BRCA1 and BRCA2, as well as by the joint multiplicative effects of many genes (polygenic component). We have now updated BOADICEA using additional family data from two UK population-based studies of breast cancer and family data from BRCA1 and BRCA2 carriers identified by 22 population-based studies of breast or ovarian cancer. The combined data set includes 2785 families (301 BRCA1 positive and 236 BRCA2 positive). Incidences were smoothed using locally weighted regression techniques to avoid large variations between adjacent intervals. A birth cohort effect on the cancer risks was implemented, whereby each individual was assumed to develop cancer according to calendar period-specific incidences. The fitted model predicts that the average breast cancer risks in carriers increase in more recent birth cohorts. For example, the average cumulative breast cancer risk to age 70 years among BRCA1 carriers is 50% for women born in 1920–1929 and 58% among women born after 1950. The model was further extended to take into account the risks of male breast, prostate and pancreatic cancer, and to allow for the risk of multiple cancers. BOADICEA can be used to predict carrier probabilities and cancer risks to individuals with any family history, and has been implemented in a user-friendly Web-based program (http://www.srl.cam.ac.uk/genepi/boadicea/boadicea_home.html).Multiple genetic loci confer susceptibility to breast and ovarian cancers. We have previously developed a model (BOADICEA) under which susceptibility to breast cancer is explained by mutations in  BRCA1 and BRCA2 account for approximately 15% of this excess familial risk . Direct evidence for the polygenic basis of the residual familial clustering not due to BRCA1 and BRCA2 mutations has more recently been provided by the identification of further loci that confer moderate risks, including mutations in CHEK2, ATM, PALB2, BRIP1  BRCA2 carriers are at an increased risk of developing breast cancer  The Anglian Breast Cancer Study . The families were identified through 1484 women with breast cancer diagnosed before the age of 55 years and registered in the East Anglian Cancer Registry between 1991 and 1996. These index cases were invited to provide blood samples and complete an epidemiological questionnaire, including family history of cancer in all first-degree relatives. The blood samples were tested for germline mutations in BRCA1 and BRCA2 using conformation-sensitive gel electrophoresis (CSGE). Mutations were confirmed by sequencing. These data were used in the initial model development and the study is described in more detail elsewhere ((b) UK National Case–Control Study (UK). Women with breast cancer were identified through two UK population-based case–control studies. The first study involved 755 patients diagnosed under the age of 36 years and registered between 1982 and 1985. The second study included 644 patients diagnosed from age 36 to 45 years and registered between 1988 and 1989. These index cases provided family history information of breast and ovarian cancer and were later contacted to provide blood samples. DNA was screened for germline mutations in BRCA1 and BRCA2 by heteroduplex analysis. Again, mutations were confirmed by sequencing. In all, 617 samples were tested for BRCA1 and BRCA2 mutations and were included in our analysis. This data set is described in detail elsewhere ((c) The Manchester Study. Women diagnosed with breast cancer at or before the age of 30 years were recruited via the North West Regional Cancer Registry (UK) between 1980 and 1997. A total of 99 index cases provided blood samples, which were screened for mutations in BRCA1 and BRCA2 using a combination of the Protein truncation test, single-strand conformation polymorphism/heteroduplex analysis and fluorescent chemical cleavage of mismatch analysis. Three-generational pedigrees were constructed through interviews and were augmented with data from hospital notes. The study is described in (d) Multiple case families: ‘British’ (B) families. In all, 156 families were ascertained in response to national publicity in the United Kingdom and by referral by oncologists or general practitioners. Eligibility was restricted to families with at least two breast cancer cases, one or more diagnosed before the age of 50 years. Occurrence of cancer and follow-up was recorded on all family members. One or more individuals from each family provided blood samples, which were analysed for BRCA1 and BRCA2 mutations using CSGE ((e) Meta-analysis families (BRCA families). This data set included pedigree data from BRCA1 and BRCA2 mutation carriers identified in 22 population-based studies of breast or ovarian cancer patients reported by BRCA1 and/or BRCA2 mutations by systematic screening, and family history information had to be available on all first-degree relatives of identified mutation carriers. To avoid replication, the families of mutation carriers identified through the ABC, UK and Manchester studies were not considered to be part of the BRCA families for the present analysis. A total of 429 families of BRCA1 and BRCA2 mutation carriers were included in the present analysis.BRCA1 and BRCA2 mutations were considered to be disease causing if they were classified pathogenic according to the generally accepted criteria (http://research.nhgri.nih.gov/projects/bic/). For consistency across the population-based studies , family history information was restricted to the first-degree relatives of the index cases.Model fitting was performed using complex segregation analysis of breast and ovarian cancer occurrences in the combined set of families described above. Individuals were followed from birth and were censored at the age of cancer occurrence, age at death or at the age of 70 years whichever occurred first. Female patients with no age information or no year of birth were censored at age 0 .BRCA1, BRCA2 and a polygenic component representing the combined multiplicative effect of multiple loci of small effect. This model is consistent with the recent discovery of multiple low-risk susceptibility genes (and the failure to identify any further ‘high-risk’ loci by linkage) =λ0(t)exp(Gi(t)+Pi(t)), where λ0(t) is the baseline incidence for the cohort, Gi(t) represents the major gene effect at age t  and Pi(t) is the polygenic effect assumed to be normally distributed with mean zero and variance σ2(t). The polygenic component was approximated by the hypergeometric polygenic model  acts on BRCA1 and BRCA2 background, the polygenic component is referred to as the ‘modifying’ component. In this analysis, we generalised the model to allow for different polygenic and modifying variances in mutation carriers and noncarriers. We also fitted models in which the polygenic and modifying variance was age dependent.The breast cancer incidence for individual ic model . More deGi(t), Pi(t)) were assumed not to vary by birth cohort. Owing to this constraint, the estimated incidences for BRCA1 and BRCA2 carriers and noncarriers were themselves cohort specific.The breast and ovarian cancer incidences were assumed to be calendar period and cohort specific, based on the incidences for England and Wales  used in the regression specifies the degree of smoothness. Various degrees of smoothness were investigated and the resulting set of incidences was compared with the original set of incidences for adherence. As a smoothness criterion, we used the sum of the absolute values of the third-order finite differences of the smoothed incidences: Published incidences are reported in 5-year intervals, which can result in large variations in the incidences between adjacent age intervals. This is particularly an issue for chniques . This meχ2 test statistic, treating the smoothed incidences as expected values. However, formal tests of significance were not performed because of the difficulty in determining the correct number of degrees of freedom for the test.Smaller values of the sum (*) correspond to smoother incidence curves. Consistency of the model with the data was assessed using a BRCA1 and BRCA2 log-relative risks (Gi(t)) for both breast and ovarian cancer. Our primary analysis involved fitting models in which the relative risks are assumed to be constant within each decade of age . Once the most parsimonious model for the form of the polygenic and modifying variance was chosen, we fitted additional models in which the log-relative hazards were piecewise linear functions of age . Variants of uncertain significance (VUSs) were assumed to be equivalent to a BRCA1- and BRCA2-negative test, since this is how they are treated in clinical genetics and in analyses testing the goodness of fit of the model. Although some such variants may be pathogenic, this effect is allowed for in the model by the mutation sensitivity parameter . For the relatives of index patients who were screened for family-specific mutations, we assumed that the test was 100% sensitive.To allow for the fact that not all mutations could be detected by the