Using machine learning to model dose-response relationships

Establishing the relationship between various doses of an exposure and a response variable is integral to many studies in health care. Linear parametric models, widely used for estimating dose-response relationships, have several limitations. This paper employs the optimal discriminant analysis (ODA) machine-learning algorithm to determine the degree to which exposure dose can be distinguished based on the distribution of the response variable. By framing the dose-response relationship as a classification problem, machine learning can provide the same functionality as conventional models, but can additionally make individual-level predictions, which may be helpful in practical applications like establishing responsiveness to prescribed drug regimens.

Using data from a study measuring the responses of blood flow in the forearm to the intra-arterial administration of isoproterenol (separately for 9 black and 13 white men, and pooled), we compare the results estimated from a generalized estimating equations (GEE) model with those estimated using ODA.

Generalized estimating equations and ODA both identified many statistically significant dose-response relationships, separately by race and for pooled data. Post hoc comparisons between doses indicated ODA (based on exact P values) was consistently more conservative than GEE (based on estimated P values). Compared with ODA, GEE produced twice as many instances of paradoxical confounding (findings from analysis of pooled data that are inconsistent with findings from analyses stratified by race).

Given its unique advantages and greater analytic flexibility, maximum-accuracy machine-learning methods like ODA should be considered as the primary analytic approach in dose-response applications.