Abstract
The analysis of time‐to‐event data typically makes the censoring at random assumption, ie, that—conditional on covariates in the model—the distribution of event times is the same, whether they are observed or unobserved (ie, right censored). When patients who remain in follow‐up stay on their assigned treatment, then analysis under this assumption broadly addresses the de jure, or “while on treatment strategy” estimand. In such cases, we may well wish to explore the robustness of our inference to more pragmatic, de facto or “treatment policy strategy,” assumptions about the behaviour of patients post‐censoring.This is particularly the case when censoring occurs because patients change, or revert, to the usual (ie, reference) standard of care. Recent work has shown how such questions can be addressed for trials with continuous outcome data and longitudinal follow‐up, using reference‐based multiple imputation. For example, patients in the active arm may have their missing data imputed assuming they reverted to the control (ie, reference) intervention on withdrawal. Reference‐based imputation has two advantages: (a) it avoids the user specifying numerous parameters describing the distribution of patients' postwithdrawal data and (b) it is, to a good approximation, information anchored, so that the proportion of information lost due to missing data under the primary analysis is held constant across the sensitivity analyses. In this article, we build on recent work in the survival context, proposing a class of reference‐based assumptions appropriate for time‐to‐event data. We report a simulation study exploring the extent to which the multiple imputation estimator (using Rubin's variance formula) is information anchored in this setting and then illustrate the approach by reanalysing data from a randomized trial, which compared medical therapy with angioplasty for patients presenting with angina.
Highlights
Survival analysis is often used to model time-to-event data in observational and clinical studies
Standard maximum likelihood methods provide valid parameter estimates and associated standard errors under censored at random (CAR). While this may be appropriate for the end of funded follow-up, in many settings, we will want to explore the robustness of our inferences to informative censoring
For our development, we take the Weibull proportional hazards model as substantive and imputation model. This is sufficiently flexible for many applications; in other settings, we suggest using a flexible spline as a parametric model for the baseline hazard, again with proportional hazards
Summary
Survival analysis is often used to model time-to-event data in observational and clinical studies. While this may be appropriate for the end of funded follow-up, in many settings, we will want to explore the robustness of our inferences to informative censoring (censoring not at random) Such sensitivity analyses should be considered when we suspect that the assumption of independence between censoring and the failure time may not hold for at least some of the patients. They should establish whether the conclusions from the study are robust to plausible departures from CAR.
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