Regression and boosting methods to inform precisionized treatment rules using data from crossover studies

The usual convention for assigning a treatment to an individual is a "one-size fits all" rule that is based on broad spectrum trends. Heterogeneity within and between subjects and improvements in scientific research convey the need for more effective treatment assignment strategies. Precisionized treatment (PT) offers an alternative to the traditional treatment assignment approach by making treatment decisions based on one or more covariates pertaining to an individual.

We investigate two methods to inform PT rules: the Maximum Likelihood Estimation (MLE) method and the Boosting method. We apply these methods in the context of a crossover study design with a continuous outcome variable, one continuous covariate, and two intervention options. We explore the methods via extensive simulation studies and apply them to a data set from a study of safety warnings in passenger vehicles. We evaluate the performance of the estimated PT rules based on the improvement in mean response (RMD), the percent of correct treatment assignments (PCC), and the accuracy of estimating the location of the crossing point (MSE((x_c )). We also define a new metric that we call the percent of anomalies (PA). We characterize the potential benefit of using PT by relating it to the strength of interaction, the location of the crossing point, and the within-person intraclass correlation (ICC). We also explore the effects of sample size and overall variance along with the methods’ robustness to violations of model assumptions. We investigate the performance of the Boosting method under the standard weight and two alternative weighting schemes.

Our investigation indicated the largest potential benefit of implementing a PT approach was when the crossover point was near the median, the strength of interaction was large, and the ICC was high. When a PT rule is used to assign treatments instead of a one-size fits all rule, an approximate 10-30% improvement in mean outcome can be gained. The MLE and Boosting method performed comparably across most of the simulation scenarios, yet in our data example, it appeared there may be an empirical benefit of the Boosting method over the MLE method. Under a distribution misspecification, the difference in performance between the methods was minor; however, when the functional form of the model was misspecified, we began to see improvement of the Boosting method over the MLE method. In the simulation conditions we considered, the weighting scheme used in the Boosting method did not markedly impact performance.

Using data to develop PT rules can lead to an improvement in outcome over the standard approach of assigning treatments. We found that in a variety of scenarios, there was little added benefit to utilizing the more complex iterative Boosting procedure compared to the relatively straightforward MLE method when developing the PT rules. The results from our investigations could be used to optimize treatment recommendations for participants in future studies.