The estimation of probability distribution for factor variables with many categorical values

With recent developments of data technology in biomedicine, factor data such as diagnosis codes and genomic features, which can have tens to hundreds of discrete and unorderable categorical values, have emerged. While considered as a fundamental problem in statistical analyses, the estimation of probability distribution for such factor variables has not studied much because the previous studies have mainly focused on continuous variables and discrete factor variables with a few categories such as sex and race. In this work, we propose a nonparametric Bayesian procedure to estimate the probability distribution of factors with many categories. The proposed method was demonstrated through simulation studies under various conditions and showed significant improvements on the estimation errors from the previous conventional methods. In addition, the method was applied to the analysis of diagnosis data of intensive care unit patients, and generated interesting medical hypotheses. The overall results indicate that the proposed method will be useful in the analysis of biomedical factor data.