Semiparametric hazard function estimation in meta-analysis for time to event data

Meta-analyses have been widely used to combine information from survival data using estimated parameters in, for example, a Cox model. A number of approaches dealing with study level random effects have been developed. However, there are far fewer meta-analysis approaches for estimating survival or hazard functions. Typical approaches are based on the cumulative survival function using the generalized estimating equation. We propose an alternative approach following Efron's discrete logistic regression (Efron, 1988), but using generalized linear mixed models. We show that spline functions can be used in fitting the models to obtain smoothed estimates for hazard functions. The models also allow a semi-parametric structure to include factors such as random study effects and treatment groups. This approach models the hazard function based on which the survival function can be estimated too. We also propose a Bayesian bootstrap approach for statistical inference for both hazard and survival functions. This approach was applied to two meta-analysis data sets as examples to illustrate its use. Copyright © 2012 John Wiley & Sons, Ltd.