Mining of gene expression data to identify genes associated with patient survival is an ongoing problem in cancer prognostic studies using microarrays in order to use such genes to achieve more accurate prognoses. The least absolute shrinkage and selection operator (lasso) is often used for gene selection and parameter estimation in high-dimensional microarray data. The lasso shrinks some of the coefficients to zero, and the amount of shrinkage is determined by the tuning parameter, often determined by cross validation. The model determined by this cross validation contains many false positives whose coefficients are actually zero. We propose a method for estimating the false positive rate (FPR) for lasso estimates in a high-dimensional Cox model. We performed a simulation study to examine the precision of the FPR estimate by the proposed method. We applied the proposed method to real data and illustrated the identification of false positive genes.