Estimating heterogeneous treatment effects from randomised trials: a comparison of the risk modelling and treatment effect modelling approaches
Abstract
Introduction Risk modelling (RM) and treatment effect modelling (EM) are two approaches to build models to estimate heterogeneous treatment effects from randomized control trials (RCT). RM is a two-stage approach; it estimates a predicted baseline risk at the first stage and then includes it as the only effect modifier in a regression model in the second stage. EM is a full treatment interaction multivariable model. Both approaches have theoretical advantages and limitations, but a thorough comparison including a simulation study is missing. Methods In a theoretical review of the two approaches, we present their underlying assumptions and theoretical advantages and disadvantages. Based on our theoretical review, we design simulation scenarios for RCTs with a dichotomous outcome and evaluate the performance of both approaches with respect to the root mean square error and the bias in the predicted risk difference. Results In the theoretical part we argue that baseline risk is a treatment effect modifier in many clinical situations. RM is a dimensionality reduction approach which, however, makes strong assumptions about the role of prognostic factors modifying the treatment effect. EM's greater flexibility is a possible advantage when the sample size is large. In most simulated scenarios RM performs better than EM, even when the assumptions underlying RM are not fully met. The advantage of RM diminishes as sample size increases. Conclusion When choosing between RM and EM the available sample size and the plausibility of their underlying assumptions should be considered.
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BibTeX
@misc{philipona2026estimating,
title = {{Estimating heterogeneous treatment effects from randomised trials: a comparison of the risk modelling and treatment effect modelling approaches}},
author = {Frederik Luca Philipona and Marta Mainetti and Orestis Efthimiou and Georgia Salanti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21526},
eprint = {2609.21526},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21526},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Estimating heterogeneous treatment effects from randomised trials: a comparison of the risk modelling and treatment effect modelling approaches
AU - Frederik Luca Philipona
AU - Marta Mainetti
AU - Orestis Efthimiou
AU - Georgia Salanti
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21526
UR - https://arxiv.org/abs/2609.21526
AB - Introduction Risk modelling (RM) and treatment effect modelling (EM) are two approaches to build models to estimate heterogeneous treatment effects from randomized control trials (RCT). RM is a two-stage approach; it estimates a predicted baseline risk at the first stage and then includes it as the only effect modifier in a regression model in the second stage. EM is a full treatment interaction multivariable model. Both approaches have theoretical advantages and limitations, but a thorough comparison including a simulation study is missing. Methods In a theoretical review of the two approaches, we present their underlying assumptions and theoretical advantages and disadvantages. Based on our theoretical review, we design simulation scenarios for RCTs with a dichotomous outcome and evaluate the performance of both approaches with respect to the root mean square error and the bias in the predicted risk difference. Results In the theoretical part we argue that baseline risk is a treatment effect modifier in many clinical situations. RM is a dimensionality reduction approach which, however, makes strong assumptions about the role of prognostic factors modifying the treatment effect. EM's greater flexibility is a possible advantage when the sample size is large. In most simulated scenarios RM performs better than EM, even when the assumptions underlying RM are not fully met. The advantage of RM diminishes as sample size increases. Conclusion When choosing between RM and EM the available sample size and the plausibility of their underlying assumptions should be considered.
ER -