关键词：
Area under the receiver operating characteristic curve
Classification
HapMap data
Heterogeneous stock mice data
Probability of correct classification
Receiver operating characteristic
Sample size determination
PREDICTION
摘要：
Background: Data on single-nucleotide polymorphisms (SNPs) have been found to be useful in predicting phenotypes ranging from an individual's class membership to his/her risk of developing a disease. In multi-class classification scenarios, clinical samples are often limited due to cost constraints, making it necessary to determine the sample size needed to build an accurate classifier based on SNPs. The performance of such classifiers can be assessed using the Area Under the Receiver Operating Characteristic (ROC) Curve (AUC) for two classes and the Volume Under the ROC hyper-Surface (VUS) for three or more classes. Sample size determination based on AUC or VUS would not only guarantee an overall correct classification rate, but also make studies more cost-effective. Results: For coded SNP data from D(>= 2) classes, we derive an optimal Bayes classifier and a linear classifier, and obtain a normal approximation to the probability of correct classification for each classifier. These approximations are then used to evaluate the associated AUCs or VUSs, whose accuracies are validated using Monte Carlo simulations. We give a sample size determination method, which ensures that the difference between the two approximate AUCs (or VUSs) is below a pre-specified threshold. The performance of our sample size determination method is then illustrated via simulations. For the HapMap data with three and four populations, a linear classifier is built using 92 independent SNPs and the required total sample sizes are determined for a continuum of threshold values. In all, four different sample size determination studies are conducted with the HapMap data, covering cases involving well-separated populations to poorly-separated ones. Conclusion: For multi-classes, we have developed a sample size determination methodology and illustrated its usefulness in obtaining a required sample size from the estimated learning curve. For classification scenarios, this methodology will help scien
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