A general method for elicitation, imputation, and sensitivity analysis for incomplete repeated binary data

Abstract

We develop and demonstrate methods to perform sensitivity analyses to assess sensitivity to plausible departures from missing at random in incomplete repeated binary outcome data. We use multiple imputation in the not at random fully conditional specification framework, which includes one or more sensitivity parameters (SPs) for each incomplete variable. The use of an online elicitation questionnaire is demonstrated to obtain expert opinion on the SPs, and highest prior density regions are used alongside opinion pooling methods to display credible regions for SPs. We demonstrate that substantive conclusions can be far more sensitive to departures from the missing at random assumption (MAR) when control and intervention nonresponders depart from MAR differently, and show that the correlation of arm specific SPs in expert opinion is particularly important. We illustrate these methods on the iQuit in Practice smoking cessation trial, which compared the impact of a tailored text messaging system versus standard care on smoking cessation. We show that conclusions about the effect of intervention on smoking cessation outcomes at 8 week and 6 months are broadly insensitive to departures from MAR, with conclusions significantly affected only when the differences in behavior between the nonresponders in the two trial arms is larger than expert opinion judges to be realistic.

Effectiveness of offering tailored text message, self‐help smoking cessation support to pregnant women who want information on stopping smoking: MiQuit3 randomised controlled trial and meta‐analysis

“…However, we assumed those lost to follow up were smoking, a likely conservative assumption given that there was more missing outcome data in the MiQuit group. Furthermore, sensitivity analyses suggested reasonably implausible assumptions regarding the unobserved abstinence data would be required before the primary analysis reached substantively different conclusions, a phenomenon documented by others [41]. Additionally, although we validated 70.4% of abstinence reports and, may have not identified some participants with positive outcomes, there was little evidence that trial groups had different rates of ‘failed’ validation therefore, it seems unlikely that this issue invalidates the principal findings.…”

How to apply variable selection machine learning algorithms with multiply imputed data: A missing discussion.

“…Most existing approaches for variable selection in the presence of missing data are developed under the MAR mechanism, which is often implausible in many settings. Although it is not widely done in practice, MI can accommodate known missing not at random (MNAR) mechanisms (i.e., the probability of a value being missing depends on the unobserved values of that variable) under the selection modeling (Beesley & Taylor,2021; Carpenter et al, 2007; Hayati Rezvan et al, 2015) and pattern-mixture modeling (Hayati Rezvan et al, 2018; Leacy et al, 2017; Tompsett et al, 2018; Tompsett et al, 2020) frameworks. Addressing challenges that arise during implementation of variable selection strategies when using MI to address MNAR missingness is an area for future development.…”

Accounting for not‐at‐random missingness through imputation stacking

“…The primary disadvantage of the proposed methodology is the need to specify values for unidentified sensitivity parameters. This is a common challenge for most MNAR adjustment methods, and existing strategies for eliciting sensitivity parameter values in the pattern mixture modeling literature can be applied to inform reasonable choices for the sensitivity parameters 18,19 . These methods will naturally become more difficult to implement as the dimension of unidentified sensitivity parameters grows, and addressing practical challenges to larger‐dimensional sensitivity parameter elicitation is an area for future development.…”

“…Since is defined in terms of the W ‐adjusted association between and , it can still be difficult to determine whether a single fixed value of the sensitivity parameter is scientifically plausible. One solution discussed in Tompsett et al 18 is to reformulate the problem in terms of more easily interpretable sensitivity parameters. Using a single set of multiple imputations obtained under MAR, we can repeat our stacked data analysis across multiple values of to characterize how values of are related to the target parameter, .…”

“…Subject matter experts can also help choose reasonable values for or some transformation, . In Tompsett et al 18 and Rezvan et al, 19 multiple subject matter experts were asked to provide their intuition regarding expected differences between subjects with missing and observed data. These expectations were then combined using a process called linear pooling to obtain a distribution of expert‐elicited values for the sensitivity parameter.…”