Additive hazards models with latent treatment effectiveness lag time

In many clinical trials for evaluating treatment efficacy, it is believed that there may exist latent treatment effectiveness lag times after which medical treatment procedure or chemical compound would be in full effect.In this paper, semiparametric regression models are proposed and studied for estimating the treatment effect accounting for such latent lag times. The new models take advantage of the invariant property of the additive hazards model in marginalising over an additive latent variable; parameters in the models are thus easily estimated and interpreted, while the flexibility of not having to specify the baseline hazard function is preserved. Monte Carlo simulation studies demonstrate the appropriateness of the proposed semiparametric estimation procedure. The methodology is applied to data collected in a randomised clinical trial, which evaluates the efficacy of biodegradable carmustine polymers for treatment of recurrent brain tumours.