Digital proximity-tracing apps have been deployed in multiple countries to assist with SARS-CoV-2 pandemic mitigation efforts. However, it is unclear how their performance and effectiveness were affected by changing pandemic contexts and new viral variants of concern.The aim of this study is to bridge these knowledge gaps through a countrywide digital proximity-tracing app effectiveness assessment, as guided by the World Health Organization/European Center for Prevention and Disease Control (WHO/ECDC) indicator framework to evaluate the public health effectiveness of digital proximity-tracing solutions.We performed a descriptive analysis of the digital proximity-tracing app SwissCovid in Switzerland for 3 different periods where different SARS-CoV-2 variants of concern  were most prevalent. In our study, we refer to the indicator framework for the evaluation of public health effectiveness of digital proximity-tracing apps of the WHO/ECDC. We applied this framework to compare the performance and effectiveness indicators of the SwissCovid app.Average daily registered SARS-CoV-2 case rates during our assessment period from January 25, 2021, to March 19, 2022, were 20 (Alpha), 54 (Delta), and 350 (Omicron) per 100,000 inhabitants. The percentages of overall entered authentication codes from positive tests into the SwissCovid app were 9.9% , 3.9% , and 4.6%  during the Alpha, Delta, and Omicron variant phases, respectively. Following receipt of an exposure notification from the SwissCovid app, 58% , 44% , and 73%  of app users sought testing or performed self-tests. Test positivity among these exposure-notified individuals was 19% (7/37) in the Alpha variant phase, 29% (2/7) in the Delta variant phase, and 41% (11/27) in the Omicron variant phase compared to 6.1% , 12% , and 41.7%  in the general population, respectively. In addition, 31% , 19% , and 30%  of exposure-notified app users reported receiving mandatory quarantine orders by manual contact tracing or through a recommendation by a health care professional.In constantly evolving pandemic contexts, the effectiveness of digital proximity-tracing apps in contributing to mitigating pandemic spread should be reviewed regularly and adapted based on changing requirements. The WHO/ECDC framework allowed us to assess relevant domains of digital proximity tracing in a holistic and systematic approach. Although the Swisscovid app mostly worked, as reasonably expected, our analysis revealed room for optimizations and further performance improvements. Future implementation of digital proximity-tracing apps should place more emphasis on social, psychological, and organizational aspects to reduce bottlenecks and facilitate their use in pandemic contexts. To contribute to mitigation efforts against the spread of SARS-CoV-2, digital proximity-tracing apps were developed and widely adopted in multiple countries. This gave rise to a novel research area within digital public health, which aims to assess the possible contribution of such apps toward disease control. Prominent examples of digital proximity-tracing apps in Europe include the United Kingdom’s National Health Service’s (NHS) COVID-19 app, the German Corona-Warn-App, and the SwissCovid app from Switzerland . In SwitThere is growing interest in further evaluating the effectiveness of digital proximity-tracing apps. However, effectiveness analyses face multiple challenges ,9. FirstEmpirical evaluations of the effectiveness of digital proximity-tracing apps remain scarce . Recent The aim of this study is to bridge these knowledge gaps through a countrywide digital proximity-tracing app effectiveness assessment, as guided by the WHO/ECDC framework. Specifically, we performed a descriptive analysis of the digital proximity-tracing app in Switzerland for 3 different periods where different SARS-CoV-2 variants of concern  were most prevalent. We performed this analysis by applying the WHO/ECDC framework to individual and public-level data, which we complemented with additional indicators of mitigative actions taken by app users after receiving an exposure notification. Accordingly, our analysis applies the WHO/ECDC framework indicators in the greater pandemic context to inform future indicator-based app monitoring and effectiveness assessment efforts.Switzerland was 1 of the first countries that launched a digital proximity-tracing app (SwissCovid) based on the DP-3T architecture on June 25, 2020 ..24].For the COVID-19 Social Monitor study, the Cantonal Ethics Commission of Zurich concluded that our study did not fall within the scope of the Human Research Act (BASEC-Nr. Req-2020-00323). All other data did not require ethics approval.The red and green lines illustrate the number of entered authentication codes by SARS-CoV-2–positive SwissCovid app users and calls to the infoline or completion of a self-assessment form upon receipt of an exposure notification, respectively. In the assessed period, the counts of these user-driven actions closely followed the incidence curve. Furthermore, they occurred in an almost stable 1:1 ratio, with 1 infoline call or completed web form per shared positive test result for the majority of the study period. However, there was a shift in this ratio deviating toward fewer user actions taken by exposed contacts during the Omicron variant phase.Indicators from the WHO/ECDC framework and selected complementary indicators from the COVID-19 Social Monitor data are illustrated in radar plots . Figure Indicator 3 represents the number of authentication codes that were shared with the SwissCovid app as a fraction of the total number of individuals with a positive SARS-CoV-2 test. This percentage was 9.9%  during the Alpha variant phase and then declined to 3.9%  and 4.6%  during the Delta and Omicron variant phases, respectively. Indicator 4 reflects the ratio of authentication codes entered into the SwissCovid app over issued authentication codes. Here, we observed a nearly twice as large proportion of entered codes during the Alpha variant phase  compared with the Delta  and Omicron variant phases . Indicator 5 represents the timing of authentication code upload into the Swisscovid app from symptom onset or positive test date if the app user was asymptomatic at the time of testing. This indicator suggests that between 50% and 56% of all entered codes were uploaded within 48 hours after symptom onset, with lower percentages observed in the following 2 variant phases.Lastly, indicator 6 represents the proportion of SwissCovid app users who completed the provided web form and called an infoline after receiving an exposure notification. Here, we observed that between 23% and 28% of exposure-notified app users contacted the infoline or completed the web form within 48 hours after the exposure date, which is provided in the exposure notification message.Test positivity following receipt of an exposure notification is considered a proxy to assess the precision of exposure detection in notifying affected individuals. The third set of indicators illustrates the extent of mitigative actions taken by SwissCovid app users following receipt of exposure notifications. Indicator 14 illustrates the ratio of users seeking contact through the infoline or completing the web form per shared positive test result. This value decreased over the course of the pandemic from 1.08 user contacts per code during the Alpha variant phase to 1.00 during the Delta variant phase and 0.50 during the Omicron variant phase. Indicator 15 illustrates the exposure risk assessment following contact with the infoline or via a web form, as well as a voluntary quarantine recommendation following receipt of exposure notifications. The proportion of quarantine recommendations per user contact was 7.4%  during the Alpha variant phase and increased to 18.5% during the Delta and 19.1% during the Omicron variant phases .Indicator 16 illustrates the standardized voluntary quarantine recommendations by the number of shared positive test results. Here, there were approximately 8 recommendations per 100 tests in the Alpha variant phase, 18 recommendations per 100 tests during the Delta variant phase, and 10 recommendations per 100 tests during the Omicron variant phase. Indicator 17 illustrates data from the COVID-19 Social Monitor and indicates that 58% (37/64), 44% (7/16), and 73% (27/37) app users sought testing or performed self-tests following an exposure notification during the Alpha, Delta and Omicron variant phases, respectively. Lastly, indicator 18 reveals that 31% , 19% , and 30%  of individuals who received exposure notifications also reported to have received mandatory quarantine orders by manual contact tracing or through a recommendation by a health care professional.Our study presented various digital proximity-tracing app performance indicators for Switzerland. These were guided by and built upon the WHO/ECDC framework for the assessment of digital proximity-tracing apps' public health effectiveness in mitigating onward transmission of SARS-CoV-2. Our analysis extends the current knowledge in the field of digital proximity tracing by comparing various pandemic periods that were characterized by different SARS-CoV-2 variants of concern, as well as by changes in public perceptions of the pandemic and public health responses. Our study further contributes to effectiveness assessments on a methodological level by introducing further indicators of interest