Binomial Likelihood Research Articles

Localized negative binomial quasi maximum likelihood estimation for time varying integer-valued processes

This paper aims to study the non parametric Negative Binomial Quasi-Maximum Likelihood Estimation (NBQMLE) for locally stationary integer valued processes. So, we have considered two locally stationary integer-valued models of negative binomial type, namely: INARCH ( p ) and INGARCH ( p , q ) models. Imposing some contraction arguments, we have extended the stationary negative-binomial QMLE to a localized one in our non-stationary environment. This estimation method is based on a kernel function that achieves the convergence rates of n h n order. Under some regularity assumptions, the consistency, as well as the asymptotic normality of the obtained estimator, are established. The performances of the established estimators are evaluated via a simulation study and an application to real data set.

The PS4-likelihood ratio calculator: flexible allocation of evidence weighting for case-control data in variant classification

BackgroundThe 2015 American College of Medical Genetics/Association of Molecular Pathology (ACMG/AMP) variant classification framework specifies that case-control observations can be scored as ‘strong’ evidence (PS4) towards pathogenicity.MethodsWe developed the PS4-likelihood...

Modelling Student Retention in Tutorial Classes with Uncertainty—A Bayesian Approach to Predicting Attendance-Based Retention

A Bayesian additive regression tree (BART) is a recent statistical method that blends ensemble learning with nonparametric regression. BART is constructed using a Bayesian approach, which provides the benefit of model-based prediction uncertainty, enhancing the reliability of predictions. This study proposes the development of a BART model with a binomial likelihood to predict the percentage of students retained in tutorial classes using attendance data sourced from a South African university database. The data consist of tutorial dates and encoded (anonymized) student numbers, which play a crucial role in deriving retention variables such as cohort age, active students, and retention rates. The proposed model is evaluated and benchmarked against the random forest regressor (RFR). The proposed BART model reported an average of 20% higher predictive performance compared to RFR across six error metrics, achieving an R-squared score of 0.9414. Furthermore, the study demonstrates the utility of the highest density interval (HDI) provided by the BART model, which can help in determining the best- and worst-case scenarios for student retention rate estimates. The significance of this study extends to multiple stakeholders within the educational sector. Educational institutions, administrators, and policymakers can benefit from this study by gaining insights into how future tutorship programme student retention rates can be predicted using predictive models. Furthermore, the foresight provided by the predicted student retention rates can aid in strategic resource allocation, facilitating more informed planning and budgeting for tutorship programmes.

Exploring odontocete depredation rates in a pelagic longline fishery.

Several odontocete species depredate catch and bait from fishing gear, resulting in their bycatch and causing substantial economic costs. There are no known mitigation methods for odontocete depredation in pelagic longline fisheries that are effective, do not harm odontocetes and are commercially viable. Understanding odontocetes' depredation strategies can contribute to mitigating this human-wildlife conflict. Using observer data from the Hawaii-based tuna longline fishery, this study summarized teleost and elasmobranch species-specific mean posterior odontocete depredation rates using a simple Bayesian binomial likelihood estimator with a Bayes-Laplace prior. Depredation rates of species with sufficient sample sizes ranged from a high of 1.2% (1.1 to 1.3 95% highest posterior density interval or HDI) for shortbill spearfish to a low of 0.002% (0.001 to 0.003 95% HDI) for blue shark. Depredation of catch is a rare event in this fishery, occurring in about 6% of sets. When depredation did occur, most frequently odontocetes depredated a small proportion of the catch, however, there was large variability in depredation rates between teleost species. For example, bigeye tuna was two times more likely to be depredated than yellowfin tuna (odds ratio = 2.03, 95% CI: 1.8-2.3, P<0.0001). For sets with depredation, 10% and 2% of sets had depredation of over half of the captured bigeye tuna and combined teleosts, respectively. All elasmobranch species had relatively low depredation rates, where only 7 of almost 0.5M captured elasmobranchs were depredated. Odontocetes selectively depredate a subset of the teleost species captured within sets, possibly based on net energy value, chemical, visual, acoustic and textural characteristics and body size, but not median length, which was found to be unrelated to depredation rate (Pearson's r = 0.14, 95% CI: -0.26 to 0.50, p = 0.49). Study findings provide evidence to support the identification and innovation of effective and commercially viable methods to mitigate odontocete depredation and bycatch.

