Predictive performance of missing data methods for logistic regression, classification trees and neural networks

Although the effect of missing data on regression estimates has received considerable attention, their effect on predictive performance has been neglected. We studied the performance of three missing data strategies-omission of records with missing values, replacement with a mean and imputation based on regression-on the predictive performance of logistic regression (I-R), classification tree (CT) and neural network (NN) models in the presence of data missing completely at random (MCAR). Models were constructed using datasets of size 500 simulated from a joint distribution of binary and continuous predictors including nonlinearities, collinearity and interactions between variables. Though omission produced models that fit better on the data from which the models were developed, imputation was superior on average to omission for all models when evaluating the receiver operating characteristic (ROC) curve area, mean squared error (MSE), pooled variance across outcome categories and calibration chi(2) on an independently generated test set. However, in about one-third of simulations, omission performed better. Performance was also more variable with omission including quite a few instances of extremely poor performance. Replacement and imputation generally produced similar results except with neural networks for which replacement, the strategy typically used in neural network algorithms, was inferior to imputation. Missing data affected simpler models much less than they did more complex models such as generalized additive models that focus on local structure. For moderate sized datasets, logistic regressions that use simple nonlinear structures such as quadratic terms and piecewise linear splines appear to be at least as robust to randomly missing values as neural networks and classification trees.