Immortal time bias from selection: a principal stratification perspective

Immortal time bias due to post-treatment definition of eligibility criteria can affect experimental and observational studies, and yet, in contrast to the extensive literature on the classical form of immortal time bias, it has seldom been the focus of methodological discussions. Here, we propose an account of eligibility-related immortal time bias that uses the principal stratification framework to explain the noncomparability of treatment arms (or exposure groups) conditional on selection. In particular, we show that the statistical estimand that conditions on observed eligibility after time zero of follow-up can be interpreted using partially overlapping principal strata. Furthermore, we show that, under this perspective, as the timing of eligibility approaches time zero of follow-up, the probabilities of the outcome for eligible individuals monotonically approach the corresponding unconditional (in absence of selection) expected potential outcomes under different treatment levels. Our study provides a potential outcomes-based explanation of eligibility-related immortal time bias, and indicates that, in addition to the target trial emulation framework, principal effects might, for some studies, be useful causal estimands.