Bayesian probabilistic sensitivity analysis of Markov models for natural history of a disease: an application for cervical cancer

Background: parameter uncertainty in the Markov model’s description of a disease course was addressed. Probabilistic sensitivity analysis (PSA) is now considered the only tool that properly permits parameter uncertainty’s examination. This consists in sampling values from the parameter’s probability distributions. Methods: Markov models fitted with microsimulation were considered and methods for carrying out a PSA on transition probabilities were studied. Two Bayesian solutions were developed: for each row of the modeled transition matrix the prior distribution was assumed as a product of Beta or a Dirichlet. The two solutions differ in the source of information: several different sources for each transition in the Beta approach and a single source for each transition from a given health state in the Dirichlet. The two methods were applied to a simple cervical cancer’s model. Results : differences between posterior estimates from the two methods were negligible. Results showed that the prior variability highly influence the posterior distribution. Conclusions: the novelty of this work is the Bayesian approach that integrates the two distributions with a product of Binomial distributions likelihood. Such methods could be also applied to cohort data and their application to more complex models could be useful and unique in the cervical cancer context, as well as in other disease modeling.

Determinants of Trade Flow in the Economic Community of Central African States (ECCAS): Does Governance Matter?

Abstract Subject and purpose of work: This study analyzes the determinants of intra-ECCAS trade, with special attention paid to the role of institutional quality from 1996 to 2021. Materials and methods: The study conducts descriptive analysis and utilizes a Negative Binomial Pseudo Maximum Likelihood to analyze the determinants of intra-ECCAS trade. Results: The results suggest that gross domestic product (GDP), population, time taken for export shipment in the exporting countries and the bilateral real exchange rate of the importing partner country enhance intra-ECCAS trade flow. On the other hand, distance, two trading partners being landlocked, time for importing countries and bilateral real exchange rate of the exporting partner discourage this. Furthermore, the findings reveal that institutions are vital to intra-ECCAS trade. Conclusions: T he key d rivers of intra-ECCAS t rade a re GDP, population, t ime t aken for export shipment in the exporting countries, bilateral real exchange rate of the importing partner country, and institutions’ quality measures.

Pembrolizumab plus lenvatinib (P+L) versus alternate therapies in first-line (1L) for advanced renal cell carcinoma (aRCC): A network meta-analysis (NMA).

422 Background: Patients with advanced renal cell carcinoma (aRCC) have poor prognosis resulting in significant burden. In the KEYNOTE-581/CLEAR trial, pembrolizumab plus lenvatinib (P+L) as 1L therapy showed statistically significant and clinically meaningful improvements in overall survival (OS), progression-free survival (PFS), and overall response rate (ORR) versus sunitinib in patients with aRCC. This NMA synthesized evidence from randomized clinical trials (RCTs) to indirectly compare the relative treatment effects of P+L vs alternate therapies in treatment-naïve aRCC. Methods: A systematic literature review was conducted to identify systemic therapies in 1L aRCC. A Bayesian NMA with fixed-effect models was performed to indirectly compare P+L to alternate therapies using sunitinib as the common comparator in 1L aRCC. Hazard ratios (HRs) for OS and PFS were calculated with 95% credible intervals (CrIs). NMAs assuming constant hazard ratios (HRs) and time-varying HRs were performed for OS and PFS. For the proportion of patients experiencing response, a binomial likelihood and logit link were used, and relative effects were expressed as odds ratios (OR). Results: A total of 33 unique RCTs met the inclusion criteria and were included in the analyses. The constant HR analysis resulted in no significant differences in OS between P+L and alternatives in network. Results showed statistically significant higher ORR for P+L compared to nivolumab + ipilimumab (N+I) (OR=3.19; 95% CrI: 2.14, 4.82) and pembrolizumab + axitinib (P+A) (OR=1.84; 95% CrI: 1.21, 2.80). The analysis also favored P+L over nivolumab + cabozantinib (N+C) (OR=1.35; 95% Crl: 0.86, 2.12) and avelumab + axitinib (A+A) (OR=1.46; 95% Crl: 0.96, 2.23), but was not statistically significant. The constant HR analysis showed that P+L resulted in a statistically significant improvement in PFS compared to N+I (HR=0.55; 95% CrI: 0.40, 0.75), A+A (HR=0.68; 95% Crl: 0.49, 0.96) and P+A (HR=0.69; 95% CrI: 0.51, 0.94). The analysis also favored P+L over N+C (HR=0.81; 95% Crl: 0.58, 1.14), but was not statistically significant. Conclusions: NMA indicates P+L has higher ORR and improved PFS compared to other regimens in 1L aRCC. No significant differences in OS were observed between P+L and competing interventions.

