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

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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 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 and N min (derived from sample size formula) were considered. The 2.5 – 97.5 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 10 000, the median 2.5 – 97.5 percentile range of risks for patients across the 1000 models was approximately 60% of their population derived risk. For example, for patients with a population derived risk of 9 - 10% or 19 - 20%, the median percentile range was 6.25% and 12.59% respectively. Using the formula derived sample size, the range was approximately 170% of their average risk score. Restricting this analysis to models with high discrimination or good calibration 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. Stability of risk estimates should be a criterion when determining the minimum sample size to develop models.

Bibliographical metadata

Original languageEnglish
JournalDiagnostic and Prognostic Research
Early online date9 Sep 2020
Publication statusE-pub ahead of print - 9 Sep 2020