title: Estimation for paired binomial data with application to radiation therapy.
abstract: 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 probabilities are nuisance parameters which may vary between pairs. The application is a meta-analysis of the treatment of rectal cancer, with observations in each study indicating the number of recurrences of the cancer in each of two groups, one with radiation therapy and one without. The ratio of the 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 approach 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 only the parameters of interest are estimated. A simulation study is performed to compare the methods and evaluate the impact of overdispersion.
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USA. jmgt@umich.edu
authors.forename: J M
authors.initials: JM
authors.lastname: Taylor
authors.forename: R E
authors.initials: RE
authors.lastname: Weiss
authors.forename: W
authors.initials: W
authors.lastname: Li
authors.forename: C H
authors.initials: CH
authors.lastname: Hsu
authors.forename: R
authors.initials: R
authors.lastname: Suwinski
mesh_terms: D001499:Bayes Theorem; D003198:Computer Simulation; D006801:Humans; D016013:Likelihood Functions; D008390:Markov Chains; D015201:Meta-Analysis as Topic; D008954:Models, Biological; D015233:Models, Statistical; D009010:Monte Carlo Method; D009364:Neoplasm Recurrence, Local; D012004:Rectal Neoplasms / Q000532:radiotherapy* / Q000601:surgery; D016896:Treatment Outcome