Pembrolizumab plus lenvatinib (P+L) versus alternative therapies in first-line (1L) advanced renal cell carcinoma (aRCC) by IMDC risk status: A network meta-analysis (NMA).

421 Background: The International Metastatic Renal Cell Carcinoma Database Consortium (IMDC) risk criteria is a widely used prognostic model in advanced RCC. Pembrolizumab plus lenvatinib (P+L) demonstrated a significant improvement in ORR, PFS, and OS versus sunitinib in subjects with cc aRCC in the KEYNOTE-581/CLEAR trial. This NMA indirectly compared the efficacy of P+L to other therapies in 1L aRCC subjects within IMDC risk groups using data from randomized clinical trials (RCTs). Methods: A systematic literature review was conducted to identify systemic therapies in 1L aRCC. Trials reporting results for IMDC favorable risk and/or intermediate+poor risk groups were included. A Bayesian NMA with fixed-effect models was performed to indirectly compare P+L to alternate therapies using sunitinib as the common comparator. Hazard ratios (HRs) for OS and PFS were calculated with 95% credible intervals (CrIs). The NMAs assuming constant hazard ratios (HRs) for OS and PFS were performed for all IMDC risk group categories. For the proportion of patients experiencing response, a binomial likelihood and logit link were used, and relative effects were expressed as odds ratios (OR). Results: For the IMDC favorable risk subgroup, P+L demonstrated statistically significant increase in ORR compared to nivolumab + ipilimumab (N+I) (OR=5.35; 95% CrI: 2.59, 11.41) and nivolumab (OR=8.41; 95% CrI: 1.84, 43.77). For PFS, P+L resulted in a statistically significant improvement in PFS compared to N+I (HR=0.31, 95% CrI: 0.17-0.56). For OS, no significant differences were observed compared to other alternatives in the network. For the IMDC intermediate+poor risk subgroup, P+L demonstrated statistically significant increase in ORR compared to nivolumab + cabozantinib (N+C) (OR=1.77; 95% CrI: 1.02, 3.10), N+I (OR=3.15; 95% CrI: 1.94, 5.10), and nivolumab + ipilimumab + cabozantinib (N+I+C) (OR=2.34; 95% CrI: 1.34, 4.12), pembrolizumab + axitinib (P+A) (OR=2.65; 95% CrI: 1.57, 4.44) and nivolumab (OR=4.68; 95% CrI: 1.84, 12.02). For PFS, P+L resulted in a statistically significant improvement compared to N+I (HR=0.59; 95% CrI: 0.41, 0.84) (P+A) (HR=0.64; 95% CrI: 0.44, 0.93), and avelumab + axitinib (A+A) (HR=0.65; 95% CrI: 0.46, 0.93). For OS, no significant differences were observed compared to other alternatives in the network. Conclusions: PFS analysis favored P+L over all alternative therapies in the network in favorable or intermediate+poor IMDC risk groups. ORR analysis favored P+L over all alternative therapies in the network in intermediate+poor IMDC risk groups. No significant difference in OS was observed between P+L and other alternative therapies in the network.

