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 mea n of the distribution of N is known. Ln this article, we develop a quasi-li kelihood technique that allows for the estimation of the means of the distr ibutions needed to define the expected value and variance of the observed r esponse and suggest a different form of the variance function. We illustrat e the results of the proposed analysis and the results obtained when the me an of the distribution of N is assumed known through the analysis of a surv iving jejunal crypt data set. Although the proposed method shows inflated s tandard errors of the parameter estimates in the cited example, the propose d method performs as well as a previously published method in all simulated conditions. Moreover, in cases where E(N) is misspecified, the proposed me thod outperforms the previously published method.