Predictive performance of machine and statistical learning methods: Impact of data-generating processes on external validity in the "large N, small p" setting

Abstract

Machine learning approaches are increasingly suggested as tools to improve prediction of clinical outcomes. We aimed to identify when machine learning methods perform better than a classical learning method. We hereto examined the impact of the data-generating process on the relative predictive accuracy of six machine and statistical learning methods: bagged classification trees, stochastic gradient boosting machines using trees as the base learners, random forests, the lasso, ridge regression, and unpenalized logistic regression. We performed simulations in two large cardiovascular datasets which each comprised an independent derivation and validation sample collected from temporally distinct periods: patients hospitalized with acute myocardial infarction (AMI, n = 9484 vs. n = 7000) and patients hospitalized with congestive heart failure (CHF, n = 8240 vs. n = 7608). We used six data-generating processes based on each of the six learning methods to simulate outcomes in the derivation and validation samples based on 33 and 28 predictors in the AMI and CHF data sets, respectively. We applied six prediction methods in each of the simulated derivation samples and evaluated performance in the simulated validation samples according to c-statistic, generalized R2, Brier score, and calibration. While no method had uniformly superior performance across all six data-generating process and eight performance metrics, (un)penalized logistic regression and boosted trees tended to have superior performance to the other methods across a range of data-generating processes and performance metrics. This study confirms that classical statistical learning methods perform well in low-dimensional settings with large data sets.

Keywords: Machine learning; Monte Carlo simulations; data-generating process; generalized boosting methods; logistic regression; random forests.

Conflict of interest statement

Declaration of conflicting interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figures

Figure 1.

AMI sample: model performance assessed using c-statistic, R-squared, Brier score, and negative log-likelihood. (There are eight panels across each pair of figures, one panel for each of the eight metrics of model performance. Each panel consists of six sets of six box plots. Each box plot describes the variation in the given performance metric across the 1,000 simulation replicates when a particular data-generating process and analytic method were used.)

Figure 2.

AMI sample: model performance assessed using ICI, E90, calibration intercept, and calibration slope.

Figure 3.

CHF sample: model performance assessed using c-statistic, R-squared, Brier score, and negative log-likelihood.

Figure 4.

CHF sample: model performance assessed using ICI, E90, calibration intercept, and calibration slope.