Semi-parametric testing for ordinal treatment effects in time-to-event data via dynamic Dirichlet process mixtures of the inverse-Gaussian distribution

Time-to-event data often violate the proportional hazards assumption under which the log-rank test is optimal. Such violations are especially common in the sphere of biological and medical data where heterogeneity due to unmeasured covariates or time varying effects are common. A variety of parametric survival models have been proposed in the literature which make more appropriate assumptions on the hazard function, at least for certain applications. One such model is derived from the first hitting time paradigm which assumes that a subject's event time is determined by a latent stochastic process reaching a threshold value. Several random effects specifications of the first hitting time model have also been proposed which allow for better modeling of data with unmeasured covariates. We propose a Bayesian model which loosens assumptions on the mixing distribution inherent in the random effects first hitting time models currently in use and we do so in a manner which is ideally suited for testing for effects of ordinal treatment variables. We demonstrate via a simulation study that the proposed model has better power than log-rank based methods in detecting ordinal treatment effects in the presence of nonproportional hazards. Additionally, we show that the proposed model is almost as powerful as log-rank based methods when the proportional hazards assumption holds. We also apply the proposed methodology to two biomedical data sets: a toxicity study in rodents and an observational study of cancer patients.