from panel survey data that assess mitigative strategies taken by individuals following receipt of exposure notifications. To the best of our knowledge, this is the first countrywide application of the WHO/ECDC performance assessment framework.A first set of indicators explored the exposure notification cascade performance throughout the 3 variant phases. A substantially higher SARS-CoV-2 incidence was observed during the Omicron variant phase, while active SwissCovid app use steadily declined between the Alpha and the Omicron variant phases. Compared to the peak use of the SwissCovid app in early 2021 with nearly 2 million active app users, the numbers decreased by approximately 600,000 users in March 2022. Furthermore, the early months of 2022 were marked by not only the highest SARS-CoV-2 incidence in Switzerland but also the highest absolute numbers of shared positive test results throughout the whole pandemic. This led to capacity issues in Switzerland, since an insufficient number of SARS-CoV-2 tests were available to meet such high demands. Combined with the public perception of a lower disease severity of Omicron, these 2 factors have likely contributed to the lower percentage of shared test results in later pandemic phases. A further notable difference between the 3 variant phases was that a comparatively lower proportion of issued authentication codes were entered into the app with variants of concern that appeared later in the pandemic. This may have resulted from changes in authentication code–issuing practices throughout the pandemic phases , as well as possibly by a decreased acceptance of the SwissCovid app .The second set of indicators focused on general test positivity in Switzerland and the proportion of individuals who tested positive for SARS-CoV-2 upon receiving an exposure notification from the SwissCovid app. The indicators illustrated a close link between test positivity and the overall SARS-CoV-2 incidence in Switzerland throughout the different phases of the pandemic. Specifically, SARS-CoV-2 case numbers and test positivity were relatively low during the Alpha variant phase but increased during the Omicron variant phase. Our individual-level analyses suggested that test positivity after receiving an exposure notification was 2-3 times higher than in the general population in the Alpha and Delta variant phases and of similar magnitude  during the Omicron variant phase. Even though this assessment is based on a relatively small sample size, the observed high test positivity is plausible in a wider context since the SwissCovid app operates on more conservative Bluetooth attenuation signal thresholds compared to the apps from other countries.The third set of indicators suggests that the mitigative actions taken by app users following the receipt of an exposure notification from the SwissCovid app may have changed over the course of the pandemic. During the Omicron variant phase, fewer people contacted the infoline or completed web forms in comparison to the Alpha and Delta variant phases. This decrease in contact attempts also resulted in relatively fewer voluntary quarantine recommendations. In the Alpha and Omicron variant phases, the proportion of reports of entering into mandatory quarantine upon receiving an exposure notification was of similar magnitude. In contrast, a higher proportion of exposure-notified app users reported to have gotten tested throughout the earlier variant phases. This may have likely been due to shifts in public perceptions regarding the disease severity of SARS-CoV-2 over time. Furthermore, it could have been a response to changing public health strategies during the Omicron variant phase, such as removing mandatory quarantine for exposed contacts in Switzerland on February 17, 2022. As suggested by the high general test positivity of 40% during the Omicron variant phase, many symptomatic or exposed individuals also relied less on SARS-CoV-2 PCR testing but, rather, self-tested or just stayed at home. Since SARS-CoV-2–infected individuals who did not get tested at official testing centers did not receive upload authentication codes, they could consequently not share their test results with proximity contacts via the SwissCovid app.The indicators also provide insights into the possible contribution of digital proximity-tracing apps, such as SwissCovid, in mitigating viral spread. For example, the ratio of shared positive test results over the upper ceiling estimate of positive tests among app users suggest that between 60% (Alpha variant phase) and 80% (Delta and Omicron variant phases) of estimated app users who tested positive did not or were unable to share their test results. The reasons for this may include that a lower number of issued authentication codes were entered into the SwissCovid app or that there were delays in issuing authentication codes. The latter can negatively affect the potential for digital proximity tracing if exposed contacts are informed faster through other means . Nevertheless, the SwissCovid app has been shown to have advantages in timeliness and efficacy in users taking mitigative actions over manual contact tracing in recent studies. For example, 1 study revealed that app users who received an exposure notification from the SwissCovid app entered quarantine, on average, 1 day earlier than contacts who did not receive an exposure notification . A simulFurthermore, relevant actions for transmission prevention were also quite frequently reported, as almost 3 out of 4 exposure-notified SwissCovid app users reported getting tested or having entered quarantine during the Omicron variant phase. These estimates fall in line with other studies using the same  or diffeOverall, our study contributes to the accumulating evidence of the possible contribution of digital proximity-tracing apps toward pandemic mitigation through quantitative evidence within an established public health indicator framework. However, our study also indicates various shortcomings of digital proximity-tracing apps that interfere with their ability to function at their full potential. In the case of the SwissCovid app, the flow of information along the exposure notification cascades was limited by various bottlenecks, such as delayed code delivery for test result sharing, complex user interfaces, or misaligned incentives for subsequent mitigative actions. This was observed with the SwissCovid app use visibly decreasing over time despite increasing prevalence with the more recent SARS-CoV-2 variants. The bottlenecks that may have contributed to decreased use of the SwissCovid app were recently illustrated by a study where case-contact pairs fulfilled all necessary conditions to enable exposure notifications , but only 6 of 10 exposed contacts ended up receiving exposure notifications . To enabOur study bears some limitations. The data and assessment methods used in this analysis cannot provide evidence for causality between digital proximity-tracing app use and transmission prevention. Due to a lack of clinical outcomes data, our findings are also not suited to extrapolate the population-level impact of digital proximity-tracing apps, such as avoided hospitalizations or deaths due to a lack of clinical outcome data. Moreover, despite drawing on an extensive database that includes almost 2700 individuals and 23,500 assessments, the number of recorded events of interest  was still relatively low. This is a common issue of population-based surveys, where the probability of occurrence at any time point remains small and thus rather represents a general methodological challenge in such research. Finally, survey-driven studies may be prone to different reporting biases, including over- or underreporting of mitigative behaviors, such as noncompliance with rules and social norms. However, this was to a degree mitigated by the longitudinal nature of our data collection and repeated surveying of SwissCovid app use and outcomes, which allowed for various quality checks and did not reveal indications for systematic reporting biases.Our study provides a comprehensive countrywide assessment of key indicators for the SwissCovid digital proximity-tracing app based on the WHO/ECDC framework and highlights the importance of considering the overall pandemic context in the assessment of the performance and effectiveness of such apps. For example, test positivity upon receipt of an exposure notification from the SwissCovid app was at least as high as (Omicron variant phase) or higher than (Alpha and Delta variant phases) general test positivity, with a high percentage of app users taking mitigative actions upon receiving an exposure notification. Furthermore, more than 200,000 individuals shared positive test results with the app over the course of the pandemic. Nevertheless, our indicator assessment also suggests room for improvement, including improving the speed and completeness of the exposure notification cascade or establishing stronger incentives for app use and test result sharing. Future implementations of digital proximity-tracing apps should place more emphasis on the social, psychological, and organizational aspects of the exposure notification cascade to improve their effectiveness in mitigating pandemic spread. In the context of constantly evolving requirements across different pandemic waves, the implementation of digital proximity-tracing apps should be regularly reviewed and revised.


