On inconsistency of the common rate difference estimators from sparse follow-up data

It has been shown that the unconditional maximum likelihood estimator of the common odds ratio, risk ratio and risk difference parameters are inconsistent in sparse statification. Under a Poisson sparse-data model, the maximum likelihood estimator for the rate difference, which is the difference of the disease incidence rates among the exposed and the unexposed, is also shown to be biased. The sparse-data asymptotic bias of the maximum likelihood estimator is evaluated numerically and compared with that of the weighted least squares estimators.