A randomized test for the conditional odds ratio of matched pairs in an inverse binomial sampling design

Abstract

Matched case-control paired data are commonly used to study the association between a disease and an exposure of interest. This work provides a consistent test for this association with respect to the conditional odds ratio (ORc), which is a measure of association that is also valid in prospective studies. We formulate the test from the maximum likelihood (ML) estimate of ORc by using data under inverse binomial sampling, in which individuals are selected sequentially to form matched pairs until for the first time one obtains either a prefixed number of index pairs with the case unexposed but the control exposed or with the case exposed but the control unexposed. We discuss the situation of possible early stopping. We compare numerically the performance of our procedure with a competitor proposed by Lui () in terms of type I error rate, power, average sample number (ASN) and the corresponding standard error. Our numerical study shows a gain in sample size without loss in power as compared to the competitor. Finally, we use the data taken from a case-control study on the use of X-rays and the risk of childhood acute myeloid leukemia for illustration.

Reducing sample size in negative binomial UMPU test

“…Setting p = π 01 π 10 +π 01 , the conditional probability of occurrence of [Y 1 < Y 2 ] when [Y 1 ̸ = Y 2 ], the testing problem is equivalent to that of testing H 0 : p = 1 2 against H 1 : p ̸ = 1 2 , which is same as the earlier one with p 0 = 1 2 . Bandyopadhyay et al (2014) work on this problem using a two-sided symmetric stopping rule. However, the present solution, based on a two-sided asymmetric stopping rule, provides the following alternative approach.…”