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Bivariate random effects models for meta-analysis of comparative studies with binary outcomes: methods for the absolute risk difference and relative risk.

ABSTRACT: Multivariate meta-analysis is increasingly utilised in biomedical research to combine data of multiple comparative clinical studies for evaluating drug efficacy and safety profile. When the probability of the event of interest is rare, or when the individual study sample sizes are small, a substantial proportion of studies may not have any event of interest. Conventional meta-analysis methods either exclude such studies or include them through ad hoc continuality correction by adding an arbitrary positive value to each cell of the corresponding 2 × 2 tables, which may result in less accurate conclusions. Furthermore, different continuity corrections may result in inconsistent conclusions. In this article, we discuss a bivariate Beta-binomial model derived from Sarmanov family of bivariate distributions and a bivariate generalised linear mixed effects model for binary clustered data to make valid inferences. These bivariate random effects models use all available data without ad hoc continuity corrections, and accounts for the potential correlation between treatment (or exposure) and control groups within studies naturally. We then utilise the bivariate random effects models to reanalyse two recent meta-analysis data sets.

SUBMITTER: Chu H

PROVIDER: S-EPMC3348438 | biostudies-literature | 2012 Dec

REPOSITORIES: biostudies-literature

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Bivariate random effects models for meta-analysis of comparative studies with binary outcomes: methods for the absolute risk difference and relative risk.

Chu Haitao H Nie Lei L Chen Yong Y Huang Yi Y Sun Wei W

Statistical methods in medical research 20101221 6

Multivariate meta-analysis is increasingly utilised in biomedical research to combine data of multiple comparative clinical studies for evaluating drug efficacy and safety profile. When the probability of the event of interest is rare, or when the individual study sample sizes are small, a substantial proportion of studies may not have any event of interest. Conventional meta-analysis methods either exclude such studies or include them through ad hoc continuality correction by adding an arbitrar ...[more]

PMID: 21177306

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Project description:BackgroundLogistic random effects models are a popular tool to analyze multilevel also called hierarchical data with a binary or ordinal outcome. Here, we aim to compare different statistical software implementations of these models.MethodsWe used individual patient data from 8509 patients in 231 centers with moderate and severe Traumatic Brain Injury (TBI) enrolled in eight Randomized Controlled Trials (RCTs) and three observational studies. We fitted logistic random effects regression models with the 5-point Glasgow Outcome Scale (GOS) as outcome, both dichotomized as well as ordinal, with center and/or trial as random effects, and as covariates age, motor score, pupil reactivity or trial. We then compared the implementations of frequentist and Bayesian methods to estimate the fixed and random effects. Frequentist approaches included R (lme4), Stata (GLLAMM), SAS (GLIMMIX and NLMIXED), MLwiN ([R]IGLS) and MIXOR, Bayesian approaches included WinBUGS, MLwiN (MCMC), R package MCMCglmm and SAS experimental procedure MCMC.Three data sets (the full data set and two sub-datasets) were analysed using basically two logistic random effects models with either one random effect for the center or two random effects for center and trial. For the ordinal outcome in the full data set also a proportional odds model with a random center effect was fitted.ResultsThe packages gave similar parameter estimates for both the fixed and random effects and for the binary (and ordinal) models for the main study and when based on a relatively large number of level-1 (patient level) data compared to the number of level-2 (hospital level) data. However, when based on relatively sparse data set, i.e. when the numbers of level-1 and level-2 data units were about the same, the frequentist and Bayesian approaches showed somewhat different results. The software implementations differ considerably in flexibility, computation time, and usability. There are also differences in the availability of additional tools for model evaluation, such as diagnostic plots. The experimental SAS (version 9.2) procedure MCMC appeared to be inefficient.ConclusionsOn relatively large data sets, the different software implementations of logistic random effects regression models produced similar results. Thus, for a large data set there seems to be no explicit preference (of course if there is no preference from a philosophical point of view) for either a frequentist or Bayesian approach (if based on vague priors). The choice for a particular implementation may largely depend on the desired flexibility, and the usability of the package. For small data sets the random effects variances are difficult to estimate. In the frequentist approaches the MLE of this variance was often estimated zero with a standard error that is either zero or could not be determined, while for Bayesian methods the estimates could depend on the chosen "non-informative" prior of the variance parameter. The starting value for the variance parameter may be also critical for the convergence of the Markov chain.

Dataset Information

Bivariate random effects models for meta-analysis of comparative studies with binary outcomes: methods for the absolute risk difference and relative risk.

Publications

Bivariate random effects models for meta-analysis of comparative studies with binary outcomes: methods for the absolute risk difference and relative risk.

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