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Notes in Case‐Control Studies with Matched Pairs under Inverse Sampling
Author(s) -
Lui KungJong
Publication year - 1996
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710380606
Subject(s) - mathematics , statistics , confidence interval , binomial (polynomial) , sample size determination , estimator , minimum variance unbiased estimator , sampling (signal processing) , negative binomial distribution , inverse , bias of an estimator , poisson distribution , computer science , geometry , filter (signal processing) , computer vision
In case‐control studies with matched pairs, the traditional point estimator of odds ratio (OR) is well‐known to be biased with no exact finite variance under binomial sampling. In this paper, we consider use of inverse sampling in which we continue to sample subjects to form matched pairs until we obtain a pre‐determined number (>0) of index pairs with the case unexposed but the control exposed. In contrast to use of binomial sampling, we show that the uniformly minimum variance unbiased estimator (UMVUE) of OR does exist under inverse sampling. We further derive an exact confidence interval of OR in closed form. Finally, we develop an exact test and an asymptotic test for testing the null hypothesis H 0 : OR = 1, as well as discuss sample size determination on the minimum required number of index pairs for a desired power at α‐level.