Pseudo-observation regression for sequentially truncated data

In observational cohort studies with complex sampling schemes, truncation arises when the time to the event of interest is observed only when it falls below or exceeds another random time, i.e., the truncation time. In more complex settings, observation may require a particular ordering of event times; we refer to this extension of the traditional paradigm as sequential truncation. Nonparametric and semiparametric maximum likelihood estimators have been developed recently to estimate the distribution of the event time of interest in the presence of sequential truncation. In this paper, we develop methods for regression modeling in this complex setting using the tool of pseudo-observations. Pseudo-observations are jackknife-like constructs that estimate an individual's contribution to an estimand. They are convenient as they are based on an estimator for the unconditional distribution of the event time. However, the simple pseudo-observation method may not be valid when the truncation depends on the covariates that also explain the time to event of interest, among other constraints. To address this limitation, we also consider a modified pseudo-observation approach. We develop both simple and modified pseudo-observation methods for Cox and accelerated failure time (AFT) models. We evaluate the proposed methods in simulation studies and apply them to an Alzheimer's disease cohort study.