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Statistical methods for fitting nonlinear functions to data generated by correlated response variates are discussed. Estimation of the model parameters is performed with an iterative two-stage scheme. The estimation procedure accommodates both within-unit and between-unit variability in fitting a response surface. Under regularity conditions the procedure yields asymptotically normal, strongly consistent estimators. If desired a patterned variance-covariance matrix can be assumed and incorporated into the model. The methods are illustrated by an analysis of data from a study of the combined effects of hepatotoxins in which between- and within-subject measurements are recorded.

In this article the problem of obtaining the maximum likelihood estimates of the parameters from a special type of linear combination of discrete probability functions is discussed. It is shown that when the sample is completely categorized the estimation problem is no more complicated that that of estimating the parameters of each of the component probability functions separately. When the sample is less than completely classified an iterative procedure must be used to obtain solutions to the likelihood equations and it is shown how the problem reduces to that of the full data case. A discussion of the asymptotic properties of the resulting estimators follows.

In this article, sufficient conditions are given for the existence of a unique solution of the likelihood equation which results from a grouped data sample. The necessary and sufficient conditions for the convergence of a sequence defined by the method of successive approximations to this unique solution are also given. Finally, it is shown that when the groups from an underlying Poisson distribution are connected the method of successive approximations will converge to the unique solution of the resulting likelihood equation regardless of the starting value chosen provided that the sample is not concentrated entirely in either or both the first and last groups.

Regression Analysis of Survival Data in Cancer Chemotherapy. By Walter H. Carter Jr, Galen L. Wampler and Donald M. Stablein. New York and Basel, Marcel Dekker, 1983. 209 p. SFr 103. (Volume 44 in Marcel Dekker Series in Statistics: Textbooks and Monographs).

In this article the effect of incomplete samples, grouped samples in particular, on the variance and bias of the estimator for the parameters from an underlying Poisson distribution is studied.