Reference Based Sensitivity Analysis for Time-to-Event Data

The analysis of time-to-event data typically makes the censoring at random assumption, i.e. that —conditional on covariates in the model—the distribution of event times is the same, whether they are observed or unobserved. When patients who remain in follow-up are compliant with the trial protocol, then analysis under this assumption can be considered to address a de-jure (“while on treatment strategy”) type of estimand. In such cases, we may well wish to explore the robustness of our inference to more pragmatic, de-facto, (“treatment policy strategy”), assumptions about the behaviour of patients postcensoring. This is particularly the case when censoring occurs if patients change, or revert, to the usual (i.e. 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. Such an approach has two advantages: (i) it avoids the user specifying numerous parameters describing the distribution of patient’s post-withdrawal data, and (ii) 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. We develop similar approaches in the survival context, proposing a class of reference based assumptions appropriate for time-to-event data. We explore the extent to which sensitivity analyses using the multiple imputation estimator (with Rubin’s variance formula) is information anchored, demonstrating this using theoretical results and simulation studies. The methods are illustrated using data from a randomized clinical trial comparing medical therapy with angioplasty in patients with angina. Causal inference methods are established as the gold standard for analysing observational (“big”) data. In a final step, we show that reference based methods can also be applied in this context by using sensitivity analysis in an investigation of the risk of opportunistic infections in a cohort of HIV positive individuals.