Model-based imputation of latent cigarette counts using data from a calibration study

In addition to dichotomous measures of abstinence, smoking studies may use daily cigarette consumption as an outcome variable. These counts hold the promise of more efficient and detailed analyses than dichotomous measures, but present serious quality issues - measurement error and heaping - if obtained by retrospective recall. A doubly-coded dataset with a retrospective recall measurement (timeline followback, TLFB) and a more precise instantaneous measurement (ecological momentary assessment, EMA) serves as a calibration dataset, allowing us to predict EMA given TLFB and baseline factors. We apply this model to multiply impute precise cigarette counts for a randomized, placebo-controlled trial of bupropion with only TLFB measurements available. To account for repeated measurements on a subject, we induce correlation in the imputed counts. Finally, we analyze the imputed data in a longitudinal model that accommodates random subject effects and zero inflation. Both raw and imputed data show a significant drug effect for reducing the odds of non-abstinence and the number of cigarettes smoked among non-abstainers, but the imputed data provide efficiency gains. This method permits the analysis of daily cigarette consumption data previously deemed suspect due to reporting error and is applicable to other self-reported count data sets for which calibration samples are available.