Improved genetic association tests for an ordinal outcome representing the disease progression process

We are interested in detecting genetic variants that influence transition between discrete stages of a disease progression process, such as the natural history of progression to cervical cancer with the following four stages: (1) normal-human papillomavirus (HPV) exposed, (2) persistent infection with oncogenic HPV, (3) cervical intraepithelial neoplasia grades 2 or 3 (CIN2/3), and (4) cervical cancer. Standard statistical tests derived from the proportional odds model or polytomous regression model can be used to study this type of ordinal outcome. But these methods are either too sensitive to the proportion odds assumption or fail to take advantage of the restriction on the parameter space for the genetic variants. Two alternative tests, the maximum score test (MAX) and the adaptive P-value combination test (Adapt-P), are proposed with the aim of striking a balance between efficiency and robustness. A simulation study demonstrates that MAX and Adapt-P have the most robust performance among all considered tests under various realistic scenarios. As a demonstration, we applied the considered tests to a genetic association study of cervical cancer.