Impact of sample size on the stability of risk scores from clinical prediction models: a case study in cardiovascular disease

Abstract

Stability of risk estimates from prediction models may be highly dependent on the sample size of the dataset available for model derivation. In this paper, we evaluate the stability of cardiovascular disease risk scores for individual patients when using different sample sizes for model derivation; such sample sizes include those similar to models recommended in the national guidelines, and those based on recently published sample size formula for prediction models. We mimicked the process of sampling N patients from a population to develop a risk prediction model by sampling patients from the Clinical Practice Research Datalink. A cardiovascular disease risk prediction model was developed on this sample and used to generate risk scores for an independent cohort of patients. This process was repeated 1000 times, giving a distribution of risks for each patient. N = 100,000, 50,000, 10,000, Nmin (derived from sample size formula) and Nepv10 (meets 10 events per predictor rule) were considered. The 5–95th percentile range of risks across these models was used to evaluate instability. Patients were grouped by a risk derived from a model developed on the entire population (population-derived risk) to summarise results. For a sample size of 100,000, the median 5–95th percentile range of risks for patients across the 1000 models was 0.77%, 1.60%, 2.42% and 3.22% for patients with population-derived risks of 4–5%, 9–10%, 14–15% and 19–20% respectively; for N = 10,000, it was 2.49%, 5.23%, 7.92% and 10.59%, and for N using the formula-derived sample size, it was 6.79%, 14.41%, 21.89% and 29.21%. Restricting this analysis to models with high discrimination, good calibration or small mean absolute prediction error reduced the percentile range, but high levels of instability remained. Widely used cardiovascular disease risk prediction models suffer from high levels of instability induced by sampling variation. Many models will also suffer from overfitting (a closely linked concept), but at acceptable levels of overfitting, there may still be high levels of instability in individual risk. Stability of risk estimates should be a criterion when determining the minimum sample size to develop models.