Ordinal responses are commonly seen in medical research. Many pathological evaluations and health status outcomes are reported on an ordinal scales. Some examples of ordinal outcomes include cancer stage (I, II, III and IV), or stage of liver disease (normal liver, chronic hepatitis, cirrhosis and end of stage liver disease or hepatocellular carcinoma (HCC)).In recent years, there has been a demand to understanding the pathogenic association between ordinal clinical outcomes and molecular characteristics. Genomic characteristics are often assayed using a high-dimensional platform where the number of interrogated sites (P) exceeds the number of samples (n). Unfortunately, traditional ordinal response models often do not perform well when the number of parameter (P) exceed the number of observations (n). A good solution to this problem is penalization, for example, least absolute shrinkage and selection operator (LASSO). Here, we extend a LASSO method, the generalized monotone incremental forward stagewise algorithm (GMIFS) method, to ordinal response models. Specifically, this research details the extension of the GMIFS method to probit link ordinal response models and the stereotype logit model.Moreover, motivated by the Bayesian LASSO proposed by Park and Casella (2008), we developed an ordinal response model that incorporates a penalty term so that both feature selection and outcome prediction are achievable. The ordinal response model we are focusing on is the cumulative logit model, and the performance will be compared with the frequentist LASSO cumulative logit model (GMIFS).In addition to GMIFS and penalized Bayesian cumulative logit model, this research also addresses filtering, which is another dimension reduction method (different from penalization). We compare filtering, or univariate feature selection methods, with penalization methods using grouped survival data.
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