Roger Bilisoly

Testing the homogeneity of the means of several groups of count data in the presence of unequal dispersions

Extra-dispersion (overdispersion or underdispersion) is a common phenomenon in practice when the variance of count data differs from that of a Poisson model. This can arise when the data come from different subpopulations or when the assumption of independence is violated. This paper develops a procedure for testing the equality of the means of several groups of counts, when extra-dispersions among the treatment groups are unequal, based on the adjusted counts using the concept of the design and size effects employed by Rao and Scott, [Rao, J.N.K., Scott, A.J., 1999. A simple method for analyzing overdispersion in clustered Poisson data. Statist. Med. 18, 1373-1385]. We also obtain the score-type test statistics based on quasi-likelihoods using the mean-variance structure of the negative binomial model, and study the properties and performance characteristics of these. The simulation results indicate that the statistic based on the adjusted count data, which has a very simple form and does not require the estimates of the extra-dispersion parameters, performs best among all the statistics considered in this paper. Finally, the proposed test statistic and the score-type statistic based on double-extended quasi-likelihood are illustrated by an analysis of a set of fetal implants in mice arising from a developmental toxicity study.

Hybrid-based confidence intervals for the ratio of two treatment means in the over-dispersed Poisson data

In many clinical trials and epidemiological studies, comparing the mean count response of an exposed group to a control group is often of interest. This type of data is often over-dispersed with respect to Poisson variation, and previous studies usually compared groups using confidence intervals (CIs) of the difference between the two means. However, in some situations, especially when the means are small, interval estimation of the mean ratio (MR) is preferable. Moreover, Cox and Lewis [4] pointed out many other situations where the MR is more relevant than the difference of means. In this paper, we consider CI construction for the ratio of means between two treatments for over-dispersed Poisson data. We develop several CIs for the situation by hybridizing two separate CIs for two individual means. Extensive simulations show that all hybrid-based CIs perform reasonably well in terms of coverage. However, the CIs based on the delta method using the logarithmic transformation perform better than other intervals in the sense that they have slightly shorter interval lengths and show better balance of tail errors. These proposed CIs are illustrated with three real data examples.