Krishna K Saha
Responses in the form of counts arise in many clinical trials and epidemiological studies, and are usually extradispersed. When one wishes to estimate the treatment effect in comparison with a placebo in clinical trials, confidence intervals are frequently used. It is of common interest in many clinical trials and epidemiological studies, to obtain the confidence interval for one of the two quantities, mean difference and mean ratio. The preference of one measure over the other depends on the design of the study. In many situations, the mean ratio is more relevant than the difference of means. Confidence interval procedures for the mean difference between treatment and control groups in the analysis of such extra-dispersed counts have been studied recently, but no attention has been paid to investigating the problem of confidence interval construction for the mean ratio. In this article, we develop several asymptotic confidence interval procedures for the mean ratio, by using the delta method, to extend the variance of a single mean estimate to the variance of the mean ratio estimate. The simulation studies indicate that all procedures perform reasonably well in terms of coverage. However, the interval based on the generalized estimating equation approach, using the logarithmic transformation, performs uniformly best in terms of coverage, expected width and location, and is preferable to the other intervals, in most of the situations considered here. Finally, three real-life examples from clinical trials are analyzed to illustrate the proposed confidence interval procedures.
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