Meta-analyses of survival outcomes commonly pool log hazard ratios or survival probabilities at selected time points. When reporting formats and observation times differ across studies, methods are needed to use available survival information for estimation at a common target time. We propose a functional random-effects model on the complementary log--log scale that synthesizes Kaplan--Meier curves and survival probabilities at discrete times as functional data. Studies that do not report survival at the target time contribute to its estimation through the use of their observed curves to estimate group-specific mean functions. The estimated between-group contrast is interpreted as a log hazard ratio under proportional hazards and as a time-specific log cumulative hazard ratio under non-proportional hazards. In simulations with delayed effects and crossing survival curves, the root mean squared error for the log cumulative hazard ratio was lower than that of the two-stage Cox method, and interval coverage was close to the nominal level. In an application to disease-free survival in resectable non-small cell lung cancer, the two-stage Cox method estimated an average hazard ratio, whereas the proposed method captured nonlinear changes in the cumulative hazard ratio over time.

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