Prediction of survival with alternative modeling techniques using pseudo values

Abstract

Background: The use of alternative modeling techniques for predicting patient survival is complicated by the fact that some alternative techniques cannot readily deal with censoring, which is essential for analyzing survival data. In the current study, we aimed to demonstrate that pseudo values enable statistically appropriate analyses of survival outcomes when used in seven alternative modeling techniques.

Methods: In this case study, we analyzed survival of 1282 Dutch patients with newly diagnosed Head and Neck Squamous Cell Carcinoma (HNSCC) with conventional Kaplan-Meier and Cox regression analysis. We subsequently calculated pseudo values to reflect the individual survival patterns. We used these pseudo values to compare recursive partitioning (RPART), neural nets (NNET), logistic regression (LR) general linear models (GLM) and three variants of support vector machines (SVM) with respect to dichotomous 60-month survival, and continuous pseudo values at 60 months or estimated survival time. We used the area under the ROC curve (AUC) and the root of the mean squared error (RMSE) to compare the performance of these models using bootstrap validation.

Results: Of a total of 1282 patients, 986 patients died during a median follow-up of 66 months (60-month survival: 52% [95% CI: 50%-55%]). The LR model had the highest optimism corrected AUC (0.791) to predict 60-month survival, followed by the SVM model with a linear kernel (AUC 0.787). The GLM model had the smallest optimism corrected RMSE when continuous pseudo values were considered for 60-month survival or the estimated survival time followed by SVM models with a linear kernel. The estimated importance of predictors varied substantially by the specific aspect of survival studied and modeling technique used.

Conclusions: The use of pseudo values makes it readily possible to apply alternative modeling techniques to survival problems, to compare their performance and to search further for promising alternative modeling techniques to analyze survival time.

Figure 1. Survival pattern 1282 patients with newly diagnosed HNSCC.

Figure 2. Censoring pattern 1282 patients with newly diagnosed HNSCC.

Figure 3. Variable importance of the models per outcome.