screening methods used, we allowed in our analysis for a sensitivity of mutation testing parameter, giving the probability of detecting a mutation if one exists. We assumed that 70 and 80%, respectively, of the disease-causing mutations in Nested models were compared against each other using the likelihood ratio test. The Akaike Information Criterion (AIC) was used to compare non-nested models .BRCA1 and BRCA2 allele frequencies in the population and the natural logarithm of the ratios of the breast and ovarian cancer incidences in BRCA1 and BRCA2 mutation carriers to the population incidences (relative hazards). Parameters were estimated by maximum likelihood, and their variances were obtained from the observed information matrix. To obtain confidence intervals for parameters with restricted ranges  we used transformations to obtain parameters that are likely to be more normally distributed . The graduated calendar- and cohort-specific incidences included the age-specific features for all cohorts observed in the general population (data not shown) . On the BRCA1 and BRCA2 relative hazards were assumed to be constant within each 10-year interval: 20–29, 30–39, 40–49, 50–59 and 60–69 years. In the first model, the polygenic and modifying variances were constrained to be equal. In the second model, the polygenic variance was allowed to be different from the modifying variance, but the latter was constrained to be the same for BRCA1 and BRCA2 carriers. In the third model, the polygenic variance and the BRCA1 and BRCA2 modifying variances were all allowed to vary. In each of these models, the polygenic and modifying variance were assumed to be constant with age. We found no evidence that the BRCA1- and BRCA2-modifying variances were different from each other (P=0.76). The modifying variance was estimated to be somewhat lower than the polygenic variance (1.55 vs 2.02), but the difference was not significant (P=0.63). When a single polygenic/modifying variance was assumed, it was estimated to be 1.99 (95% CI: 1.54–2.57). This model had the lowest AIC value of the three models (7948.284). The BRCA1 and BRCA2 parameter estimates for this model are given in We first fitted three models, with different assumptions about the polygenic and modifying variances . For theP=0.30). The other two models assumed separate constant modifying variances, which were either constrained to be equal or different among BRCA1 and BRCA2 mutation carriers. These models also did not improve the fit significantly, compared with the model with a constant polygenic/modifying variance (P=0.53 and 0.65). The latter two models assumed constant modifying variances because models with varying modifying variances resulted in unbounded estimates.We then fitted three further models, for which the polygenic variance was allowed to vary by age group =σm2(t)=α+βt, where t represents the age in years, and estimated the parameters α  and β . Compared with the model with a constant variance, there was some marginal evidence that this model fitted better (P=0.049).Despite the lack of a significant improvement in fit, the parameter estimates suggest that the polygenic variance may decrease with age. We explicitly allowed for this hypothesis by fitting a model in which the polygenic and modifying variances were the same linear function of age, that is, To investigate further the properties of these models, we computed the age-specific familial relative risks (FRRs) for an individual with an affected mother predicted by these two models as described elsewhere . The preBRCA1 and BRCA2 log-relative hazards to be piecewise linear functions of age  and 0.10% (95% CI: 0.07–0.16%), respectively. These correspond to population carrier frequencies of 0.12% for BRCA1 and 0.20% for BRCA2. The average cumulative risks of breast and ovarian cancer in BRCA1 and BRCA2 mutation carriers based on this model are shown in BRCA1 carriers over all possible modifiers was estimated to be 46% by the age of 70 years for women born before 1920, rising to 59% for women born after 1950. On the basis of the 5th and 95th percentiles of the distribution of the polygenic/modifying component, the estimated cumulative breast cancer risks were 7.2 and 98%, respectively, for carriers born before 1920, rising to 12.0 and 99.9% for carriers born after 1950. The average cumulative risks of breast cancer in BRCA2 mutation carriers by the age of 70 years were estimated to be lower, 39% for women born before 1920  rising to 51% for those born after 1950 . The estimated ovarian cancer risks were highest for women born between 1930 and 1939, but the variation across the birth cohorts was smaller than for breast cancer. For BRCA1 mutation carriers, the ovarian cancer risk by the age of 70 years was estimated to be 33% for women born prior to 1920, rising to 36% for those born between 1920 and 1939, and then dropping to 34%. For BRCA2 mutation carriers, the corresponding risks were estimated to be 11, 12 and 11%, respectively. The predicted age-specific FRRs under this model are shown in The model with a linearly decreasing polygenic/modifying variance was extended to allow for the BRCA1 and BRCA2 mutation carriers were obtained by multiplying the cohort and calendar period age-specific incidence rates from the general population. Noncarriers were assumed to develop these cancers according to the population incidences.Since reliable data on these additional cancer types were not available in the main data set used to derive BOADICEA, we used instead estimated risks derived from the largest published studies see . We incoBRCA1 and BRCA2 alone cannot explain all the observed FRRs , was entirely due to the susceptibility as defined by the model . On the basis of this assumption, the contralateral breast cancer incidence after the first breast cancer, given the genotype, is half the breast incidence assumed in the standard model (since only one breast is at risk). Similarly, the incidence of a cancer at another site, after a first cancer diagnosis, was assumed to be the same as if the preceding cancer had not occurred, consistent with the assumption that the site-specific cancer risks are independent conditional on the genotype. The transition model for female patients in this extended BOADICEA model is depicted in BRCA1 and BRCA2 mutation carriers are now based on a much larger number of mutation-carrying families and are, therefore, more reliable; the variance of the polygenic component is now age dependent as opposed to constant; and the incidences vary gradually with age and are cohort and calendar period specific. In addition, the model has been extended to allow for the risks of male breast, prostate and pancreatic cancer, and the risks of other cancers after a first diagnosis.In this report, we have updated and extended our previously published model BOADICEA using additional data. There are several additional features in the updated model. The breast and ovarian cancer incidences in FGFR2 and TNRC9), the per allele odds ratio was higher below the age of 40 years, although not significantly so. Other studies have found that the relative risks associated with CHEK2 1100delC and ATM mutations are somewhat higher at young ages  variances for carriers . HoweverBRCA1 and BRCA2 carriers. The majority of the current data came from families of unselected series of cases that had been previously used to estimate the BRCA1 and BRCA2 penetrance . In contrast, the estimates in BRCA1 and BRCA2 mutation carriers who have an affected first-degree relative (affected with breast cancer in most cases). Under the BOADICEA model, these women would be expected to have higher than average breast cancer risks, as demonstrated elsewhere . Users can either create a pedigree online, or can upload a pedigree file. The program allows for families of any size or structure; pedigrees built online are restricted to first- and second-degree relatives but uploaded files can be of arbitrary complexity. It has been shown that relatives more distant than second degree can provide important information for risk models  of developing breast or ovarian cancer for unaffected individuals, or the risk of contralateral breast cancer or ovarian cancer for those who have already developed a first breast cancer. The code has also been modified to allow for the possibility that the individual is of Ashkenazi Jewish origin. This case requires separate consideration owing to the high prevalence of three founder mutations in this population  reported in BRCA1 and BRCA2 mutation carriers, and the polygenic variance, were assumed to be the same in the Ashkenazi and non-Ashkenazi versions. Similar modification will be required for other populations where the frequencies of BRCA1 and BRCA2 mutations are different . These will be implemented at a later stage.The current version of BOADICEA has now been implemented as a user-friendly Web-based program ; tumour histological characteristics; and the inclusion of hormonal, reproductive and lifestyle risk factors.


