Classification Trees with Mismeasured Responses

Classification trees are a popular machine learning tool for studying a variety of problems, including prediction, inference, risk factors identification, and risk groups classification. Classification trees are basically developed under the assumption that the response and covariate variables are accurately measured. This condition, however, is often violated in practice. Ignoring this feature commonly yields invalid analysis results. In this paper, we study the impact of mismeasured responses on the performance of standard classification trees and propose a novel classification trees algorithm for mismeasured responses. Our study is directed to settings with binary responses which are subject to mismeasurement. To address the effects of mismeasured responses, we modify the decision rules which are valid for tree building in the mismeasurement-free settings by introducing new measures for the node impurity and misclassification cost. To characterize the magnitude of mismeasurement in responses, we consider two data scenarios. In the first scenario, the mismeasurement rates are known, either from previous studies of the same nature or being set by researchers who are interested in conducting sensitivity analyses to assess the impact of mismeasured responses. In the second scenario, the mismeasurement rates are unknown and are estimated from a validation dataset which contains both accurate measurements and mismeasurements for responses. We conduct a variety of simulation studies to assess the performance of the proposed classification trees algorithm, in comparison to the usual classification trees algorithms which ignore response mismeasurement. It is demonstrated that ignoring response mismeasurement can yield seriously erroneous results and that our proposed method provides superior performance with the mismeasurement effects accommodated. To illustrate the usage of the proposed method, we analyze the data arising from the National Health and Nutrition Examination Surveys (NHANES) by conducting sensitivity analyses to assess how classification results may be affected by different misclassification costs.