Estimating time-varying effects for overdispersed recurrent events data with treatment switching

In the analysis of multivariate event times, frailty models assuming time-independent regression coefficients are often considered, mainly due to their mathematical convenience. In practice, regression coefficients are often time dependent and the temporal effects are of clinical interest. Motivated by a phase III clinical trial in multiple sclerosis, we develop a semiparametric frailty modelling approach to estimate time-varying effects for overdispersed recurrent events data with treatment switching. The proposed model incorporates the treatment switching time in the time-varying coefficients. Theoretical properties of the proposed model are established and an efficient expectation-maximization algorithm is derived to obtain the maximum likelihood estimates. Simulation studies evaluate the numerical performance of the proposed model under various temporal treatment effect curves. The ideas in this paper can also be used for time-varying coefficient frailty models without treatment switching as well as for alternative models when the proportional hazard assumption is violated. A multiple sclerosis dataset is analysed to illustrate our methodology.