A Multiple-Imputation-Based Approach to Sensitivity Analyses and Effectiveness Assessments in Longitudinal Clinical Trials

Abstract

It is important to understand the effects of a drug as actually taken (effectiveness) and when taken as directed (efficacy). The primary objective of this investigation was to assess the statistical performance of a method referred to as placebo multiple imputation (pMI) as an estimator of effectiveness and as a worst reasonable case sensitivity analysis in assessing efficacy. The pMI method assumes the statistical behavior of placebo- and drug-treated patients after dropout is the statistical behavior of placebo-treated patients. Thus, in the effectiveness context, pMI assumes no pharmacological benefit of the drug after dropout. In the efficacy context, pMI is a specific form of a missing not at random analysis expected to yield a conservative estimate of efficacy. In a simulation study with 18 scenarios, the pMI approach generally provided unbiased estimates of effectiveness and conservative estimates of efficacy. However, the confidence interval coverage was consistently greater than the nominal coverage rate. In contrast, last and baseline observation carried forward (LOCF and BOCF) were conservative in some scenarios and anti-conservative in others with respect to efficacy and effectiveness. As expected, direct likelihood (DL) and standard multiple imputation (MI) yielded unbiased estimates of efficacy and tended to overestimate effectiveness in those scenarios where a drug effect existed. However, in scenarios with no drug effect, and therefore where the true values for both efficacy and effectiveness were zero, DL and MI yielded unbiased estimates of efficacy and effectiveness.

An efficient monotone data augmentation algorithm for multiple imputation in a class of pattern mixture models

“…In the controlbased PMMs, Rubin's variance estimator tends to overestimate the variance of the estimated treatment effect (Lu, 2014;Ayele et al, 2014) because the imputation and data analysis models are uncongenial (Meng, 1994;Nielsen, 2003). Specifically, dropouts and completers in the active arm are assumed to follow different mean response trajectory in the imputations, but the mean response curves are assumed to be the same for all active subjects in the analysis.…”

“…Two types of PMMs that are commonly used as MNAR sensitivity analyses in confirmatory trials are the control-based PMMs and the delta-adjusted PMMs (Little and Yau, 1996;Carpenter et al, 2013;Ratitch et al, 2013;Mallinckrodt et al, 2013). The control-based methods assume that the statistical behavior of active subjects after dropout is similar to that of control subjects since subjects no longer receive the active treatment after discontinuation (Little and Yau, 1996;Carpenter et al, 2013;Ayele et al, 2014). The control-based method may not be suitable if after dropout, the active subjects perform worse than the control subjects .…”

“…To the best of our knowledge, no formal Markov chain Monte Carlo (MCMC) algorithm has been developed for the control-based PMMs and the delta-adjusted PMMs in the literature (Ayele et al, 2014). The purpose of the paper is to propose an efficient MCMC algorithm for missing data imputation in a class of PMMs including the control-based PMMs and the deltaadjusted PMMs.…”

“…It is often challenging to specify in advance some range of clinically plausible values for ∆ without knowledge of the actual data . These PMMs provide estimates of the effectiveness of a drug, A c c e p t e d M a n u s c r i p t 4 which is essentially the maintained benefit attributable to the randomized medication taken during the trial (Ayele et al, 2014), and reflects the fact that the subjects may no longer receive the assigned medication after dropout. These effectiveness estimates have been referred to as de facto estimands by Carpenter et al (2013).…”

“…For example, in some controlled imputations(Lu, 2014;Ayele et al, 2014), φ is estimated using only data from the control arm. One advantage of scheme C is that step C1 can be implemented under MAR using the standard software.…”