Missing data imputation using statistical and machine learning methods in a real breast cancer problem

Missing data imputation is an important task in cases where it is crucial to use all available data and not discard records with missing values. This work evaluates the performance of several statistical and machine learning imputation methods that were used to predict recurrence in patients in an extensive real breast cancer data set.

Imputation methods based on statistical techniques, e.g., mean, hot-deck and multiple imputation, and machine learning techniques, e.g., multi-layer perceptron (MLP), self-organisation maps (SOM) and k-nearest neighbour (KNN), were applied to data collected through the "El Álamo-I" project, and the results were then compared to those obtained from the listwise deletion (LD) imputation method. The database includes demographic, therapeutic and recurrence-survival information from 3679 women with operable invasive breast cancer diagnosed in 32 different hospitals belonging to the Spanish Breast Cancer Research Group (GEICAM). The accuracies of predictions on early cancer relapse were measured using artificial neural networks (ANNs), in which different ANNs were estimated using the data sets with imputed missing values.

The imputation methods based on machine learning algorithms outperformed imputation statistical methods in the prediction of patient outcome. Friedman's test revealed a significant difference (p=0.0091) in the observed area under the ROC curve (AUC) values, and the pairwise comparison test showed that the AUCs for MLP, KNN and SOM were significantly higher (p=0.0053, p=0.0048 and p=0.0071, respectively) than the AUC from the LD-based prognosis model.

The methods based on machine learning techniques were the most suited for the imputation of missing values and led to a significant enhancement of prognosis accuracy compared to imputation methods based on statistical procedures.