Two Nearest Means: A New Case Based Reasoning Method

Objective: Case-based reasoning predicts outcomes based on matching to training cases and without modeling the relationship between features and outcome. This study compares the accuracy of the two nearest means (2NM), a case-based reasoning, to regression, a feature-based reasoning. Data Sources: The accuracy of the two methods was examined in predicting mortality of 296,051 residents in Veterans Health Affairs nursing homes. Data was collected from 1/1/2000 to 9/10/2012. Data was randomly divided into training (90%) and validation (10%) samples. Study Design: Case-control observational study Data Collection/Extraction Methods: In the 2NM algorithm, first data was transformed so that all features are monotonely related to the outcome. Second, all means that violate monotone order were set aside; to be processed as exceptions to the general algorithm. Third, for predicting a new case, the means in the training set are divided into “excessive” and “partial” means, based on how they match a new case. Finally, the outcome for the new case is predicted as the average of two means: the excessive mean with minimum outcome and the partial mean with maximum outcome. For regression, we predicted mortality from age, gender, and 10 disabilities. Principal Findings : In cases set aside for validation, the 2NM had a McFadden Pseudo R-squared of 0.51. The linear logistic regression, trained on the same training sample and predicting to the same validation cases, had a McFadden Pseudo R-squared of 0.09. The 2NM was significantly more accurate (alpha <0.001) than linear logistic regression. Conclusions : 2NM, a Case-Based reasoning method, captured nonlinear interactions in the data.