Estimation for paired binomial data with application to radiation therapy

We compare and contrast several different methods for estimating the effect of treatment when responses are paired binomial observations. The ratio of binomial probabilities is the parameter of interest, while the binomial pr obabilities are nuisance parameters which may vary between pairs. The appli cation is a meta-analysis of the treatment of rectal cancer, with observati ons in each study indicating the number of recurrences of the cancer in eac h of two groups, one with radiation therapy and one without. The ratio of t he probabilities of recurrence in the radiation to non-radiation groups is of substantive interest, and is modelled as a logistic or complementary log -log function of an unknown linear combination of the covariates. The three methods we consider are maximum likelihood, a Bayesian approach and an app roach based on estimating equations. For the MLE and Bayesian approach the potentially large number of nuisance parameters are estimated together with the parameters of interest, whereas for the estimating equation approach o nly the parameters of interest are estimated. A simulation study is perform ed to compare the methods and evaluate the impact of overdispersion. Copyri ght (C) 2001 John Wiley & Sons, Ltd.