Background. Minor digestive symptoms are common and dietary approaches such as probiotic administration or fibre and fermentable carbohydrate intake adjustments are often recommended. A Fermented Milk Product (FMP) containing Bifidobacterium animalis subsp. lactis CNCM I-2494 and lactic acid bacteria has been shown to improve digestive symptoms after 4 weeks of consumption, but the speed of onset of this effect and its dependence on fibre intake or physical activity is unknown. To answer these questions, data from two previously published trials on FMP for minor digestive symptoms were combined. Methods. In total, 538 participants provided weekly assessments of bloating, abdominal pain/discomfort, flatulence, borborygmi/rumbling stomach from which a composite score was calculated. At baseline in one study (n = 336), dietary fibre consumption was recorded and physical activity classified as high, moderate or low. The speed of the FMP’s effect was assessed by a repeated measure analysis of variance measuring the change from baseline for the composite score of digestive symptoms. Results. FMP consumption resulted in a significant decrease in the composite score of symptoms after only 2 weeks in both studies and the pooled data at week 1 , week 2 , week 3  and week 4 . The interactions fibre intake-by-product group, physical activity-by-product group and time-by-product group were not statistically significant. Conclusion. FMP consumption leads to a rapid improvement in symptoms which is likely to encourage adherence to this dietary intervention. This effect is independent of dietary fibre and physical activity. Irritable bowel syndrome (IBS) as well as minor digestive symptoms place a significant burden on the health of the general population ,2. DietaBifidobacterium infantis 35,624 have been shown to improve symptoms in patients with IBS [Bifidobacterium lactis CNCM I-2494 and lactic acid bacteria has been shown to improve IBS symptoms [Evidence that probiotics improve digestive discomfort is presently limited to a relatively limited number of products ,5,6. Thewith IBS  and the with IBS . A Fermesymptoms . It alsosymptoms ,12. HoweB. lactis CNCM I-2494 and to establish whether lifestyle components such as fibre intake or physical exercise may influence this effect.This work aimed to explore the available data from two previously published studies to determine the speed of improvement of abdominal discomfort with a FMP containing 2, complaining of minor abdominal discomfort and with a bowel movement frequency within 3–21 per week . Subjects were excluded if they had a clinical diagnosis of any digestive disease including IBS, or they received drugs for digestive symptoms, or they had any significant systemic disease. Subjects were not allowed to consume any other probiotic than the study products and were asked to not change their usual dietary intake and or level of physical activity. The consumption of fibre was measured at baseline during a phone interview with a dietician in study 2 (n = 336) and subjects were divided into four levels corresponding to quartiles of fibre consumption. Physical activity was assessed at baseline in study 2 using the international physical activity questionnaire (IPAQ) which allows the classification of subjects into three categories of physical activity  [The datasets analysed in this research were obtained during two double-blind randomised controlled trials using the same design, products and endpoint derivation ,12. The and low) .Bifidobacterium animalis subsp. lactis CNCM I-2494, Streptococcus salivarius subsp. thermophilus CNCM I-1630, Lactobacillus delbrueckii subsp. bulgaricus CNCM I-1632 and I-1519, and Lactococcus lactis subsp. lactis CNCM I-1631 twice a day for 4 weeks. Both products were prepared at Danone Research facilities, Palaiseau, France, and shipped in blinded packaging with refrigeration to the study sites. The randomisation was generated in well-balanced blocks using envelopes for study 1 by an external contract research organization (LC2) and using Interactive Web Response Systems for study 2 developed by another external contract research organization . Blinding was accomplished by ensuring that test and control products were of identical appearance, taste and texture. The randomisation code was not to be broken until all assessments had been performed, all data had been entered into the database, and the database had been locked after a clean file procedure.Subjects self-evaluated weekly the frequency of four individual digestive symptoms  using a 5-point Likert scale. A composite score of discomfort ranging from 0 to 16 was calculated as the sum of those four symptom scores. After a 2-week run-in period, subjects were randomised in a 1:1 ratio to consume 125 g of either a non-fermented dairy product without bacterial strains (control product) or a FMP containing Statistical analyses were performed using mixed procedure available in the SAS System package  version 9.3. All the analyses were performed on the intention to treat (ITT) principle based on all randomised subjects. No imputation techniques were used to handle for missing data on endpoint assessment.To assess the FMP’s effect on the frequency of digestive symptoms, a secondary endpoint in both studies, we used a repeated-measure analysis of variance (ANOVA) on the change from baseline with fixed effect of study, time (in week) and product group, as well as time-by-product group interaction effect. Additional covariates were included such as baseline digestive symptoms composite score and study-by-product group interaction (Model 1 on pooled data).t-test p-values comparing the LS-Means difference between study product groups were estimated globally and by time point. Although this analysis was exploratory, we performed as multiple comparisons the hierarchical stepdown multiple-testing strategy starting from timepoint Week 4 (W4) and going back week-by-week until Week 1 (W1). The results are graphically displayed with series plots showing LS-Means difference (FMP-Control) with 95% CI.For exploratory purposes, the Least Squares (LS)-Means and their 95% Confidence Interval (CI) were produced by study product group and by study product group per time. Two-sided approximate p-value lower than 0.1 was used as the threshold to display the LS-Means and their 95% CI by interaction groups.For the dietary fibre consumption and physical activity impact on the change from baseline of digestive symptoms and the interaction with study product group, we added separately in two repeated-measure ANOVA the qualitative covariate fibre or physical activity as well as the interaction fibre—or physical activity-by-time and fibre—or physical activity-by-product group . An interaction type 3 test of fixed effect The analyses to assess the speed of the FMP’s effect on abdominal discomfort were performed on the pooled dataset representing 538 subjects (pooled ITT population). The number of subjects with missing data for the frequency of digestive symptoms was too low  to use any missing data strategy for replacement. Dietary intake of fibre and Physical Activity (PA) data were only gathered in Study 2, so we performed the analyses of the impact of fibre intake and physical activity on response to FMP consumption on a set of 336 subjects (study 2 ITT population). The number of missing data for fibre intake and physical activity was 28 (8.3%) and 39 (11.6%), respectively. The model was run with the subjects having available information .The subjects’ characteristics are shown in p-value = 0.003). This greater reduction of CS by FMP was already present and significant after 2 weeks of product consumption (FMP led to a significantly greater reduction of the LS-Means difference of Composite Score (CS) over the 4-week consumption period as compared to the Control product  (p = 0.25) or physical activity (p = 0.75) with the study product.The greater reduction observed for FMP as compared to the Control of the Composite Score (CS) over the 4-week consumption period was not affected by the adjustment for baseline levels of fibre intake and physical activity  . There wIn the two studies, no adverse events or serious adverse events were reported as being related to the study product. Overall clinical safety was good.This research indicates that consumption of a FMP over 4 weeks can improve digestive symptoms after only 2 weeks of product consumption. Furthermore, the data suggest that this effect is not influenced by dietary fibre intake or physical activity at the start of study.14 Furthermore, the observation that the intestinal and central aspects of the disorder can be transmitted by faecal transplantation in animal models and potentially modulated by probiotics, especially bifidobacteria, opens space for the development of new treatments [Abdominal discomfort and irritable bowel syndrome (IBS) are common disorders with the latter being characterised by similar but more intense symptoms on a chronic basis. The pathophysiology of IBS is multifactorial and includes disturbances of gastrointestinal motility and sensitivity as well as psychological influences. In addition, there is now evidence that the gut microbiota is disturbed (dysbiosis) in at least some patients with the disorder.eatments ,6,14.In the present study, we used data collected in two randomised controlled studies which had shown that a FMP was more effective than a non-fermented control product in improving discomfort over a 4-week period of consumption, which is the time frame recommended in guidelines for trials in functional gastrointestinal disorders. We considered it to be of interest to explore how fast this effect occurred as it might be anticipated that the absence of measurable effect after 2 weeks could result in poor compliance or even the cessation of consumption by participants. We found that the FMP had a rapid effect and interestingly a similarly fast response has been observed in other treatments aimed at modifying the microbiota, such as rifaximin .B. lactis CNCM I-2494 has been shown to modulate intestinal physiology in healthy subjects [9,10 as well as those with minor digestive symptoms [B. infantis 35624 improved symptom scores in patients with IBS but not in subjects without diagnosed gastrointestinal disorder with less severe symptoms [It is noteworthy that the FMP containing subjects ,16 and isymptoms ,12. Convsymptoms ,8,17. Hosymptoms  and othesymptoms .Fibre intake can modulate digestive symptoms and lowering the consumption of fibre  as well The present research has some limitations. Firstly, we do not have information on the effect of the FMP consumption on a long-term basis and it would be useful to know whether improvement is sustained after discontinuation of treatment or whether continued consumption is necessary. Secondly, this was an exploratory post-hoc analysis based on secondary endpoints from previously published studies. Thirdly, neither study, alone or combined, was prospectively designed to confirm the absence of an interaction between the product effect and level of physical activity or fibre intake at baseline. As such, the associated interactions tests may lack statistical power. Lastly, there was no assessment of the effect on the gut microbiota or its metabolites which might improve understanding of the mechanisms behind the observed clinical effect.In conclusion, early phase studies of potential new products for minor digestive symptoms should probably assess the speed of onset of any beneficial effect, as this is likely to have a major impact on whether it is likely to be widely used in this setting. In addition, it would be useful to know whether response to dietary intervention is maintained after discontinuation of the intervention or whether maintenance consumption is necessary. However, the feasibility of such long-term studies with a randomised controlled design is questionable. Real-world evidence studies might be an option in this context.


