Missing data sensitivity analysis for recurrent event data using controlled imputation

Abstract

Statistical analyses of recurrent event data have typically been based on the missing at random assumption. One implication of this is that, if data are collected only when patients are on their randomized treatment, the resulting de jure estimator of treatment effect corresponds to the situation in which the patients adhere to this regime throughout the study. For confirmatory analysis of clinical trials, sensitivity analyses are required to investigate alternative de facto estimands that depart from this assumption. Recent publications have described the use of multiple imputation methods based on pattern mixture models for continuous outcomes, where imputation for the missing data for one treatment arm (e.g. the active arm) is based on the statistical behaviour of outcomes in another arm (e.g. the placebo arm). This has been referred to as controlled imputation or reference-based imputation. In this paper, we use the negative multinomial distribution to apply this approach to analyses of recurrent events and other similar outcomes. The methods are illustrated by a trial in severe asthma where the primary endpoint was rate of exacerbations and the primary analysis was based on the negative binomial model.

Sensitivity analyses for partially observed recurrent event data

“…The work presented here is an extension of the work by Keene et al , where only constant event intensities are considered for the imputation and analysis models. This assumption may be too strict in practice and a relaxation of this assumption – at least for the imputation model – is advisable.…”

“…Note that using this MNAR assumption in other active controlled settings may be implausible and difficult to justify.Applying this MNAR assumption will generally result in conservative inference compared with an MAR analysis as treatment differences are diluted. Using the taxonomy in previous publications , this approach corresponds to the copy reference method. MNAR‐2 After discontinuation, the event intensity for patients in the investigational arm is a certain percentage higher than the MAR intensity. That is, for patients in the investigational arm, we use the rate function , where , to impute event occurrences in the time interval ( C i , T ].…”

“…Applying this MNAR assumption will generally result in conservative inference compared with an MAR analysis as treatment differences are diluted. Using the taxonomy in previous publications , this approach corresponds to the copy reference method.…”

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

“…For recurrent event data, Keene et al() specified a log‐linear NB model with offset and samples the jump‐to‐reference and copy‐reference imputation parameters from the posterior distribution using a noninformative prior. Akacha and Ogundimu() considered copy‐reference and tipping point control‐based imputation for recurrent event data, where the count after dropout is imputed from a posterior predictive distribution using asymptotic or bootstrap imputation to approximate the Bayesian data argumentation scheme.…”

“…In this paper, we implement control‐based imputation in analyzing clinical trials with recurrent event data by sampling the parameters from the posterior distribution similar to that from Keene etal() However, we assume a piecewise exponential proportional intensity model with frailty for the recurrent events. We correct the variance estimation through a bootstrap approach.…”