Expected Value of Sample Information Calculations for Risk Prediction Model Validation.

Abstract

Background: The purpose of external validation of a risk prediction model is to evaluate its performance before recommending it for use in a new population. Sample size calculations for such validation studies are currently based on classical inferential statistics around metrics of discrimination, calibration, and net benefit (NB). For NB as a measure of clinical utility, the relevance of inferential statistics is doubtful. Value-of-information methodology enables quantifying the value of collecting validation data in terms of expected gain in clinical utility.

Methods: We define the validation expected value of sample information (EVSI) as the expected gain in NB by procuring a validation sample of a given size. We propose 3 algorithms for EVSI computation and compare their face validity and computation time in simulation studies. In a case study, we use the non-US subset of a clinical trial to create a risk prediction model for short-term mortality after myocardial infarction and calculate validation EVSI at a range of sample sizes for the US population.

Results: Computation methods generated similar EVSI values in simulation studies, although they differed in numerical accuracy and computation times. At 2% risk threshold, procuring 1,000 observations for external validation, had an EVSI of 0.00101 in true-positive units or 0.04938 in false-positive units. Scaled by heart attack incidence in the United States, the population EVSI was 806 in true positives gained, or 39,500 in false positives averted, annually. Validation studies with >4,000 observations had diminishing returns, as the EVSIs were approaching their maximum possible value.

Conclusion: Value-of-information methodology quantifies the return on investment from conducting an external validation study and can provide a value-based perspective when designing such studies.

Highlights: In external validation studies of risk prediction models, the finite size of the validation sample leads to uncertain conclusions about the performance of the model. This uncertainty has hitherto been approached from a classical inferential perspective (e.g., confidence interval around the c-statistic).Correspondingly, sample size calculations for validation studies have been based on classical inferential statistics. For measures of clinical utility such as net benefit, the relevance of this approach is doubtful.This article defines the expected value of sample information (EVSI) for model validation and suggests algorithms for its computation. Validation EVSI quantifies the return on investment from conducting a validation study.Value-based approaches rooted in decision theory can complement contemporary study design and sample size calculation methods in predictive analytics.