Covariate adjustment in a randomised trial with time-to-event outcomes

Covariate adjustment in a randomised trial aims to provide more powerful comparisons of randomised groups. We describe the challenges of planning how to do this in the ODYSSEY trial, which compares two HIV treatment regimes in children. ODYSSEY presents three challenges: (1) the outcome is time-to-event (time to virological or clinical failure); (2) interest is in the risk at a landmark time (96 weeks after randomisation); and (3) the aim is to demonstrate non-inferiority (defined as the risk difference at 96 weeks being less than 10 percentage points). The statistical analysis plan is based on the Cox model with predefined adjustment for three covariates. We describe how to use the margins command in Stata to estimate the marginal risks and the risk difference. This analysis does not allow for uncertainty in the baseline survivor function. We compare confidence intervals produced by normal theory and by bootstrapping, and (for the risks) using the log-log transform. We compare these methods with Paul Lambert's standsurv, which is based on a parametric survival model. We also discuss an inverse probability of treatment weighting approach, where the weights are derived by regressing randomised treatment on the covariates.