Choice of link functions for generalized linear mixed models in meta-analyses of proportions

Two-step approaches for synthesizing proportions in a meta-analysis require first transforming the proportions to a scale where their distribution across studies can be approximated by a normal distribution. Commonly used transformations include the log, logit, arcsine, and Freeman-Tukey double-arcsine transformations. Alternatively, a generalized linear mixed model (GLMM) can be fit directly on the data using the exact binomial likelihood. Unlike popular two-step methods, this accounts for uncertainty in the within-study variances without a normal approximation and does not require an ad hoc correction for zero counts. However, GLMMs require choosing a link function; we illustrate how the AIC can be used to choose the best fitting link when different link functions give different results. We also highlight how misspecification of the link function can introduce bias; using an empirical sandwich estimator for the standard error may not sufficiently avoid undercoverage due to link function misspecification. We demonstrate the application of GLMMs and choice of link function using data from a systematic review on the prevalence of fever in children with COVID-19.

Evaluation of Bayesian spatiotemporal infectious disease models for prospective surveillance analysis

BackgroundCOVID-19 brought enormous challenges to public health surveillance and underscored the importance of developing and maintaining robust systems for accurate surveillance. As public health data collection efforts expand, there is a critical need for infectious disease modeling researchers to continue to develop prospective surveillance metrics and statistical models to accommodate the modeling of large disease counts and variability. This paper evaluated different likelihoods for the disease count model and various spatiotemporal mean models for prospective surveillance.MethodsWe evaluated Bayesian spatiotemporal models, which are the foundation for model-based infectious disease surveillance metrics. Bayesian spatiotemporal mean models based on the Poisson and the negative binomial likelihoods were evaluated with the different lengths of past data usage. We compared their goodness of fit and short-term prediction performance with both simulated epidemic data and real data from the COVID-19 pandemic.ResultsThe simulation results show that the negative binomial likelihood-based models show better goodness of fit results than Poisson likelihood-based models as deemed by smaller deviance information criteria (DIC) values. However, Poisson models yield smaller mean square error (MSE) and mean absolute one-step prediction error (MAOSPE) results when we use a shorter length of the past data such as 7 and 3 time periods. Real COVID-19 data analysis of New Jersey and South Carolina shows similar results for the goodness of fit and short-term prediction results. Negative binomial-based mean models showed better performance when we used the past data of 52 time periods. Poisson-based mean models showed comparable goodness of fit performance and smaller MSE and MAOSPE results when we used the past data of 7 and 3 time periods.ConclusionWe evaluate these models and provide future infectious disease outbreak modeling guidelines for Bayesian spatiotemporal analysis. Our choice of the likelihood and spatiotemporal mean models was influenced by both historical data length and variability. With a longer length of past data usage and more over-dispersed data, the negative binomial likelihood shows a better model fit than the Poisson likelihood. However, as we use a shorter length of the past data for our surveillance analysis, the difference between the Poisson and the negative binomial models becomes smaller. In this case, the Poisson likelihood shows robust posterior mean estimate and short-term prediction results.

Conjugate priors and bias reduction for logistic regression models

We address the issue of divergent maximum likelihood estimates for logistic regression models by considering a conjugate prior penalty which always produces finite estimates. We show that the proposed method is closely related to the reduced-bias approach of Firth (1993), and that the induced penalized likelihood can be expressed as a genuine binomial likelihood, replacing the original data with pseudo-counts.

Seasonal and Spatial Distribution of Walleye Sex Ratios in a Large Nebraska Reservoir

