Analysis of binary outcomes with missing data: missing = smoking, last observation carried forward, and a little multiple imputation

Abstract

Analysis of binary outcomes with missing data is a challenging problem in substance abuse studies. We consider this problem in a simple two-group design where interest centers on comparing the groups in terms of the binary outcome at a single timepoint. We describe how the deterministic assumptions of missing = smoking and last observation carried forward (LOCF) can be relaxed by allowing missingness to be related imperfectly to the binary outcome, either stratified on past values of the outcome or not. We also describe use of multiple imputation to take into account the uncertainty inherent in the imputed data. Data were analyzed from a published smoking cessation study evaluating the effectiveness of adding group-based treatment adjuncts to an intervention comprised of a television program and self-help materials. Participants were 489 smokers who registered for the television-based program and who indicated an interest in attending group-based meetings. The measurement of the smoking outcome was conducted via telephone interviews at post-intervention and at 24 months. The significance of the group effect did vary as a function of the assumed relationship between missingness and smoking. The 'conservative' missing = smoking assumption suggested a beneficial group effect on smoking cessation, which was confirmed via a sensitivity analysis only if an extreme odds ratio of 5 between missingness and smoking was assumed. This type of sensitivity analysis is crucial in determining the role that missing data play in arriving at a study's conclusions.