Incorporating Hardy–Weinberg Equilibrium Law to Enhance the Association Strength for Ordinal Trait Genetic Study

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The conventional method to examine whether genetic variants are associated with the ordinal traits is the proportional odds model. Such analyses are often conducted by assuming an additive genetic mode of inheritance. However, how the genetic variants influence the risk of occurrence of a disease is impossible to know in practice. Using an improper model might result in a low-power test, thus it reduces the probability of detecting the deleterious genetic markers. To address these concerns, we propose a two-phase procedure (TPP) for ordinal trait genetic studies. In the first phase, we used a linear combination to weight the Hardy–Weinberg equilibrium tests in case groups and formed an omnibus test to classify the genetic models. Then based on the chosen model, the corresponding score test was used to identify the associations. To control the false positive rate, we derived the joint distribution of the test used for selecting the genetic model and that used for identifying the associations. We also obtained the closed forms of two other robust tests, MAX3 and CHI2. Extensive computer simulations were carried out and the results showed that the true selection rates of genetic models are satisfactory and the proposed TPP is more robust than MAX3 and CHI2. Finally, we demonstrated the advantage of our proposed method by applying it to analyse the antibody reactivity to cyclic citrullinated peptides data.

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