Comparison of Imputation Methods for Categorical Real-World Prostate Cancer Data with Natural Order

Missing values (NA) often occur in cancer research, which may be due to reasons such as data protection, data loss, or missing follow-up data. Such incomplete patient information can have an impact on prediction models and other data analyses. Imputation methods are a tool for dealing with NA. Cancer data is often presented in an ordered categorical form, such as tumour grading and staging, which requires special methods. This work compares mode imputation, k nearest neighbour (knn) imputation, and, in the context of Multiple Imputation by Chained Equations (MICE), logistic regression model with proportional odds (mice_polr) and random forest (mice_rf) on a real-world prostate cancer dataset provided by the Cancer Registry of Rhineland-Palatinate in Germany. Our dataset contains relevant information for the risk classification of patients and the time between date of diagnosis and date of death. For the imputation comparison, we use Rubin's (1974) Missing Completely At Random (MCAR) mechanism to remove 10%, 20%, 30%, and 50% observations. The results are evaluated and ranked based on the accuracy per patient. Mice_rf performs significantly best for each percentage of NA, followed by knn, and mice_polr performs significantly worst. Furthermore, our findings indicate that the accuracy of imputation methods increases with a lower number of categories, a relatively even proportion of patients in the categories, or a majority of patients in a particular category.