Background and Objectives: Recent studies in humans and dogs have shown that ventricular repolarization exhibits a low-frequency (LF) oscillatory pattern following enhanced sympathetic activity, which has been related to arrhythmic risk. The appearance of LF oscillations in ventricular repolarization is, however, not immediate, but it may take up to some minutes. This study seeks to characterize the time course of the action potential (AP) duration (APD) oscillatory behavior in response to sympathetic provocations, unveil its underlying mechanisms and establish a potential link to arrhythmogenesis under disease conditions.Materials and Methods: A representative set of human ventricular computational models coupling cellular electrophysiology, calcium dynamics, β-adrenergic signaling, and mechanics was built. Sympathetic provocation was modeled via phasic changes in β-adrenergic stimulation (β-AS) and mechanical stretch at Mayer wave frequencies within the 0.03–0.15 Hz band.Results: Our results show that there are large inter-individual differences in the time lapse for the development of LF oscillations in APD following sympathetic provocation, with some cells requiring just a few seconds and other cells needing more than 3 min. Whereas, the oscillatory response to phasic mechanical stretch is almost immediate, the response to β-AS is much more prolonged, in line with experimentally reported evidences, thus being this component the one driving the slow development of APD oscillations following enhanced sympathetic activity. If β-adrenoceptors are priorly stimulated, the time for APD oscillations to become apparent is remarkably reduced, with the oscillation time lapse being an exponential function of the pre-stimulation level. The major mechanism underlying the delay in APD oscillations appearance is related to the slow IKs phosphorylation kinetics, with its relevance being modulated by the IKs conductance of each individual cell. Cells presenting short oscillation time lapses are commonly associated with large APD oscillation magnitudes, which facilitate the occurrence of pro-arrhythmic events under disease conditions involving calcium overload and reduced repolarization reserve.Conclusions: The time course of LF oscillatory behavior of APD in response to increased sympathetic activity presents high inter-individual variability, which is associated with different expression and PKA phosphorylation kinetics of the IKs current. Short time lapses in the development of APD oscillations are associated with large oscillatory magnitudes and pro-arrhythmic risk under disease conditions. In brief, differential phosphorylation kinetics of calcium (ICa) and potassium (IK) currents upon phasic β-AS as well as changes in calcium cycling and the action of stretch-activated channels (SACs) in response to phasic mechanical stretch have been shown to generate LF oscillations in cellular action potential (AP) duration (APD) , are major ionic modulators of such inter-individudal differences  augments LF oscillations of APD  oscillatory pattern following enhanced sympathetic activity. In humans, this has been demonstrated by quantification of so-called periodic repolarization dynamics in the T-wave vector of the electrocardiogram (ECG) , as compared to the very fast activation of the ICa current, has been demonstrated to be behind such APD lag following sudden ISO exposure. The distinctively slow response of IKs to β-AS and its implications in terms of APD adaptation time have been also described in other species, like the rabbit , both being commonly present in failing hearts.The present study investigates the cellular ventricular APD response to phasic, rather than constant, β-AS and mechanical stretch, in closer correspondence with the experimentally reported LF patterns of efferent sympathetic nerve activity  epicardial model  at 90|50% repolarization corresponding to 1 Hz pacing (expressed in ms); RMP, representing resting membrane potential (in mV); Vpeak, representing peak membrane potential measured in the AP upstroke (in mV); and ΔAPD90, representing the percentage of change in APD90 with respect to baseline following individual inhibitions of IKs, IKr, or IK1 currents (measured in ms). Of the initial 500 models, only 218 meeting all the calibration criteria were selected. Additionally, models showing pro-arrhythmic behavior at baseline and/or under sympathetic provocation were discarded, which led to a population of 188 models for the analysis of this study.Initially, 500 models were generated by using the Latin Hypercube Sampling method to sample the conductances of the above described currents in the range ±100%  affinity for the intracellular Na+ concentration. In the modified Xie et al.  and Caa[k], where the discrete index k represents cycle number. Thus, k varies from 0 to K, with K being the number of cycles following β-AS and/or mechanical stretch.APD was evaluated at 90% repolarization in both simulations and experiments. The simulated or experimentally measured APD time series following β-AS and/or mechanical stretch is denoted by APD, for APD to reach a new steady-state following application of β-AS and/or stretch was defined as the time taken by the APD time series to attain convergence, with convergence characterized by the derivative of the APD time series being below a predefined threshold. Specifically, the following steps were used to compute the APD time lapse:Smoothinga[k] to obtain a smooth version of it, To remove short-term variability and make the estimation of the convergence time more robust, moving average smoothing was applied onto the APD time series T was set to the period in cycles of the sympathetic activity, T = 20 cycles.where Numerical derivatived[k] was numerically estimated by computing the central difference for the interior data points of From Time lapse calculationkAPD, for APD convergence following β-AS and/or stretch was defined as:A threshold on the maximum allowed variation in the derivative of the APD time series for convergence to be attained was defined in this study by setting θ = 0.5 ms. The number of cycles, APD was obtained by converting kAPD into minutes:The time lapse τCL is the cycle length in seconds (constant period between stimuli applied to the cells to elicit APs).where APD equal to 0 represent cases where convergence of the APD time series was immediate.Values of τThe time lapse, τAPD = 139 s, whereas for the second virtual cell, τAPD = 0 s. The characteristics of these two cells in terms of ionic current conductances are presented in APD, which ranged from just a few seconds for some virtual cells to more than 3 min for other cells. Similarly, 2, although most cells present PLF values below 5 ms2.The individual and combined contributions of phasic β-AS and mechanical stretch to the time lapse in the occurrence of LF oscillations of APD is presented in Additionally, Based on the results presented in sections 3.1 and 3.2 and the fact that LF oscillations of APD are superimposed to the general trend of APD decrease following enhanced sympathetic activity, the time lapse for the development of APD oscillations can equivalently be determined by the time required for APD to converge to steady-state following constant β-AS.The temporal evolution of APD following constant application of an ISO dose of 10 nM was investigated in simulations based on our generated population of cells and compared with our experimental data recorded by using the same β-AS protocol with the same ISO dose. The possibility that prior stimulation of β-adrenoceptors could reduce the time required for APD to develop LF oscillations in response to enhanced sympathetic activity was next explored. IKs current, and ryanodine receptors, RyR.To ascertain the ionic mechanisms underlying the time required for APD to develop LF oscillations following phasic β-AS, the effect of phosphorylation and dephosphorylation kinetics of all cellular PKA substrates was investigated. IKs influenced the time for development of APD oscillations, simulations were run where the IKs phosphorylation and dephosphorylation rate constants were increased to the values described in Soltis and Saucerman  for the groups of cells presenting and not presenting arrhythmogenic events are shown in When disease conditions were simulated as accompanied by an increase in the conductance of non-specific cationic SACs in accordance with experimental evidences .The important role of 2+ overload, has been found to dramatically reduce the time lapse for sympathetically-induced oscillatory behavior. This can be understood on the basis that under RRR the amount of IKs current is reduced and, provided phosphorylation kinetics are not varied, this leads to a reduction in the oscillation time lag of the APD. Since the above holds for each of the virtual cells in the population built this study, the time lapse values measured under pathological conditions are lower than the ones corresponding to non-pathological conditions.RRR, individually or combined with Cain silico studies (Pueyo et al., in vivo research on a CAVB dog model (Sprenkeler et al., A comparison for time lapses calculated for cells under healthy conditions has been established while considering two groups of interest, one composed of cells presenting and the other one not presenting arrhythmogenic events after simulation of disease conditions. Results have been shown to be comparable. However, in both the pro-arrhythmic and non-pro-arrhythmic groups, there is an inverse relationship between the magnitude of LF oscillations of APD, measured by PLF, and the time required for such oscillations to develop. These findings indicate that cells in which APD oscillations appear rapidly in response to enhanced sympathetic activity are associated