expression patterns, SELDI-TOF MS data, and SNPs (single nucleotide polymorphisms) profiles in a case-control study. While the general procedure to validate a classifier will be discussed, the emphasis is manly placed on assessing prediction confidence and chance correlation, two critical aspects that, unfortunately, have not been extensively discussed in the field.

ISSUES, CHALLENGES, AND RECOMMENDATIONS

Developing classifiers from omics data is difficult because (1) there are many more predictor variables than the sample size (the number of subjects); (2) the sample size is often small with a skewed patient/healthy individual distribution; and (3) the signal/noise ratio in both clinical outcomes (dependent variables) and omics profiles (independent variables) are low.

Most molecular classification approaches reported in the literature have focused on developing and validating a single classifier. Although many successes have been demonstrated, the single classifier approach is inherently susceptible to the data quality and size; as the sample size and/or the signal/noise ratio of a data set decrease, the quality of a single classifier declines rapidly. Another aspect that is unique, or at least very significant, to molecular classification is that redundant information is normally present in an omics profile. The nature of the data reflects biologic phenomena where multiple molecular expression patterns are often equally important as biomarkers in diagnosis/prognosis. Unfortunately, a single classifier tends to optimize a single pattern for classification.

Consensus modeling, that combines multiple classifiers to reach a consensus conclusion, is theoretically less prone to data quality and size and more robust to handle an unbalanced data set. Most importantly, consensus modeling makes full use of the redundant information presented in omics data to explore all possible biomarkers. Thus, consensus modeling offers a unique opportunity in molecular classification.

The critical and implicit assumption in consensus modeling is that multiple classifiers will effectively identify and encode more aspects of the variable relationships than will a single classifier. The corollaries are that combining several identical classifiers produces no gain, and benefits of combining can only be realized if individual classifiers give different results. In other words, benefits of combining are only expected if separate classifiers encode differing aspects of disease-omics pattern associations. More recently, we also found that the information gained



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