A fully Bayesian approach for the imputation and analysis of derived outcome variables with missingness

Derived variables are variables that are constructed from one or more source variables through established mathematical operations or algorithms. For example, body mass index (BMI) is a derived variable constructed from two source variables: weight and height. When using a derived variable as the outcome in a statistical model, complications arise when some of the source variables have missing values. In this paper, we propose how one can define a single fully Bayesian model to simultaneously impute missing values and sample from the posterior. We compare our proposed method with alternative approaches that rely on multiple imputation with examples including an analysis to estimate the risk of microcephaly (a derived variable based on sex, gestational age and head circumference at birth) in newborns exposed to the ZIKA virus.