Abstract The ratio of female to male Walleye Sander vitreus across the spatial scale of large reservoirs and during nonspawning times receives little attention, even though standardized sampling occurs during this time. This study evaluated whether the proportion of female Walleye collected from seasonal sampling at different spatial areas within a large reservoir fell within the 0.450–0.550 range, which would closely reflect a 1:1 female-to-male sex ratio. We used a Bayesian generalized linear mixed-effects model with a binomial probability distribution to assess the proportion of female Walleye, using season (spring and fall) and reservoir zone (riverine, transitional, and lacustrine) as fixed effects and year (2015 and 2016) as a random effect. We collected a total of 2,163 Walleye using standardized Nebraska Game and Parks Commission gill-netting methodology and determined sex on a random subsample of fish (n = 989) collected throughout each reservoir zone. There was no meaningful deviation from the 0.450–0.550 range in the mean posterior estimate of the proportion of female Walleye caught in the riverine and transitional zones during either spring or fall. The mean (SD) posterior estimate of the proportion of female Walleye in the lacustrine zone was 0.182 (0.024) in the spring and 0.621 (0.032) in the fall. These results are consistent with previous observations of increased male presence near spawning locations in the spring and demonstrate that increased fall female catch in the lacustrine zone could potentially bias sampling results. This study provides further insight into the distribution of sexes across the spatial gradient of a large Great Plains reservoir and demonstrates a need to sex Walleye during standardized fall surveys.

Ensemble Methods in Customer Churn Prediction: A Comparative Analysis of the State-of-the-Art

In the past several single classifiers, homogeneous and heterogeneous ensembles have been proposed to detect the customers who are most likely to churn. Despite the popularity and accuracy of heterogeneous ensembles in various domains, customer churn prediction models have not yet been picked up. Moreover, there are other developments in the performance evaluation and model comparison level that have not been introduced in a systematic way. Therefore, the aim of this study is to perform a large scale benchmark study in customer churn prediction implementing these novel methods. To do so, we benchmark 33 classifiers, including 6 single classifiers, 14 homogeneous, and 13 heterogeneous ensembles across 11 datasets. Our findings indicate that heterogeneous ensembles are consistently ranked higher than homogeneous ensembles and single classifiers. It is observed that a heterogeneous ensemble with simulated annealing classifier selection is ranked the highest in terms of AUC and expected maximum profits. For accuracy, F1 measure and top-decile lift, a heterogenous ensemble optimized by non-negative binomial likelihood, and a stacked heterogeneous ensemble are, respectively, the top ranked classifiers. Our study contributes to the literature by being the first to include such an extensive set of classifiers, performance metrics, and statistical tests in a benchmark study of customer churn.

Non-optimal apparent temperature and cardiovascular mortality: the association in Puducherry, India between 2011 and 2020

BackgroundCardiovascular diseases (CVDs), the leading cause of death worldwide, are sensitive to temperature. In light of the reported climate change trends, it is important to understand the burden of CVDs attributable to temperature, both hot and cold. The association between CVDs and temperature is region-specific, with relatively few studies focusing on low-and middle-income countries. This study investigates this association in Puducherry, a district in southern India lying on the Bay of Bengal, for the first time.MethodsUsing in-hospital CVD mortality data and climate data from the Indian Meteorological Department, we analyzed the association between apparent temperature (Tapp) and in-hospital CVD mortalities in Puducherry between 2011 and 2020. We used a case-crossover model with a binomial likelihood distribution combined with a distributed lag non-linear model to capture the delayed and non-linear trends over a 21-day lag period to identify the optimal temperature range for Puducherry. The results are expressed as the fraction of CVD mortalities attributable to heat and cold, defined relative to the optimal temperature. We also performed stratified analyses to explore the associations between Tapp and age-and-sex, grouped and considered together, and different types of CVDs. Sensitivity analyses were performed, including using a quasi-Poisson time-series approach.ResultsWe found that the optimal temperature range for Puducherry is between 30°C and 36°C with respect to CVDs. Both cold and hot non-optimal Tapp were associated with an increased risk of overall in-hospital CVD mortalities, resulting in a U-shaped association curve. Cumulatively, up to 17% of the CVD deaths could be attributable to non-optimal temperatures, with a slightly higher burden attributable to heat (9.1%) than cold (8.3%). We also found that males were more vulnerable to colder temperature; females above 60 years were more vulnerable to heat while females below 60 years were affected by both heat and cold. Mortality with cerebrovascular accidents was associated more with heat compared to cold, while ischemic heart diseases did not seem to be affected by temperature.ConclusionBoth heat and cold contribute to the burden of CVDs attributable to non-optimal temperatures in the tropical Puducherry. Our study also identified the age-and-sex and CVD type differences in temperature attributable CVD mortalities. Further studies from India could identify regional associations, inform our understanding of the health implications of climate change in India and enhance the development of regional and contextual climate-health action-plans.

