Predicting survival in patients with metastatic kidney cancer by gene-expression profiling in the primary tumor -- Data Supplement - HTML Page - 1754SuppText.htslp -- Proceedings of the National Academy of Sciences

Supporting Text
Explanation of Statistical Methods
Identification of Array Elements Significant for Survival.
To test the statistical significance of the large number of genes that were associated with survival, a permutation test was used. We randomly permuted the patients’ survival outcomes such that each patient’s gene expression is associated with a random survival outcome. We then fit the Cox proportional-hazards model to each gene and assessed the significance of the association of that gene with the permuted survival outcome. We determined the number of genes that were associated with survival at the 0.001 significance level. This procedure was repeated 1,000 times. Leave-One-Out Cross-Validation Procedure for Survival Analysis.
For each training set obtained by omitting one patient, we screened all the genes to identify those statistically significant (P < 0.001) for survival. We clustered the patient expression profiles in the training set with regard to the significant genes for that training set, cutting the dendrogram to obtain two clusters. We labeled those two clusters as good or poor prognosis based on which cluster had the better survival outcome. We classified the test patient into one of these clusters based on k-nearest neighbor classification using as similarity metric the Pearson correlation coefficient based on the significant genes for that training set and k = 5. We classified the test patient for that training set as to good or poor prognosis based on which cluster the majority of the test patient’s nearest neighbors belonged to. After completing the cross validation, we plotted Kaplan–Meier survival curves for the two prognosis groups determined by the cross-validation procedure. Assessing the Difference Between Two Survival Curves Generated by the Cross-Validation Procedure.
The usual log-rank test for comparing survival distributions would not be valid for comparing these curves, because the prognosis groups were determined by a cross-validation procedure rather than a priori. Consequently, we performed a permutation test to evaluate the significance of the difference between survival curves. For each random permutation of survival to expression profile, we repeated the complete cross-validation procedure, obtained a good and poor prognosis group, and computed a log-rank c ² value. We used a c ² statistic from the log-rank test between the two groups as the test statistic. We repeated this entire procedure for 5,000 random permutations to estimate the distribution of the c ² statistic under the null hypothesis that survival is independent of expression profile. The proportion of this null distribution beyond the c ² value for the two cross-validated survival curves in the actual data was taken as the P value.