Abstract
We present a novel Bayesian approach to random effects meta analysis of binary data with excessive zeros in two-arm trials. We discuss the development of likelihood accounting for excessive zeros, the prior, and the posterior distributions of parameters of interest. Dirichlet process prior is used to account for the heterogeneity among studies. A zero inflated binomial model with excessive zero parameters were used to account for excessive zeros in treatment and control arms. We then define a modified unconditional odds ratio accounting for excessive zeros in two arms. The Bayesian inference is carried out using Markov chain Monte Carlo (MCMC) sampling techniques. We illustrate the approach using data available in published literature on myocardial infarction and death from cardiovascular causes. Bayesian approaches presented here use all the data, including the studies with zero events and capture heterogeneity among study effects, and produce interpretable estimates of overall and study-level odds-ratios, over the commonly used frequentist’s approaches. Results from the data analysis and the model selection also indicate that the proposed Bayesian method, while accounting for zero events, adjusts for excessive zeros and provides better fit to the data resulting in the estimates of overall odds-ratio and study-level odds-ratios that are based on the totality of the information.
Highlights
An arm is a standard term for describing clinical trial and it represents a treatment group or a set of subjects
The results suggest that when the data has a high percentage of observed zeros, zero-inflated Binomial (ZIB) model is a more appropriate model to use
5 Discussion Binary data naturally arise in clinical trials in health sciences
Summary
An arm is a standard term for describing clinical trial and it represents a treatment group or a set of subjects. In a two-arm trial with binary outcomes, it is typically assumed that YT1 , ..., YTk and YC1 , ..., YCk are random samples from YTi ∼ Bin nTi , PTi and YCi ∼ Bin nCi , PCi respectively, where k is the number of studies.
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