It has been shown that clinical information such as disease stage and histologic classification is insufficient for predicting disease progression and clinical outcome for cancer patients. Omics technologies have made it possible to apply a molecular signature for establishing a more precise prediction for disease. Risk score, a linear combination for the intensities of selected features, is a common way to define a molecular-based signature. Due to the nature of using the training data set more than once, the p-value calculated from naive chi-square distribution with 1 degree of freedom inflates the type I error. Permutation test is a conventional method for assessing the statistical significance of the association between risk score and the outcome of interest. Permutation test can be computer intensive, especially for a large data set. We applied the first order Taylor approximation to derive the approximated null distribution for the test statistic of risk score for the training set. Comparing to the permutation test, our proposed method provides a more computationally efficient alternative for calculating a reliable p-value for the risk score of a training set.