Restricted Mean Analysis Across Multiple Follow-up Intervals.

Abstract

The restricted mean survival, first proposed by Irwin (1949) is the expected survival time within a fixed follow-up window. This measure has a meaningful interpretation for both physicians and patients in a clinical setting that motivates its further exploration. The first paper provides a nonparametric estimate of Tau-restricted mean survival that uses additional follow-up information beyond Tau, when appropriate, to improve precision. The variance of our estimate must account for correlation between incorporated follow-up windows and we follow an approach by Woodruff (1971) that linearizes random components of the estimate to simplify calculations. Both asymptotic closed form calculations and simulation studies recommend selection of follow-up intervals spaced approximately Tau/2 apart. In the second paper we develop two recurrent events testing procedures. We take advantage of the properties of time-to-first event analyses and use events beyond the first by combining data across multiple follow-up windows in two different ways. The first pools the data before estimating the Tau-restricted mean survival and the second uses the area under the Tau-restricted mean residual life function. We consider multiple scenarios of treatment effect in simulation studies and find our testing procedures perform favorably, especially when events are correlated, compared to the robust proportional rates model proposed by Lin et al. (2000) and the nonparametric Ghosh and Lin test. A component of the lung allocation score, used to order patients for transplant offers, is the 1-year restricted mean survival on waitlist. In the third paper we develop a restricted mean survival model that combines data from multiple 1-year follow-up windows spaced six months apart to incorporate time-dependent patient risk data, extending work by Xiang et al. (2013) to multiple follow-up intervals. Model parameters are estimated by multiply imputing censored time-to-event data using an inverse transform method; the complete dataset is analyzed using standard methods. The systematic removal of patients from the lung transplant waitlist based on their daily updated LAS results in dependent censoring, which we account for using inverse probability of censoring weights when estimating survival functions. Simulation studies show that our proposed method performs well and incorporating additional follow-up improves efficiency.