Meta‐analysis methodology for combining treatment effects from Cox proportional hazard models with different covariate adjustments

In Cox proportional hazard models with censored survival data, estimates of treatment effects with some important covariates omitted will be biased toward zero (Gail et al ., Biometrika 71 : 431–444). This can be especially problematic in meta‐analyses that combine estimates of parameters from studies where different covariate adjustments are made. Presently, few constructive solutions have been provided to address this issue. In this paper, we review the existing meta‐analysis methodologies for aggregated patient data (APD) and propose two meta‐regression models (meta‐ANOVA model and meta‐polynomial model) with indicators of different covariates in Cox proportional hazard models to adjust the heterogeneity of treatment effects due to omitted covariates across studies. Both parametric and nonparametric estimators for the pooled treatment effect and the heterogeneity variance are presented and compared. We illustrate the advantages of our proposed analytic procedures over the existing methodologies by simulation studies and real data analysis. The existing methodologies yield large estimation bias in the presence of an “incomparability” issue, whereas our proposed models can adjust the bias and thus provide an accurate estimation.