Polyester fibers are widely employed in a multitude of sectors and applications from the technical textiles to everyday life thanks to their durability, strength, and flexibility. Despite these advantages, polyester lacks in dyeability, adhesion of coating, hydrophilicity, and it is characterized by a low wettability respect to natural fibers. On this regard, beyond the harmful hydrophobic textile finishings of polyester fabrics containing fluorine-compounds, and in order to avoid pre-treatments, such as laser irradiation to improve their surface properties, research is moving towards the development of fluorine-free and safer coatings. In this work, the (3-glycidyloxypropyl)trimethoxysilane (GPTMS) and various long alkyl-chain alkoxysilanes were employed for the fabrication in the presence of a catalyst of a water-based superhydrophobic finishing for polyester fabrics with a simple sol-gel, non-fluorinated, sustainable approach and the dip-pad-dry-cure method. The finished polyester fabrics surface properties were investigated by static and dynamic water repellency tests. Additionally, the resistance to common water-based liquids, abrasion resistance, moisture adsorption, and air permeability measurements were performed. Scanning electron microscopy was employed to examine the micro- and nano-morphology of the functionalized polyester fabrics surfaces. The obtained superhydrophobic finishings displayed high water-based stain resistance as well as good hydrophobicity after different cycles of abrasion. Polyester fiber textiles are popular among customers because of their durability, strength, flexibility, and resilience to climatic conditions, making them perfect for long-term usage in outdoor applications. Furthermore, the greatest benefit of polyester fibers is that they can be mass-produced in massive quantities at a low cost, resulting in lower costs for the customer as well ,2,3. On In order to increase the coating durability, it is crucial to increase the coating adhesion capability of polyester textiles themselves. In some investigations, polyester fibers were altered by UV irradiation, plasma pre-treatment or chemical hydrolysis to add functional groups to the surface, increasing the polymer’s hydrophilicity before the application of chemicals and functionalization ,10. As a matter of fact, fluorine and silicon finishing compounds are the most often used finishing agents ,12. In tAlthough opportunely coated fabrics can generate a water repellent surface with lower surface tension on the exterior of polyester fibers as in the case of silicone and polysiloxane water repellent agents, featuring the advantages of good biocompatibility and inexpensive raw material costs, the washing resistance is still insufficient ,20. Long-chain alkane compounds represent one of the existing water repellent finishing techniques able to introduce on cotton fabrics good water repellent properties. Unfortunately, due to the lack of functional groups able to bind to cotton fibers, they lead to the formation of finishings characterized by poor washing resistance, negative impact on hand feel, and poor air permeability ,22.One commonly explored strategy for producing superhydrophobic textiles is first to increase surface roughness by functionalizing the surface with proper inorganic precursors and nanoparticles via the sol-gel technique and then to reduce surface energy by attaching a hydrophobic groups . FurtherHerein, in this study, a facile and eco-friendly sol-gel approach, to obtain superhydrophobic and breathable polyester fabrics, is presented; the chosen sol-gel reaction pathway is based on the hydrolysis and condensation of (3-glycidyloxypropyl)trimethoxysilane (GPTMS), crosslinked to different long alkyl-chain alkoxysilanes. The treated fabrics exhibited excellent superhydrophobicity useful for the assessment of their potential contribution to sustainable water repellent and fluorine-free textile coatings for a wide range of sectors, as shown in In particular, (3-glycidyloxypropyl)trimethoxysilane (G) was co-condensed with various non-fluoro substances, such as triethoxy(ethyl)silane (C2), triethoxy(octyl)silane (C8), and hexadecyltrimethoxysilane (C16), in the presence of HCl and 1-methylimidazole as catalysts for the GPTMS epoxy ring opening, to prepare nanohybrid cross-linked polyalkylsiloxanes coatings that were applied on polyester surfaces by the dip-pad-dry-cure deposition approach. The features of the finished polyester fabrics were additionally tested and examined by different chemical, physical, and mechanical techniques. In particular, the static and dynamic water repellency, resistance to conventional water-based liquids, abrasion resistance, moisture absorption, and air permeability of the coated polyester fabrics were analyzed, and the micro and nano-morphology of the functionalized fabrics surfaces were observed by scanning electron microscopy (SEM). Finally, a possible mechanism of the super hydrophobic behavior of the obtained micro- nano-structured hybrid coating was evaluated and proposed.As for the cotton fiber substrates, water repellent finishing of polyester fabrics is often conducted using physical or chemical procedures that involve lowering surface energy and modifying the roughness and surface morphology of the fabrics specimens ,34,35. UIn this study, in order to avoid surface pre-treatments, e.g., laser irradiation, the polyester samples (PL) were treated with the silane precursor (3-glycidyloxypropyl)trimethoxysilane as a crosslinker to encourage the formation of a tridimensional hybrid functional organic-inorganic network that displayed adhesive electrostatic and covalent interactions with the treated substrate. The development of these chemical contacts between the alkoxysilane precursors and fibers, however, can be aided by the presence of functional groups (hydroxyl and/or carboxyl) at the polyester polymeric ends . TherefoIn a first step, the bifunctional (3-glycidyloxypropyl)trimethoxysilane and one of the C2, C8, or C16 alkylsilanes, each characterized by an alkyl chain of a different length, were combined by a “grafting onto” approach to create the functional 3D polymeric matrix a throughAccording to earlier reports ,40, the Five functional treated polyester specimens were produced by performing a second dip-pad-dry-cure step and using selected C2, C8, or C16 alkylsilanes, separately, in order to create more efficient hydrophobic finished polyester fabrics b. As a mIn this regard, WCA analysis was employed to study the static hydrophobicity of the functionalized polyester specimens. Moreover, spray tests were performed to determine their dynamic water repellence. Using a reagent test, created in accordance with AATCC test method 193-2007, the contact angles of some aqueous liquids (characterized by various surface tensions) were measured to determine the degree of anti-wettability or repellency of the fabrics . The watTo be considered successful, the fabrics must be capable to reject the solution for 10 s . This teThe sessile drop method is frequently used to directly measure the contact angle in order to test the wettability of specified coatings by distilled water . In thisFurthermore, in the case of fabrics modified by combining short and long hydrocarbon chains, high WCA values, as those achieved for the samples PL_G_C2_C16 and PL_G_C8_C16, are obtained. In fact, by creating an asymmetric nanostructured hyperbranched polymeric coating with both long and short chain C2 or C8 and C16 co-monomers, it was able to replicate a brush effect that increased roughness while simultaneously reducing surface wettability . The droMoreover, in order to compare the reported results with other published data, different examples of hydrophobic treatments for polyester fabrics and the relative WCA values are given in The dynamic wettability of the treated polyester fabric was further investigated using spray testing (AATCC 22-2005) . Spray tOnly a few droplets of the employed water volume (250 mL) that had been in touch with the treated textile samples remained quickly dispersed after that. The results show that polyester fabrics have high hydrophobicity and a low surface energy.In contrast, the polyester fabrics exhibit greater surface energy when coated with GPTMS-based sol without the further addition of functional alkylsilane precursors. A water droplet placed upon the untreated polyester fabric spreads rapidly as well. The self-cleaning property of coated fabric (sample PL_G_C16_C16) is demonstrated in Additionally, as revealed in The micro-morphology of the water repellent fiber surface was observed by scanning electron microscopy. The surface morphology of the polyester fabric fibers, before and after water repellent coatings application, was studied after the gold coating of samples. The surface appearance of the fibers was detected and analyzed in order to study the relationship between the surface micro-morphology and water repellence features . Figure The results exhibited the rougher surface of the functionalized fabrics. The insets in SEM images of A thin film is therefore covering the surface of polyester fibers consisting in the long alkyl-chain polysiloxanes grafted onto the GPTMS-based 3D matrix. In comparison with traditional fluoro-based materials, the developed functional and fluorine-free coating has higher water repellency, which can successfully reduce the surface energy of the polyester fabric specimen and improve the hydrophobicity of the fabric .Microparticle aggregates coated the polyester fibers, thus significantly influencing the development of coated polyester fabrics with excellent hydrophobicity and water repellency.As the number of Martindale cycles increased up to 5000 cycles (end-point of the test because the control fabrics shows some defects), the wettability of the specimens gradually decreased. While this had no valuable effect on the general sample resistance, a more comprehensive analysis of the abrasion resistance behavior of treated textile supports displays that the appearance of the fabrics remains almost the same. In this regard, the quantity of catalyst is playing a key role. In fact, for polyester, the best behavior was achieved for the sample PL_G_C8_C8, showing a limited decrease of the static contact angle water even after 5000 cycles of abrasion.Moisture content has a crucial role in both cost and quality in a wide range of products, coatings and finishings. Compared to other synthetic fibers, polyester has a greater ability to avoid moisture absorption; this is one of the reasons why some types of polyester often tend to dry quickly ,60. DespThe WVT values of the polyester fabric samples, treated with GPTMS, are lower than those of the original untreated samples. This water absorption was the same when using pure GPTMS-sol, since the modified GPTMS-based coating may still be hydrophilic. These GPTMS-sols must be changed with stronger hydrophobic components addition, such as hexadecyltriethoxysilane , to significantly alter their reaction to water absorption. The addition of the alkylsilane monomers therefore intensifies this decrease in proportion to the lengthening of the alkylchain.The treatment of polyester fabrics, using first a hybrid