Mantle cell lymphoma (MCL) is an aggressive B-cell non-Hodgkin lymphoma that is incurable with existing therapies, and therefore presents a significant unmet clinical need. The ability of this disease to overcome therapy, including those that target the B cell receptor pathway which has a pathogenic role in MCL, highlights the need to develop new treatment strategies. Herein, we demonstrate that a distinguishing feature of lymph node resident MCL cells is the expression of phosphatidylinositol 3-kinase γ (PI3Kγ), a PI3K isoform that is not highly expressed in other B cells or B-cell malignancies. By exploring the role of PI3K in MCL using different PI3K isoform inhibitors, we provide evidence that duvelisib, a dual PI3Kδ/γ inhibitor, has a greater effect than PI3Kδ- and PI3Kγ-selective inhibitors in blocking the proliferation of primary MCL cells and MCL cell lines, and in inhibiting tumour growth in a mouse xenograft model. In addition, we demonstrated that PI3Kδ/γ signalling is critical for migration of primary MCL cells and cell lines. Our data indicates that aberrant expression of PI3Kγ is a critical feature of MCL pathogenesis. Thus, we suggest that the dual PI3Kδ/γ duvelisib would be effective for the treatment of mantle cell lymphoma. MCL is genetically characterised by the t11;14 translocation which results in overexpression of cyclin D1. Although the translocation and consequence overexpression of cyclin D1 is not sufficient to induce lymphomagenesis it probably facilitates the process by deregulating the cell cycle4. It has been long been known that MCL has two distinct clinical entities described as classical  MCL, and a leukaemic  variant. The malignant lymphocytes of classical MCL express the transcription factor SOX11 and the BCR has unmutated IGHV genes7 with up to 60% of cases using the same 6 genes within the IGHV3 and IHGV4 antigen recognition sequences9. The leukaemic variant has a more indolent clinical course; cells lack SOX11 and express mutated IGHV genes10. Expression of TP53 results in an aggressive phenotype5 and is found in a higher proportion of leukaemic cases7.MCL is an aggressive B-cell non-Hodgkin’s lymphoma (B-NHL) which is incurable with current treatment options, and overall survival (OS) ranges between 3 and 5 years11. BCR signalling is also upregulated in vitro in MCL cell lines where the most abundant upregulated phosphoproteins are those involved in this signalling pathway12. Moreover, in a transgenic mouse model, SOX11 overexpression in B cells leads to amplified BCR signalling and the development of a MCL-like lymphoma11. Therefore, inhibitors of the BCR proximal signalling molecules PI3Kδ  and BTK  have been used to treat MCL. Treatment with idelalisib is effective in other B-NHL, however the response in MCL was poor with a progression-free survival (PFS) of 3.5 months13. Ibrutinib and acalabrutinib15 have been approved for treatment of MCL however they do not improve PFS, or the overall response rate compared to conventional chemoimmunotherapy (CIT)4.The importance of the BCR in the pathogenesis of MCL is highlighted by the fact that signalling through the receptor is significantly upregulated in the lymph node (LN)-resident MCL cells as compared to those found in the peripheral blood. Furthermore, patients with the highest levels of BCR signalling have a significantly poorer prognosis16. MCL lymphocytes model the LME, recruiting cells such as lymphoma-associated macrophages; and T-cells which secrete CD40L and IL-418 and induce MCL-cell proliferation19. Part of the efficacy of BTK inhibitors has been attributed to the fact that they block signals emanating from the LME as well as from the BCR22. Despite this, signalling from the BCR and the LME play a major role in the resistance/failure of currently available therapies26.The lymphoma microenvironment (LME) also plays an important role in the pathogenesis of MCL. Signals generated by the LME are important for MCL cell proliferation and survival28. PI3Kδ is important for BCR signalling and T-cell activation, whilst PI3Kγ is important for activation of macrophages, and trafficking of myeloid cells30. Duvelisib has been approved for the treatment of the B-NHLs follicular lymphoma (FL) and chronic lymphocytic leukaemia (CLL) where it has the combined properties of inhibiting tumour cell proliferation and survival, as well as modulating the LME31. Herein we show that MCL cells, in contrast to other B-NHL cells, express high levels of PI3Kγ and that the kinase is important for both the proliferation and migration of MCL cells. Our data therefore provide a functional rationale for the treatment of MCL patients with the dual PI3Kδ/γ inhibitor duvelisib.An effective therapeutic strategy for MCL would therefore need to involve more successful targeting of signals from both the LME and the BCR pathway. The dual PI3Kδ/γ inhibitor duvelisib was developed with this in mind- cells of the LME. PI3Kγ staining was not seen in the CD20 positive areas of the two control normal SLO cores taken from tonsil . Similar levels of PI3Kγ were found in cells from the Maver-1 and Mino cell lines, and in purified primary malignant peripheral blood cells from patients with both nodal and leukaemic MCL , PI3Kδ , PI3Kγ (CZC24832), and the dual PI3Kδ/γ inhibitor (duvelisib). The concentration of inhibitors was determined by inhibition of AKT phosphorylation in response to appropriate stimulation  and Mino cells (P = 0.004), as did CZC24832 incubation on Maver-1 (P = 0.038). In contrast, idelalisib and A66 had no effect . In contrast, inhibition in response to CZC24832 and idelalisib was only seen in some patients (3 and 2 respectively) and was not significant when taking the patient group as a whole (P > 0.06). Treatment with A66 had no effect The MCL cell lines Maver-1, Mino and Jeko-1 and the HS-5 stromal cell line  were used.A standardised scoring method was used for TMA analysis. The scores for the percentage of positive lymphocytes were as follows: none (0), 1–24% (1), 25–49% (2), 50–74% (3) and 75–100% (4). For IHC the intensity of the stained lymphocytes was scored as weak (1), moderate (2) or strong (3); for RNAscope intensity was defined by the number of positive dots/cell—none (0), 1–3 (1), 4–10 (2), > 10 (3). The total score = percentage score × intensity score. A minimum of two cores were evaluated for each patient by two independent researchers, and the scores were averaged. A patient was considered to express PI3Kγ in their SLO when ≥ 50% of the cells were positive and the mean intensity was ≥ 1.5.Antibodies to the following targets were used: PI3Kγ ; PI3Kδ ; CD19, CD105, CCR7, CXCR4, CXCR5 ; CD20 .For the TMA, the EnVision™ staining method was used . Slides were then stained for PI3Kγ, CD20 and PI3Kδ on adjacent sections using DAB (brown) as the chromogenic substrate. Slides were then counter stained with haematoxylin (blue).RNAscope staining was performed according to the manufacturer’s instructions ; using probes to PIK3CG  together with a positive (PPIB) and negative control. Cores where the positive control showed no staining were excluded from analysis; the negative control did not stain in any of the tissue sections.Cells were stained by direct immunofluorescence and analysed by flow cytometry .The expression of PI3Kγ (p110γ) on the MCL cell lines and PBMC from MCL patients was analysed by western blotting. Primary cells were purified by MACS  to remove non-B cells as T cells and monocytes are known to express PI3Kγ . The monocyte cell line THP-1 was used as a positive control for PI3Kγ expression.34.In order to determine the efficacy of the PI3K inhibitors MCL cells were incubated for 1 h with inhibitors to different PI3K isoforms . The effects of the inhibitors on the phosphorylation of AKT in response to BCR cross-linking with goat anti-human IgM  and chemokine signalling with CLL21  were then examined by western blotting. Inhibitors were titrated using the following concentrations 100 nM; 500 nM; 1 μM and 2 μM. AKT phosphorylation was inhibited by 1 μM  method (ThermoFisher), according to the manufacturer’s instructions. Briefly, 10 μM EDU was added for the last 4 h of the incubation. Cells were then harvested, fixed and permeabilised, before incubation with the ClickIT™ EDU reaction cocktail. Finally, the DNA binding dye 7′AAD (ThermoFisher) was added in order also to measure the cell cycle phase. The proportion of cells which were proliferating, as well as the cell cycle stage, were then analysed by flow cytometry. The number of cells was also counted manually.19, MCL cells stained with CFSE (ThermoFisher) were cultured with irradiated cells stromal cells (HS-5) in the presence of IL-4  together with PI3K inhibitors. Every 4 days half the medium was removed and replaced with fresh medium containing IL-4 plus the appropriate PI3K inhibitor. MCL cells were harvested at days 7, 10 and 14 and the MCL cells were stained with CD19 and HS5 cells with CD105. The percentage of MCL cells (CD20+CD105-) which had decreased CFSE staining was then measured by flow cytometry.Since primary mantle cells undergo rapid apoptosis in vitro when cultured in the absence of stromal cell support6 Maver-1 or Mino cells subcutaneously in 50% Matrigel (0.2 ml mixture). When the tumours had reached 60–160 mm3 mice were sorted into 3 groups (10 mice/group) and treated by oral gavage with either vehicle (5% DMSO + 40% PEG400 + 55% water) PO BID, duvelisib 50 mg/kg PO BID or idelalisib 50 mg/kg PO BID. Tumour volume and body weights were measured twice weekly for the duration of the study. Tumour sizes (mm3) were measured with a calliper in two dimensions and calculated using the formula: (a × b2)/2. Where a = half of length and b = half of width of the tumours.All the procedures related to animal handling, care and the treatment in this study were performed according to the guidelines approved by the Institutional Animal Care and Use Committee (IACUC) of Shanghai Chempartner following the guidance of the Association for Assessment and Accreditation of Laboratory Animal Care (AAALAC). Moreover, the reporting of the data in the manuscript follows the recommendations in the ARRIVE guidelines. CB17 SCID mice were injected with 5 × 10MCL cells were cultured for up to 72 h and cell death was measured using Anexin V-FITC (BD) and 7’AAD (ThermoFisher) staining followed by flow cytometry.+) B cells that had migrated to the bottom wells was counted. Since the migration of primary cells differed greatly between patients, migration of treated cells was normalised to migration in response to chemokine alone.MCL cells which had been incubated with inhibitors to PI3K isoforms were placed on the inserts of Transwell plates . CCL21 (1 μg/ml) was added to the bottom wells at a concentration which had been shown to induce maximum migration (data not shown) and MCL cells were added to the inserts. After 6 h the number of  for 1 h. Cells were then washed prior to incubation with PI3K inhibitors, and then incubated for 2 h on plates which had been coated with VCAM-1 (1 μM) ± CXCL13 [(500 ng/ml) R&D]. After washing to remove non-adherent cells, fluorescence was measured on a plate reader . The number of adherent cells was calculated with reference to a calibration curve.To determine whether there were any differences between the different subtypes of B-NHL on the TMAs the Krurskal-Wallis test was used, where statistical significance was suggested at the 0.05 level, Tukey’s method was used to correct for multiple comparisons. Post-hoc pair-wise comparisons were performed using the Mann–Whitney U-test where significance was maintained at the 0.05 level. Pearson’s correlation coefficient was used to analyse the relationship between TMA staining of protein (IHC) and mRNA (RNAscope). The paired Student’s T-test was used to determine if there were any statistically significant differences between the different PI3K inhibitors in the in vitro assays; the unpaired T-test was used in the mouse experiments.Supplementary Information 1.Supplementary Information 2.


