Control‐based imputation for sensitivity analyses in informative censoring for recurrent event data

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.

Section: Introductionmentioning

confidence: 99%

Reference‐based sensitivity analysis for time‐to‐event data

Atkinson

Kenward²,

Clayton

et al. 2019

“…Estimates and confidence intervals can be transformed to the rate scale for reporting. Alternatively, one could bootstrap sample subjects from the original data and repeat the whole procedure for each bootstrap sample, and then derive a mean estimate across bootstrap samples and a bootstrap confidence interval following the approach of Gao …”

Section: Imputing Off‐treatment Datamentioning

confidence: 83%

“…For instance, a simple sinusoidal model might then be added. Alternatively changes in rate across the length of study could be accommodated by splitting periods based on the time since treatment initiation using a piecewise model similar to Gao et al …”

Section: Discussionmentioning

confidence: 99%

“…Alternatively changes in rate across the length of study could be accommodated by splitting periods based on the time since treatment initiation using a piecewise model similar to Gao et al. 8 The method described above is for analysis of recurrent event data using negative binomial models. Methods for continuous repeated measures data are under development and it will be important for a consensus to emerge on which of the alternative approaches being proposed are considered the most robust for the primary analysis of confirmatory trials.…”

Section: Discussionmentioning

confidence: 99%

“…Alternatively, one could bootstrap sample subjects from the original data and repeat the whole procedure for each bootstrap sample, and then derive a mean estimate across bootstrap samples and a bootstrap confidence interval following the approach of Gao. 8 The negative binomial analysis model suggested here pools the number of events from on and off treatment periods within a subject to answer a treatment policy estimand. This is in line with analysis of final outcome data where subjects are pooled within the randomised treatment group irrespective of whether their final outcome measurement is taken on or off treatment.…”

Section: Imputing Off-treatment Datamentioning

confidence: 99%

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Treatment policy estimands for recurrent event data using data collected after cessation of randomised treatment

Roger

Bratton

Mayer

et al. 2018

SUMMARY In the past, many clinical trials have withdrawn subjects from the study when they prematurely stopped their randomised treatment and have therefore only collected ‘on‐treatment’ data. Thus, analyses addressing a treatment policy estimand have been restricted to imputing missing data under assumptions drawn from these data only. Many confirmatory trials are now continuing to collect data from subjects in a study even after they have prematurely discontinued study treatment as this event is irrelevant for the purposes of a treatment policy estimand. However, despite efforts to keep subjects in a trial, some will still choose to withdraw. Recent publications for sensitivity analyses of recurrent event data have focused on the reference‐based imputation methods commonly applied to continuous outcomes, where imputation for the missing data for one treatment arm is based on the observed outcomes in another arm. However, the existence of data from subjects who have prematurely discontinued treatment but remained in the study has now raised the opportunity to use this ‘off‐treatment’ data to impute the missing data for subjects who withdraw, potentially allowing more plausible assumptions for the missing post‐study‐withdrawal data than reference‐based approaches. In this paper, we introduce a new imputation method for recurrent event data in which the missing post‐study‐withdrawal event rate for a particular subject is assumed to reflect that observed from subjects during the off‐treatment period. The method is illustrated in a trial in chronic obstructive pulmonary disease (COPD) where the primary endpoint was the rate of exacerbations, analysed using a negative binomial model.

An illness–death multistate model to implement delta adjustment and reference‐based imputation with time‐to‐event endpoints

García‐Hernandez,

Pérez,

del Carmen Pardo

et al. 2023

With a treatment policy strategy, therapies are evaluated regardless of the disturbance caused by intercurrent events (ICEs). Implementing this estimand is challenging if subjects are not followed up after the ICE. This circumstance can be dealt with using delta adjustment (DA) or reference‐based (RB) imputation. In the survival field, DA and RB imputation have been researched so far using multiple imputation (MI). Here, we present a fully analytical solution. We use the illness–death multistate model with the following transitions: (a) from the initial state to the event of interest, (b) from the initial state to the ICE, and (c) from the ICE to the event. We estimate the intensity function of transitions (a) and (b) using flexible parametric survival models. Transition (c) is assumed unobserved but identifiable using DA or RB imputation assumptions. Various rules have been considered: no ICE effect, DA under proportional hazards (PH) or additive hazards (AH), jump to reference (J2R), and (either PH or AH) copy increment from reference. We obtain the marginal survival curve of interest by calculating, via numerical integration, the probability of transitioning from the initial state to the event of interest regardless of having passed or not by the ICE state. We use the delta method to obtain standard errors (SEs). Finally, we quantify the performance of the proposed estimator through simulations and compare it against MI. Our analytical solution is more efficient than MI and avoids SE misestimation—a known phenomenon associated with Rubin's variance equation.