sol prepared by hydrolysis and condensation of GPTMS under acidic condition and in the presence of 1-methylimidazole as catalyst and long chain alkoxysilanes, and then hydrolyzed long chain alkoxysilanes, imparts a super-hydrophobic behavior to the coated polyester textiles. The results of the wettability test, as evidenced by the overall experimental data, led us to conclude that the addition of long alkyl-chain alkoxysilanes resulted in rougher surfaces, which decreased the surface free energy of the functionalized fabrics. As a matter of fact, the better alignment of the different long alkyl chains on the coated polyester surface and the increase in the textiles surface roughness are two explanations for the better featured water repellency. Furthermore, the treatment of the polyester fabrics causes a limited reduction in moisture adsorption and air permeability. Moreover, the treated polyester fabrics retain most of the hydrophobic properties even after 5000 abrasion cycles. The proposed two-step coatings system highlights that the use of fluorine-containing compounds is not strictly necessary and it can be easily replicated and extended towards a more sustainable preparation of transparent water-repellent functionalized surfaces over a large area. Last but not least, it may also offer a convenient alternative to traditional methods for the production of hydrophobic and superhydrophobic textile fabrics. Furthermore, in the case of polyester surfaces, this method has been shown to be an efficient and stable way to obtain functional coated fabrics, even in the absence of conventional polyester chemical and physical pre-treatments.The obtained good water repellency, shown by the developed coatings, led us to conclude that this environmentally friendly, cost-effective, and relatively simple synthetic procedure may have positive effects on the production of a wide variety of textile fabrics featuring extremely high hydrophobicity and water-based anti-stain performance.A commercial plain weave PET fabric (multifilament) provided by TEXOVERSUM School of Textiles  was used for the experiments. The fabric has mass per unit area of 65.5 g/sqm, a thickness of 0.1 mm and a yarn fine of 5.1 tex (tex = g/km) (the average filament diameter is 11 µm). The warp and weft density are 50/cm and 75/cm respectively. Deionized water was employed in all the experiments. Highest purity level (3-glycidyloxypropyl)trimethoxysilane (G), hexadecyltrimethoxysilane (C16), triethoxy(octyl)silane (C8) and triethoxy(ethyl)silane (C2) were purchased from Merck Co.  and employed without further purification. Hydrochloric acid (HCl 37% wt.) and 1-methylimidazole were used as sol-gel and GPTMS epoxy ring opening catalysts respectively. Ethanol (96% vol.) and isopropanol were provided from Sigma Aldrich. Three distinct alkoxysilanes  with progressively longer hydrocarbon chains were separately employed and combined with an equimolar amount of the G precursor (1 mol) to create the desired functional final sol-gel solution. Ethanol was gradually added to the prepared mixture while being stirred at room temperature. The hydrolysis-condensation reaction was induced by adding dropwise HCl (1.5 mol) and 1-methylimidazole . The final mixture was vigorously agitated for 24 h at room temperature. The dip-pad-dry-cure procedure was used to impregnate 15 × 15 cm squares of polyester fabrics, as shown in 2 to achieve about 70% of wet gain. The polyester fabric specimens were first submerged in the functional sols for 5 min at room temperature and padded using an automatic padder  at a nip pressure of 2 kg/cmAfter drying at 80 °C for a duration of 6 min, the step was repeated a total of three times and the padded fabrics were finally put in oven and cured at 130 °C for 6 min, in a convection oven. Based on an initial study, the best curing conditions (temperature and time) for polyester fabric were selected in order to avoid the thermal degradation of polymers and to achieve the siloxane cross-linking degree typical for robust xerogel coating. Additionally, polyester fabrics were immersed for 5 min in an alkylsilane-based ethanol solution , resulting in the deposition of the double-treated specimens .Finally, the specimens were dried in the oven until constant weight at 130 °C for approximately 5 min. The fabrics were then climatized for 24 h in a typical climate chamber and subsequently weighted.A wt.%), by weighing every sample before (W1) and after being impregnated with the functional formulation and after being subjected to an additional thermal treatment (W2) and calculated using Equation (1).The total dry-solid add-on was measured through the weight gain  were measured using the sessile drop technique  using a 5 µL water droplet at room temperature. The average of ten readings was used to create one representative WCA.The spray testing was carried out to assess the dynamic wettability of the treated specimens using the AATCC Test Method 22-2005, appropriate to any textile material substrate. For the spray testing, three fabric samples 150 mm × 150 mm in size were needed to produce one representative standard. A sample of polyester was sprayed with 250 mL of distilled water that has been poured into the tester’s funnel at a 45° angle. The sample was knocked three times before being taken out. The degree of the wetting was evaluated using the water repellency rating (WRR). By evaluating the wetted sample’s appearance with the wetted standard polyester sample, the measurement was elaborated. A higher value indicates greater hydrophobicity.A scanning electron microscope  was used to study the morphology fiber surface. In particular, the pristine and treated polyester fabrics were observed at 2.0 kV and a magnification of 1000 and 4000 for the insets. Prior to testing, gold was sputter-coated onto each sample.Several water solutions, such as of coffee, milk, tea, methylene blue dyed water, pH = 1 acid (HCl), pH = 14 alkali (NaOH), and salt solution (NaCl), were separately applied to the G_C16_C16 modified polyester fibers in order to assess the wetting behavior. The self-cleaning properties of the functionalized polyester fibers were evaluated by applying soil to their surface and washing it with blue-dyed water.M/W). Equation (2) was employed to compute the hygroscopicity ratio, which served as a scale for assessing the hygroscopicity of the different polyester specimens. In the following Equation (2), BM represents the weight of the conditioned specimen and AM the starting weight of pristine sample.All of the polyester fabric samples’ ability to carry moisture was assessed using the KERN DBS moisture meter (KERN & SOHN GmbH-TYPE DBS60-3). The thermogravimetry approach was used to assess the moisture-transfer capabilities of each polyester fabric specimen. Each substrate was weighed before and after drying in this procedure to ascertain the variation in moisture. The radiation in the KERN DBS moisture meter passes through the specimen and was converted to thermal energy, which causes the sample to heat up from the inside out. The sample does reflect some radiation, but it does so more strongly in dark samples than in light ones. Since bright samples reflect more thermal radiation than dark ones, they need to be dried at a higher temperature. For this reason, the analysis was performed using a drying temperature of 130 °C and a moisture measurement protocol  and 125 Pa of air pressure.


Clear-cell sarcoma (CCS) was first described in 1968. It partly overlaps morphologically, immunohistochemically, and ultrastructurally with malignant melanoma (MM), hence its name "soft tissue melanoma." Nevertheless, there are sufficient cytogenetic differences between cutaneous melanoma and clear-cell sarcoma to consider clear-cell sarcoma as a separate entity. Clear-cell sarcoma of soft tissue is different from clear-cell sarcoma of the kidney. It is classified as a tumor of uncertain differentiation in the WHO 2020 classification of soft tissue tumors. It is an aggressive, rare malignant tumor that is involved in the deep soft tissues of the extremities and trunk. We report a case of primary clear-cell sarcoma of unusual presentation in a 31-year-old young man, mimicking metastatic melanoma. gene, which led to a diagnosis of primary clear cell sarcoma in the skin.A 31-year-old man presented with a heel mass of 2.5 cm. Histologically, it was a dermal and hypodermal nodular proliferation of spindle cells of 23 mm with a grenz zone under the epidermis. There was no necrosis area or lymphovascular invasion. Surgical margins were free. There were no clinically suspicious lymph nodes. The tumor cells were stained for S100 protein, MELAN A, and HMB45, which led to an initial diagnosis of metastatic malignant melanoma. However, analysis by fluorescence in situ hybridization (FISH) found a rearrangement of the Ewing sarcoma region 1 (EWSR1)This case highlights the importance of considering the diagnosis of a clear-cell sarcoma in front of any dermal lesions with morphological and immunohistochemical melanocytic features that do not have an in situ component and of atypical presentation, especially in young patients, hence the interest in performing fluorescence in situ hybridization for EWSR1, which remains the key to the diagnosis of cutaneous clear-cell sarcoma. Clear-cell sarcoma (CCS) of soft tissue is a malignant tumor involving deep soft tissue and is characterized by Ewing sarcoma region 1 (EWSR1) rearrangement. It overlaps morphologically, immunohistochemically, and ultrastructurally with malignant melanoma (MM), hence its name "soft tissue melanoma," which is not recommended . It is cA 31-year-old man presented with a 2.5 cm heel mass nodule. An MRI was performed, showing a grossly well-defined subcutaneous tumor of benign appearance compatible with an angioleiomyoma Figure -5. AccorClear-cell sarcoma was first described in 1965 by F. Enzinger. It overlaps morphologically, immunohistochemically, and ultrastructurally with malignant melanoma, hence its name "soft tissue melanoma." Nevertheless, there are sufficient cytogenetic differences between cutaneous melanoma and clear-cell sarcoma to consider clear-cell sarcoma as a separate entity . This tuWide surgical excision with negative margins is the gold standard of CCS treatment. Adjuvant therapy is not necessary when the margins are clear. If the resection is close to the resection margins, adjuvant radiation is required. Chemotherapy is typically reserved for metastatic disease . PrognosThe clinical presentation, histological, and immunohistochemical features of this case were compatible with melanoma. However, the young age and the absence of detected primary melanoma led us to perform fluorescence in situ hybridization that allowed for the detection of EWS (22q12) gene rearrangement which prompted a diagnosis of clear cell sarcoma. So, this case highlights the importance of considering the diagnosis of a clear-cell sarcoma in front of any dermal lesions with melanocytic features that do not have an epidermal component and of atypical presentation, especially in young patients, hence the interest in performing fluorescence in situ hybridization for EWSR1, which remains the key to the diagnosis of clear-cell sarcoma.


