Estimation of haplotype associated with several quantitative phenotypes based on maximization of area under a receiver operating characteristic (ROC) curve

An algorithm for estimating haplotypes associated with several quantitative phenotypes is proposed. The concept of a receiver operating characteristic (ROC) curve was introduced, and a linear combination of the quantitative phenotypic values was considered. This set of values was divided into two parts: values for subjects with and without a particular haplotype. The goodness of its partition was evaluated by the area under the ROC curve (AUC). The AUC value varied from 0 to 1; this value was close to 1 when the partition had high accuracy. Therefore, the strength of association between phenotypes and haplotypes was considered to be proportional to the AUC value. In our algorithm, the parameters representing a degree of association between the haplotypes and phenotypes were estimated so as to maximize the AUC value; further, the haplotype with the maximum AUC value was considered to be the best haplotype associated with the phenotypes. This algorithm was implemented by using R language. The effectiveness of our algorithm was evaluated by applying it to real genotype data of the Calpine-10 gene obtained from diabetics. The results showed that our algorithm was more reasonable and advantageous for use with several quantitative phenotypes than the generalized linear model or the neural network model.