Re-calibration and discrimination in survival risk prediction functions
Risk prediction models are important tools intended to help clinicians make optimal treatment decisions. They are often developed on large reference samples for applications in different local cohorts. For example, consider transporting the US Framingham risk prediction function for coronary heart disease (CHD) to populations in Europe or Asia. In this process it is necessary to correctly re-calibrate the existing function for future applications. In this thesis we propose a new re-calibration method which could be used when transporting the risk function from a reference to the local cohort. This new method is compared with the existing re-calibration methods through numerical simulations under various assumptions and on real-life population data. In a majority of settings it outperforms the existing methods. We also explore the strengths and limitations of each re-calibration method and provide guidance for practical use of these methods. The re-calibration methods described can be used for any risk prediction models based on Cox proportional hazard regression. To facilitate convenient application we present an easy to use SAS macro. Another essential feature of a successful risk prediction model is characterized by its discrimination or its ability to separate those with events from those without events. One of the most popular measures of discrimination is the area under the Receiver Operating Characteristic (ROC) curve, often called the c statistic or just area under the curve (AUC). Various authors have extended the AUC from binary outcome applications to survival data. However, these extensions are not unique. In this thesis we compare four of these extensions using simulations and practical applications to the Framingham risk functions as well as a breast cancer risk model. We conclude that the extension proposed by Harrell and described in detail by Pencina & D'Agostino is a metric that is most consistent with the most appropriate definition of discrimination in survival. We construct a SAS code for its consistent estimator based on the work of Uno et al. We also notice large differences in magnitude between various C indices calculated on the same data and caution against comparisons across different C indices.