A computer program for the analysis of over-dispersed counts and proportions

Over-dispersed binary and count data occur frequently in many fields of application. Examples include occurrence of cavities in one or more teeth, and development of tumors in one or more animals of a litter. Methods of statistical analyses that ignore correlation between observations underestimate the standard errors. Consequently, coverage proportions of confidence intervals and significance levels of tests are distorted. To implement methods for the analysis of correlated binary or count data requires a level of sophistication for data analysis such that one can specify a model for over-dispersion and the correlation between observations. To analyze the over-dispersed binary or count data, one could postulate a specific statistical model and use maximum likelihood methods for the estimation of parameters. However, it may be preferable to employ an approach that does not rely on modeling because the true model is hard to know with confidence. Rao and Scott (J.N.K. Rao and A.J. Scott, Biometrics 48 (1992) 577-585) and Scott and Rao (A.J. Scott and J.N.K. Rao, submitted for publication, 1995) proposed simple methods for analyzing correlated binary and count data exhibiting over-dispersion relative to a binomial and homogeneous Poisson model. This paper presents the SAS program to implement their methods to analyze over-dispersed binary and count data. To demonstrate the implementation and the usefulness of their methods, we present an application involving sensitivity of a monoclonal antibody and the number of mammary tumors developing in rats.