Survival prognosis and variable selection: A case study for metastatic castrate resistant prostate cancer patients

Abstract

Survival prognosis is challenging, and accurate prediction of individual survival times is often very difficult. Better statistical methodology and more data can help improve the prognostic models, but it is important that methods and data usages are evaluated properly. The Prostate Cancer DREAM Challenge offered a framework for training and blinded validation of prognostic models using a large and rich dataset on patients diagnosed with metastatic castrate resistant prostate cancer. Using the Prostate Cancer DREAM Challenge data we investigated and compared an array of methods combining imputation techniques of missing values for prognostic variables with tree-based and lasso-based variable selection and model fitting methods. The benchmark metric used was integrated AUC (iAUC), and all methods were benchmarked using cross-validation on the training data as well as via the blinded validation. We found that survival forests without prior variable selection achieved the best overall performance (cv-iAUC = 0.70, validation-iACU = 0.78), while a generalized additive model was best among those methods that used explicit prior variable selection (cv-iAUC = 0.69, validation-iACU = 0.76). Our findings largely concurred with previous results in terms of the choice of important prognostic variables, though we did not find the level of prostate specific antigen to have prognostic value given the other variables included in the data.

Keywords: generalized additive models; imputation; lasso; stability selection; survival forests; survival prognostic models.

Figure 1.. Correlation plot (left) for all binary predictors.

See Supplementary Figure 1 for the correlation plot with labels. Correlations (right, below the diagonal) and pairwise associations as given by loess scatter plot smoothers (right, above the diagonal) for the numerical predictors.

Figure 2.. Integrated AUC for different combinations of methods evaluated by three replications of 5-fold cross-validation.

Results are shown for individual folds (light blue filled circles) and averaged over all folds (red filled circles). The figure also shows iAUC on the validation data (purple filled squares) and iAUC for the reference model on the validation data (purple dashed line). The four methods marked with a * used variables chosen via stability selection, whereas the other four methods relied on implicit variable selection.

Figure 3.. Selection proportions for the 20 most stably selected variables stratified by imputation method.

The threshold of 50% (red line) was used for the final variable selection.

Supplementary Figure 1.. Correlation plot for all binary predictors.