Parametric methods for confidence interval estimation of overlap coefficients

Overlap coefficient (OVL), the proportion of overlap area between two probability distributions, is a direct measure of similarity between two distributions. It is useful in microarray analysis for the purpose of identifying differentially expressed biomarkers, especially when data follow multimodal distribution which cannot be transformed to normal. However, the inference methods about OVL are quite sparse. This article proposes two methods, a generalized inference (GI) approach and a parametric bootstrapping (PB) method, to construct confidence intervals of OVL under the assumption of normality. In conjunction with the EM algorithms, these methods are extended to mixture Gaussian (MG) distributions. The performances of these methods are evaluated empirically under a variety of distributions including normal, gamma and mixture Gaussian. At last, the proposed approaches are applied to a published microarray dataset from a gene expression study of three most prevalent adult lymphoid malignancies.