A framework for meta-analysis of prediction model studies with binary and time-to-event outcomes

It is widely recommended that any developed—diagnostic or prognostic—prediction model is externally validated in terms of its predictive performance measured by calibration and discrimination. When multiple validations have been performed, a systematic review followed by a formal meta-analysis helps to summarize overall performance across multiple settings, and reveals under which circumstances the model performs suboptimal (alternative poorer) and may need adjustment. We discuss how to undertake meta-analysis of the performance of prediction models with either a binary or a time-to-event outcome. We address how to deal with incomplete availability of study-specific results (performance estimates and their precision), and how to produce summary estimates of the c-statistic, the observed:expected ratio and the calibration slope. Furthermore, we discuss the implementation of frequentist and Bayesian meta-analysis methods, and propose novel empirically-based prior distributions to improve estimation of between-study heterogeneity in small samples. Finally, we illustrate all methods using two examples: meta-analysis of the predictive performance of EuroSCORE II and of the Framingham Risk Score. All examples and meta-analysis models have been implemented in our newly developed R package “metamisc”.