Baseline information in structural failure time estimators for the effect of observed treatment compliance

Structural accelerated failure time models allow expression of the effect of treatment actually received in placebo-controlled randomized trials with non-compliance. Without further assumptions, the structural parameter is typically estimated via a series of auxiliary logrank tests, searching for the structural parameter that back-transforms treated survival times to latent treatment-free survival times which are equally distributed between randomized arms. In this paper we investigate to what extent score tests involving baseline covariates provide more powerful auxiliary tests and lead to more precise estimates of the structural parameter without compromising the alpha-level. We propose a set of estimating equations which combines score components for covariate effects based on the control arm only, with a log-likelihood score for treatment effect based on both arms. Analytic results for exponential models as well as simulation studies for the semi-parametric approach indicate that in many practical situations this incorporation of baseline covariates leads to more precise estimators of the structural effect. Relative efficiency is shown to depend on the selective nature of compliance. In a leukaemia trial we find the length of the 95 per cent confidence interval for the structural parameter is reduced to two-thirds of the original length by incorporating baseline covariates in this way.