Exact Tests for Epidemiological Risks under Independent Negative Binomial Sampling for Rare Events in Clinical Trials
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Exact Tests for Epidemiological Risks Under Independent Negative Binomial Sampling for Rare Events in Clinical Trials
Srrmg-Ho Kang, PhD Department of Statistics, Ewha Womans University, Seoul, Korea
Kry Words Exact unconditional power; 2 x 2 contingency table; Epidemiology; Rare event; Vaccine Corrrspondrntr Addrrss Seung-Ho Kang. Department ofstatistics, Ewha Womans LJniversiv, I1 - I , DaeHyun-Dong. SeoDaeMun-Gu. Seoul, KOREA, 120-750 (email: [email protected]).
2 x 2 contingency tables are fresuently obtained fiom independent binomial sampling. Howevq when the probabilities of the outcome of interest are small, we may use independent negative binomial sampling in which sampling stops aftera predetermined number of the outcome of interest ocmn. f i e obtained 2 x 2 contingency tables are likely to be unbalanced, and the asymptotic tests could be unreliable. In
INTRODUCTION The analysis of adverse event data in clinical trials is an important part of the development, postmarket characterization and safety of pharmaceutical products. Epidemiologic methods have often been used in the investigation of adverse efiects of approved drugs and vaccines. In epidemiology, it is important to compare the risk of a group with a risk factor to one without a risk factor. The risk difference, the risk ratio and the odds ratio are frequently used indices to measure the extent of association between a risk factor and an outcome in epidemiology. In this article, we focus on hypothesis testing of the risk difference, the risk ratio, and the odds ratio when independent negative binomial sampling is employed. For more information on the three indices, see Fleiss et al. (1). Independent binomial sampling is frequently employed to compare proportions from two populations. That is, the sample sizes from two populations are determined in advance, and then binary responses are observed and the numbers of outcomes of interest are recorded. The data are summarized in the form of 2 x 2 contingency tables. When the probabilities of the outcome of interest are small, the number of the outcome of interest can be very small or even zero under independent binomial sam-
this arii.de, we develop exact conditional tests for the risk difference, the risk ratio, and the odds ratio in 2 x 2 contingency tables obtained fiom independent negative binomial sampling. We investigate the exact unconditional powers of the exact tests. f i e main advantage of exact test is that it is gumanteed to contrd type I erron under the nominal level unconditionally.
pling. In such cases, we may employ independent negative binomial sampling in which we continue sampling subjects until we obtain a predetermined number of the outcome of interest. An advantage of independent negative binomial sampling is to ensure that we obtain an appropriate number of the outcome of interest in our samples. Independent negative binomial sampling has a long history (2,3),but it is not until recently that many studies have been conducted to address statistical issues under indepen
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