Hypothesis Testing in a Mixture Case-Control Model

Jing Qin, Kung Yee Liang

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 ofλ= 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.

Original languageEnglish (US)
Pages (from-to)182-193
Number of pages12
Issue number1
StatePublished - Mar 2011
Externally publishedYes


  • Case-control
  • Chi-squared distribution
  • Clinical trial
  • Gene mutation
  • Microarray study
  • Mixture models

ASJC Scopus subject areas

  • Statistics and Probability
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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