Logistic regression models for patient-level prediction based on massive observational data: Do we need all data?

Abstract

Objective: Provide guidance on sample size considerations for developing predictive models by empirically establishing the adequate sample size, which balances the competing objectives of improving model performance and reducing model complexity as well as computational requirements.

Materials and methods: We empirically assess the effect of sample size on prediction performance and model complexity by generating learning curves for 81 prediction problems (23 outcomes predicted in a depression cohort, 58 outcomes predicted in a hypertension cohort) in three large observational health databases, requiring training of 17,248 prediction models. The adequate sample size was defined as the sample size for which the performance of a model equalled the maximum model performance minus a small threshold value.

Results: The adequate sample size achieves a median reduction of the number of observations of 9.5%, 37.3%, 58.5%, and 78.5% for the thresholds of 0.001, 0.005, 0.01, and 0.02, respectively. The median reduction of the number of predictors in the models was 8.6%, 32.2%, 48.2%, and 68.3% for the thresholds of 0.001, 0.005, 0.01, and 0.02, respectively.

Discussion: Based on our results a conservative, yet significant, reduction in sample size and model complexity can be estimated for future prediction work. Though, if a researcher is willing to generate a learning curve a much larger reduction of the model complexity may be possible as suggested by a large outcome-dependent variability.

Conclusion: Our results suggest that in most cases only a fraction of the available data was sufficient to produce a model close to the performance of one developed on the full data set, but with a substantially reduced model complexity.

Keywords: Learning curve; Logistic regression; Model complexity; Observational data; Prediction model; Sample size.