Stepped wedge designs have uni-directional crossovers at randomly assigned time points (steps) where clusters switch from control to intervention condition. Incomplete stepped wedge designs are increasingly used in cluster randomized trials of health care interventions and have periods without data collection due to logistical, resource and patient-centered considerations. The development of sample size formulae for stepped wedge trials has primarily focused on complete designs and continuous responses. Addressing this gap, a general, fast, non-simulation based power procedure is proposed for generalized estimating equations analysis of complete and incomplete stepped wedge designs and its predicted power is compared to simulated power for binary and continuous responses. An extensive set of simulations for six and twelve clusters is based upon the Connect-Home trial with an incomplete stepped wedge design. Results show that empirical test size is well controlled using a t-test with bias-corrected sandwich variance estimator for as few as six clusters. Analytical power agrees well with a simulated power in scenarios with twelve clusters. For six clusters, analytical power is similar to simulated power with estimation using the correctly specified model-based variance estimator. To explore the impact of study design choice on power, the proposed fast GEE power method is applied to the Connect-Home trial design, four alternative incomplete stepped wedge designs and one complete design. The open-cohort design, however, allows the attrition of members from and addition of new members to an existing cohort in each period. We will mainly focus on the cross-sectional and closed-cohort designs in this article. Most study planning methods are for complete SW-CRTs where all clusters have outcome data in all periods. However, incomplete stepped wedge designs are increasingly used in cluster randomized trials, whereby some cluster-periods do not record data due to logistical, resource and patient-centered considerations. Specifically, researchers do not collect data in a closed-cohort design or enroll new participants in a cross-sectional design during some cluster-periods. Hemming et al.3 described two types of incompleteness in stepped wedge designs, one involving implementation periods and the other staggered study entry or termination of clusters. In the first instance, implementation periods are the transition phases between control and intervention periods in which no data collection or participant enrollment occurs because a block of time is needed before the intervention can be implemented. In the second instance, when the initiation of baseline data collection or study termination is delayed for some clusters according to different periods, there will be staggered entry or end-of-follow-up, correspondingly. Both types of incompleteness may be introduced in the design of a single study. There is a need for the explication of statistical methodology and the development of software tools for a general, non-simulation-based, power calculation procedure based on the generalized estimating equations (GEE) to quickly and accurately calculate power for incomplete stepped wedge designs with a small or large number of clusters.A stepped-wedge cluster randomized trial (SW-CRT) is a type of uni-directional crossover design in which clusters switch from control condition to treatment at randomly assigned time points.1.24 Use of GLMMs with non-identity link functions in the analysis of CRTs carries a couple of important caveats. First, the interpretation of the intervention effect is dependent upon the random effects included in the GLMM. For example, the treatment effect parameter in the logistic random effects model for binary outcomes in SW-CRTs has a conditional odds ratio interpretation. Whereas the intervention effect odds ratio is cluster-specific in a random intercept model, its interpretation in a model including cluster-period random effects applies to a conceptual population of cluster-periods possessing the same values of the latent random-effect variables.5 Second, while GLMMs are flexible insofar as accounting for the dependence of observations within clusters via random effects, with few exceptions, they do not adequately describe the pattern and magnitude of within-cluster correlation on the natural measurement scale of the responses. This is because exact expressions for the marginal mean and the marginal within-cluster correlation structure for CRTs and SW-CRTs are generally lacking.68 Perhaps for this reason, while GLMMs are frequently used in the analysis of SW-CRTs with binary and other categorical responses, they are seldom used as the basis for planning SW-CRTs other than computing power by simulation.9Generalized Linear Mixed Models (GLMMs) based on the maximum likelihood estimation methods and population-averaged (PA) models estimated with GEE are the two most widely used statistical analysis methods for stepped wedge and other CRTs.1012 In contrast to GLMMs, the intervention effect from a marginal (PA) model describes how the average response changes across the subsets of population defined by the treated and control cluster-periods. Because models for the mean and correlation structures are separately specified, the interpretation of the marginal mean regression parameters remains the same regardless of the correlation specification. The link function is chosen to obtain inference on the target parameters of choice; for binary responses, this could be the odds ratio via the logit link, the risk ratio via the log link, or the risk difference via the identify link. A second advantage in using GEE for SW-CRTs is that inference for mean model parameters is robust to misspecification of the ICC structure in large samples when the sandwich variance estimator is used.12 Feng et al.13 conducted extensive simulation studies to show that sandwich variance estimator with GEE analysis had good performance for CRTs with 50 or more clusters, even with the misspecification of correlation structures. A third advantage of marginal models is that, unlike GLMMs, they produce estimates of correlations that can be directly used in sample size determination for several outcome types and target parameters for intervention effectiveness, which addresses Item 7a of the CONSORT extension for the SW-CRT14 that calls for reporting of “assumptions made about correlations between responses of participants from the same cluster.” For the aforementioned reasons, there is a need for the development of statistical power methods and computational tools based on marginal models for discrete and continuous responses in planning and analysis of SW-CRTs for a selection of intra-cluster correlation structures that reflect the longitudinal and clustered aspects of complete and incomplete cross-sectional and closed-cohort designs.Population-averaged models have several advantages for the design and analysis of SW-CRTs. Because SW-CRTs are often used in health care research to inform policy decisions, marginal models carry a straightforward PA interpretation and may be preferred in such settings.15 Barker et al.4 found 46/102 had fewer than 10 clusters and Grayling et al.16 reported that the median number of clusters in SW-CRTs is 21. For their analysis with marginal models, use of bias-corrected sandwich variance estimators is recommended to improve the accuracy of inference regarding tests of the intervention effect including control of Type I error.17 In simulation studies, these bias-corrected GEE methods performed similarly well under correctly specified and mis-specified ICC matrices for as few as 10 clusters.18 Additionally, to address the finite-sample bias of correlation parameter estimates, Matrix-adjusted Estimating Equations (MAEEs) incorporates a matrix-based finite-sample bias adjustment in a second set of estimating equations for correlation parameters solved simultaneously with the usual GEE for the marginal mean parameters.19A distinguishing characteristic of SW-CRTs and other CRTs, which should be considered in statistical analysis, is that they frequently have a small number of clusters.1.32022 In the random-cluster-intercepts linear model1 and a nested exchangeable three-level model extension,23 Hemming et al.3 developed formulae for statistical power for continuous responses through 24 implemented the power and sample size calculation procedures for CRTs with linear mixed models into an R shiny app for complete and incomplete SW-CRT.Because CRTs are less powerful than individually randomized trials, determination of the proper number and allocation of study participants in SW-CRTs is critically important. However, most sample size methods for SW-CRTs are for continuous responses and complete designs. In particular, there is substantial literature on sample size and power calculation procedures for continuous responses in complete SW-CRTs based on linear mixed models (LMMs) estimated by maximum likelihood or generalized least squares.10 The methods extend earlier sample size formulae for GEE analysis of parallel-groups CRTs, including cross-sectional and cohort CRTs26 and multi-level CRTs.28 Prior work29 has shown that the analytical power for marginal mean (e.g. intervention) parameters in complete SW-CRTs agrees well with simulated power for as few as eight clusters, when PA models are analyzed using GEE with bias-corrected sandwich standard errors concurrently with MAEE estimation of ICCs.19 Chen et al.30 proposed a R package swdpwr to calculate the analytical power for complete SW-CRTs with binary or continuous outcomes.In the case of population-averaged models, simple-to-use sample size formulae based on PA models for continuous responses and non-simulation procedures for binary responses have recently been proposed for complete, cross-sectional and closed-cohort SW-CRTs within the framework of GEE.10 to SW-CRTs with incomplete designs. The article is organized as follows. Section 2, motivates our work with the description of a real-world small sample incomplete stepped wedge design. Section 3, describes the population-averaged models of interest consisting of marginal mean and within-cluster correlation models with special consideration of correlation structures suitable for cross-sectional and closed-cohort SW-CRTs, respectively. Estimation is presented within a GEE framework involving a pair of estimating equations for the marginal means and correlation parameters. To accommodate a small number of clusters, MAEE for correlation parameter estimation and bias-corrected covariance estimators are employed. Section 4, proposes the general power procedure for GEE analysis of discrete and continuous responses for completed and incomplete stepped wedge designs. Section 5, presents a simulation study of empirical type I error and power based on GEE/MAEE analysis for incomplete SW-CRTs based on Connect-Home trial with six or 12 clusters, which is compared to predicted power from the non-simulation fast GEE power method.10 Section 6, describes the application of the proposed fast GEE method to study planning based on the Connect-Home trial and the final section discusses results and their implications.In