Semiparametric methods for multistate survival models in randomised trials

Transform methods have proved effective for networks describing a progression of events. In semi-Markov networks, we calculated the transform of time to a terminating event from corresponding transforms of intermediate steps. Saddlepoint inversion then provided survival and hazard functions, which integrated, and fully utilised, the network data. However, the presence of censored data introduces significant difficulties for these methods. Many participants in controlled trials commonly remain event-free at study completion, a consequence of the limited period of follow-up specified in the trial design. Transforms are not estimable using nonparametric methods in states with survival truncated by end-of-study censoring. We propose the use of parametric models specifying residual survival to next event. As a simple approach to extrapolation with competing alternative states, we imposed a proportional incidence (constant relative hazard) assumption beyond the range of study data. No proportional hazards assumptions are necessary for inferences concerning time to endpoint; indeed, estimation of survival and hazard functions can proceed in a single study arm. We demonstrate feasibility and efficiency of transform inversion in a large randomised controlled trial of cholesterol-lowering therapy, the Long-Term Intervention with Pravastatin in Ischaemic Disease study. Transform inversion integrates information available in components of multistate models: estimates of transition probabilities and empirical survival distributions. As a by-product, it provides some ability to forecast survival and hazard functions forward, beyond the time horizon of available follow-up. Functionals of survival and hazard functions provide inference, which proves sharper than that of log-rank and related methods for survival comparisons ignoring intermediate events.