Meta-analysis of time-to-event data has proved difficult in the past because consistent summary statistics often cannot be extracted from published results. The use of individual patient data allows for the re-analysis of each study in a consistent fashion and thus makes meta-analysis of time-to-event data feasible. Time-to-event data can be analysed using proportional hazards models, but incorporating random effects into these models is not straightforward in standard software. This paper fits random-effects proportional hazards models by treating the random effects as missing data and applying the expectation-maximisation algorithm. This approach has been used before by using Markov chain Monte Carlo methods to perform the expectation step of the algorithm. In this paper, the expectation step is simplified, without sacrificing accuracy, by approximating the expected values of the random effects using simple shrinkage estimators. This provides a robust method for fitting random-effects models that can be implemented in standard statistical packages.