Neisseria gonorrhoeae. We compared its gastrointestinal side effects using 1 g single, 2 g single or 2 g split (i.e. 1 g plus 1 g 6–12 h later) dosing, representing our clinic’s changing guidelines over the study period.Azithromycin is commonly used to treat We recruited consecutive sexual health clinic patients who received azithromycin (and 500 mg ceftriaxone) for uncomplicated gonorrhoea. Each patient received a text message 48 h after their attendance to complete a questionnaire.n = 271), 2 g single (218) or 2 g split (105) doses. Vomiting was less common for 1 g versus 2 g single dose  and 2 g split versus 2 g single dose . Nausea was less common for 1 g versus 2 g single dose  and 2 g split versus 2 g single dose . Diarrhoea was less common for 1 g versus 2 g single dose  and 2 g split versus 2 g single dose . Almost all were willing to retake the same dosing for gonorrhoea in the future: 97% for 1 g single; 94% for 2 g single; and 97% for 2 g split dose.Patients received 1 g single (Azithromycin 2 g split dose for gonorrhoea resulted in significantly less vomiting, nausea and diarrhoea than a 2 g single dose. However, the increasing resistance to azithromycin now challenges its inclusion in dual therapy for gonorrhoea.4 Some countries have recently returned to ceftriaxone monotherapy as recommended first-line treatment for uncomplicated gonorrhoea, e.g. the UK and the USA , when a chlamydial infection has been excluded.6 The 2020 European gonorrhoea guideline recommends ceftriaxone 1 g plus azithromycin 2 g as a single dose. If side effects are anticipated, azithromycin can be given as a 2 g split dose, that is 1 g then 1 g after 6–12 h.7 However, ceftriaxone 1 g monotherapy is recommended as an option for anorectal gonorrhoea in well-controlled settings and circumstances .7Over time, gonorrhoea has become resistant to multiple classes of antibiotics. Ceftriaxone is currently the only antibiotic that remains fully effective against gonorrhoea. When occasional cases of treatment failure with ceftriaxone emerged over the last one to two decades, dual antimicrobial therapy was introduced using ceftriaxone (250 mg to 1 g single intramuscular dose) with azithromycin  internationally.8 and predicted to be more common based on pharmacokinetic/pharmacodynamic (PK/PD) modelling.9 In Australia, ceftriaxone 500 mg intramuscularly is given with azithromycin 1 g orally to treat genital and anorectal gonorrhoea and with azithromycin 2 g single dose to treat pharyngeal gonorrhoea.10 The azithromycin 2 g dose appears more effective than the azithromycin 1 g dose for treating ceftriaxone-resistant gonorrhoea or when azithromycin is used alone in the absence of azithromycin resistance.11 However, gonococcal isolates are now increasingly considered to be resistant to azithromycin internationally.4The main rationale for maintaining azithromycin in the dual therapy is to avoid treatment failure with ceftriaxone monotherapy, which has been sporadically documented, particularly with pharyngeal infection,13 There are no studies comparing the gastrointestinal side effects using different dosing of azithromycin, particularly for the 2 g split dose. Bergan et al.14 found that after 12 h, blood levels post a 1 g dose were about 10% of peak levels, and Hoffler et al.15 found that after 6 and 12 h, blood levels after a 1 g dose were 10%–25% of peak levels. Thus, taking the second 1 g dose 6–12 h post the first 1 g dose may reduce side effects since high blood levels are minimized. Notably, studies confirming a higher cure rate for gonococcal infections with azithromycin 2 g split dose treatment compared with azithromycin 1 g single dose therapy are lacking.At Melbourne Sexual Health Centre (MSHC), the largest public sexual health centre in Australia, we administer azithromycin 2 g single dose, as recommended for pharyngeal gonorrhoea, but are concerned about a possible increase in gastrointestinal side effects.10 We were interested in gastrointestinal side effects  using the different azithromycin dosing.We aimed to compare the side-effect profile of azithromycin 1 g single dose, 2 g single dose and 2 g split dose to treat uncomplicated urogenital and extragenital gonorrhoea. Azithromycin was used together with ceftriaxone 500 mg, as per Australian STI Management Guidelines.16 Verbal consent was received, and each patient was given an information leaflet and received a unique, secure link to the online questionnaire via text message 48 h after receiving the ceftriaxone injection at MSHC.This was a quasi-experimental study (before-and-after design) where consecutive patients attending MSHC received treatment for uncomplicated urogenital and extragenital gonorrhoea in three phases: (1) azithromycin 1 g single dose for both urogenital and extragenital gonorrhoea (3 June 2019 to 24 May 2020); (2) azithromycin 2 g single dose for pharyngeal gonorrhoea ; and (3) azithromycin 2 g split dose for pharyngeal gonorrhoea (25 May 2020 to 21 May 2021). Pharmacy staff at MSHC invited patients diagnosed with gonorrhoea to participate in the survey when they dispensed the antibiotics. The survey was an anonymous online survey hosted on Research Electronic Data Capture (REDCap), a secure web-based software platform for research studies.N. gonorrhoeae; (3) had reasonable command of English and could provide informed consent; and (4) treated with ceftriaxone plus azithromycin for gonorrhoea. Pharmacy staff provided all patients (regardless of whether they agreed to participate or not) with standard advice on how to take the azithromycin tablets when giving out the medication; this advice included information about taking the medicine straight after food and commonly occurring side effects. Patients are advised to be sexually abstinent for 7 days for all dosing regimens.Inclusion criteria included: (1) aged 18 years or over; (2) diagnosed with 17 Studies assessing the tolerability of a 2 g oral dose of azithromycin indicate that up to 7% will experience vomiting when given on an empty stomach,13 but this could be reduced after food. This study compared the proportion of patients experiencing gastrointestinal side effects between the three azithromycin doses. A sample size of approximately 210 in each group provided 80% power to detect a difference in vomiting between the 1 g dose and the 2 g dose if the proportion with vomiting was 1% and 6% or more, respectively .We also examined a third group whereby patients given 2 g azithromycin split their dose, i.e. 1 g followed 6–12 h later by 1 g. We initially planned to recruit 210 individuals into this third group, but due to the impact of the COVID-19 pandemic causing reductions in gonorrhoea cases and delays in recruitment, we decided to stop recruitment at 100 patients for the 2 g split dose during the study when the data showed a significant difference between the three groups.We anticipated that approximately 1% of patients taking a 1 g dose of azithromycin would experience vomiting.Ethics approval was received from the Alfred Hospital Ethics Committee (256/19).Participants were sent a text message 48 h after being prescribed the medication and asked whether they had experienced any nausea, diarrhoea or vomiting since taking the antibiotic. Participants given the 2 g split dose were not sent a prompt to take the second dose. We asked about the following: the time between eating food and taking the antibiotics; the time between taking the first 1 g dose and the next 1 g dose (for the 2 g split dose group); the time between taking the antibiotics; the experience of any side effects; and the duration of the side effects. We used a Likert scale  to measure the severity of each side effect. Besides gastrointestinal side effects, we asked whether participants experienced any other side effects. Finally, we asked whether they would accept the same treatment if they needed treatment for gonorrhoea again. Concurrent medications were extracted from their current pharmacy records, and the site of gonorrhoea infection was extracted from their electronic health record. Test of cure was not conducted because failure with ceftriaxone is rare.P value of <0.05 was considered to be statistically significant. Box plots were created to summarize the time to side effects. All analysis was performed using Stata .We used descriptive statistics to summarize the proportion of people experiencing various side effects: vomiting, nausea and diarrhoea. We calculated the 95% CIs for the difference in proportions using exact binomial (Clopper–Pearson) CIs. We also present an adjusted risk difference (RD) including gender, age and weight as potential confounders. A A total of 1067 individuals agreed to receive the follow-up SMS, with 594 consenting and completing the survey: 271 (azithromycin 1 g single dose), 218 (2 g single dose) and 105 (2 g split dose). All individuals in the 2 g split dose group reported that they took the second dose. The median time interval between doses was 8 h (IQR: 6.5–11.5). Most  were male with a mean age of 32.0 years (SD 9.1). Further details of the study population are shown in Table Table Vomiting was less common with azithromycin 2 g split versus 2 g single dose . Nausea was less common with azithromycin 2 g split versus 2 g single dose  and diarrhoea was less common with azithromycin 2 g split versus 2 g single dose . Our results did not change when adjusted for gender, age and weight.When comparing 2 g split with 1 g single dose, there was no significant difference in reports of vomiting  or nausea . However, there was significantly more diarrhoea for 2 g split compared with 1 g single dose . When adjusted for gender, age and weight, the difference in diarrhoea was no longer significant (95% CI: −6.4 to 40.6).n = 3), two had a score of 1 and one had a score of 4. For those who took the 2 g single dose (n = 8), three had a score of 2, three had a score of 3 and two had a score of 4. No score was reported for the person who took the 2 g split dose.Only 11 people reported vomiting, so we did not perform any statistical analysis of the differences in the timing between taking azithromycin and onset of vomiting. In terms of the severity of vomiting , of those who took the 1 g dose , nausea (P = 0.959) or diarrhoea (P = 0.428).For the 1 g single dose, the median number of diarrhoea episodes was 3 (IQR 2–4). For the 2 g single dose, the median number was 3 (IQR 2–4). For the 2 g split dose, the median number after the first dose was 2 (IQR 1–3) and the median number after the second dose was 2 (IQR 1–3). There was no difference between people who had food within 1 h and those who did not with regard to vomiting  for the 1 g single dose; 94%  for the 2 g single dose; and 97%  for the 2 g split dose.In this study of 594 people treated for gonorrhoea, we found significant differences in the frequency of gastrointestinal side effects reported, depending on the dosing of azithromycin administered. Within this population, who also received a ceftriaxone 500 mg intramuscular single dose, increasing azithromycin from a 1 g single to a 2 g single dose resulted in more vomiting, nausea and diarrhoea. Splitting the 2 g dose (two 1 g doses 6–12 h apart) compared with the 2 g single dose significantly reduced all gastrointestinal side effects to levels similar to those seen with a 1 g single dose. Despite the high proportion of gastrointestinal side effects in this study population, almost all patients would still take the same medication if they were infected with gonorrhoea in the future.5 the UK6 and Europe,7 2 g azithromycin is still recommended by Australian guidelines for treating oropharyngeal gonorrhoea10 and US guidelines recommend gentamicin plus 2 g azithromycin as an alternative when there is cephalosporin allergy.5 The European guideline also recommends 1 g ceftriaxone plus 2 g azithromycin for uncomplicated gonorrhoea in some situations, including the presence of ceftriaxone resistance, lack of test of cure or no administration of doxycycline if C. trachomatis infection has not been excluded.7 