Comparison of Ordinal Response Modeling Methods like Decision Trees, Ordinal Forest and L1 Penalized Continuation Ratio Regression in High Dimensional Data

Response variables in most medical and health-related research have an ordinal nature.Conventional modeling methods assume predictor variables to be independent, and consider a large number of samples (n) compared to the number of covariates (p). Therefore, it is not possible to use conventional models for high dimensional genetic data in which p > n. The present study compared the predictive performance of decision trees, ordinal forest, and L1 penalized continuation ratio regression.

In the present study, three data sets were used. The B-cell data contained 12,625 gene expression data related to 128 patients with four ordinal levels of response variables. The HCC data related to liver cancer included 1469 genes of 56 patients with three ordinal levels of response variables. The Heart data contained information of five variables in 294 patients undergoing angiography with five ordinal levels of response variables. The performance of the methods was compared based on the same training and test datasets using indicators such as accuracy, gamma, and kappa.

For two high-dimensional data sets, the ordinal forest model had a higher predictive ability while for the low-dimensional data set, the L1 penalized continuation ratio model had a better predictive performance.

The selection of the best prediction model depends on the data set, and for each data, different methods should be considered to achieve the best model.