Outcome risk model development for heterogeneity of treatment effect analyses: a comparison of non-parametric machine learning methods and semi-parametric statistical methods
Authors: Xu Edward , Vanghelof Joseph , Wang Yiyang , Patel Anisha , Furst Jacob , Raicu Daniela Stan , Neumann Johannes Tobias , Wolfe Rory , Gao Caroline X. , McNeil John J. , Shah Raj C. , Tchoua Roselyne 
Published: July 2024

Abstract
Background
In randomized clinical trials, treatment effects may vary, and this possibility is referred to as heterogeneity of treatment effect (HTE). One way to quantify HTE is to partition participants into subgroups based on individual’s risk of experiencing an outcome, then measuring treatment effect by subgroup. Given the limited availability of externally validated outcome risk prediction models, internal models (created using the same dataset in which heterogeneity of treatment analyses also will be performed) are commonly developed for subgroup identification. We aim to compare different methods for generating internally developed outcome risk prediction models for subject partitioning in HTE analysis.

Methods
Three approaches were selected for generating subgroups for the 2,441 participants from the United States enrolled in the ASPirin in Reducing Events in the Elderly (ASPREE) randomized controlled trial. An extant proportional hazards-based outcomes predictive risk model developed on the overall ASPREE cohort of 19,114 participants was identified and was used to partition United States’ participants by risk of experiencing a composite outcome of death, dementia, or persistent physical disability. Next, two supervised non-parametric machine learning outcome classifiers, decision trees and random forests, were used to develop multivariable risk prediction models and partition participants into subgroups with varied risks of experiencing the composite outcome. Then, we assessed how the partitioning from the proportional hazard model compared to those generated by the machine learning models in an HTE analysis of the 5-year absolute risk reduction (ARR) and hazard ratio for aspirin vs. placebo in each subgroup. Cochran’s Q test was used to detect if ARR varied significantly by subgroup.

Results
The proportional hazard model was used to generate 5 subgroups using the quintiles of the estimated risk scores; the decision tree model was used to generate 6 subgroups (6 automatically determined tree leaves); and the random forest model was used to generate 5 subgroups using the quintiles of the prediction probability as risk scores. Using the semi-parametric proportional hazards model, the ARR at 5 years was 15.1% (95% CI 4.0–26.3%) for participants with the highest 20% of predicted risk. Using the random forest model, the ARR at 5 years was 13.7% (95% CI 3.1–24.4%) for participants with the highest 20% of predicted risk. The highest outcome risk group in the decision tree model also exhibited a risk reduction, but the confidence interval was wider (5-year ARR = 17.0%, 95% CI= -5.4–39.4%). Cochran’s Q test indicated ARR varied significantly only by subgroups created using the proportional hazards model. The hazard ratio for aspirin vs. placebo therapy did not significantly vary by subgroup in any of the models. The highest risk groups for the proportional hazards model and random forest model contained 230 participants each, while the highest risk group in the decision tree model contained 41 participants.

Conclusions
The choice of technique for internally developed models for outcome risk subgroups influences HTE analyses. The rationale for the use of a particular subgroup determination model in HTE analyses needs to be explicitly defined based on desired levels of explainability (with features importance), uncertainty of prediction, chances of overfitting, and assumptions regarding the underlying data structure. Replication of these analyses using data from other mid-size clinical trials may help to establish guidance for selecting an outcomes risk prediction modelling technique for HTE analyses.