this article, computationally fast, non-simulation procedures for determining sample size and statistical power for GEE analysis of binary and continuous responses are extended from complete SW-CRTs in Li et al.231 The primary component of the intervention is an individualized Transition Plan of Care that SNF staff create to support the patient and caregiver at home. The incomplete design with six SNFs (clusters) and four patients per cluster-period , shown in 25 are particularly useful for discrete responses when population-averaged interpretations are desired, this article focuses on binary responses, although continuous responses are also considered.The Connect-Home trial uses an incomplete, cross-sectional stepped wedge design to test an intervention to improve outcomes for rehabilitation patients transitioning from skilled nursing facilities (SNFs) to home-based care.10 Next, the number of SNFs or clusters Our investigation considers that the Connect-Home study design is distinct from that of the typical SW-CRT in several aspects. First, the number of periods 33.132 However, we mainly focus on cross-sectional and closed-cohort designs in this article and assume a common set of time points.A unifying population-averaged model framework is described for the design and statistical analysis of stepped wedge designs. The following notations apply to both cross-sectional and cohort SW-CRT designs where there are average intervention effects model10 and the incremental intervention effects model.33 In the average intervention effects model, 10 While not considered in this article, other models are possible such as those with higher order polynomials  for time.Two types of marginal mean models are investigated in the article, the widely used the me trial . Finally10 On the other hand, the proportional decay correlation structure34 allows for correlation decay over time, where the intra-individual correlation 1 specifies that within- and between-period correlations are equal. For cross-sectional designs, this means that Specification of the marginal model is completed with the covariance structure of a cluster’s response. The variance of the response is nsidered . Specifi19The GEE/MAEE method formalizes estimation of correlation parameters through specification of a second generalized linear model for intracluster correlations:3.219 to reduce the finite-sample bias of the correlation parameter estimates.29 We denote the response vector as 19 which is described briefly in the paper to reduce redundancy. Finally, in the case of continuous responses, an additional step is required to update the dispersion parameter 10Estimation of marginal models for SW-CRTs is based on GEE with MAEE35 When both 36 referred to as BC0, which tends to underestimate the variances. We also consider three bias-corrected sandwich covariance estimators29 to reduce finite sample bias. Setting 35 or 37 Next, setting 38 or referred as 19 Finally, setting 39 or 19 while finite-sample bias corrections are recommended in GEE/MAEE marginal model analysis for CRTs, they are not required for estimating the sample size and power in the design stage, as discussed in the next section.With regard to the variance estimators of the marginal regression parameters in the SW-CRTs, the model-based variance d, whereΣ^0=∑i=1I44.110 In turn, the Wald-test statistic 40 as fast GEE power or predicted power.The 4.210 Motivated by the Connect-Home trial, we describe its implementation for incomplete SW-CRTs with application to a marginal mean model with linear period effects. Because the proposed method is based on the general GEE power method of Rochon40, it applies to generalized linear models for correlated binary and continuous responses with arbitrary link functions, variance functions and correlation matrices. A key step in the application of the fast GEE power computation is the generation of the cluster-level design matrices, 3 In order to efficiently compute power for incomplete SW-CRT designs, we additionally propose a Completeness Matrix (CM) to represent the planned missingness pattern. Both DP and CM matrices have dimension 3 has 40 is applied to account for staggered entry/dropout or, as in this example, implementation periods. For an incremental intervention effects model for the SW-CRT design with CRTFASTGEEPWR41 implements the fast GEE power method for CRTs with complete and incomplete designs that can be described by DP and CM matrices. It is available at http://www.bios.unc.edu/~preisser/personal/software.html.The fast GEE power procedure for SW-CRTs has been previously investigated for complete SW-CRTs for the average intervention effects marginal mean model with categorical period effects.510 empirical test size and power of GEE Wald-tests are simulated for binary responses and continuous responses. Specifically, motivated by the Connect-Home trial design, data are simulated for sample sizes of 6 or 12 clusters assuming equal allocation of clusters across sequences, with 4 or 2 patients per cluster-period, respectively, so that the total number of patients is fixed at 360. In Web Appendix A, the DP and CM matrices are displayed for the Connect-Home trial. The design matrices Simulation studies are conducted to demonstrate that the proposed fast GEE power method gives predicted power similar to that of time-intensive simulations for binary and continuous responses in incomplete cross-sectional and closed-cohort SW-CRTs. We also compare power between the five correlation structures in 42 Baseline prevalence 10 The effect sizes for the average intervention effects model are Clustered binary data are randomly generated from marginal models from Section 3.1. with a logit link function for the marginal mean in equation , the actual power of the study design and planned sample size as represented by empirical power is of paramount importance. In this regard, use of the clusters . For six5.3For continuous responses (Web Appendix D), the type I error results under the average intervention effects model  also show that BC1 using the 66.1The fast GEE power calculation method is applied to compare power among six SW-CRTs designs (Web Appendix F) based on the Connect-Home trial for continuous and binary outcomes. The purpose of this exercise is to illustrate how the fast power method may be used to compare power among several complete and incomplete stepped wedge designs under consideration during study planning. Each design has a fixed total of 360 patients, six treatment sequences and from 16 to 22 periods. Design A is the incomplete SW-CRT for Connect-Home trial and Design F is a complete SW-CRT. The other four designs show alternative incomplete SW-CRTs and vary according to the length of implementation periods, the use of staggered study entry and termination of clusters. Each study includes six or 12 clusters or SNFs with four or two patients per cluster-period, respectively, so that the total number of patients is always 360. As in the simulation study, the power using the For binary responses, power with 6 clusters and a cluster-period size of 4 is always much smaller than 12 clusters and a cluster-period size of 2 because power of the clusters . Thus, 1CRTFASTGEEPWR. Descriptions of the inputs and outputs of the SAS macro are provided in Section G of the Web Appendix along with three examples of its application to incomplete and complete SW-CRTs.Comparative results for power for binary responses under the six designs is notably different for the incremental intervention effects model. The power of Designs D/E/F is consistently greater than those of Designs A/B/C, respectively. Thus, the introduction of staggered study entry and termination of clusters into the stepped wedge designs has a greater negative impact on power than the introduction of implementation periods under the incremental interventions effects model. While this result is the opposite from what was observed under the average interventions effects model, power under both marginal means models was always best under the complete design F, and almost always worst under Design A that used staggered entry/termination and two implementation periods. The pattern of GEE power with respect to the correlation structures was similar for the two marginal mean models. Finally, the results for continuous responses (Web Table 7) align well with those for binary responses. All power results in this section and the next were produced by the SAS macro 6.2Although Design A was the overall worst performer in terms of power among the six study designs in Section 6.1., it was nonetheless chosen for the Connect-Home trial because, as noted in Section 2., logistical considerations dictated both staggered entry/termination and two implementation periods. Results of the simulation study and the application of the fast GEE power method in me trial  is consiFrom 7This article proposes a fast GEE power method for binary and continuous responses in complete and incomplete stepped wedge cluster randomized trials. Extensive simulation studies demonstrate that the fast GEE power method can reliably predict power in real-world cross-sectional and closed-cohort incomplete stepped wedge trials when the statistical analysis is based upon GEE with bias-corrected sandwich variance estimators. The fast GEE power approach was illustrated in the planning of an incomplete stepped wedge design for Connect-Home, an intervention to improve outcomes for rehabilitation patients transitioning from skilled nursing facilities to home care. A SAS macro 3 and Rochon,40 the general GEE power method is implemented for complete and incomplete stepped wedge designs, thereby extending the power methods for complete designs of Li et al.10 to designs with staggered enrollment of clusters, implementation periods, and planned early withdrawal of clusters, as applications shown in Section 6. Indeed, the lack of closed-form formula for non-continuous outcomes motivates the fast, numerical approach for power calculation. While this article focuses on linear time trends in the marginal mean model based on the Connect-Home trial, our approach accommodates categorical and any other time trends. Moreover, the SAS macro 43 reviewed 18 power calculators for SW-CRTs based on GLMMs or GEEs and report that four calculators41 which may cover most scenarios of interest, including our SAS macro This study is novel in several aspects. Through specification of the “Design Pattern” matrix and “Completeness Matrix” in the spirit of Hemming et al.10 who restrict attention to the average intervention effects model for continuous and binary responses with categorical period fixed effects and an exchangeable or nested exchangeable correlation structure for complete cross-sectional stepped wedge designs. In the current work, the specification of linear period effects allows use of the 45 Additionally, the present article considers two distinct marginal mean models, the popular average intervention effects model and the incremental intervention effects model. The latter model allows for a gradual uptake of intervention across periods which is similar to the linear-time-on-treatment effect representation within the linear mixed model framework.33In