Improving precision of cumulative incidence estimates in randomized controlled trials with external controls

Augmenting the control arm in clinical trials with external data can improve statistical power for demonstrating treatment effects. In many time-to-event outcome trials, participants are subject to truncation by death. Direct application of methods for competing risks analysis on the joint data may introduce bias, for example, due to covariate shifts between the populations. In this work, we consider transportability of the conditional cause-specific hazard of the event of interest under the control treatment. Under this assumption, we derive semiparametric efficiency bounds of causal cumulative incidences. This allows for quantification of the theoretical efficiency gain from incorporating the external controls. We propose triply robust estimators that can achieve the efficiency bounds, where the trial controls and external controls are made comparable through time-specific weights in a martingale integral. We conducted a simulation study to show the precision gain of the proposed fusion estimators compared to their counterparts without utilizing external controls. As a real data application, we used two cardiovascular outcome trials conducted to assess the safety of glucagon-like peptide-1 agonists. Incorporating the external controls from one trial into the other, we observed a decrease in the standard error of the treatment effects on adverse non-fatal cardiovascular events with all-cause death as the competing risk.