Ceftriaxone monotherapy has variable bioavailability in the oropharynx, which potentially could lead to more treatment failures and an increased likelihood of antimicrobial resistance.18Although there is a general move to remove azithromycin as first-line therapy from sexually transmitted infection (STI) guidelines in the USA,19 Our finding of the low reports of vomiting  is similar to the product monograph for azithromycin reporting that in adult patients (n = 904) 1.7% reported vomiting for 1 g single, 6.7% for 2 g single dose and 1% when patients received azithromycin  over 3 or 5 days.17 These findings are consistent with the theory that vomiting may be related to blood levels of azithromycin, so reducing peak levels would theoretically reduce this. In a study of 431 participants receiving a 2 g single dose of azithromycin for gonorrhoea, 7% reported vomiting.13 In another study of 202 participants receiving gentamicin with a 2 g single dose of azithromycin, 7.4% reported vomiting, and in 199 participants who received gemifloxacin with a 2 g single dose of azithromycin, 5% reported vomiting .12 It is important to note that from these dual therapy studies (like our study), it is not possible to ascertain the contribution of azithromycin to gastrointestinal side effects separately from concomitant antibiotics. We did not find any significant difference between the timing of food and the report of vomiting within an hour of taking azithromycin, although our sample size may be too small to detect a statistically significant difference.The frequency of vomiting, particularly in the first hour, is important for a drug with low oral bioavailability, such as azithromycin.17 This might be because there is no standard method for measuring the severity of diarrhoea. Furthermore, the addition of ceftriaxone may add to the reports of diarrhoea.20 Azithromycin has a prokinetic effect on the gastrointestinal system, explaining the high frequency of diarrhoea. Our study’s reports of nausea  are also higher than the data from the product monograph .17 This could also be due to the additional impact of taking ceftriaxone.20Our study also reported a high frequency of other gastrointestinal side effects. Azithromycin absorption may be suboptimal when patients have vomiting or diarrhoea, but we did not have data to examine the impact on the microbiological cure. Our reports of diarrhoea  are higher compared with those reported in the product monograph .The strength of our study is that we prospectively followed a large cohort of individuals treated for gonorrhoea who actively reported their experience of side effects. We minimized recall bias by sending the survey via text message 48 h after the patient took azithromycin. Our findings should be read in the light of several limitations. First, our study population is from a single clinic in Australia. Our results should be verified in studies of other populations. Second, there is a possibility of detection bias; those who experienced a side effect may have been more likely to respond to the survey. All participants were aware they were given azithromycin with no placebo as a control. Third, the exceptionally high acceptability to retake the same medication despite significant side effects may be due to social desirability bias or the perception that they had no other option to cure gonorrhoea. Finally, as this was not an experimental study design, we did not randomize patients so there could be unmeasured confounders between the three groups; nor did we mandate patients to have a test of cure, so we could not comment on whether different azithromycin regimens impacted microbiological cure.In conclusion, we found differing side-effect profiles, particularly regarding nausea and diarrhoea, depending on the azithromycin dosing regimens in the treatment of gonorrhoea. Azithromycin 1 g single or 2 g split dose for the treatment of gonorrhoea resulted in significantly less vomiting, nausea and diarrhoea than 2 g single dose. Despite a high proportion of individuals who reported gastrointestinal side effects, almost all patients would still take the same medication if they were infected with gonorrhoea in the future.


The XRD, SEM‐EDS, and XPS measurements indicate that chalcopyrite reacts to form copper(I) chloride (CuCl). After the reductive treatment, the mineral products are leached by iron(III) sulfate to demonstrate the complete extraction of copper. The chromium(II) ion may be regenerated by an electrolysis unit inspired by an iron chromium flow battery in a practical industrial process.A hydrometallurgical process is developed to lower the costs of copper production and thereby sustain the use of copper throughout the global transition to renewable energy technologies. The unique feature of the hydrometallurgical process is the reductive treatment of chalcopyrite, which is in contrast to the oxidative treatment more commonly pursued in the literature. Chalcopyrite reduction by chromium(II) ion is described for the first time and superior kinetics are shown. At high concentrate loadings of 39, 78, and 117 g L 2+ ion is electrochemically generated by leveraging advances in iron chromium flow battery technologies. The Cr2+ ion reduces chalcopyrite (CuFeS2) to copper(I) chloride (CuCl) for the sustainable production of copper.The Cr The pyrometallurgical process is generally used in industry to convert CuFeS2 to metallic Cu despite relatively high investment and operating costs.The increasing demand for copper coincides with declining grades of copper reserves, and consequently, a global peak in copper production is expected to arise in the coming decades.2 bioleaching, and leaching in general, from ores or concentrates in a sulfate (or sulfuric acid) medium are hindered by a passivating sulfur‐like or metal‐deficient layer; consequently, leaching efficiency is poor. High temperature pressure leaching overcomes the passivation, but such conditions are often uneconomical in many plants. The galvanox process is a promising alternative to enhance copper recovery at atmospheric pressure and relatively low temperature but has not seen widespread adoption by industry. It should be noted that there are other processes in various phases of development that may become promising alternatives. are in direct competition with the hydrogen evolution reaction, and therefore typically operate at Faradaic efficiencies below 40 %. These slurry reactions also present potential engineering challenges such as reactor plugging and electrode fouling.2 may be advantageous because it obviates the hydrogen evolution reaction and circumvents engineering challenges associated with slurry electrodes. The chemical reduction of CuFeS2 has been tested with Fe,22+ was tested as a reductant for the first time and superior kinetics are demonstrated. Although the cost of chromium is high relative to copper, an electrolysis unit inspired by an iron chromium flow battery (ICFB)[2+ at high current densities.The chemical reduction of CuFeS2 concentrate to the solution of 1 m CrCl2 and 4 m HCl. Reaction 3 [Eqs. (3)] is postulated to be taking place and is discussed throughout this section.A violent reaction was observed upon adding the CuFeSm CrCl2, 4 m HCl, and 78 g L−1 CuFeS2 concentrate after 0, 2, 3, 5, and 60 s of reaction time. The pictures show the rapid release of H2S gas, which was qualitatively measured with a Sensorcon detector. The release of gas ensued immediately upon the addition of the concentrate and concluded within a minute of reaction time. The liquid phase samples were measured with gas chromatography–mass spectroscopy (GC‐MS) to confirm the presence of dissolved H2S for similar experiments.Figure 2S coincided with the release of Fe2+ ions to solution, which is consistent with Reaction 3 [Eqs. (3)]. Figure 2+ released as a function of time for a slurry comprising 1 m CrCl2, 4 m HCl, and CuFeS2 concentrate loadings of 39, 78, 117, and 234 g L−1. The reaction kinetics were rapid considering that approximately 100 % of Fe2+ was released from CuFeS2 within 5 min for the CuFeS2 concentrate loadings of 39, 78 and 117 g L−1. The release of Fe2+, however, was limited for the CuFeS2 concentrate loading of 234 g L−1 suggesting the complete utilization of Cr2+. Measurements of Fe2+ release exceeding 100 % may indicate a minor error in the estimation of composition shown in Table 2+ to any significant level. The release of copper ions to solution during the progression of the reaction was measured, but the quantitative results were inconsistent due to the precipitation of the ions out of solution, which is discussed below. The copper ions are thought to be released in the form of Cu+, rather than Cu2+, due to the reductive conditions of the electrolyte and presence of the chloride ion for stability. The pH of the solutions after the reduction experiments were below zero, ensuring that these reactions were not pH limited. The Cu2+ ion is not thought to be present due to the reductive conditions in the electrolyte.The evolution of gaseous H2+ released as a function of time for slurries comprising 1 m CrCl2, 39 g L−1 of CuFeS2 concentrate, and initial HCl concentrations of 0 m, 0.5 m, 1 m, and 4 m. The pH of the solution after the reduction step was approximately 2.5 for the slurries with initial HCl concentrations of 0 m, 0.5 m, 1 m, indicating that these reactions were pH limited. The pH of the solution after the reduction step may be leveraged to facilitate a separation between Fe2+ and Cr3+, which may be desirable prior to the reduction of Cr3+ to Cr2+ by an electrolysis unit. These results suggest that the proton has a greater stoichiometric number than CuFeS2, which is consistent with Reaction 3 [Eqs. (3)]. The experiments conducted with initial HCl concentrations of 2 m and 3 m were found not to be pH limited.Figure 2+ ion obtained with a Keyence VHX‐5000 microscope. The results indicate that the mineral product is affected by the CuFeS2 concentrate loading. The 39 g L−1 CuFeS2 loading yielded a green product, which is consistent with the appearance of CuCl as well as other potential Cu−Cl complexes. The various mineral products were characterized and shown to yield different amounts of copper recovery, which is discussed below. The mineral products post reaction with various HCl concentrations yielded the same trend in appearance.Figure 2+ ion, and Figure 2+ ion and various initial HCl concentrations. The predominant peaks of the unreacted CuFeS2 concentrate were consistent with CuFeS2, FeS2, and SiO2, as shown in Table 2 diminished for the reacted mineral products, consistent with the Fe2+ release measured by AAS. The peaks associated with the reaction products emerged for the mineral products with high conversion of CuFeS2. The predominant mineral product was determined to be copper chloride (CuCl) from the spectra. Secondary products, such as Cu2(OH)3Cl, were consistent with the spectra. Reaction 4 [Eqs. (4)] shows the precipitation of CuCl out of solution, which is the primary product formed. Reaction 4 is shown for simplicity whereas the chemistry taking place is more complicated and a variety of Cu−Cl complexes precipitate. The precipitation of CuCl out of the solution containing 4 m HCl was unexpected considering that the molar ratio of Cl/Cu was 36 in the system. However, the molar ratio of Cl/Cr was 6, and therefore, complexes formed between Cl− and Cr3+ may lower the number of Cl− ions available to stabilize Cu+. The concentration of Cu+ in solution after 60 min of reduction was approximately 0.07 m, which is close to the solubility limit of 0.233 m reported at 2 m HCl in the literature.