A framework for meta-analysis through standardized survival curves

Meta-analyses of survival studies aim to reveal the variation of an effect measure of interest over different studies and present a meaningful summary. They must address between study heterogeneity in several dimensions and eliminate spurious sources of variation. Forest plots of the usual (adjusted) hazard ratios are fraught with difficulties from this perspective since both the magnitude and interpretation of these hazard ratios depend on factors ancillary to the true study-specific exposure effect. These factors generally include the study duration, the censoring patterns within studies, the covariates adjusted for and their distribution over exposure groups. Ignoring these mentioned features and accepting implausible hidden assumptions may critically affect interpretation of the pooled effect measure. Risk differences or restricted mean effects over a common follow-up interval and balanced distribution of a covariate set are natural candidates for exposure evaluation and possible treatment choice. In this paper, we propose differently standardized survival curves over a fitting time horizon, targeting various estimands with their own transportability. With each type of standardization comes a given interpretation within studies and overall, under stated assumptions. These curves can in turn be summarized by standardized study-specific contrasts, including hazard ratios with more consistent meaning. We prefer forest plots of risk differences at well chosen time points. Our case study examines overall survival among anal squamous cell carcinoma patients, expressing the tumor marker $p16^{INK4a}$ or not, based on the individual patient data of six studies.