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Cancer survival studies are commonly analyzed using survival-time prediction models for cancer prognosis. A number of different performance metrics are used to ascertain the concordance between the predicted risk score of each patient and the actual survival time, but these metrics can sometimes conflict. Alternatively, patients are sometimes divided into two classes according to a survival-time threshold, and binary classifiers are applied to predict each patient’s class. Although this approach has several drawbacks, it does provide natural performance metrics such as positive and negative predictive values to enable unambiguous assessments.
We compare the survival-time prediction and survival-time threshold approaches to analyzing cancer survival studies. We review and compare common performance metrics for the two approaches. We present new randomization tests and cross-validation methods to enable unambiguous statistical inferences for several performance metrics used with the survival-time prediction approach. We consider five survival prediction models consisting of one clinical model, two gene expression models, and two models from combinations of clinical and gene expression models.
A public breast cancer dataset was used to compare several performance metrics using five prediction models. 1) For some prediction models, the hazard ratio from fitting a Cox proportional hazards model was significant, but the two-group comparison was insignificant, and vice versa. 2) The randomization test and cross-validation were generally consistent with the p-values obtained from the standard performance metrics. 3) Binary classifiers highly depended on how the risk groups were defined; a slight change of the survival threshold for assignment of classes led to very different prediction results.
1) Different performance metrics for evaluation of a survival prediction model may give different conclusions in its discriminatory ability. 2) Evaluation using a high-risk versus low-risk group comparison depends on the selected risk-score threshold; a plot of p-values from all possible thresholds can show the sensitivity of the threshold selection. 3) A randomization test of the significance of Somers’ rank correlation can be used for further evaluation of performance of a prediction model. 4) The cross-validated power of survival prediction models decreases as the training and test sets become less balanced.