The emergence of advanced gene sequencing technologies has transformed the study of structural and genetic variations within the human genome. This has spurred increased research into the genetic underpinnings of complex diseases. While medical research often utilizes ordinal response variables to reflect stages or severity of diseases, most existing methods focus on binary or continuous traits, neglecting vital ordinal data. To address this gap, this article introduces the Partial Linear Cumulative Logistic (PLCL) method within a mixed model framework, designed to accurately process ordinal traits and explore their genetic correlations with diseases. The PLCL method employs B-spline functions for modeling, uses Sieve maximum likelihood estimation for regression coefficients, and determines P-values via a likelihood ratio test. An aggregated Cauchy association test then combines these P-values for comprehensive analysis. Simulation results affirm PLCL's robustness, efficiency in P-value computation without permutations, strict Type I error control, and superior performance compared to traditional methods.
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Zhou et al. (2024) studied this question.