We propose a method for estimating parameters in binomial regression models when the response variable is missing and the missing data mechanism is nonignorable. We assume throughout that the covariates are fully observed. Using a logit model for the missing data mechanism, we show how parameter estimation can be accomplished using the EM algorithm by the method of weights proposed in Ibrahim (1990, Journal of the American Statistical Association 85, 765-769). An example from the Six Cities Study (Ware et al., 1984, American Review of Respiratory Diseases 129, 366-374) is presented to illustrate the method.