Our results also highlight, in the context of two sub-phenotypes, that the multinomial regression-based test of heterogeneity has equivalent power to a direct comparison of the two case groups via logistic regression.
We have performed simulations to investigate the power of the multinomial regression framework to test for disease association and heterogeneity in allelic odds ratios between sub-phenotypes, and to compare its performance to existing logistic regression-based approaches.
Predictors of these classes were identified using one-way ANOVA, Chi Square tests and multinomial regression analysis.
The remaining 3 tests use multinomial regression techniques to allow each categorization of G to be the response variable, with E as the predictor variable: A logistic regression (this test is the same as that examined by Kraft et al. (9)), a proportional odds regression, and a multinomial regression are performed for binary, ordinal, and nominal codings of G.
Although the rs4673 allele frequency was not significant between the groups (P > 0.5), chi square test and multinomial regression analysis showed an observed high risk for rs13306294 A allele among patients.
For the comparison study between patients with IP and the general population, a multinomial regression analysis was performed to test the difference in smoking rates between patients with IP and the general population.
Within the multinomial regression framework, we can also perform formal tests of heterogeneity in allelic odds ratios between sub-phenotypes.
In the statistical analysis we used chi-squared test, t-test, permutation test, analysis of covariance, multivariate logistic regression analysis and multinomial regression model.
According to the likelihood ratio test, the fit of the multinomial regression model was good (χ2 (18, 2826) = 275.9, p < 0.001).
To address this issue, we have developed a novel test of association within a multinomial regression modeling framework, allowing for heterogeneity of genetic effects between sub-phenotypes.
