Interval censored PH survival models for longitudinal data: precision of estimators

We present a general likelihood for interval censored survival data arising in longitudinal studies such as longitudinal randomized controlled clinical trials (RCTs) and give some general formulae for inference in parametric, interval censored, proportional hazards, regression survival models. For the exponential regression model we compare the performance of the general likelihood with a commonly used proxy likelihood, which ignores the interval censoring by treating the interval censored times to events as if they were exact. We show analytically that use of the proxy likelihood leads to estimators (for example, of the treatment effect) which are artificially precise and we quantify the extent of the resulting biases in a simulation study.