with larger oscillatory magnitudes. Although the inverse relationship between PLF and the oscillatory time lapse holds true for both groups, such a relationship is steeper in the pro-arrhythmic group, with given low time lapse values associated with larger oscillatory magnitudes. Those enhanced magnitudes may facilitate the occurrence of arrhythmic events that can act as triggers for arrhythmias and at the same time they may contribute to a more vulnerable substrate by increasing spatial repolarization inhomogeneities between regions being at different oscillating phases. This increased arrhythmia susceptibility associated with elevated LF oscillations of repolarization has been postulated by IKs expression and phosphorylation dynamics in pro-arrhythmia that has been uncovered in the present study is in line with previous studies investigating ventricular repolarization response to β-AS. The slow IKs phosphorylation kinetics as compared to the fast ICa kinetics have been reported to be behind the generation of transient arrhythmogenic early afterdepolarizations (Liu et al., IKs conductance in determining τAPD, as IKs conductance modulates the relevance of IKs dynamics on APD time course during β-AS. Additionally, differential IKs and ICa activation kinetics in response to sudden β-AS have been shown to promote the transition from ventricular tachycardia to ventricular fibrillation by transiently steepening APD restitution in simulated ventricular tissues (Xie et al., The role of in vitro data from isolated canine ventricular myocytes in response to sudden administration of a β-adrenergic agonist. Despite differences between species, experimental studies have shown that ventricular repolarization characteristics of canine cardiomyocytes closely resemble those of human cardiomyocytes (Szabó et al., in vitro and/or in vivo data became available to analyze the time required for ARI or APD oscillations to become manifest following sympathetic provocation, further validation of the results obtained in the present study could be performed.In this study, simulations have been run to quantify the time lapse for development of sympathetically-mediated LF oscillations of APD in a large population of human ventricular AP models developed based on available experimental data. After confirming the role of β-AS, over the role of mechanical stretch, in determining such oscillatory time lapse, our simulated results were compared with available The simulated results presented in this study correspond to single cells. As a continuation of this investigation, tissue models built on the basis of the present population of AP models could be used to assess whether other tissue-specific factors could play a relevant role in the time required for APD oscillations to develop, in the magnitude of such oscillations as well as in the associated consequences in terms of pro-arrhythmic risk.The population of human ventricular computational models built in this study used the O'Hara et al.  model asThe developed population of human ventricular AP models was deterministic. Future work could include incorporation of stochasticity into the main ionic currents active during AP repolarization. This would allow accounting for beat-to-beat repolarization variability, which might have an effect in the time course for development of LF oscillations of APD.An ISO dose of 0 μM was used to represent β-AS under baseline conditions. Although results are anticipated to be very similar to those obtained for a low ISO dose slightly above 0, somewhat different time lapse values for APD oscillations might be quantified.IKs current. Prior stimulation of β-adrenoceptors reduces the time required for the development of repolarization oscillations. Short time lapses are associated with large APD oscillatory magnitudes, particularly in cells susceptible to develop arrhythmogenic events in response to sympathetic stimulation.Human ventricular repolarization presents low-frequency oscillations that develop following enhanced sympathetic activity at time lapses varying from a few seconds to more than 3 min depending on individual cells characteristics. The latency in the oscillatory development is due to the slow ventricular response to β-adrenergic stimulation and, specifically, it is associated with the slow phosphorylation kinetics of the The datasets generated for this study are available on request to the corresponding author.EP and PT devised the project, the main conceptual ideas and proof outline, and were responsible for overseeing the research and providing critical insight and recommendations regarding the focus, structure and content of the paper. DS-P and JF-B performed computational simulations and analyzed the data results. NS and PN contributed with technical details and analysis support. All authors participated in writing and proofreading throughout the publication process.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


ELF5 as a potential modulator of estrogen action and driver of endocrine resistance, and here we provide the first insight into the mechanisms by which ELF5 modulates estrogen sensitivity. Using chromatin immunoprecipitation sequencing we found that ELF5 binding overlapped with FOXA1 and ER at super enhancers, enhancers and promoters, and when elevated, caused FOXA1 and ER to bind to new regions of the genome, in a pattern that replicated the alterations to the ER/FOXA1 cistrome caused by the acquisition of resistance to endocrine therapy. RNA sequencing demonstrated that these changes altered estrogen-driven patterns of gene expression, the expression of ER transcription-complex members, and 6 genes known to be involved in driving the acquisition of endocrine resistance. Using rapid immunoprecipitation mass spectrometry of endogenous proteins, and proximity ligation assays, we found that ELF5 interacted physically with members of the ER transcription complex, such as DNA-PKcs. We found 2 cases of endocrine-resistant brain metastases where ELF5 levels were greatly increased and ELF5 patterns of gene expression were enriched, compared to the matched primary tumour. Thus ELF5 alters ER-driven gene expression by modulating the ER/FOXA1 cistrome, by interacting with it, and by modulating the expression of members of the ER transcriptional complex, providing multiple mechanisms by which ELF5 can drive endocrine resistance.Acquired resistance to endocrine therapy is responsible for half of the therapeutic failures in the treatment of breast cancer. Recent findings have implicated increased expression of the ETS transcription factor  Two thirds of breast cancers are initially treated with endocrine therapy because they are likely to rely on estrogen for their proliferation. Understanding why this therapy ultimately fails in 2/3 of cases offers the chance of durable treatment. In 2012 we hypothesised that normal developmental cell fate decisions taken by mammary progenitor cells persist in tumours that are maintained by instances of a cancerous progenitor, and that a change in the relative influence of the two major transcription factors that drive progenitor cell fate, ER to specify the hormone sensing lineage, and ELF5 to specify the ER- alveolar lineage, may allow a cancer to shift control of proliferation from estrogen to ELF5. Here we show that these transcription factors are often co located at super enhancers, enhancers and at the promoters of differentially regulated genes. When the levels of ELF5 were increased this caused ER and its pioneer factor FOXA1 to move to new regions of the genome associated with resistance to hormonal therapy. We also showed that ELF both regulated and bound directly to members of the ER-transcriptional complex. These findings provide the first indication of the mechanisms by which an increase in ELF5 could drive the acquisition of endocrine resistance. Estrogen receptor (ER) positive breast cancer is initially treated using endocrine therapy to withdraw estrogen, destroy its receptor, or alter ER-driven transcription . ER+ breELF5 to be expressed We are sorry that we cannot be more positive about your manuscript at this stage. Please do not hesitate to contact us if you have any concerns or questions.Yours sincerely,Matthew L. FreedmanAssociate EditorPLOS GeneticsDavid KwiatkowskiSection Editor: Cancer GeneticsPLOS GeneticsReviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: Piggen et al., present a valuable study on the role of ELF5 in mediating endocrine resistance. Several novel aspects include: 1) ELF5 ChIP-seq, 2) Insights gained from FOXA1/ER displacement and potential role in distinct gene regulation, 3) Insight into the ELF5 protein complexes. Major comments which may strengthen the findings/conclusions of this study are:1) It’s not clear from this study whether the protein expression levels of ELF5 are consistent with expression in tumor samples upon DOX induction. My concern is whether ELF5 expression is elevated to an extent that is not observed in disease - and therefore also resulting effects on FOXA1/ER cistrome.2) In other disease systems, super enhancers have been used to define and predict activity of core TFs that regulate cell (disease state) identity. Are these associated with the 20+ (line 166) TFs ? or perhaps defines a distinct subset overlapping with ER-transcriptional complex members.3) As FOXA1 is known to have pioneering activity, following ELF5 over-expression are de novo FOXA1 binding sites established at previously closed/open chromatin ?Reviewer #2: The authors aimed to investigate the mechanism by which the alveolar lineage transcription factor ELF5 may drive endocrine therapy resistance. They use multiple ‘omics approaches to do so (with many replicates), however the data often felt like a laundry list of