addition to the focus on incomplete stepped wedge designs, this article builds upon Li et al.17 with GEE analysis for SW-CRTs under a small number of clusters in Web Table 11. According to Web Table 11, the majority of studies advised using the 17 recently demonstrated that the average of BC1 and BC2 standard errors could best maintain valid type I error rate; however, the empirical power of their bias-correction remains unexplored. Future work is needed to study whether their average standard error estimator provides empirical power close to a prediction formula such as proposed here under incomplete SW-CRTs.The simulation studies support the use of the 10 to six clusters. However, performance results for BC3 in the current article are poorer compared to Li et al.10 and Scott et al.12 The different performance of BC3 could be related to the incomplete design characteristics of the Connect-Home trial. Scott et al.12 and Thompson et al.18 showed that the BC3 tended to have a similar empirical power with BC1 under the complete SW-CRT. Notably, BC3 is constructed by a diagonal matrix for finite-sample correction that might be more easily affected by the information loss and have greater variances due to the missingness under the incomplete SW-CRTs compared to BC0, BC1, and BC2. In short, our results lead to a recommendation not to use the BC3 correction for incomplete stepped wedge designs with a small number of clusters.Importantly, the analytical power by the fast GEE power method agrees well with simulated power in complete and incomplete SW-CRTs having twelve clusters with cluster-period sizes of two when data are analyzed using GEE with the bias-corrected sandwich variance estimator BC1. For designs of six clusters with cluster-period sizes of four, the analytical power using t-test is similar to the simulated power with correctly specified model-based variance estimator and is more conservative compared to the power with BC1 variance estimator. Thus, the results support the use of fast GEE power methods with t-test for 12 clusters and extend the minimal number of clusters to have valid simulated GEE power with BC1 variance estimator from eight clusters in Li et al.19 As discussed in Section 1.2, marginal mean modeling facilitates the estimation and reporting of ICC estimates in cluster randomized trials, as recommended by the CONSORT statement for stepped wedge trials.47 While the use of MAEE produces better ICC estimates, bias-correction for the ICC estimates has been found to have negligible impact on the analysis of the intervention effect in marginal mean models for cluster randomized trials.48In assessing the validity of the fast GEE power method, its predicted power was compared to simulated power using statistical analysis based on GEE with MAEE finite-sample adjustment for correlation estimates. Estimation of correlation parameters by MAEE, which was not a focus of the current work, has been shown to substantially reduce bias and improve coverage for intraclass correlations in clustered randomized trials including those with stepped wedge designs.29Nevertheless, we further extended the MAEE to accommodate the exponential decay and proportional decay correlation structure for cross-sectional and closed-cohort, respectively, by using the log link in the generalized linear model for the correlation parameters. However, the convergence rate of estimation results under exponential decay and proportional decay correlation were lower than the other correlation structures (Web Appendix E). Because the simulation study was motivated by the Connect-Home SW-CRT, which has six clusters, the relatively low convergence rate was not unexpected. With a higher number of clusters, the convergence rate increases for ED but not for PD. For convergence failures under decay correlation structures, the estimation of correlations out of their natural boundary and non-convergence under Newton–Raphson method are the main causes. In order to lessen the chance of a convergence failure, the range of feasible correlation parameters in terms of positive-definite correlation matrices should be checked in the design phase of SW-CRTs. Future work could be done to improve the convergence rate under decaying correlation structures with the GEE/MAEE procedure for small numbers of clusters, such as replacing Newton–Raphson method with the quasi-least squares approach in Li.The proposed fast GEE power method was applied in a hypothetical study planning scenario where six prospective stepped wedge designs were compared with respect to their power given a fixed number of clusters and total sample size. This demonstration enabled an assessment of the impact on power of certain features of incomplete stepped wedge designs. While the relative impact of staggered enrollment and implementation periods depended upon the assumptions of the marginal mean model and within-cluster correlation structure, the general finding suggested that the use of incomplete SW-CRT designs decreases power relative to comparable complete designs. While power tended to be the greatest for the nested exchangeable correlation matrix among the five correlation structures studied, this finding may not apply to other settings such as SW-CRTs with large cluster-period sizes. Importantly, the choice of correlation structure in power analysis should be based on the study design, population and outcomes, for example, cross-sectional versus closed-cohort design and whether correlation decay is expected based on trial duration.3 and cluster crossover trials.46In conclusion, the fast GEE power method provides a computationally efficient, non-simulation approach to determine the power and sample size of complete and incomplete SW-CRTs. Both the fast GEE power method and the GEE/MAEE analysis procedure can also be applied to count responses and to marginal models with individual level covariates. For example, open-cohort studies are a possible extension of the methods, without the restriction of a constant number of patients across periods and allowing for missing observations common in real-life data analysis. Finally, the procedures could also be adapted to the design and analysis of various types of complete and incomplete parallel trials, including staggered incomplete parallel CRTsClick here for additional data file.Supplemental material, sj-pdf-1-smm-10.1177_09622802221129861 for A general method for calculating power for GEE analysis of complete and incomplete stepped wedge cluster randomized trials by Ying Zhang, John S Preisser, Elizabeth L Turner, Paul J Rathouz, Mark Toles and Fan Li in Statistical Methods in Medical Research


Advantages of three-dimensional (3D) computed tomography-based navigation system has recently been used for safe, accurate, reliable spinal tumour excision. This study presents two cases, a 33-year-old male and a 17-year-old male presented in the clinic with mid-back and low back ache, respectively with change in posture. Radiology suggested an osteoid osteoma. Accurate localisation and complete extirpation of the lesion were performed using a translaminar approach with O-arm Navigation. After follow-up of one year, both did not complain of back pain or radiation, scoliosis had improved in both cases and their VAS was 0 and ODI was 0%. 3D navigation with the O-arm system provided an easy and accurate localisation of the lesion, reducing the risk of instability subsequently and avoiding instrumented stabilisation. This technique also provided for histopathological confirmation of the diagnosis. Over the decades, surgical techniques of the spine have evolved, and minimally invasive procedures are now utilised for excision of osteoid osteoma with high precision. We report two cases of osteoid osteoma of spine managed with surgical excision with O-arm guided navigation. Case 1 had osteoid osteoma at superior articular process of the D11 vertebra while Case 2 had osteoid osteoma of the L4 right pars interarticularis, both treated with surgical excision with O-arm guided navigation.Osteoid osteoma is a primary benign bone lesion that commonly occur in the second decade of life, but also varies from the first to fourth decade with a male to female predominance of 2:1. The clinical symptom reported is night pain, caused by nidus induced prostaglandin/prostacyclin production. Patients also present with painful scoliosis due to soft tissue and muscle irritation, leading to asymmetrical spasm. Surgical excision is the definitive method of treatment for patients unresponsive to nonsteroidal anti-inflammatory drugs like aspirinA 33-year-old male presented with dull mid-back pain radiating to the left side of the chest for 7 months. Pain was aggravated at night and relieved by taking nonsteroidal anti-inflammatory drugs (NSAIDS). Pain progressively increased to the point of causing difficulty in daily activities. On clinical examination, he had dorsolumbar scoliosis with convexity to the right, tenderness, and paraspinal spasm in that region. The scoliosis was partially corrected on bending forward. His back visual analog scale (VAS) score was 8 with Oswestry Disability Index 40%. Neurological examination was normal. Radiographs of the dorsolumbar spine suggested sclerosis in the D10 and D11 facet joint on the left side with scoliosis with convexity to the right. Pre- and post-contrast magnetic resonance imaging of the dorsolumbar spine was performed. The dynamic evaluation was performed with contact using time-intensity curves and correlated with plain CT. There was a well-defined lytic lesion seen involving the superior articular process of the D11 vertebra measuring 11mm x 11mm x 9mm being hypointense on T2 and mildly hyperintense on T1 with central sclerosis on CT scan scalloping the inferior articular process of the D10 vertebra. It showed rapid early uptake of contrast on arterial phase with slow washout. These findings favoured a diagnosis of osteoid osteoma .A 17-year-old male presented with low-back pain for eight months. Pain was aggravated at night and relieved by taking nonsteroidal anti-inflammatory drugs (NSAIDS). Pain progressively increased to the point of causing difficulty in daily activities. Clinical examination showed lumbar scoliosis with convexity to left, tenderness, and paraspinal spasm in that region. The scoliosis was partially corrected on bending forward. His back visual analog scale (VAS) score was 9 with Oswestry Disability Index 44%. Neurological examination was normal. Radiographs of the lumbar spine suggested sclerosis in the L4 right pars interarticularis and lumbar scoliosis with convexity to the left. Pre- and post-contrast magnetic resonance imaging of the lumbar spine was performed. The dynamic evaluation was performed with contact using time-intensity curves and correlated with plain CT. There was an area of well-defined radiolucency with central sclerotic focus seen involving the L4 right pars interarticularis measuring 4mm. It showed rapid early uptake of contrast on arterial phase with slow washout. These findings favoured a diagnosis of osteoid osteoma which was confirmed on histopathology .The patient was positioned prone on the Jackson table . After taking safe surgical precautions, a