Tutorial: statistical methods for the meta-analysis of diagnostic test accuracy studies.

This tutorial shows how to perform a meta-analysis of diagnostic test accuracy studies (DTA) based on a 2×2 table available for each included primary study. First, univariate methods for meta-analysis of sensitivity and specificity are presented. Then the use of univariate logistic regression models with and without random effects for e.g. sensitivity is described. Diagnostic odds ratios (DOR) are then introduced to combine sensitivity and specificity into one single measure and to assess publication bias. Finally, bivariate random effects models using the exact binomial likelihood to describe within-study variability and a normal distribution to describe between-study variability are presented as the method of choice. Based on this model summary receiver operating characteristic (sROC) curves are constructed using a regression model logit-true positive rate (TPR) over logit-false positive rate (FPR). Also it is demonstrated how to perform the necessary calculations with the freely available software R. As an example a meta-analysis of DTA studies using Procalcitonin as a diagnostic marker for sepsis is presented.

Correlated Chained Gaussian Processes for Modelling Citizens Mobility Using a Zero-Inflated Poisson Likelihood

Modelling the mobility of people in a city depends on counting data with inherent problems of overdispersion. Such dispersion issues are caused by massive amounts of data with zero values. Though traditional machine learning models have been used to overcome said problems, they lack the ability to appropriately model the spatio-temporal correlations in data. To improve the modelling of such spatio-temporal correlations, in this work we propose to model the citizens mobility, for the Chinese city of Guangzhou, by means of a Zero-inflated Poisson likelihood in conjunction with Gaussian process priors generated from convolution processes. We follow the idea of chaining the likelihood’s parameters to latent functions drawn from Gaussian process priors; this way allowing a higher flexibility to model heteroscedasticity. Additionally, we derive a stochastic variational inference framework that allow us to use two types of convolution process models in the context of large datasets: correlated chained Gaussian processes with a convolution processes model, and correlated chained Gaussian processes with variational inducing kernels. We present quantitative and qualitative results comparing the performance between Negative Binomial and Zero-inflated Poisson likelihoods, both in combination with three types of Gaussian process priors: a linear model of coregionalisation, and our two proposed methods based on a convolution processes model and variational inducing kernels.

Institutional Quality and Intra-Regional Trade Flows: Evidence from ECOWAS

Since institutional quality can either create or destroy incentives for individuals to engage in trade, it has become a source of worry to policymakers, as it can limit both intra- and extra-regional trade. Based on this, we empirically analyzed the extent to which national institutional quality affects bilateral trade flows in ECOWAS based on a gravity model for the period from 2000 to 2018. Specifically, the study employs the negative binomial pseudo-maximum likelihood estimator (NBPML). The results reveal that institutional variables with both aggregated and disaggregated measures of the quality of institutions have a significant and positive impact on trade flows in ECOWAS and on its sub-samples, WAEMU and WAMZ. The results further indicate that for both importing and exporting countries, reduced corruption, effective rule of law, and effective government coincide with more trade among member countries. The degree of regional integration is an important determinant of intra-ECOWAS trade, as are GDP, GDP per capita, common language, and landlockedness.

Raising the bar for patient experience during care transitions in Canada: A repeated cross-sectional survey evaluating a patient-oriented discharge summary at Ontario hospitals.

Patient experience when transitioning home from hospital is an important quality metric linked to improved patient outcomes. We evaluated the impact of a hospital-based care transition intervention, patient-oriented discharge summary (PODS), on patient experience across Ontario acute care hospitals. We used a repeated cross-sectional study design to compare yearly positive (top-box) responses to four questions centered on discharge communication from the Canadian Patient Experience Survey (2016-2020) among three hospital cohorts with various levels of PODS implementation. Generalized Estimating Equations using a binomial likelihood accounting for site level clustering was used to assess continuous linear time trends among cohorts and cohort differences during the post-implementation period. This research had oversight from a public advisory group of patient and caregiver partners from across the province. 512,288 individual responses were included. Compared to non-implementation hospitals, hospitals with full implementation (>50% discharges) reported higher odds for having discussed the help needed when leaving hospital (OR = 1.18, 95% CI = 1.02-1.37) and having received information in writing about what symptoms to look out for (OR = 1.44, 95% = 1.17-1.78) post-implementation. The linear time trend was also significant when comparing hospitals with full versus no implementation for having received information in writing about what symptoms to look out for (OR = 1.05, 95% CI = 1.01-1.09). PODS implementation was associated with higher odds of positive patient experience, particularly for questions focused on discharge planning. Further efforts should center on discharge management, specifically: understanding of medications and what to do if worried once home.

