Hypothesis Testing in a Mixture Case–Control Model
Article first published online: 25 MAR 2010
© 2010, The International Biometric Society
Volume 67, Issue 1, pages 182–193, March 2011
How to Cite
Qin, J. and Liang, K.-Y. (2011), Hypothesis Testing in a Mixture Case–Control Model. Biometrics, 67: 182–193. doi: 10.1111/j.1541-0420.2010.01409.x
- Issue published online: 25 MAR 2010
- Article first published online: 25 MAR 2010
- Received November 2008. Revised January 2010. Accepted January 2010.
- Chi-squared distribution;
- Clinical trial;
- Gene mutation;
- Microarray study;
- Mixture models
Summary We consider a problem of testing mixture proportions using two-sample data, one from group one and the other from a mixture of groups one and two with unknown proportion, λ, for being in group two. Various statistical applications, including microarray study, infectious epidemiological studies, case–control studies with contaminated controls, clinical trials allowing “nonresponders,” genetic studies for gene mutation, and fishery applications can be formulated in this setup. Under the assumption that the log ratio of probability (density) functions from the two groups is linear in the observations, we propose a generalized score test statistic to test the mixture proportion. Under some regularity conditions, it is shown that this statistic converges to a weighted chi-squared random variable under the null hypothesis of λ= 0, where the weight depends only on the sampling fraction of both groups. The permutation method is used to provide more reliable finite sample approximation. Simulation results and two real data applications are presented.