+ and 60 % precipitated out of solution for the experiments conducted with a concentrate loading of 39 g L−1 and an acid concentration of 4 m HCl.Figure 2 and silicates were inert during the reductive treatment. Experiments were conducted between 39 g L−1 CuFeS2 concentrate, 1 m CrCl2, 4 m HCl and initial ferrous chloride (FeCl2) concentrations of 0, 0.5 m, 1 m, and 2 m. It was determined that the reduction process can tolerate initial FeCl2 concentrations of 1 m and below. The Fe2+ precipitated out of solution for the experiment conducted with an initial FeCl2 concentration of 2 m.The XRD data, in conjunction with the AAS data, indicate that the FeSm CrCl2 and 4 m HCl for 60 min. The mineral products develop some mossy features, which may be related to the growth of CuCl. Figure 2+ ion. The unreacted CuFeS2 concentrate samples show peaks corresponding to Cu, Fe, S, Si, and O. The reacted samples show the diminishment in the Fe and S peaks, which is consistent with the release of Fe2+ to solution and the release of H2S as a gas. The minor S peak present in the 39 g L−1 sample may be related to the presence of unreacted FeS2 in the mineral products. The reacted samples also show the emergence of the Cl peak, which is consistent with the formation of CuCl. The Cu peak elongates for the reacted samples due to the increasing mass fraction of Cu within the samples. No peak corresponding to Cr was observed in the spectra, indicating that the presence of Cr within the samples is minor. The samples were digested in aqua regia and the mass fraction of Cr within the samples was estimated to be 1–3 %. The presence of chromium is thought to be an artifact of the procedure used to filter and dry the mineral products.Figure 2+ ion. The Cr element was not observed on the mineral products, which further indicates that the samples were not comprised of chromium. Similarly, Fe and S were not observed on the surface of the mineral reaction products, which is consistent with the release of Fe2+ and H2S from the surface of the particles into the solution phase. The XPS data indicate the absence of a sulfur passivation layer, which may account for the rapid kinetics of the reduction reaction. The various copper peaks indicate the presence of several copper‐containing products leading to convoluted spectra. For instance, the peaks at the binding energies of 944 and 935 eV are assigned to Cu2(OH)3Cl and CuCl, respectively. The Cu scans also show an observable shift in binding energy from the CuFeS2 concentrate standard. The emergence of a Cl peak for the reacted samples is consistent with the formation of Cu−Cl complexes.Figure 2+ from the mineral products by 0.5 m Fe2(SO4)3. Reaction 5 [Eqs. (5)] shows the leaching reaction of CuCl by the Fe3+ oxidant, which goes to completion within minutes.Figure 2+ can be extracted from the 39 g L−1 mineral product. The aqueous solution may subsequently undergo solvent extraction and electrowinning for the production of metallic copper. In experiments, not shown, the 39 g L−1 sample was solubilized to the same extent in 1 m H2SO4, and therefore, the ferric ion may not be required for the extraction of copper. The incomplete copper extraction for higher pulp densities is partly related to the incomplete conversion of CuFeS2 shown in Figure 2(OH)3Cl, may be refractory for copper leaching and undesirable. It is shown that virtually no Cu2+ is extracted from the CuFeS2 concentrate, and therefore, the reductive treatment directly leads to the extraction of copper.The results show that virtually all of the Cu2 in acid solution for the first time and superior kinetics were shown at room temperature and ambient pressure. AAS was used to measure the complete release of Fe2+ from CuFeS2 within minutes during its reduction. XRD and SEM‐EDS were used to characterize the predominant mineral product to be CuCl. The measurements also indicate that pyrite and silicates were inert during the reductive treatment. XPS was used to measure the surface of the mineral products and the results suggest that the rapid kinetics may be related to the lack of a passivation layer during the reduction step. The mineral products were leached by the ferric ion to demonstrate complete copper recovery.Chalcopyrite concentrate was reduced by CrClFreeport‐McMoRan. It was analyzed by the supplier with energy dispersion X‐ray diffraction to have the following composition as shown in Table Chalcopyrite mineral concentrate was kindly provided by 2 concentrate was sieved (−140+270 mesh) to confine the particle size to be within 53–106 μm. An amount of 50 g of the concentrate was subsequently rinsed with 1 L of DI water and 1 L of 1 m H2SO4 to remove any soluble iron and copper ions generated during natural concentrate oxidation occurring in transport and storage. CuFeS2 concentrate pulp densities of 39, 78, 117, or 234 g L−1 were added to a 250 mL Erlenmeyer flask containing 25 mL of a solution comprising of 1 m CrCl2 and 4 m HCl. For other experiments, a CuFeS2 concentrate pulp density of 39 g L−1 was added to a solution comprising 1 m CrCl2 and various HCl concentrations. Thirdly, for other experiments, a CuFeS2 concentrate pulp density of 39 g L−1 was added to a solution comprising of 1 m CrCl2, 4 m HCl, and various concentrations of FeCl2. It was imperative for the reaction to be conducted in a fume hood due to the rapid release of H2S gas, as shown in Figure 2+ and Cu+ contents. After the reduction, the mineral particles were filtered from solution and allowed to air dry prior to characterization.The CuFeSiCE 3300 AAS was used to measure the release of Fe2+ and Cu+ ions into solution from CuFeS2 during its reduction. The characteristic wavelengths for the iron and copper measurements were 248.3 nm and 324.8 nm, respectively. Standards ranging from 0–4 ppm were measured immediately before the samples to construct linear (R2>0.995) calibration curves.An Ka radiation (k=0.15418 nm), a tube voltage of 45 kV, and a current of 40 mA. The mineral products were placed on a silicon crystal zero‐diffraction plate (MTI Corporation) and were adhered in place with Apiezon grease. The samples were scanned continuously in the range of 10–100° with a step size of 0.0065° on a spinning plate with a revolution time of 2.0 s. A PIXcel1D detector was used to record the peak intensity for the subsequent analysis of the mineral composition.A PANalytical XPert3 Powder XRD was used to measure the bulk mineral phase of the reaction products. The XRD was operated with filtered Empyrean Cu PHI 5500 XPS equipped with an Al X‐ray source was used to measure the elemental composition of the reaction product surfaces. The base pressure of the chamber was approximately 1×10−8 torr. Samples were supported on carbon tape.A Zeiss Sigma VP SEM was used to capture images of the mineral products after reaction. The SEM‐EDS analysis was operated at an accelerating potential of 6 kV and base pressure of approximately 1×10−5 torr. Samples were supported on carbon tape and were coated with gold using a Cressington 108 Auto Sputter Coater. The sputtering was conducted under argon gas flow with 0.1 mbar of pressure for 20 s. A Bruker XFlash Detector was used for EDS analysis to analyze elemental composition.A m Fe2(SO4)3 in 1 m H2SO4. The percent of copper released was determined by the ratio of copper extracted by the two leachants.A sample of the mineral products was digested in aqua regia for complete copper extraction, and an equivalent sample of the mineral products was leached in a solution comprising 0.5 The authors declare no conflict of interest.1


In both tables, the row “Source (1 hr maximum: 177 μg/m3)” incorrectly listed the value for the nonhypertensive group as 46 instead of 446. This article has been corrected.1In the Original Investigation titled “Association of Deepwater Horizon Oil Spill Response and Cleanup Work With Risk of Developing Hypertension,”


We have exploited the fact that benzene has a relatively high photoabsorption cross section in the vacuum ultraviolet region to study this dilute mixture of benzene. Before irradiation with 1 keV electrons, we observed that the benzene electronic transition bands in the C6H6 : CO2 mixture exhibits a blueshift in band position towards energies observed in the gas-phase compared with that of pure, amorphous benzene and we have attributed this to a matrix isolation effect. After irradiation, a lowering in intensity of both the carbon dioxide and benzene electronic transition bands was observed, as well as the formation of the small irradiation product, carbon monoxide. A residue was obtained at 200 K which showed characteristic features of the benzene electronic transition of 1E1u ← 1A1g, but with additional structure suggesting the formation of a benzene derivative.We present the first vacuum ultraviolet spectroscopic study of an interstellar ice analogue of a 1 : 100 benzene (C 6H6) : carbon dioxide (CO2) (1 : 100) mixture which has been energetically processed with 1 keV electrons.We present the first vacuum ultraviolet spectroscopic study of an interstellar ice analogue of a benzene (C The structure of most PAHs makes them difficult to observe using rotational spectroscopy and observations with infrared spectroscopy generally lack the resolution to distinguish between different PAHs.Polycyclic aromatic hydrocarbons (PAHs) have attracted considerable attention in the astrochemistry community due to their ubiquitous presence in the interstellar medium (ISM). It is thought that up to 10% of the interstellar carbon budget is in the form of PAHs3 and the Large Magellanic Cloud object SMP LMC 11.4 Recently a derivative of benzene, benzonitrile, was detected in the gas-phase in the molecular cloud TMC-1.5 Formation routes for PAHs in the diffuse ISM include the top-down processes of SiC dust grain destruction from the intense UV radiation field and sputtering from shockwaves.6,7 Alternative bottom-up processes include the formation of PAHs from benzene derivatives or radicals in the gas-8 or solid-phase which are more likely in low temperature, molecular cloud environments. Within our own Solar System, PAHs and benzene derivatives have been detected on some Saturnian moons,9 interplanetary dust grains10 and meteorites. In fact, some of the PAHs and benzene derivatives detected in meteoritic materials show deuterium enrichment indicating that the formation origin of these molecules may be from molecular cloud environments.11Nevertheless, benzene, a prototypical aromatic molecule and building block of PAHs, has been detected in the gas-phase in the protoplanetary nebula CRL 618 12 Within molecular clouds, the icy mantles of interstellar dust grains may be subjected to energetic processing  which could induce molecular synthesis within the ice. Several experimental studies have looked at the formation of PAHs or benzene derivatives within interstellar ice analogues.13–15 In particular, aromatic molecules with the carboxylic acid moiety (–COOH) have been studied because of their role as precursors to amino acids with non-aromatic carboxylic acids detected in the ISM in the form of formic acid (HCOOH)16 and acetic acid (CH3COOH).17 Carboxylic acids with varying degrees of complexity have also been detected in the Tagish Lake,18–20 Murchison21,22 and Orgueil22,23 carbonaceous meteorites.Although PAHs, benzene and its derivatives have not been directly identified in the solid-phase, which is most likely due to their weak infrared absorption features overlapping with intense ice absorption bands, they are believed to be incorporated into icy mantles around interstellar dust grains or operate as nucleation sites for the condensation of other species.2, as an interstellar ice analogue, with 1 keV electrons using vacuum ultraviolet (VUV) spectroscopy. While mid-IR spectroscopy is the more commonly used in situ laboratory technique for investigating the structure and composition of interstellar ices, and any changes upon energetic processing, this is the first time that VUV spectroscopy has been used to study the benzene : CO2 system. With VUV spectroscopy we can take advantage of the fact that benzene has appreciatively high photoabsorption cross sections due to strong electronic π → π* transitions compared to that of other interstellar ice constituents such as H2O and CO2. For example, cross sections of benzene at wavelengths <200 nm reach 50 Mb 24 which is almost 40 times more intense compared to that of the CO2 peak cross section of around 1.3 Mb.25 In contrast, the mid-IR band strength  of the strongest vibrational transition of solid benzene, the C–C stretch (v19), is 1.4 × 10−18 cm per molecule26 which is approximately 90 times less intense compared to the C–O stretch (v3) of CO2 with a band strength of 1.3 × 10−16 cm per molecule.27 This makes VUV spectroscopy a potentially more favourable region of the electromagnetic spectrum to study very dilute mixtures of benzene in ice matrices (e.g. benzene and water). In this paper we present the results of the first experimental study using VUV spectroscopy to investigate an electron irradiated, 1 : 100 C6H6 : CO2 mixture as an interstellar ice analogue.In this paper we investigate the energetic processing of a dilute mixture of benzene in CO228 This set-up has been used before for the investigation of condensed phase molecules and is described in detail elsewhere by Dawes et al.24 and only a brief description is given here.Experiments were carried out using The Open University's Portable Astrochemistry Chamber (PAC) attached to the AU-UV beamline at the ASTRID2 Synchrotron Facility in Aarhus, Denmark.