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The odds ratio (OR) is a statistical measure used extensively in epidemiology and research to quantify the strength of association between exposure and outcome across different groups. Unlike relative risk, which compares the probabilities of an event occurring, the odds ratio compares the odds of an event occurring in the exposed group to the odds of it occurring in the unexposed group. The odds, in this context, are calculated as the probability of the event happening divided by the...
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Related Experiment Video

Updated: Aug 25, 2025

Candidate Gene Testing in Clinical Cohort Studies with Multiplexed Genotyping and Mass Spectrometry
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Likelihood ratio test for genetic association study with case-control data under Probit model.

Zhen Sheng1,2, Yukun Liu1,2, Pengfei Li3

  • 1Key Laboratory of Advanced Theory and Application in Statistics and Data Science, MOE, Shanghai, People's Republic of China.

Journal of Applied Statistics
|October 17, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces novel Probit mixed-effects models for analyzing case-control genetic data. These models offer significant power gains for disease association studies compared to traditional methods.

Keywords:
Case–control dataProbit modelempirical likelihoodlikelihood ratio testmixed-effects model

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Area of Science:

  • Biostatistics
  • Statistical Genetics
  • Epidemiology

Background:

  • Probit and Logit models are widely used for binary disease classification in genetic association studies.
  • While effective for prospective data, Probit models have limitations with retrospective case-control data, particularly with random effects.

Purpose of the Study:

  • To systematically investigate the performance of Probit mixed-effects models for case-control genetic data.
  • To develop and evaluate novel likelihood ratio tests for genetic association using these models.

Main Methods:

  • Developed Probit mixed-effects models for retrospective case-control data.
  • Derived a closed-form retrospective likelihood.
  • Proposed four likelihood ratio tests based on disease prevalence availability.
  • Determined the limiting distribution of the tests under the null hypothesis.

Main Results:

  • The developed likelihood ratio tests demonstrate a significant power gain over Logit-model-based score tests.
  • Incorporating disease prevalence information further enhances the power of these tests.
  • Simulations confirm the effectiveness of the proposed Probit models.

Conclusions:

  • Probit mixed-effects models provide a powerful approach for genetic association studies with retrospective case-control data.
  • The proposed likelihood ratio tests are superior to existing methods, especially when disease prevalence is known.
  • The study identified a significant association between the ABO gene and malaria in Kenyan data, a finding missed by conventional methods.