genes or proteins  without a clear mechanism by which ELF5 acts. While the title and abstract of this paper are provoking in terms of a potential mechanism by which ELF5 can act to promote breast cancer, especially in the context of resistance to estrogen blockade, the data unfortunately fall short in actually demonstrating this. Many of the conclusions are overstated based on what the data demonstrates, the data are largely correlative, and overall lacks a clear mechanism for which ELF5 might reorganize the epigenome, and as such, the manuscript in its current state is not sufficient for publication.1. By ChIP-seq the authors found that genomic regions of genes bound by ELF5 were also binding sites for ER and FOXA1. It is not shown anywhere what ELF5 ectopic expression looks like in either BrCa cell line, and T47D data is largely ignored throughout the manuscript. The RNA-seq data is not shown in its own right for both cell lines. These data are critical as the authors later call ELF5 DEGs. Are ER and FOXA1 regulated transcriptionally by ELF5 expression? How do we know that the ER and FOXA1 new binding sites are not merely caused by transcriptional upregulation of these TFs, which in turn causes ectopic binding? Overall, the authors need to better describe their ELF5 expression system and the RNA-seq data.2. The authors also describe overlap of ELF5 with repetitive elements, with dedicated main figures to this point, but the context of this is completely unclear as they never come back to this finding later in the paper. What is the significance of this? Does it help to understand newly acquired binding sites? .3. They further studied ELF5 binding partners and suggested that it interacted with the ER transcription complex, such as DNA-PKcs. What does this interaction mean? It is unclear how it was chosen for study (besides being one of two identified through RIME) and it was not validated by co-IP. Also, the changes on gene expression upon its KD are not striking. The authors might consider other interactors to study – e.g. splicing or replications proteins (MCMs). More generally, why did the RIME data only produce 3 proteins from 5 replicates?4. Many points are overstated in the paper based on the data presented.-For example, the authors say at line 90 that “An ELF5 motif was present at sites of increased binding ”. Even though there is signal of ELF5 at the SFig.5C, it is not a peak or clearly biologically significant.-The authors compare ELF5 expression in primary and metastatic patient samples. They state “This tumor collection contained 7 ER-positive cancers, 5 of which showed increased ELF5 expression”. This is an overstatement, since only 2 tumors showed increased in ELF5 expression. The others presented small increases at low levels that it might even be considered baseline. Moreover, claiming that the ELF 5 signature is significant in these patients should be validated in another patient cohort in order to make such generalizations.-The authors also overstate the effects of ELF5 induction in some of key genes analyzed in Supp. Fig. 10, e.g. GRHL3 did not show significant regulation by ELF5.-The authors also state at line 322 that “ELF5 diminishes the transcriptional effects of estrogen”. That again is an overstatement. To be able to draw this conclusion, the authors should perform an experiment using ELF5NoDox and ELF5Dox treated with estrogen and then compare the results to be able to conclude this.-Also the title and main conclusions suggests reorganization of the ER cistrome, but how this occurs, which is the most interesting questions here, is not clear.5. The Materials and Methods section falls short of how experiments were performed compromising the rigor and reproducibility of this study. For example, the authors should make clear how the dox treatment was done and what is being compared. It’s difficult to find the information whether the comparison is done on MCF-7 cells or T47D, as well as dox treatment for 24 or 48h. What do the authors actually ChIP with? ELF5 itself or via the V5 tag? What does ELF no dox look like, was it Chip’d as a negative control? Was the data normalized to this? etc, etc.Minor points:1. Supp Fig 8 is impossible to read leaving the reader without a clear understanding of the data presented.2. Some of the Supp data could be brought into the main figures. The reader is constantly having to move into the Supp figures to understand the main figures. For example, some of the ChEA analysis in Supp 9A could be moved into main figures.3. The Upset plots are sometimes very busy and difficult to follow.4. In line 220-221 the authors compared genes up-regulated or down-regulated upon estrogen deprivation to the ELF5 gene dataset. However, they do not specify where in Fig. 3A each of these datasets are and where the data for long-term estrogen deprivation is from.5. On line 255-256, MCMs are part of replication complexes not transcription complexes.6. On line 258-259, the authors cite 6 genes implicated in endocrine resistance that are differentially expressed by FOXA1 or ER1, however they are not at the list presented on Fig. 3D. Are these handful of genes enough for driving the phenotype?Reviewer #3: The authors provide a carefully done and interesting study with findings that very well support the role of the transcription factor ELF5 in playing a contributing role in endocrine resistance and breast cancer metastasis. ELF5 is known to have key roles in the development of the mammary gland and other tissues, and the authors now show that it also plays an important role in breast cancer in the acquisition of endocrine resistance and cancer progression to metastatic cancer.To investigate the mechanism by which ELF5 engenders endocrine resistance and metastasis, the authors examine genomic binding sites (ChIP-seq) of ELF5, ER, and FOXA1, gene expression by RNA-seq in breast cancer cells with dox-inducible elevated ELF5 expression, and use RIME and PLA to identify interacting proteins and to analyze and derive information and make correlations with RNA-seq and ChIP-seq publically available datasets from breast tumors displaying endocrine sensitivity or resistance, and metastases from endocrine-resistant patients. These analyses appear to be done rigorously and well and yield valuable new information on ELF5, ER, and FOXA1 cistromes and transcriptomes in MCF-7 and T47D cells with dox-inducible increased ELF5 expression and correlations with data from clinical breast cancers.While other studies have shown that the ER cistrome can be modulated by other nuclear receptor transcription factors including progesterone receptor and retinoic acid receptor (RAR), this is the first study to examine the impact of elevated developmental transcription factor ELF5 on the ER- and FOXA1-regulated cistrome and transcriptome in breast cancer that underlie endocrine resistance and cancer progression. Elevated ELF5 changed the cistrome binding sites of ER and FOXA1, moving them to new genomic regions similar to those seen in breast cancers that have acquired resistance to endocrine therapy. RIME and PLA showed that ELF5 interacted with components of the ER transcriptional complex including members of the CoREST complex and DNA-PKcs, and that knockdown of DNA-PKcs altered ELF5-driven gene expression implicating their relevance in ELF5 activity. RNA-seq revealed that ELF5 also changed the expression of members of the ER transcription complex and of genes known previously to drive the acquisition of endocrine therapy resistance. Overall, the studies are well done and provide mechanistic insight on the role of ELF5 in altering estrogen action and engendering endocrine therapy resistance in cancer.Questions1. Why is the isoform 2 of ELF5 used in the cell lines in this study?2. Do the antibodies used detect all ELF5 isoforms, and are other isoforms present and of relevance in human tumors?**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Geneticsdata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #1: YesReviewer #2: YesReviewer #3: Yes**********what does this mean?). 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PLOS Genetics may also choose to issue a press release for your article. If there's anything the journal should know or you'd like more information, please get in touch via  18 Dec 2019PGENETICS-D-19-01119R1 ELF5 modulates the estrogen receptor cistrome in breast cancer. Dear Dr Ormandy, We are pleased to inform you that your manuscript entitled "ELF5 modulates the estrogen receptor cistrome in breast cancer." has been formally accepted for publication in PLOS Genetics! Your manuscript is now with our production department and you will be notified of the publication date in due course.The corresponding author will soon be receiving a typeset proof for review, to ensure errors have not been introduced during production. Please review the PDF proof of your manuscript carefully, as this is the last chance to correct any errors. 