Estimating classification probabilities in high-dimensional diagnostic studies

Motivation: Classification algorithms for high-dimensional biological data like gene expression profiles or metabolomic fingerprints are typically evaluated by the number of misclassifications across a test dataset. However, to judge the classification of a single case in the context of clinical diagnosis, we need to assess the uncertainties associated with that individual case rather than the average accuracy across many cases. Reliability of individual classifications can be expressed in terms of class probabilities. While classification algorithms are a well-developed area of research, the estimation of class probabilities is considerably less progressed in biology, with only a few classification algorithms that provide estimated class probabilities. Results: We compared several probability estimators in the context of classification of metabolomics profiles. Evaluation criteria included sparseness biases, calibration of the estimator, the variance of the estimator and its performance in identifying highly reliable classifications. We observed that several of them display artifacts that compromise their use in practice. Classification probabilities based on a combination of local cross-validation error rates and monotone regression prove superior in metabolomic profiling.