−8 mbar. Benzene  was degassed via three freeze–pump–thaw cycles prior to use and pre-mixed with CO2  in the gas line. The mixture was then vapour deposited onto a cold (20 K) MgF2 (Crystran) substrate held in a copper holder attached to a closed cycle helium cryostat (Sumitomo). VUV spectra were acquired in the range 120–340 nm with 0.05 to 1 nm wavelength step size depending on the width of the spectral features to be resolved. Absorbance spectra were calculated from the recorded incident and transmitted intensities as a function of wavelength (nm).The experiments were carried out at a base pressure of low 10in situ laser interferometry measurements from the use of a HeNe laser beam reflected off the substrate during deposition. Deposition rates were between 0.12 and 0.55 nm s−1 depending on the thickness of the ice being grown. The final thickness of the films were 349 nm for the unirradiated mixture and a 1.28 μm for the irradiated mixture. For the unirradiated mixture a thinner ice was prepared to avoid saturation of the electronic transition bands, to allow for accurate band assignments and observe any changes in the band profiles upon annealing. A thicker ice was prepared for irradiation to ensure a sufficient quantity of products were formed for observation/monitoring and to ensure that the ice thickness was greater than the penetration depth of electrons so that there was no substrate effect. This thicker ice was grown in stages to confirm that no thickness-dependent effects were present until saturation of the peaks was observed.Film thickness was determined from −2. The electron flux at the sample was approximately 1.77 × 1013 electrons per cm2 per s. After 180 min of irradiation this corresponded to a fluence of 1.91 × 1017 electrons per cm2. A penetration depth of 40 nm for 1 keV electrons was estimated using Monte Carlo simulations from the CASINO code.29The mixture was irradiated with 1 keV electrons  with a current of 10 μA and the bombarded area was about 3.5 cm−1 by heating the sample using a Kapton heater and regulated with a temperature controller (Oxford Instruments). The samples were held at the required temperature for 2 min and then returned to base temperature (20 K) prior to measuring the spectra.Samples were annealed gradually at a rate of 1 K min324,30 we know that when solid-phase benzene is diluted with amorphous solid water a blueshift in the electronic bands compared to that of pure benzene is observed. We therefore used an unirradiated control sample to characterise the 1 : 100 C6H6 : CO2 mixture and any effects annealing might produce, the results of which are discussed in Section 3.1. In Section 3.2 we discuss the results of irradiating the 1 : 100 C6H6 : CO2 mixture with 1 keV electrons for 180 min and in Section 3.2.1 we discuss the results on the residue left at 200 K.From previous studies3.13.1.16H6 : CO2 mixture deposited at 20 K compared with spectra of a 1 : 100 C6H6 : H2O mixture deposited at 24 K,30 pure benzene deposited at 24 K and gas-phase benzene.24 Two broad bands centred around 127 and 142 nm are due to CO2 and correspond to the  and  transitions respectively. The higher energy  transition exhibits vibronic structure the positions of which are in good agreement (to within 10 meV) with a study conducted by Mason et al.25 where pure CO2 was deposited at 20 K.6H6 : CO2 mixture are observed in 1E1u ← 1A1g, 1B1u ← 1A1g and 1B2u ← 1A1g transitions. The 1E1u ← 1A1g transition is the most intense benzene band and it is blueshifted by 0.30 eV from 191.8 nm (6.47 eV) in pure benzene to 183.2 nm (6.77 eV) in the 1 : 100 C6H6 : CO2 mixture. The 1B1u ← 1A1g transition appears as a structured shoulder on the long wavelength side of the 1E1u ← 1A1g transition  of C6H6 : H2O were studied and as the benzene was diluted, successive blueshifts from pure benzene were observed and attributed to a matrix isolation effect. Also, the 1 : 100 C6H6 : H2O mixture showed structure within in the 1E1u ← 1A1g transition band which resembled the band profile of gas-phase benzene and was not observed in the less diluted benzene mixtures. This gas-phase like band profile is also observed in the 1 : 100 C6H6 : CO2 mixture of the 1E1u ← 1A1g transition band and further supports the theory of matrix isolation as a cause of the shifts observed in the electronic band rather than a solvent effect. While the vibronic peaks of the 1B2u ← 1A1g electronic transition are not completely resolved, the data is sufficient to suggest a blue shift in position towards energies observed in the gas-phase in a similar fashion to that of the 1 : 100 C6H6 : H2O mixture.Three benzene bands in the 1 : 100 C3.1.26H6 : CO2 mixture as it is annealed to 80, 90 and 140 K corresponding to the temperature at which pure CO2 is crystalline (>80 K), pure benzene begins to crystallise and pure CO2 desorbs (75–90 K), and, pure benzene desorbs (140 K). At 80 K the CO2 and  transition bands are still present in the same position as that of spectra taken at 20 K, albeit with lower intensity, and by 90 K they have disappeared due to desorption of CO2. At 80 K the 1E1u ← 1A1g transition of benzene has lowered in intensity and the band profile is showing signs of the splitting characteristic of that of crystallisation of benzene. The 1B1u ← 1A1g vibronic structure appears less well defined than at 20 K and may be due to desorption of CO2 which is also occurring at 80 K. When the CO2 is fully desorbed at 90 K the 1E1u ← 1A1g has shifted from 183.4 nm to 192.8 nm with a well defined splitting in the band (190.6 nm and 194.6 nm) observed. Additionally the 1B1u ← 1A1g vibronic features have sharpened compared to that at 80 K and shifted to pure, crystalline benzene positions.24 At 140 K all the benzene has been removed from the substrate.3.2via the vibronic structure of the A1Π ← X1∑+ transition, the assignments are shown in via VUV irradiation of CO2. Davydov splitting observed in the lower energy bands  of pure CO are not observed in CO formed from irradiation of electrons, consistent with that of the CO formed from VUV photons in a study by Cruz-Diaz et al.31 Additionally the vibronic bands have blueshifted compared to that of pure CO, which is also consistent with that of Cruz-Diaz et al.31 The  transition of CO2 is also present after irradiation but at lower intensity, which might be due to a combination of dissociation from electron irradiation and sputtering. The  transition of CO2 is not observable due to the overlapping A1Π ← X1∑+ CO band which has a much higher cross section. The 1E1u ← 1A1g and 1B1u ← 1A1g transitions of benzene are also present in the same position as the unirradiated benzene, albeit with lower intensity due to formation of products or sputtering.After irradiating with 1 keV electrons there is a noticeable difference in the spectrum compared to that of the unirradiated spectrum as shown in  transition of CO2 as it is close to the desorption temperature of CO2. At 80 K it is expected that the CO would have desorbed, as pure CO desorbs between 28–36 K depending on the original deposition temperature .32 However, the A1Π ← X1∑+ transition is still clearly observable although the intensity is lowered somewhat, with the  band no longer visible and the  band less well defined. Like the unirradiated sample discussed in Section 3.1.2 the benzene transition bands are present with a lower intensity for both electronic transitions and the vibronic structure of the 1B1u ← 1A1g transition are less well defined compared to that of spectrum taken at 20 K. At 90 K CO2 and CO have desorbed and interestingly the benzene band has increased in intensity. The 1E1u ← 1A1g transition shows signs of splitting similar to that observed in the unirradiated sample indicating crystallisation of benzene, however, this is less well defined compared to that of the unirradiated sample and may be due to the bands in the sample being saturated as the sample is thicker than the unirradiated sample. At 140 K the spectrum looks relatively flat; however, when zoomed in the 1E1u ← 1A1g transition is present, indicating that benzene is still desorbing at this temperature.Upon annealing to 80 K there is a further decrease in intensity of the 3.2.133 on toluene, which is a derivative of benzene, we know that the electronic transitions of toluene redshift compared to that of benzene. Additionally, a study by Hashimoto and Akimoto34 showed that when UV spectra of several derivatives of benzene  in oxygen matrices were taken the absorption maxima of the absorption bands shift from 238 nm for benzene to 266 nm for durene (the most substituted ring). This may suggest that the additional feature at 230 nm is due to the addition of a functional group on the benzene ring, in this case a carboxyl group. Furthermore, the mid-IR results obtained in the study by McMurtry et al.15 at 180 K show evidence of benzoic acid, isophthalic acid and terephthalic acid present, which also leads us to believe that our residue at 200 K contains benzene derivatives. However, further studies on benzene derivatives in the VUV are still required for more definitive identification of products as such data, to our knowledge, is not available in the literature.By 200 K all of the benzene has desorbed and a residue is left as shown in 46H6 : CO2 mixture. Benzene is a prototypical, aromatic molecule believed to be present in the icy mantles of interstellar dust where simple molecules such as H2O, CO, CO2, CH4 and NH3 are known to reside. These icy mantles will be subjected to energetic processing which can alter the composition of the icy mantles and possibly form benzene derivatives which may later be released into the gas-phase through thermal or photo-induced desorption. Benzene has a relatively high photoabsorption cross section in the vacuum ultraviolet part of the electromagnetic spectrum making it an attractive spectroscopic technique to use for the study of interstellar ice analogues containing dilute mixtures of benzene. Characterisation of the interstellar ice analogue before irradiation suggests that when benzene is diluted into CO2 a matrix-isolation effect takes place. This is evidenced through the shift in the 1E1u ← 1A1g and 1B1u ← 1A1g electronic transition towards gas-phase values of benzene compared to that of pure, solid benzene and the change in band profile to resemble a more gas-like character. Benzene derivatives are predicted to form after irradiation of the interstellar ice analogue15 and the residue at 200 K observed in this study shows that a benzene-like structure has formed. However, definitive assignment begs the need for further VUV spectroscopic work of condensed molecular films of potential irradiation products formed as such data has not yet been published.We have presented the results of the first vacuum ultraviolet spectroscopic study of the interstellar ice analogue of a 1 : 100 CThere are no conflicts to declare.


