Accounting for informatively missing data in logistic regression by means of reassessment sampling

We explore the 'reassessment' design in a logistic regression setting, where a second wave of sampling is applied to recover a portion of the missing data on a binary exposure and/or outcome variable. We construct a joint likelihood function based on the original model of interest and a model for the missing data mechanism, with emphasis on non-ignorable missingness. The estimation is carried out by numerical maximization of the joint likelihood function with close approximation of the accompanying Hessian matrix, using sharable programs that take advantage of general optimization routines in standard software. We show how likelihood ratio tests can be used for model selection and how they facilitate direct hypothesis testing for whether missingness is at random. Examples and simulations are presented to demonstrate the performance of the proposed method.