Statistical methods for the restricted mean survival time and lifetime risk
Embargo Date
2023-10-06
OA Version
Citation
Abstract
In observational studies or non-randomized studies with censored data, associations are commonly measured with adjusted hazards ratios from multivariable proportional hazards models. The difference in restricted mean survival times (RMST) up to a pre-specified time point is an alternative measure that offers a clinically meaningful interpretation. However, existing methods for the difference in RMST do not address statistical challenges common in observational research, such as time-varying confounding or competing risks. Several regression-based methods exist to estimate an adjusted difference in RMSTs, but they digress from the model-free method of taking the area under the survival function. The lifetime risk is another widely reported metric for disease incidence in the presence of censoring and the competing risk of death. The lifetime risk is usually estimated by the Aalen-Johansen estimator allowing delayed entry, but there are no methods to directly model the lifetime risk. These gaps in statistical methodology may limit the applications of the difference in RMST and lifetime risk. By addressing these methodological gaps, we aim to promote the reporting of the RMST and lifetime risk in observational and non-randomized studies.
In this dissertation, we present novel statistical methods for the difference in RMST, difference in restricted mean time lost (RMTL), and lifetime risk. First, we introduce an estimator and the associated variance for the adjusted difference in RMST using inverse probability weighting (IPW). Second, we demonstrate how to estimate the adjusted difference in RMST accounting for time-varying confounding with the parametric g-formula. We also demonstrate how to address missing data challenges with sequential multiple imputation. Third, we introduce an IPW-based estimator and the associated variance for the adjusted difference in RMTL in the presence of competing risks. We also propose a regression model of the RMTL conditional on covariates with inverse probability of censoring weighting. Finally, we present a new regression model for the lifetime risk using pseudo-observations of the Aalen-Johansen estimator. In simulation studies, we demonstrate our proposed estimators are unbiased and perform well under various settings. We illustrate the methods for incident coronary heart disease and atrial fibrillation in the Framingham Heart Study.