A quasi-likelihood approach for overdispersed binomial data when N is unobserved

Several methods for the analysis of binomial data when the denominator, N. is unknown have been developed. Each of these methods requires that the mean of the distribution of N is known. In this article, we develop a quasi-likelihood technique that allows for the estimation of the means of the distributions needed to define the expected value and variance of the observed response and suggest a different form of the variance function. We illustrate the results of the proposed analysis and the results obtained when the mean of the distribution of N is assumed known through the analysis of a surviving jejunal crypt data set. Although the proposed method shows inflated standard errors of the parameter estimates in the cited example, the proposed method performs as well as a previously published method in all simulated conditions. Moreover, in cases where E(N) is misspecified. the proposed method outperforms the previously published method.