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Predicting health outcomes from longitudinal health histories is of central importance to healthcare. Observational healthcare databases such as patient diary databases provide a rich resource for patient-level predictive modeling. In this paper, we propose a Bayesian hierarchical vector autoregressive (VAR) model to predict medical and psychological conditions using multivariate time series data. Compared to the existing patient-specific predictive VAR models, our model demonstrated higher accuracy in predicting future observations in terms of both point and interval estimates due to the pooling effect of the hierarchical model specification. In addition, by adopting an elastic-net prior, our model offers greater interpretability about the associations between variables of interest on both the population level and the patient level, as well as between-patient heterogeneity. We apply the model to two examples: 1) predicting substance use craving, negative affect and tobacco use among college students, and 2) predicting functional somatic symptoms and psychological discomforts. Analyses of patient-level observational healthcare databases underpin much of the current evidence base for healthcare practice. Administrative claims, electronic health record (EHR), and patient diary databases in particular have seen increased use in the past decade owing to greater availability at lower costs and technological advances that made computational processing on large-scale data more feasible . BecauseNeither administrative claims nor EHRs represent the ideal information required to generate reliable evidence. For example, diagnoses recorded on medical claims are used to support justification for the payment for a given visit or procedure and “up-coding” may occur, or, a given diagnosis could represent the condition that the procedure was used to rule out or could be an administrative artifact. Some diagnosis codes have been studied through source record verification and have demonstrated impressive performance characteristics )4]), whePatient diary databases capture fewer variables and smaller numbers of patients but offer significant advantages. In particular, diaries can capture longitudinal data about activities of daily living, mood, and personal habits and not just when a patient is seeking healthcare. Patient diaries support significant research activities in chronic disease management , 9], , . ElectroMajor use cases for observational healthcare databases include inferences about the causal effects of healthcare interventions , healthcare characterization , and paMany researchers have considered the problem of developing predictive models from patient-level data . ). 13]). Some authors have attempted to incorporate explicit temporal information into patient-level predictive models. In the context of stroke prediction, Shahn et al. 2015) proposed a “relational random forests” (RRF) that capture “motifs” in the medical history that are predictive of specific future events . Motifs 15 proposIn this paper, we approach PLPM as a multivariate time series modeling problem and consider a temporal generative model for the medical record. We adopt a Bayesian approach and consider applications to patient diary data in the context of drug and alcohol treatment and functional somatic symptoms. We explore the predictive performance of this model. Since the model offers advantages in terms of interpretability as compared with alternatives such as random forests and deep learning, we explore insights derived from the model.Vector autoregressive (VAR) models represent a mainstay of multivariate time analysis . Previouall patients using a hierarchical model. Bayesian VAR models have been widely applied in various fields of study such as economics , . He. He32]. Finally, we use AIC as a criterion to select the optimal order of the VAR model.www.aa.org) and is a frequently used treatment modality for various types of addictions. The intraindividual variability of relevant psychological states combined with the “one day at a time” nature of sustained abstinence warrants a day-to-day investigation of substance use recovery. Zheng et al. (2013) fit first-order vector autoregression models to each individual predicting daily levels of substance use craving, negative affect and tobacco use.College and university students experience high rates of substance use disorders, with 22.9% meeting the diagnostic criteria versus 8.5% of the general population . Recognition of this problem has led at least 20 colleges and universities to develop collegiate recovery communities (CRC)  that proExtensive research has established the relevance of craving, negative affect, and tobacco use as key criteria in recovery research . In turZheng et al. (2013) present a series of conclusions finding overall that the study revealed “substantial person-level heterogeneity in the day-to-day processes that challenge continued abstinence within a college recovery community, providing a picture of accumulated daily recovery risk that could threaten abstinence over both the short and long term.”The original data in Zheng et al. (2013) comprise 55 adult addict patients from CRC at a Southwestern university. In this study, we included 25 patients from the same sample, excluding 12 of the 55 who are non-smokers, 4 whose diary records exhibit no day-to-day variance, and 14 who have 3 or more missing daily records. All participants were fully anonymized before accessing the data. All are non-Hispanic White. All had received professional alcohol/drug dependency treatment. All had received inpatient care, most for 3 months or more. All considered themselves 12-step group members and reported that they read 12-step literature and applied the steps to their lives on a daily basis. Participants provided an average of 25.56 days’ worth of data each (ranging from 10 to 33 days), with the average participant missing 0.8 days (ranging from 0 to 2 days). Notice that we used slightly different criteria than Zheng et al. (2013) to include the patients, leading to a slightly different sample in the current study.Tobacco use. Daily tobacco use was measured with one item asking, “How many cigarettes did you smoke today?” Responses ranged from 0 (no cigarettes), 1 (1 or 2), 2 (2 to 5), 3 (5 to 10), 4  to 5 (full pack plus).Substance use craving. Daily substance use craving was measured with seven items modified from the Desires for Alcohol Scale and the Alcohol Urges Questionnaire to accommodate daily assessment and polydrug use. A sample item reads, “For a moment today I missed the feeling of drinking or drugging.” Responses were 1 (strongly disagree) to 5 (strongly agree).Negative affect. Zheng et al. (2013) used the 10-item negative affect scale from the Positive and Negative Affect Schedule to assess daily negative affect. Example emotions including “Stressed,” “Upset,” “Scared,” “Hostile,” and “Irritable”. Responses ranged from 1, very slightly or not at all to 5, very much. Zheng et al. (2013) provided descriptive statistics for the three variables and the number of observations of each participant.Our pre-processing step includes missing data imputation using the mean of the non-missing consecutive days, log-transformation of all three variables to improve normality, standardization to mean 0 and variance 1 and removal of linear trend for each time series for each patient by regressing individual variables against the “day” variable  and taking the residuals.k2,, k = 1, …, R2p follow Γ and Γ distributions respectively. The diagonal elements of Θv are assumed to follow Γ. The precision matrix of the error term Λ is assumed to follow Wishart((R − 1)IR, 1). We assume the multiplicative variables  and regularized linear regression model, a state-of-the-art machine learning-based approach for patient level prediction modeling . ). 36]). n = 1, …, N is generated by the posterior samples of the VAR coefficients and the error precision matrix:We use the posterior predictive distributions to predict the test data for the Bayesian model (see  for detaL1 and L2 norms) was fitted for each patient to predict the current value of each individual variable based on the previous values of all three variables. 3-fold cross validation in conjunction with the “one standard error” criterion was used to train the model, select the tuning parameters and perform the future data prediction  are used to predict the test observation for each individual patient. For the regularized linear regression model, elastic-net regularization . Mean slized in . Note thlized in .We fit two hierarchical VAR models with order one and two, respectively. The posterior sampling procedure was implemented in R. Specifically, we ran 10,000 iterations across 4 chains and used the first half of the iterations as warmup iterations. The second half was thinned by every 20 iterations to diminish the autocorrelation in the posterior samples, ending up with 500 samples per chain for posterior inference. All 4 chains mixed well and converged to similar stationary distributions for all parameters  and is favored. Since the second order model underperformed the first order model (AIC = 3466.319), we did not pursue higher orders. We note that Zheng et al. (2013) fit VAR(1) models to each individual patient. In fact, since there is one patient who has only 9 days of daily records in the training data, maximum likelihood estimation of models of higher order than one results in singularity problems requiring a Bayesian and/or regularized approach.L1 and L2 tuning parameters for different coefficients) while the regularized linear regression model uses the same tuning parameters for all coefficients. The latter leads to aggressive shrinkage in the coefficient estimates. In fact, most of the estimated coefficients given by the regularized linear regression model are zero, meaning that no variables are selected for the majority of the patients. Therefore, compared to the patient-specific VAR model that has no shrinkage and the regularized linear regression model that has aggressive shrinkage, our model provides decent amount of shrinkage and improves interpretation (see The advantage of the sparsity induced by the elastic-net prior over the existing patient-specific VAR model is that it reduces spurious relationships between the variables  and onlyv). The solid arrows show the associations with large patient-level heterogeneity: the largest one is the effect of previous tobacco use on current tobacco use, followed by previous craving on current negative