Ranking Candidate Genes for the Biomarker Development in a Cancer Diagnostics

Recently, Pepe et al. (2003) employed the receiver operating characteristic (ROC) approach to rank candidate genes from a microarray experiment that can be used for the biomarker development with the ultimate purpose of the population screening of a cancer, In the cancer microarray experiment based on n patients the researcher often wants to compare the tumor tissue with the normal tissue within the same individual using a common reference RNA. This design is referred to as a reference design or an indirect design. Ideally, this experiment produces n pairs of microarray data, where each pair consists of two sets of microarray data resulting from reference versus normal tissue and reference versus tumor tissue hybridizations. However, for certain individuals either normal tissue or tumor tissue is not large enough for the experimenter to extract enough RNA for conducting the microarray experiment, hence there are missing values either in the normal or tumor tissue data. Practically, we have $n_1$ pairs of complete observations, $n_2$ 'normal only' and $n_3$ 'tumor only' data for the microarray experiment with n patients, where n=$n_1$+$n_2$+$n_3$. We refer to this data set as a mixed data set, as it contains a mix of fully observed and partially observed pair data. This mixed data set was actually observed in the microarray experiment based on human tissues, where human tissues were obtained during the surgical operations of cancer patients. Pepe et al. (2003) provide the rationale of using ROC approach based on two independent samples for ranking candidate gene instead of using t or Mann -Whitney statistics. We first modify ROC approach of ranking genes to a paired data set and further extend it to a mixed data set by taking a weighted average of two ROC values obtained by the paired data set and two independent data sets.