A study of sequential inference for the risk ratio and measure of reduction of two binomials

Abstract

A STUDY OF SEQUENTIAL INFERENCE FOR THE RISK RATIO AND MEASURE OF REDUCTION OF TWO BINOMIALS by Zhou Wang Dr. Hokwon Cho , Examination Committee Chair Associate Professor of Statistics University of Nevada, Las Vegas, USA The binomial distribution is one of the most commonly and widely occurring probabilistic phenomena in our lives. Since observations from independent Bernoulli trials yield a dichotomous type, the distribution of sequences provides the basis and clue for statistical formulations of a wide variety of problems. Occasionally, the core of biomedical studies is related to the comparison and evaluation of the risks of events or outcomes of interest in comparing populations under study. For instance, one wishes to compare two groups of subjects drawn from two independent populations. Then, two sample proportions play central roles in those comparisons. One of the most useful ways to make comparisons for the relative risk is to take a ratio, also referred to as the risk ratio. In addition, a measure of reduction of the two proportions is considered. In this thesis, we consider sequential methods of inferences for the ratio of two independent binomial probabilities, the risk ratio, in two populations for comparison. We obtain approximate confidence intervals and optimal sample sizes for the risk ratio and measure of reduction, respectively. Since there does not exist an unbiased estimator of the risk ratio, the procedure is developed based on a slightly modified