In the absence of an indirect effect, they all estimate the direct effect of the intervention. Otherwise, r1, r2, and r3 estimate the total effect, which comprises the direct and indirect effects, whereas r4 and r5 estimate the direct effect only. We derive the conditions under which each estimator is more precise or powerful than its alternatives. To control bias in studies with a small number of clusters, we propose a set of approximately unbiased estimators. We evaluate their properties by simulation and apply the methods to a trial of seasonal malaria chemoprevention. The approximately unbiased estimators are practically unbiased and their confidence intervals usually have coverage probability close to the nominal level; the asymptotically unbiased estimators perform well when the number of clusters is approximately 32 or more per trial arm. Despite its simplicity, r1 performs comparably with r2 and r3 in trials with a large but realistic number of clusters. When the variability of baseline event rate is large and there is no indirect effect, r4 and r5 tend to offer higher power than r1, r2, and r3. We discuss the implications of these findings to the planning and analysis of cluster randomized trials.We consider five asymptotically unbiased estimators of intervention effects on event rates in non‐matched and matched‐pair cluster randomized trials, including ratio of mean counts  Methods for individual‐level analysis of CRTs include random‐effects models and generalized estimating equations. As compared to cluster‐level analysis, individual‐level analysis has the relative advantage of efficiency and ease in covariate adjustment. However, it has the relative disadvantage of being less robust, especially when the number of clusters is small.r1.An estimator of the intervention effect in terms of incidence rate ratio, also called relative incidence, that only uses event data is a ratio of the arithmetic mean of the number of outcome events per cluster in the intervention arm to that in the control arm. We call this the “ratio of mean counts”, denoted by cij=yij/pij, where yij and pij are the number of events and person‐time in the jth cluster in the ith trial arm, respectively. Then, the arithmetic means of the cluster‐level event rates in the intervention and control arms are calculated, denoted by c‾1 and c‾0, respectively. The ratio of the two means, r2=c‾1/c‾0 is a popular estimator of the incidence rate ratio.CVcij = 0, 0.125, and 0.25, where CVcij is the coefficient of variation of the cluster‐level event rate in the ith trial arm and CVc0j is known as “k” in the literature.r2. However, another simulation study considered a broader range of CVcij.r2 was practically unbiased when CVcij = 0.05 and 0.15, but it was biased when CVcij = 0.4. Analytical investigation and simulation evaluation in a broad range of parameter values are warranted.The denominator of event rates, that is, units of person‐time, in CRTs is usually variable across clusters. The person‐time for estimation of an event rate is sometimes approximated by the population size at some point of the study duration. In this article we use the phrases person‐time and population size interchangeably. Typical statistical practice makes comparison of event rates instead of mean number of events between trial arms. It requires extra resources in the collection of person‐time data. A demographic surveillance system, a population census, or rounds of community surveys may be required for this purpose. With both the number of events and person‐time collected for each cluster, one may calculate a cluster‐level event rate for each cluster, denoted by r3. While c‾i  is an unweighted average of cluster‐level event rates in the ith trial arm, the alternative estimator of event rate here can be seen as a weighted average of cluster‐level event rates, with the clusters' population sizes as weights.An alternative estimator of incidence rate ratio can be obtained by first calculating the event rate in each trial arm as the sum of the number of events divided by the sum of person‐time over the clusters,r4, by replacing the sums of person‐time in r3 by the sums of number of events in the non‐target groups. Note that this estimator is defined even if the number of events in the non‐target group is zero in some clusters, which is a realistic situation because usually the reason of it being a non‐target group is that the disease incidence is relatively low. The motivation for considering this estimator arises from not only concerns of feasibility and cost of data collection but also concerns of precision and power. From an epidemiological point of view, sometimes we anticipate that the event counts in the target and non‐target groups are highly correlated, because they are both the manifestation of the disease burden in the clusters. In particular, some events are highly localized, for example, infectious diseases occurring in small outbreaks. For such events, the correlation between number of events in the target and non‐target groups, say children inside and outside a vaccination age range, is likely to be much stronger than the correlation between the number of events and amount of person‐time in the target group. This advantage in correlation offers a potential for improved precision. Note that r4 and the three estimators aforementioned have different targets of estimation (estimands): r1, r2, and r3 estimate the total effect of the intervention whereas r4 estimates the direct effect. Details will be discussed in the next section.In CRTs, interventions are often provided only to a specific group of the cluster members instead of all cluster members. For example, in studies of vaccines for pediatric infectious diseases, usually only young children in a specific age range are offered the interventions or its control comparators. Older children and adults are not. We refer to the two groups of cluster members as the target and non‐target groups. The outcome events may occur in both groups. In studies based on passive surveillance, the event data may be collected for the non‐target group in addition to the target group without much additional resources required, because the capital cost and infrastructure are already invested for the target group anyway. We consider an estimator that we call “double ratio of counts”, denoted by r5. It has the ratio of event rates between the target and non‐target groups in the intervention arm as the numerator and its counterpart in the control arm as the denominator. Details in statistical notations will be provided in the next section. We hypothesize that this estimator will out‐perform r4 in precision and power.We also propose a new estimator that we call “double ratio of event rates”, denoted by r2 aforementioned.Donner and Klar pointed out that CRTs of binary outcomes may regard a proportion as a ratio and then an appropriate variance estimate can be obtained from sample survey theory.This study aims to (a) evaluate and compare the performance of the five estimators aforementioned and (b) develop, evaluate, and compare bias‐corrected version of them. In Section For brevity, we will focus on CRTs that randomize clusters individually, that is, non‐matched CRTs. Where necessary we also provide the details for matched‐pair CRTs in which one cluster per matched pair is randomized to receive the intervention and the other serves as the control. Introduction to the two types of CRTs can be found in, for example, Hayes and Moulton22.1βT, βD, and βI are the total, direct, and indirect effects in terms of log incidence rate ratio. If there is no indirect effect, βI=0 and βT=βD. The presence of an indirect effect depends on various factors including the nature of the interventions and outcome events. For example, even though vaccines are often anticipated to generate some degree of indirect effect on efficacy endpoints, they are usually anticipated to have no indirect effect on safety endpoints.An intervention may have a direct effect and an indirect effect, for example, via reducing disease transmission in the community.Yijk and Pijk be the number of events and total person‐time in the kth group of the jth cluster in the ith trial arm in the population, respectively, where k = 1 and 0 represent the target and non‐target groups, respectively, i = 1 and 0 represent intervention and control trial arms, respectively. We consider a data generating process that is often used in epidemiologic modeling, that the expected value of Yijk given Pijk is:βD,ik and βI,i represent direct and indirect effects , αij is a random cluster effect with standard deviation SDαij ≥ 0 that represents variation in event rates between clusters within each trial arm, and γk represents the difference in event rates between the target and non‐target group . Note that SDαij≅CVcij, the coefficient of variation in cluster‐level event rate.αij and Pijk are identical in expectation between the intervention and control arms. From Equation  provides an asymptotically unbiased estimator of the direct effect:r4 is:r2 vs r4 and r3 vs r4 are meaningful only if the indirect effect is absent or trivial and the estimates r2≅r4 and r3≅r4. In Section A of Online Supplementary Material 1 we show that Varr4<Varr2 if in both trial arms:Varr4<Varr3 if in both trial arms:r4 over r2 and r3 in terms of precision.In contrast, with large r2=ζr4, then tr2<tr4 if in both trial arms :r3=ξr4, then tr3<tr4 if in both trial arms:ζ=1 or ξ=1, Equations :corryij1quations  and 10)∣tr2∣=∣rr4, the ratio of event rates estimator, r5=R1†/R0†=R11′/R10′R01′/R00′, where Rik′=∑jyijk∑jpijk, also provides an asymptotically unbiased estimator of the direct effect. The variance of r5 is:p‾i⋅k=∑j=1nipijk/ni.Similar to Varr5<Varr4 if in both trial arms :Varr5<Varr4 in many studies.Furthermore,n1=n0=n is the number of pairs of clusters. Within the jth pair of clusters, one cluster is randomized to receive intervention (i = 1) and the other is the control cluster (i = 0). The paired design version of the five estimators, rlpaired, and their variances are shown in Appendix Table For matched‐pair CRTs, 2.3r1paired.r3paired or r4paired.n−1; bias‐reduction methods were proposed. Useful though they are, they do not deal with non‐matched CRTs and r2paired and r5paired.The literature about bias in ratio estimators and the mitigation methods has very much focused on paired observations, mostly concerning an estimator in the form of One solution is to determine the expectation and therefore bias of a ratio estimator, and then subtract the bias from the estimator. See, for example, van Kempen and van Vliet2.3.1r1 and approximately unbiased estimator r1* of the ratio of means estimator are, respectively:Y‾0⋅1 approximated by the sample mean y‾0⋅1 to form the sample CV.The expectation of the asymptotically unbiased estimator 2.3.2r2 and approximately unbiased estimator r2* are, respectively:C‾0 replaced by the sample estimate to form the sample CV.The expectation of the asymptotically unbiased estimator 2.3.3Y‾i⋅1 and P‾i⋅1 replaced by their sample estimates to form the sample CVs.2.3.4Er4 and r4* can be obtained by replacing r3, pij1 and P‾i⋅1 by r4, yij0, and Y‾i⋅0 in the formula in the previous sub‐section on ratio of event rates.2.3.52.3.6r1* is:Varrl*=Varrl for l= 2, 3, 4, and 5 as well.The variance of lnrl*∀l. Using the delta method and the result above, Varlnrl*=Varrl/rl*2∀l, where Varrl have been given in Equations t‐distribution with n1+n0−2 degrees of freedom for non‐matched CRTs and n−1 degrees of freedom for matched‐paired CRTs.The distribution of ratios is not normal. For calculation of confidence intervals, we calculate Varr3 involves an asymptotic variance estimator of VarRi=Var∑j=1niyij1/∑j=1nipij1. Similarly, in Equations *, l= 3, 4, and 5, to denote the estimators when used together with this Jackknife‐based variance estimation method.In Equation , the calquations  and 13)Varr3 inv33.1kth group in the jth cluster in the ith trial arm, conditional on the person‐time pijk, by using a Poisson distribution with expected value given by Equation  expβD=0.5 and expβI=0.75; (c) expβD=1 and expβI=1. We set γ=1 for the difference in event rate between the target and non‐target groups. We set person‐times pij1,pij0 as following a bivariate distribution with means 100, coefficient of variation CVpijk= 0.2, 0.4, or 0.6, skewness 1.5, kurtosis 4, and correlation 0.8. Our choice of CVpijk takes into account the findings from a recent systematic review of CRTs that the first quartile, median, and third quartile of CVpijk were 0.22, 0.41, and 0.52, respectively.rmvnonnormal macro in Stata for the non‐normal data generation.CVpijk= 0.2 or 0.4, as symmetric distribution is possible under modest CV. A small number of observations  with person‐time either below 5 or above 350 were replaced by 5 or 350, respectively. This is because CRTs often exclude clusters that are very small in size and exclude or sub‐divide very large clusters due to operational and efficiency considerations.