Effects of medical intervention are increasingly studied in distributed research settings, using multiple clinical data sources such as electronic health records and administrative claims. Sharing individual patient data is seldom allowed, and instead only summary statistics can be used to combine evidence across the network. Many studies in such a distributed setting use a Cox proportional hazards model to estimate the effect of a treatment on the time to some outcome of interest, and current practice combines the per-database estimates through traditional meta-analysis techniques which assume the likelihood is normally distributed. We show that this approach can lead to large bias when outcome counts are small or zero in one of the treatment cohorts due to violation of this assumption. We use real and simulated data to evaluate four approximations of the likelihood: normal, skew-normal, a one-dimensional grid, and a custom function designed to mimic the Cox likelihood function shape. We demonstrate how these approximations can be used in fixed-effects and (Bayesian) random-effects models. Results show that using the grid or custom approximation avoids the aforementioned bias.