Semiparametric Methods for Estimating Cumulative Treatment Effects in the Presence of Non-proportional Hazards and Dependent Censoring.

The research in this thesis focuses on methods for estimating the cumulative treatment effect on time to an event in the setting when the treatment-specific hazards are not proportional. In clinical studies of time to event data, non-proportional hazards are very common. The Cox model is frequently used, assuming that thetreatment effect is constant or a specific function of time. However, it is often difficult to assess whether the functional formchosen for the treatment effect is correct. Even if the correct form is chosen, the cumulative (as opposed to the instantaneous) treatment effect is preferred in many applications. For example, theinvestigator may be interested in the contrast in 5-year survival between the treatment groups. We propose three novel methods forestimating cumulative treatment effects. In Method I, we propose atreatment-stratified Cox model. The ratio of cumulative hazardscomparing treatment categories is proposed to estimate thecumulative treatment effect. This measure has a hazard ratiointerpretation when proportional hazard holds. In Method II, weconsider the setting where, in addition to the treatment effect, theeffect of the adjustment covariates may be non-proportional. Wepropose an inverse probability of treatment weighting (IPTW) methodto balance the distribution of adjustment covariates among treatmentgroups. The ratio of cumulative hazards, relative risk anddifference in restricted mean lifetime are proposed as measures ofthe cumulative treatment effect for Method II. Method III deals withthe setting where the event time and censoring time are dependent.We employ double inverse weighting, with an inverse probability ofcensoring weight (IPCW) to counteract the dependent censoring fromtime-varying covariates, and IPTW to adjust for baseline covariates.Each of Methods I, II and III is applied to organ failure data.