Statistical Models In The Study Of Joint Association Analysis Of Bivariate Qualitative Traits

When people study the relationship between gene and diseases,they usually work on figuring out if the gene influences one single disease or not.In fact,as the different types of genotypes may have some correlations and because of pleiotropy,it is meaningful to jointly analysis associated multivariate qualitative traits,which turns out better power than analysing just one single trait.In the study of this field,many scholars have studied gene tests on quantitative traits or qualitative traits which are associated with quantitative traits.We creatively focus on joint association analysis of multivariate qualitative traits,specially bivariate traits and in order to study it we construct there statistical models.The first model is traditional logistic regression model,we use the experience of gene tests for multivariate traits one by one and build joint score function to jointly analysis associated multivariate qualitative traits.The second model is based on an assumption that there exits a latent continuous variable which determines the value of the qualitative variable,then we can analysis associated multivariate qualitative traits by analysing associated continuous variables.The third model is based on conditional logistic model,we assume that one of the associated multivariate qualitative traits has logistic regression relation to the others and the gene to test.It helps to give the probability distribution of multiple traits.In this way,we simplify the model and improve the testing power.The first part of the article introduces the research background and research signifi-cance of genetic correlation detection,and we also introduce some popular test methods according to recent reference,we divide these methods into two aspects.The second part of the article examines binary variables on a single gene,we put forward three kinds of model and under each model gives one kind of practical test methods,we also theoreti-cally proved the rationality of the there kinds of methods and give the test statistics.In the third part of the article,we simulate data to check whether the type I error of the there kinds of testing method can be controlled and compare their test powers for different val-ues of parameters.According to the results,we give the advantages and disadvantages of there kinds of test method.In the fourth part of the article we made a conclusion accord-ing to the simulation results,that is the second model has the best power but the question is it is hard to operate.When the two diseases have a positive effect on each other,the third model behaves better.