single two-dimensional fluoroscopy image was taken from the O-arm  to mark the incision and a stab incision was made cranially to attach the reference probe to the spinous process, extending caudally to the dorsolumbar region. Subsequent dissection was performed to reach the left D10 D11 facet joint for first case. For the second case, the Medtronic METRx 14mm tube system was used with Wiltse approach. With O-arm setting changed to minimise the radiation dose; a CT scan was taken within 15s. The navigation system used was StealthStation S8 . The basic data used for navigation consisted of pre-operative CT data, which were transferred and recorded on the system computer and reconstructed into three-dimensional (3D) images.After registering the navigation with a 1.5mm ball-tipped reference probe, the accuracy of the images was verified by point merging and surface merging. The lesion was identified and accurately localised with the probe. Under neurosurgical microscope OPMI Pentero 900  careful drilling was initiated with 3mm diamond tip MIDAS Navidrill  till the lesion wall was reached as identified with the probe. The lesion was extirpated en masse in both cases. Further drilling was done in the walls of the articular process taking care not to breach the pedicle and keeping the dura safe.Adequacy of extirpation was checked using the Navigation probe. Total amount of blood loss was less than 30ml in both cases. The operative time for the first case was 90min and the second case was 75min. Surgical wound was closed. Both patients walked 4h after the surgery. On the second day of surgery, the back VAS improved to 2, and patients were discharged home. Histopathological examination confirmed osteoid osteoma diagnosis. After follow-up of one year, both did not complain of back pain or radiation, scoliosis had improved in both cases VAS was 0 and ODI was 0%2. CT-guided percutaneous resection technique has limitations such as accurate localising the drill tip leading to malposition and inadequate drilling with increased risk of inadvertent dural and spinal cord injury, or increased risk of infection due to substandard sterility precautions in radiological suites. CT-guided percutaneous radiofrequency thermal ablation and laser photocoagulation for the treatment of osteoid osteomas located in the extremities has been used successfully. However, proximity to neural structures makes this modality conflicting in the spine. Thermal damage to the neural structures due to the heating tip has always raised concerns. Inadvertent injury to adjacent neural structures, high failure rates in the spine and lack of histologic confirmation of diagnosis makes it less ideal for treating osteoid osteomas in the spine.Treatment of an osteoid osteoma involves complete intralesional excision of the nidus, either by surgical or radiological intervention after failure of adequate medical management. Although, intra-operative nidus localisation is challenging and can lead to extensive resection of the adjacent normal bone structure leading to risk of iatrogenic fracture and extended period of healing, instability requiring stabilisation, or neurovascular injury. Accuracy of intra-operative localisation of the nidus include radionuclide localisation with a gamma probe, intra-operative CT-guided localisation, or a combination of scintigraphy and computer navigation3. Gasbarrini et al4 studied 81 patients operated for osteoid osteoma either by conventional excision therapy or minimally invasive surgery (six of 81). They concluded that minimally invasive surgery has advantages of reducing soft tissue morbidity and the collateral damage caused by conventional surgical approach, it allows patients a more rapid and complete return to normal function. Considering accuracy of 3D fluoroscopic navigation, Mason et al5 analysed 30 studies for accuracy of pedicle screws. They reported accuracy of conventional fluoroscopy as 68.1%; accuracy of 2D fluoroscopic navigation as 84.3%; and with 3D fluoroscopic navigation accuracy as 95.5%. They concluded that accuracy rates of 3D as compared with 2D fluoroscopic navigation were consistently higher throughout all individual spinal levels. This result show that 3D fluoroscopic navigation can help surgical excision of osteoid osteoma more accurately.Advantages of a three-dimensional (3D) computed tomography-based navigation system has recently been used for safe, accurate, reliable spinal tumour excisionLimitations of this study includes lack of long-term follow-up to evaluate for recurrence. Also, large group of patients is required to make this a standardised treatment for osteoid osteoma.This study of 3D navigation with the O-arm system provided precise, safe, accurate, reliable localisation of the lesion, reducing approach related morbidity, the risk of iatrogenic instability and subsequent instrumented stabilisation, thereby reducing the hospital stay and cost of treatment. An intra-operative verification O-arm spin confirmed complete tumour excision and a low dose protocol of the O-arm significantly reduced the radiation exposure to the patient. Histopathological confirmation of the diagnosis can also be provided by this technique.


In this paper, a MEMS -based frequency-tunable metamaterial absorber for millimeter-wave application was demonstrated. To achieve the resonant-frequency tunability of the absorber, the unit cell of the proposed metamaterial was designed to be a symmetric split-ring resonator with a stress-induced MEMS cantilever array having initial out-of-plane deflections, and the cantilevers were electrostatically actuated to generate a capacitance change. The dimensional parameters of the absorber were determined via impedance matching using a full electromagnetic simulation. The designed absorber was fabricated on a glass wafer with surface micromachining processes using a photoresist sacrificial layer and the oxygen-plasma-ashing process to release the cantilevers. The performance of the fabricated absorber was experimentally validated using a waveguide measurement setup. The absorption frequency shifted down according to the applied DC (direct current) bias voltage from 28 GHz in the initial off state to 25.5 GHz in the pull-down state with the applied voltage of 15 V. The measured reflection coefficients at those frequencies were −5.68 dB and −33.60 dB, corresponding to the peak absorptivity rates of 72.9 and 99.9%, respectively. Metamaterials, artificially engineered composites of periodic or non-periodic structure, show a peculiar and exotic electromagnetic behavior, unlike materials found in nature . Thanks One of the ways to overcome this drawback is to actively reconfigure the resonant frequency of the metamaterial with tunable elements. Some tuning methods have been reported to demonstrate frequency-reconfigurable metamaterial absorbers. Electrical tuning using varactor or PIN (positive-intrinsic-negative) diodes allows a fast tuning speed and a wide tuning range to be obtained ,20,21, bIn this paper, a frequency-tunable metamaterial absorber targeting millimeter-wave frequency (Ka-band) applications using MEMS cantilever actuators was designed. Electrostatically driven metal MEMS cantilevers were implemented in the split-ring resonators (SRRs) of the metamaterial unit cell as variable capacitors to reconfigure the resonant frequency. In order to achieve a large capacitance change with a lower driving voltage, MEMS cantilevers were fabricated on the capacitive area in the form of an array structure with a bent-up curvature using stress gradients induced by the oxygen-plasma-release process of the cantilevers. The proposed absorber with two unit cells was designed through full-wave simulation, fabricated via surface micromachining processes on a glass wafer, and experimentally characterized using a relatively simple waveguide measurement setup. The effects of the nonuniform bending of the fabricated cantilevers on the operating voltage and absorption performances were considered using the measured profiles of the fabricated cantilever beams.In general, an incident electromagnetic wave is divided into reflection, transmission, and absorption. Thus, the absorbance  response of the proposed absorber, commercial full-wave EM simulation software  was used. The parameters of the proposed MEMS-based metamaterial absorber are shown in The simulation model including the overall structures was constructed by designing a pair of waveguides with the proposed absorber sample sandwiched between them, as shown in θ of the MEMS cantilever beam with respect to the substrate surface. As expected from The initial EM simulation results of the designed absorber are shown in 2SO4) and hydrogen peroxide (H2O2) to remove contaminants. On the backside of the wafer, a 300 nm thick aluminum layer was deposited by means of metal sputtering as a ground layer . The typical deformation plot of 12 cantilevers in one array of cantilevers from an SRR unit cell, for example, is shown in xHy bond into CO, CO2, and H2O via the reaction of active oxygen with the photoresist sacrificial layer. This heat effect can create the temperature gradient between the top and bottom surface of the beam structures, which can result in the permanent bending of the beams if it is too large. In addition, the microstructural change in the surface of the thin film exposed to plasma particles at a high energy level could be another factor leading to residual stress and thus the deflection of the cantilever beam [The nonuniform bending of each cantilever beam in the sample might have been caused by various factors of the oxygen-plasma-ashing process we used to release the cantilever beams. It is known that heat is generated during the oxygen plasma ashing by decomposing the Cver beam .In order to measure the absorption characteristics of the fabricated sample, a measurement setup was constructed, as shown in The measured reflection coefficients of the fabricated absorber sample according to the applied DC bias voltages  and were estimated to be 24.6, 14.6, and 6.7 V for beams A, B, and C, respectively. In addition, the deformed profiles of these beams just before switching to the pull-down state were estimated with a COMSOL Multiphysics® simulation and are illustrated as dotted lines in The typical finite element method (FEM) model of a single cantilever beam constructed using the measured profile is shown in In In this study, we proposed and demonstrated a MEMS-driven frequency-tunable metamaterial absorber operating at millimeter-wave frequencies. A surface-micromachined MEMS cantilever array as a part of the unit cell was fabricated to have process-induced stress gradients for a large tuning ratio with a relatively low actuation voltage. Both numerical and experimental demonstrations were performed on our metamaterial absorber. The absorptivity of the fabricated sample changed from 72.9% in the initial off state to 99.9% in the pull-down state, while the absorption frequency shifted from 28.0 to 25.5 GHz. The proposed MEMS-based metamaterial absorber could be employed to millimeter-wave applications where actively controlled electromagnetic absorbers are required but it is difficult to find effective tuning methods.