Efficient Testing Procedure in a Randomized Trial with Survival Outcome

Specialeforsvar: Sara Nørgård Jensen

TItel: Efficient Testing Procedure in a Randomized Trial with Survival Outcome

Abstract: This thesis develops a new testing procedure for assessing treatment effect on survival time in randomized trials with potentially right-censored data. Traditional methods, such as the log-rank test and the Cox Proportional Hazards model, rely on restrictive assumptions that may not hold in practice, limiting their robustness. Motivated by these limitations, we adopt an assumptionlean approach by introducing a novel, model-free estimand. The estimand reduces to the main exposure effect parameter from the Cox model under correct specification and, importantly, remains valid even when the Cox model is misspecified, thus provides a robust measure of the treatment effect on survival time. To achieve assumption-lean inference, we derive the efficient influence function for the estimand. This derivation proceeds in three stages; beginning with a fully nonparametric model without assuming randomization or right censoring, incorporating covariates and non-informative censoring, and finally transitioning to a semiparametric model with randomization. Leveraging results from the literature and deriving additional properties of influence functions, we construct an One-Step estimator for the estimand, facilitating hypothesis testing through variance estimation and Wald test statistics. The thesis concludes with an implementation of the One-Step and plug-in estimators. While the One-Step estimator did not consistently outperform the plug-in estimator, future improvements using data-adaptive methods, such as random forests combined with cross-fitting, are suggested.

Vejledere: Niels Richard Hansen, Torben Martinussen, SUND
Censor:     Søren Wengel Mogensen, Lund Universitet