Development and validation of a prognostic model for survival time data: application to prognosis of HIV positive patients treated with antiretroviral therapy.

The process of developing and validating a prognostic model for survival time data has been much discussed in the literature. Assessment of the performance of candidate prognostic models on data other than that used to fit the models is essential for choosing a model that will generalize well to independent data. However, there remain difficulties in current methods of measuring the accuracy of predictions of prognostic models for censored survival time data. In this paper, flexible parametric models based on the Weibull, loglogistic and lognormal distributions with spline smoothing of the baseline log cumulative hazard function are used to fit a set of candidate prognostic models across k data sets. The model that generalizes best to new data is chosen using a cross-validation scheme which fits the model on k-1 data sets and tests the predictive accuracy on the omitted data set. The procedure is repeated, omitting each data set in turn. The quality of the predictions is measured using three different methods: two commonly proposed validation methods, Harrell's concordance statistic and the Brier statistic, and a novel method using deviance differences. The results show that the deviance statistic is able to discriminate between quite similar models and can be used to choose a prognostic model that generalizes well to new data. The methods are illustrated by using a model developed to predict progression to a new AIDS event or death in HIV-1 positive patients starting antiretroviral therapy.