A practical framework for exploring non-linear dose–response using adherence data in complex interventions
Abstract
Background: Randomised trials of complex interventions commonly estimate the effect of being offered treatment using intention-to-treat (ITT) analyses. However, in many settings, particularly psychological therapies, participants adhere to varying amounts of treatment. Estimating causal effects of treatment dose is challenging because dose received is a post-randomisation variable that may be confounded by patient’s characteristics associated with both adherence and outcomes. Existing approaches rely on parametric assumptions, such as linear dose–response relationships, which may be unrealistic. We propose a practical framework for exploring non-linear dose–response relationships using non-adherence.
Methods: We introduce the Dose-Specific Average Treatment Effect (DS-ATE), a principal causal estimand defined within strata of potential treatment dose. To estimate this, we propose the Dose Outcome with Stratified Estimation and Random Forest (DOSE-RF) framework. In stage one, a random forest model predicts potential dose under treatment using baseline covariates. In stage two, participants are grouped into predicted dose strata and the effect of randomisation on outcomes is estimated within each stratum, producing dose-specific effects that can be visualised as a dose–response curve. Performance was evaluated using Monte Carlo simulations across varying dose distributions, predictor strengths and levels of unmeasured confounding. The framework was demonstrated using data from the SoCRATES trial of cognitive behavioural therapy for early psychosis.
Results: DOSE-RF recovered the underlying dose–response shape without requiring pre-specification of its functional form. Performance was strongest when dose strata were sufficiently populated, with low bias and nominal coverage. The method showed relatively stable identification of non-linear patterns, including threshold and quadratic relationships, under moderate prediction error in dose classification.
Conclusions: DOSE-RF provides a practical framework for exploring dose–response relationships in trials with variable adherence. It enables flexible, non-parametric visualisation of treatment effects and is intended to complement ITT analyses and support hypothesis generation.
Related
- Computational Taxonomy for visualizing and exploring systems with functional response dynamics: soybean's O2-respiration example
- Phase oscillator networks with multiple and state-dependent delays: A framework for exploring white matter plasticity in neurodynamics
- A Liouville dynamical modelling and control framework for oesophageal cancer-induced immune response
- An efficient estimation framework for sensitive data under randomized response with real-world applications
- MIMO and Multi-Group Comparison Problem in Process Control: A Multivariate Statistical Framework for Systems Represented with Frequency Response Functions
BibTeX
@article{payne2026practical,
title = {{A practical framework for exploring non-linear dose–response using adherence data in complex interventions}},
author = {Mollie Payne and Amy Hardy and Ben Carter and Richard Emsley},
journal = {Trials},
year = {2026},
month = oct,
doi = {10.1186/s13063-026-10043-8},
url = {https://link.springer.com/article/10.1186/s13063-026-10043-8},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A practical framework for exploring non-linear dose–response using adherence data in complex interventions
AU - Mollie Payne
AU - Amy Hardy
AU - Ben Carter
AU - Richard Emsley
PY - 2026
DA - 2026/10/16
JO - Trials
DO - 10.1186/s13063-026-10043-8
UR - https://link.springer.com/article/10.1186/s13063-026-10043-8
AB - Background: Randomised trials of complex interventions commonly estimate the effect of being offered treatment using intention-to-treat (ITT) analyses. However, in many settings, particularly psychological therapies, participants adhere to varying amounts of treatment. Estimating causal effects of treatment dose is challenging because dose received is a post-randomisation variable that may be confounded by patient’s characteristics associated with both adherence and outcomes. Existing approaches rely on parametric assumptions, such as linear dose–response relationships, which may be unrealistic. We propose a practical framework for exploring non-linear dose–response relationships using non-adherence. Methods: We introduce the Dose-Specific Average Treatment Effect (DS-ATE), a principal causal estimand defined within strata of potential treatment dose. To estimate this, we propose the Dose Outcome with Stratified Estimation and Random Forest (DOSE-RF) framework. In stage one, a random forest model predicts potential dose under treatment using baseline covariates. In stage two, participants are grouped into predicted dose strata and the effect of randomisation on outcomes is estimated within each stratum, producing dose-specific effects that can be visualised as a dose–response curve. Performance was evaluated using Monte Carlo simulations across varying dose distributions, predictor strengths and levels of unmeasured confounding. The framework was demonstrated using data from the SoCRATES trial of cognitive behavioural therapy for early psychosis. Results: DOSE-RF recovered the underlying dose–response shape without requiring pre-specification of its functional form. Performance was strongest when dose strata were sufficiently populated, with low bias and nominal coverage. The method showed relatively stable identification of non-linear patterns, including threshold and quadratic relationships, under moderate prediction error in dose classification. Conclusions: DOSE-RF provides a practical framework for exploring dose–response relationships in trials with variable adherence. It enables flexible, non-parametric visualisation of treatment effects and is intended to complement ITT analyses and support hypothesis generation.
SN - 1745-6215
ER -