External validity of risk models: Use of benchmark values to disentangle a case-mix effect from incorrect coefficients.

Various performance measures related to calibration and discrimination are available for the assessment of risk models. When the validity of a risk model is assessed in a new population, estimates of the model's performance can be influenced in several ways. The regression coefficients can be incorrect, which indeed results in an invalid model. However, the distribution of patient characteristics (case mix) may also influence the performance of the model. Here the authors consider a number of typical situations that can be encountered in external validation studies. Theoretical relations between differences in development and validation samples and performance measures are studied by simulation. Benchmark values for the performance measures are proposed to disentangle a case-mix effect from incorrect regression coefficients, when interpreting the model's estimated performance in validation samples. The authors demonstrate the use of the benchmark values using data on traumatic brain injury obtained from the International Tirilazad Trial and the North American Tirilazad Trial (1991-1994).