A note on the bias of estimators with missing data.

It is well known that many standard analyses, including maximum likelihood estimation and the generalized estimating equation approach (Liang and Zeger, 1986, Biometrika 73, 13-22) can result in biased estimation when there are missing observations. In such cases it is of interest to calculate the magnitude of the bias incurred under specific assumptions about the process generating the full data and the nonresponse mechanism. In this paper we give a condition that identifies the limit in probability of estimators that are solutions of estimating equations computed from the incomplete data. With discrete data, this condition suggests a simple algorithm to compute the asymptotic bias of these estimators that can be easily implemented with existing statistical software. We illustrate our approach with asthma prevalence data in children.