Multivariate Bayesian Arm-Based Network Meta-Analysis of Pharmacological Interventions for the Treatment of Acute Bipolar Mania in Adults.

In a network meta-analysis (NMA), multiple treatments can be compared simultaneously by aggregating pieces of evidence from direct as well as indirect treatment comparisons in different randomized controlled trials (RCTs). Conventional NMA are performed using a normal approximation approach and can be applied for arm-level binary outcome data as well. This study aimed to estimate the treatment effects within a Bayesian framework using a binomial likelihood for a multivariate NMA model. The dataset consists of 57 RCTs comparing the effect of ten pharmacological drugs and a placebo for acute bipolar mania in adults. The binary outcomes of interest were treatment response and all-cause dropouts measured three weeks from the baseline. Binomial distribution was adopted for the number of events and the probability of event occurrence modeled on the logit scale. Jeffrey's Beta prior was considered for the heterogeneity and inconsistency of standard deviation (SD) parameters. Cholesky and spherical decomposition strategies were adopted for the between-study variance-covariance matrix. Deviance information criterion (DIC) indices were computed to determine the model fit. All results pertaining to Markov chain Monte Carlo simulations and all analyses were carried out in WinBUGS software. The estimated common heterogeneity SDs were similar, and the DIC values did not provide any evidence for superiority between the two decomposition strategies. The correlation (95% credible interval) between the outcomes was estimated as -0.31 (-0.71, -0.02) and -0.37 (-0.73, -0.03) for the Cholesky and spherical decompositions, respectively. Gelman-Rubin convergence statistics were stable, and Monte Carlo errors for all the parameters were around 0.005. Overall, olanzapine, paliperidone, and quetiapine were both significantly more effective and acceptable than a placebo when both the study outcomes were considered simultaneously. The findings favoring olanzapine, paliperidone, and quetiapine possess an excellent concordance with the one adopted in clinical practice, and the Canadian Network for Mood and Anxiety Treatments and Royal Australian and New Zealand College of Psychiatrists guidelines recommend these as first-line drugs for treating bipolar disorder.

Use of copula to model within-study association in bivariate meta-analysis of binomial data at the aggregate level: ABayesian approach and application to surrogate endpoint evaluation.

Bivariate meta-analysis provides a useful framework for combining information across related studies and has been utilized to combine evidence from clinical studies to evaluate treatment efficacy on two outcomes. It has also been used to investigate surrogacy patterns between treatment effects on the surrogate endpoint and the final outcome. Surrogate endpoints play an important role in drug development when they can be used to measure treatment effect early compared to the final outcome and to predict clinical benefit or harm. The standard bivariate meta-analytic approach models the observed treatment effects on the surrogate and the final outcome outcomes jointly, at both the within-study and between-studies levels, using a bivariate normal distribution. For binomial data, a normal approximation on log odds ratio scale can be used. However, this method may lead to biased results when the proportions of events are close to one or zero, affecting the validation of surrogate endpoints. In this article, we explore modeling the two outcomes on the original binomial scale. First, we present a method that uses independent binomial likelihoods to model the within-study variability avoiding to approximate the observed treatment effects. However, the method ignores the within-study association. To overcome this issue, we propose a method using a bivariate copula with binomial marginals, which allows the model to account for the within-study association. We applied the methods to an illustrative example in chronic myeloid leukemia to investigate the surrogate relationship between complete cytogenetic response and event-free-survival.