Multivariate statistical analyses are used to evaluate a wide range of factors in predicting relapse and survival for 429 children enrolled in the National Wilms' Tumor Study. Anaplastic or sarcomatous histology, specimen weight over 250 grams, positive regional lymph nodes, treatment with only a single drug and age over two years are the most important predictors of relapse. The first three factors also predict mortality. Laterality, capsular penetration, intrarenal vascular invasion, direct regional extension and operative spillage have lesser effects which do not contribute significantly to the multivariate prediction equations, while sex, race and the presence of a tumor thrombus in the renal vein have essentially no effect. Treatment with combination chemotherapy is confirmed to be efficacious regardless of what prognostic factors are operating. A statistical model allows prediction of relapse and death for each of 24 patient subgroups, with the estimates of percentage relapsed ranging from 3% to 100%.