αij, as following a normal distribution with mean − 2 and SDαij= 0.05, 0.2, and 0.5. The three levels of SDαij correspond to approximately CVcij = 0.05, 0.2, and 0.5.CVc0j is “often ≤ 0.25 and seldom exceeds 0.5 for most health outcomes”.For non‐matched CRTs, we generated the number of events in the Equation . We consith trial arm in the jth paired cluster  by using a Poisson distribution with expected value expβD,ik+βI,i+αij+γpij1 in the target group and expβI,i+αijpij0 in the non‐target group. We set the paired cluster effects α1j,α0j as following a bivariate normal distribution with means −2 and SDs 0.05, 0.2, or 0.5 and correlation 0.8. The person‐time parameter in the kth group in the jth pair of clusters pijk followed a multivariate non‐normal distribution with means 100, CVpijk= 0.2, 0.4, or 0.6, skewness 1.5, kurtosis 4, and correlation 0.8. Additionally, multivariate normal distribution was used in the case of CVpijk= 0.2 or 0.4. The other parameters in the matched‐pair CRTs were the same as those in the non‐matched CRTs.For matched‐pair CRTs, we generated the number of events in the In the literature, it has been suggested that non‐matched CRTs should include at least four clusters per trial arm and matched‐pair CRTs should include at least six pairs of clusters.In each scenario, we conducted 10 000 replicates of data generation and in each of them calculated the five asymptotically unbiased estimators and the five approximately unbiased estimators and their variances. We report the relative bias of the mean estimates of the incidence rate ratio, root mean square error (RMSE), coverage probability (CP) of the 95% confidence intervals (CI) and power to reject the null hyperthesis of the respective ratio equals one (or type 1 error when the null hyperthesis is true). Calculation of CIs was based on log‐transformation and then exponentiate back to the original scale, which were used for statistical inference. Calculations of relative bias and RMSE were based on the ratios themselves without transformation.3.2expβD=0.5 and expβI=1, and CVpij=0.4, which was approximately the median level of variability in cluster size found by a systematic review.r1, r2, r3, r1*, r2*, and r3* (upper panel) and r4, r5, r4*, and r5* (lower panel).In Figures ni) increased. Furthermore, the bias of r1, r2, and r3 increased as SDαij increased. In scenarios with SDαij≤0.2, r2, and r3 only showed very mild bias and the two curves mostly overlapped. In contrast, the approximately unbiased estimators, r1*, r2*, and r3*, were practically unbiased under all situations considered. The relative bias of r4 and r5 was stable in relation to SDαij. The approximately unbiased estimators r4* and r5* were practically unbiased under all situations considered.Figure r2* and r3* had smaller RMSE than r1*, but they converged as ni increased. r2* had slightly smaller RMSE than r3* when SDαij=0.5 and ni was small. Otherwise they were almost indistinguishable from each other. r5* had smaller RMSE than r4*. Their difference was stable across level of SDαij but they converged as ni increased. The asymptotically unbiased estimators had RMSE similar to or slightly larger than their respective approximately unbiased counterparts', but the difference vanished as ni increased.In Figure SDαij was large *, gave improved CP that was closer to the nominal 95% level than r3*. In the lower panel, r4, r5, r4*, and r5* had varying degree of under‐coverage in different scenarios. However, using the Jackknife‐based variance estimators for r4* and r5*, denoted by r4(J)* and r5(J)*, respectively, the CP was close to the nominal level in all situations.The estimators tended to have coverage probability (CP) smaller than the nominal 95% level, especially when e Figure . The CP expβD=1 and expβI=1. Otherwise, the parameters are the same as those in Figures SDαij≥ 0.2 and ni< 32. The inflation reduced as ni increased. In the upper panel, r2 and r2*, followed by r3(J)* and r1*, performed better than the others. In the lower panel, r4, r5, r4*, and r5* had varying level of inflation of type 1 error under different parameter settings. In contrast, r4(J)* and r5(J)* performed well. In no circumstances did they show more than 1% deviation from the 5% target.Figure r2* and r3(J)*, vs selected estimators that use event counts in the non‐target group as denominators, r4(J)* and r5(J)*. We focused on them because they performed well in terms of CP and type 1 error rate. The lower panel introduced an indirect effect, expβI=0.75, in addition to a direct effect, expβD=0.5. Otherwise, the parameters here are the same as those in Figures r2* and r3(J)* were more powerful than r4(J)* and r5(J)* for SDαij≤0.2. In contrast, r4(J)* and r5(J)* were more powerful when SDαij=0.5. Furthermore, r5(J)* was more powerful than r4(J)* in all the scenarios considered. With the addition of the indirect effect, r2* and r3(J)* were more powerful than r4(J)* at all levels of SDαij, but similar to r5(J)* at SDαij=0.5.Figure r1 and r4 increased substantially as CVpij1 increased except when the number of cluster was about 32 or above. In contrast, r2, r3, r5 and the approximately unbiased estimators were much less sensitive to the magnitude of CVpij1 * reduced to about 93% and its type 1 error rate increased to about 7% when CVpij1 = 0.6, SDαij = 0.5 and the number of clusters was 6 or below *,paired performed well in these aspects while r2*,paired had somewhat inflated type 1 error rate and below target CP  in Senegalese children to illustrate.A passive surveillance system was implemented in health facilities to determine the number of clinical malaria episodes confirmed by rapid malaria test (primary endpoint) in each cluster, by four age groups . The data was at the cluster, not individual, level. Mortality data was collected for all age groups but only data for children aged 9 years or below was used in the previously published analysisFor the purpose of illustration, we used the 2008 data from the 18 clusters that resembled a non‐matched CRT. Children aged between 3 to 59 months were the target group. We considered children aged 5 to 9 years the non‐target group.CVcij1>1 in both arms. In the target group, the CVs of malaria episodes approximately doubled the CVs of the population size, with θ=CVpij1/CVyij1≈0.60/1.37=0.44. The correlation coefficient between malaria episodes and population size of the target group, corryij1,pij1, was weak, with average across trial arms being only 0.03. The estimates of malaria incidence rate in the SMC and control arms were c‾1=0.0029>R1=0.0028 and c‾0=0.0031>R0=0.0020, respectively. In contrast, the correlation between malaria episodes in the target and non‐target group, corryij1,yij0, was strong, averaged at 0.76.Table l = 3, 4, and 5, the SE's based on rl(J)* were only slightly larger than rl*. All confidence intervals were quite wide. Although corryij1,pij1 was weak, the estimated r1 was much larger than r2 and r3, leading to standard error SEr1 larger than SEr2 and SEr3. Given c‾i>Ri in both trial arms, SEr2<SEr3. As expected from Equations l = 3, 4,Equation , Varr4≅VCVcij1 in the two arms averaged at 0.79. Furthermore, in the target group, the CVs of death approximately doubled the CVs of the population size, with θ=CVpij1/CVyij1≈0.60/1.00=0.60. Unlike malaria episodes, the correlation coefficient between deaths and population size of the target group was more substantial, with average across trial arms being 0.59. The estimates of mortality rate in the SMC and control arms were c‾1=0.0022<R1=0.0025 and c‾0=0.0018>R0=0.0017, respectively. The correlation between deaths in the target and non‐target group was moderate, with average corryij1,yij0 at 0.51; this was weaker than that for malaria episodes.Table SE's based on rl(J)* were only slightly larger than those based on rl*. All confidence intervals were quite wide. Since corryij1,pij1 was substantial and the estimated r1 was much larger than r2 and r3, SEr2 and SEr3 were smaller than SEr1. With fairly similar values of corryij1,yij0 and corryij1,pij1 and relatively large θ, SEr2 and SEr3 were smaller than SEr4. There was no clear difference between corryij1,pij1+corryij0,pij0 and corryij1,pij0+corryij0,pij1 in either trial arm, so Varr4≅Varr5.Estimation results on mortality are available in Table 5r1 has performance very similar to r2 and r3. At the study planning stage, investigators may take into account this finding when they consider the cost and benefit of collecting person‐time data.The proposed approximately unbiased estimators successfully reduce the bias when the number of clusters is small. They also have advantages in terms of smaller RMSE and more accurate coverage probability than the asymptotically unbiased estimators. For studies with fewer than 60 clusters per arm, we recommend the use of the approximately unbiased estimators. Some CRTs do have a large number of clusters per trial arm, for example, a trial of influenza vaccination had over 400 nursing homes per armr2.r2 is a non‐linear function of the between‐cluster variability of event rate. From simulation, the bias of r2 became obvious as the variability increased, especially when the number of clusters per trial arm was below 16 or so. In the SMC study of malaria episodes, where the variability was large, the r2 estimate was much larger than r2*. In those situations, the use of our proposed bias‐corrected estimator r2* is preferable over r2.Previous simulation studies evaluated the performance of the estimator r3* performs well in terms of bias and RMSE, its variance estimator under‐estimates the true variability as the CV of cluster size or event rate increases; it approaches the target CP as the number of clusters increases. The under‐coverage can be corrected by plugging the Jackknife estimates of VarRi into the estimator for Varr3. We found that r2* and r3(J)* have similar performance except when CVpijk = 0.6 or SDαij = 0.5. In those settings, r3(J)* had type 1 error rate up to about 2% higher than the nominal 5% level when the number of clusters was six or below, and r2* may be preferred. However, in matched‐pair CRTs, r2*,paired did not out‐perform r3(J)*,paired. Furthermore, previous studies had shown that the estimator of cluster‐level event rate in a trial arm, c‾i, is a biased estimator, and the level of bias does not reduce in relation to increase in number of clusters.Ri can be used to obtain an asymptotically unbiased estimate of disease incidence.r2* is used to estimate incidence rate ratio, Ri is preferable over c‾i as an estimator of the incidence rate in each trial arm.While r4 and r5 was in part motivated by an evaluation of a malaria vaccine where indirect effects were unlikely and the incidence of some outcomes such as meningitis (a safety outcome) could be highly variable between clusters, and where balanced randomization with respect to access to health care facilities (where passive surveillance took place) was difficult to ensure.SDαij is large, the number of events in the target group is likely to be more strongly correlated with the number of events in the non‐target group than with the person‐time in the target group. Furthermore, it is typical that vaccine studies anticipate no indirect effect on safety endpoints. So, these