affect and tobacco use. This is consistent with the findings in To further investigate what constitutes the patient-level heterogeneity for each of the associations between the three variables, we separate the entire sample of 25 participants by gender and age into 3 groups: young female, young male and old male. We then look at the distribution of the posterior modes of the patient-level lag-1 coefficients , the three groups tend to have similar medians with the young female group having a slightly higher median than the other two groups. However, the young male group has the greatest variance than the other two groups. Many of them also have strong negative patient-level coefficients, as apposed to the old male group, which has strong positive patient-level coefficients. This suggests that while increase in tobacco use in the previous day tends to increase tobacco use in the current day for the general population , the old male group seems to have a higher value than the other two groups. This suggests that for males older than 22 years, more craving in the previous day correlates to more negative affect in the current day than young females and young males. Moreover, for the effect of craving in the previous day on tobacco use in the current day , the old male group has lightly greater variance than the other two groups. This suggests that the effect of craving in the previous day on tobacco use in the current day can be more different between individual old males than between the younger participants.The estimated coverage probabilities of 95% predictive intervals are, respectively, 97%, 93% and 33.3% for the Bayesian model, the patient-specific VAR model and the regularized linear regression model. For a nominal level of 95%, we would expect about 95% of the predictive intervals to contain the true values. Both the Bayesian model and the patient-specific VAR model are close to the nominal level, whereas the regularized linear regression model is substantially undercovered. Further, 68% of the Bayesian intervals are narrower than those given by the patient-specific VAR model. This shows that the Bayesian method can not only provide more accurate point estimates but also a more satisfactory range estimate as well. Note that the majority of the intervals (more than 95%) given by regularized linear regression model are narrower than the other two methods. Both the undercover issue and the short length of these intervals are due to the aggressive nature of the shrinkage of this model.Approximately 20% to 50% of the physical symptoms presented in primary care and hospital settings cannot be fully explained by organic pathology  40] [41 [4140]  43] [44 [4443]  46] in  in 46] iTo investigate bidirectional relationship and temporal precedence between stress and FSS’s within individual patients, van Gils et al. (2014) adopted a VAR modeling framework on data from a diary study with patients who had multiple, persistent FSS’s, including external and internal body pain and other symptoms related to the autonomic nervous system . A patie26 patients with persistent FSS’s and psychological discomforts were recruited by medical practitioners in a 12-week study between January 2004 and February 2006. Standard handheld personal digital assistant (PDA) computers with the Palm operating system were used to record daily diary on 14 FSS’s  and 5 psychological discomforts . Patients entered 1-3 records on each day, with each data entry consisting of 3 most severe symptoms out of the 14 FSS’s and all 5 psychological discomfort measures . All participants were fully anonymized before accessing the data.FSS’s. Diary questions with respect to FSS’s were phrased as follows: “How much have you been bothered by symptom X? Please mark a point on the line between severe symptom X and no symptom X at all.” (1-150).Psychological discomforts. The level of stress and other psychological discomforts were assessed using the following question: “How stressful  are people and things around you? Please mark a point on the line between very stressful  and not stressful  at all.” (1-150).N = 12, 12, 10, 15, respectively). All patients in these subsets are included in the analysis. The age of the patients included in the four models ranges from 29 to 59 years old and there is only 1 male in the first 3 models and 4 males in the fourth model. For each of the 4 FSS’s, we extend the previous work where the relationship between one FSS and stress was considered ).In the examples, we used weakly informative hyperpriors which are conjugate but almost flat on the parameter space. This provides convenient derivation of the conditionals used in the Gibbs sampler while enforcing little prior information. We also tried different values of the hyperparameters but these yielded very similar results.Furthermore, in the examples, we used posterior modes as parameter estimates for better interpretability and visualization. However, we also tried posterior median. Due to the fact that the posterior distributions are symmetric and unimodal for most of the parameters, the results were very similar in terms of both parameter estimation and future data prediction, although sparsity in the parameter estimation then no longer exists.Moreover, we used a relatively simple missing data imputation scheme in the applications. This is to facilitate computational speed. Certainly more elaborate imputation procedure could be employed. Due to the fact that there are only a very small portion of missingness in both applications, different imputation approaches should not lead to drastically different results.We also notice that the point estimates of the future observations in both applications are close to zero, while the true values can be quite far away from zero. We suspect two reasons for this phenomenon: 1) the Bayesian method has bias-variance trade-off, that is, it increases bias by shrinking the prediction towards zero but greatly reduces variance, leading to smaller prediction errors in general; 2) the test data contains a lot of variability and both existing state-of-the-art models and the proposed model need more covariates to improve prediction. In future work, we hope to include more covariates  that may be predictive about the outcomes in order to improve the prediction accuracy for cases like this.In addition, due to the limited duration of observation in the first application, we used only 1 day as test data for each patient. As such, this probably has limited clinical utility. For the second application, however, 10 days  are used as test data. We believe this can prove meaningful in clinical practice.Lastly and equally importantly, in the current application, we derive associations, rather than causal interpretations, between the variables. If causation is warranted, confounding must be addressed in the model. Adding covariates, for example, might allow one to address confounding and derive a more interpretable model for causal inference.All code that generated the analyses in the paper and the data used in the first application are provided as online supplementary files Click here for additional data file.S2 AppendixTo draw from posterior distribution using Gibbs sampler, one draws each parameter from its conditional distribution given all other parameters at their current values. We provide full conditionals for all parameters.(PDF)Click here for additional data file.S1 Figw1 to w9 indicate the 9 population-level coefficients. The 4 chains are displayed by different colors in each panel.(TIF)Click here for additional data file.S2 Figw1 to w9 indicate the 9 population-level coefficients. The 4 chains are displayed by different colors in each panel.(TIF)Click here for additional data file.S3 Figw1 to w9 indicate the first 9 population-level coefficients. The 4 chains are displayed by different colors in each panel.(TIF)Click here for additional data file.S4 Figw1 to w9 indicate the 9 population-level coefficients. The 4 chains are displayed by different colors in each panel.(TIF)Click here for additional data file.S5 Figw1 to w9 indicate the first 9 population-level coefficients. The 4 chains are displayed by different colors in each panel.(TIF)Click here for additional data file.S6 Figw1 to w9 indicate the 9 population-level coefficients. The 4 chains are displayed by different colors in each panel.(TIF)Click here for additional data file.S7 Figw1 to w9 indicate the first 9 population-level coefficients. The 4 chains are displayed by different colors in each panel.(TIF)Click here for additional data file.S8 Figw1 to w9 indicate the 9 population-level coefficients. The 4 chains are displayed by different colors in each panel.(TIF)Click here for additional data file.S9 Figw1 to w9 indicate the first 9 population-level coefficients. The 4 chains are displayed by different colors in each panel.(TIF)Click here for additional data file.S10 Figw1 to w9 indicate the 9 population-level coefficients. The 4 chains are displayed by different colors in each panel.(TIF)Click here for additional data file.S1 TableEach row is for one patient and each column is for one VAR coefficient.(PDF)Click here for additional data file.S2 TableEach row is for one patient and each column is for one VAR coefficient.(PDF)Click here for additional data file.S3 TableEach row is for one patient and each column is for one VAR coefficient.(PDF)Click here for additional data file.S1 RcodeThis zip file contains all R code to generate the analysis, including the functions of the posterior sampling procedure for the proposed Bayesian model and the analysis on the real data.(ZIP)Click here for additional data file.S1 DataThis zip file contains the data used in the first application. All datasets are in csv format.(ZIP)Click here for additional data file.