Meta-analysis of single-arm survival studies: a distribution-free approach for estimating summary survival curves with random effects

In epidemiologic studies and clinical trials with time-dependent outcome (for instance death or disease progression), survival curves are used to describe the risk of the event over time. In meta-analyses of studies reporting a survival curve, the most informative finding is a summary survival curve. In this paper, we propose a method to obtain a distribution-free summary survival curve by expanding the product-limit estimator of survival for aggregated survival data. The extension of DerSimonian and Laird's methodology for multiple outcomes is applied to account for the between-study heterogeneity. Statistics I(2) and H(2) are used to quantify the impact of the heterogeneity in the published survival curves. A statistical test for between-strata comparison is proposed, with the aim to explore study-level factors potentially associated with survival. The performance of the proposed approach is evaluated in a simulation study. Our approach is also applied to synthesize the survival of untreated patients with hepatocellular carcinoma from aggregate data of 27 studies and synthesize the graft survival of kidney transplant recipients from individual data from six hospitals.