estimators are expected to estimate the same target as far as safety is concerned. In simulation studies of scenarios that the intervention only had a direct effect, we have seen that when SDαij was ≤0.2, r2* and r3(J)* tended to be more powerful than r4(J)* and r5(J)*. When SDαij increased to 0.5 and in the malaria data in the SMC trial, r4(J)* and r5(J)* had substantially smaller SE than r2* and r3(J)*. For situations like this, r4(J)* and r5(J)* are our estimators of choice. In various scenarios we evaluated, r5(J)* gave higher level of statistical power than r4(J)*, except that they had similar performance when CVpijk was small. In that case, the magnitude of the benefits may not justify the extra cost in collection of person‐time data in both the target and non‐target groups. Otherwise, r5(J)* tends to be preferable over r4(J)*.Our consideration of r2 or r3 or their extensions may be used in efficacy analysis while r4 and r5 or their extensions may be used in safety analysis.We foresee that the estimators that use person‐time in the target group and estimators that use number of events in the non‐target groups as a denominator may be used in different parts of the same CRT, depending on the considerations aforementioned. For example, r4 and r5 are generic quantities in the sense that yij0 may be replaced by quantities other than the number of events in non‐target groups to achieve other purposes. For example, there has been interest in the use of “negative control events” to remove the bias arising from differential ascertainment of outcome events in non‐blinded CRTs.r4, with y1j0 and y0j0 replaced by the number of negative control events in the intervention and control arm, respectively.yij0 by the baseline event count, r4 becomes a baseline adjusted estimator of the total effect. It offers a robust alternative to the analysis of CRT‐BA trials.Furthermore, The strengths of the present study include coverage of both non‐matched and matched‐pair CRTs, analytic evaluation of the bias of existing asymptotically unbiased estimators, proposal of estimators that capitalize on denominators other than cluster population size and their potential applications, development of a bias‐corrected version of these estimators for use in studies with a small number of clusters, and simulation evaluation of the estimators with a realistic range of variability in cluster size. A limitation is that the methods do not handle covariate adjustment. However, good use of restricted randomization may reduce the need for covariate adjustment in the analysis stage.r1 and r2, whose calculation begins with getting an event count and event rate per cluster, respectively. This is different from the calculation of r3 to r5, which begins with generating an estimate for a trial arm. For example, in r3, the incidence rate in a trial arm is the sum of events over clusters divided by the sum of person‐time over clusters within the trial arm. There is not a summary value for every cluster. Furthermore, when the purpose is to estimate rate ratio instead of rate difference, the ANCOVA approach would need to analyze the log‐transformed values instead. The exponentiated intervention effect estimate is then interpreted as a ratio of geometric means, which is not the same as the widely used estimator of ratio of arithmetic means (including r1 and r2). In CRTs with a small number of clusters, the bias and bias‐correction for ratios of geometric means of event counts and event rates have yet to be investigated. Another approach is to use Poisson regression analysis with cluster‐level covariates  without using the intervention variable as predictors to obtain an expected number of events for each cluster.yij0 in r4 or pijk in r5 are replaced by this expected number of events, they become covariate adjusted estimators of the total or direct effect, respectively. The bias‐correction method may then be applied to obtain covariate adjusted r4* or r5*. But the variance estimators may not work well as they do not account for the uncertainty in the prediction of the expected number of events. In short, while there are several candidate approaches available, challenges remain. Further research is needed to develop and evaluate these or other approaches to covariate adjustment.In non‐matched CRTs, one approach for controlling covariate effects is stratified analysis and pooling of stratum‐specific estimates using weights inversely proportional to variances. The limitation is that it is not practical to stratify for multiple covariates and it requires categorization of continuous covariates. Another approach is to apply ANCOVA to cluster‐level data. However, it only works for methods that generate a summary value per cluster, such as corryij1,pij1 is important in determining the relative strength of the different estimators. A large SDαij tends to dilute this correlation. As such, pilot data and careful consideration of the between‐cluster variability in event rate is important not only for sample size determination but also for choice of study design and statistical analysis procedures.The size of The authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.Online Supplementary Material 1: Comparisons of asymptotically unbiased estimators and derivations of approximately unbiased estimatorsClick here for additional data file.Online Supplementary Material 2: Further simulation results, by number of clusters per trial arm and three levels of SD (αij); mean population size per cluster is 100Click here for additional data file.


When triethylsilane was used as a substrate, the system revealed the largest kinetic isotopic effect (KIESi−H/Si−D=346±4) ever reported for this type of reaction. This unexpectedly high KIE, measured at room temperature, together with the calculated Arrhenius preexponential factor ratio (AH/AD=0.0004) and difference in the observed activation energy [(EaD−EaH)=34.07 kJ mol−1] are consistent with the participation of quantum tunneling in the catalytic process. DFT calculations have been used to unravel the reaction pathway and identify the rate‐determining step. Aditionally, isotopic effects were considered by different methods, and tunneling effects have been calculated to be crucial in the process.An unprecedented quantum tunneling effect has been observed in catalytic Si−H bond activations at room temperature. The cationic hydrido‐silyl‐iridium(III) complex, {Ir[SiMe(o‐C A “giant” kinetic isotope effect (KIE=346) has been observed for the generation of hydrogen from the hydrolysis of silanes catalyzed by a silyl‐iridium(III) complex. This and other experimental evidence together with theoretical calculations have been used to demonstrate the participation of hydrogen quantum tunneling in this catalytic process. The parent iridium dimer [Ir(cod)Cl]2 has also been included in the initial screening for comparative purposes.2 vs time) are shown in Figure Iridium(III) compounds 2 was used as precatalyst. This result indicates that a vacant coordination site on the catalyst is required for the reaction to proceed. In contrast, compound 1, containing a labile solvent molecule, was a very effective catalyst for the hydrolysis of Et3SiH, liberating 1 equiv of H2 in only 35 seconds (Table 1/2) was 2.8 times larger than that observed for the dimeric iridium precursor [Ir(cod)Cl]2 under identical reaction conditions. 1H and 1H‐29Si HMBC NMR analysis of evaporated samples at the end of the reaction permitted us to identify triethylsilanol as the only silane‐containing product . The robustness of the catalytic system derived from 1 was confirmed through successive additions of Et3SiH. The sequential reaction profiles obtained showed that the catalyst maintained its activity for at least 10 successive cycles . The results obtained showed a clear electronic influence of the silane substituents on the reaction rate .The hydrolytic reaction with precatalyst 1 towards the alcoholysis of Et3SiH was also explored . The reaction proceeded at similar rates for the primary alcohols assayed  was used as a nucleophile.The catalytic activity of compound 1 among the most active catalytic systems for the hydrolysis and alcoholysis of organosilanes. [Et3SiH]) . Kinetic isotopic effect (KIE) was analyzed, using compound 1, on both the hydrolysis and the methanolysis of Et3SiH. The results obtained showed no effect on the reaction rate when a deuterated nucleophile was used (KIEH2O/D2O=KIEMeOH/MeOD=1), which is consistent with the zero‐order dependence of the reaction rate on H2O concentration (see above). Surprisingly, extraordinarily high KIEs (25 °C) were calculated when the reaction rate using Et3SiD was compared to that of Et3SiH (KIEEt3SiH/Et3SiD(25 °C)=346±4 (hydrolysis); KIEEt3SiH/Et3SiD(25 °C)=143±1 (methanolysis), see Figures S14 and S16, Supporting Information. These results clearly point to H−Si bond activation being involved in the rate‐determining step (RDS) of the catalytic reaction, and suggest the possible participation of hydrogen quantum tunneling in this step of the process.2 was used as precatalyst, KIEH2O/D2O=1.10±0.03 and KIEEt3SiH/Et3SiD=2.26±0.06  were measured. These results also pointed to a related mechanism, with H−Si bond activation being involved in the RDS, but hydrogen quantum tunneling could not be claimed in this case. In fact, a comparison of rate constants between precatalysts 1 and [Ir(cod)Cl]2 using Et3SiD as a nucleophile (k(1)=0.101 s−1 M−1; k([Ir(cod)Cl]2)=8.45 s−1 M−1) reinforces the idea that the high activities observed for our system are caused by a quantum tunneling mechanism, strongly inhibited when deuterosilanes were used as nucleophiles. No tunneling has been observed for the methanolysis of Et3SiH(D) using the cationic iridium(III) complex [IrCp*(phenylpiridine)(MeCN)]+.H/AD<0.7) and a difference in the observed activation energy larger than the ones expected from zero‐point energy (EaD−EaH>5.02 kJ mol−1) would support this idea.+,2O molecule to the silylium cation. This front side H2O is oriented like in 1C, keeping the silylium cation close to the dihydrido‐iridium complex. The so‐formed intermediate is labelled as 2C. In this complex, the electrostatic (H∂+−H∂−) interaction remains, as it may be concluded from the distance between the protic H−OH the hydride H−Ir, 1.57 Å, and the partial charges 0.547 and −0.118 e, respectively. From this intermediate, the protic H atom is ready to be transferred from the front‐side H2O to the dihydrido‐iridium complex through 2TS, leading to the formation of an iridium‐H2 complex (3C) and Et3Si−OH species after the decomplexation of the back‐side H2O.The next step would be the formation of a pentacoordinated silylium cation +, 2C in scheme Summarizing the computational results, they confirm the key role of hydrogen tunneling in the reaction mechanism, and provide a detailed mechanism for this reaction Scheme . Slight eme 3SiOH2]+, C2 III complex 1, behaved as an efficient precatalyst for the hydrolysis/alcoholysis of tertiary silanes leading to the release of one equivalent of dihydrogen and the corresponding silanols/silylethers. Kinetic studies on the process revealed kSi‐H/kSi‐D=346, which represents the largest one involving Si−H/D bonds observed up to date. This huge KIE in addition to the calculated Arrhenius factor and the difference in the observed activation energy are experimental indications of the participation of hydrogen quantum tunneling in the RDS of the process at room temperature. Detailed DFT calculation on the reaction mechanism allowed us to propose a slightly modified electrophilic mechanism for the reaction compared to the previously reported ones. In addition to this, theoretically calculated KIEs at different temperatures using the WKB one‐dimensional tunneling correction, support the importance of quantum tunneling. To the best of our knowledge, this is the first reported case of hydrosilane activation with the participation of quantum tunneling.The cationic hydrido‐silyl‐IrThe authors declare no conflict of interest.1As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.Supporting InformationClick here for additional data file.