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Evaluating Predictive Modeling Strategies for Predicting Individual Treatment Effects in Precision Medicine

Pamela M. Chiroque-Solano, M Lee Van Horn, Thomas Jaki

TL;DR

The study addresses reliable estimation of Predicted Individual Treatment Effects (PITEs) in precision medicine, where counterfactuals are unobserved. It compares 30+ modeling strategies across a structured simulation varying $n$, $p$, $\rho$, and $\mu_{\beta_\Delta}$, evaluating with RMSE and Direction (DIR) and formal PITE decompositions. The results show that regularized linear and projection-based approaches (e.g., ridge, lasso, elastic net, PLS, PCR) provide robust PITE estimates across diverse conditions, while flexible learners require favorable data characteristics; external validation is essential to reveal weaknesses. The findings yield practical do/avoid guidance for method selection and highlight the need to balance predictive accuracy, calibration, and robustness to support actionable, patient-level treatment decisions in precision medicine.

Abstract

Precision medicine seeks to match patients with treatments that produce the greatest benefit. The Predicted Individual Treatment Effect (PITE)-the difference between predicted outcomes under treatment and control-quantifies this benefit but is difficult to estimate due to unobserved counterfactuals, high dimensionality, and complex interactions. We compared 30+ modeling strategies, including penalized and projection-based methods, flexible learners, and tree-ensembles, using a structured simulation framework varying sample size, dimensionality, multicollinearity, and interaction complexity. Performance was measured using root mean squared error (RMSE) for prediction accuracy and directional accuracy (DIR) for correctly classifying benefit versus harm. Internal validation produced optimistic estimates, whereas external validation with distributional shifts and higher-order interactions more clearly revealed model weaknesses. Penalized and projection-based approaches-ridge, lasso, elastic net, partial least squares (PLS), and principal components regression (PCR)-consistently achieved strong RMSE and DIR performance. Flexible learners excelled only under strong signals and sufficient sample sizes. Results highlight robust linear/projection defaults and the necessity of rigorous external validation.

Evaluating Predictive Modeling Strategies for Predicting Individual Treatment Effects in Precision Medicine

TL;DR

The study addresses reliable estimation of Predicted Individual Treatment Effects (PITEs) in precision medicine, where counterfactuals are unobserved. It compares 30+ modeling strategies across a structured simulation varying , , , and , evaluating with RMSE and Direction (DIR) and formal PITE decompositions. The results show that regularized linear and projection-based approaches (e.g., ridge, lasso, elastic net, PLS, PCR) provide robust PITE estimates across diverse conditions, while flexible learners require favorable data characteristics; external validation is essential to reveal weaknesses. The findings yield practical do/avoid guidance for method selection and highlight the need to balance predictive accuracy, calibration, and robustness to support actionable, patient-level treatment decisions in precision medicine.

Abstract

Precision medicine seeks to match patients with treatments that produce the greatest benefit. The Predicted Individual Treatment Effect (PITE)-the difference between predicted outcomes under treatment and control-quantifies this benefit but is difficult to estimate due to unobserved counterfactuals, high dimensionality, and complex interactions. We compared 30+ modeling strategies, including penalized and projection-based methods, flexible learners, and tree-ensembles, using a structured simulation framework varying sample size, dimensionality, multicollinearity, and interaction complexity. Performance was measured using root mean squared error (RMSE) for prediction accuracy and directional accuracy (DIR) for correctly classifying benefit versus harm. Internal validation produced optimistic estimates, whereas external validation with distributional shifts and higher-order interactions more clearly revealed model weaknesses. Penalized and projection-based approaches-ridge, lasso, elastic net, partial least squares (PLS), and principal components regression (PCR)-consistently achieved strong RMSE and DIR performance. Flexible learners excelled only under strong signals and sufficient sample sizes. Results highlight robust linear/projection defaults and the necessity of rigorous external validation.
Paper Structure (33 sections, 1 theorem, 48 equations, 8 figures, 8 tables, 1 algorithm)

This paper contains 33 sections, 1 theorem, 48 equations, 8 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Evaluated Approaches
  4. Diagnostic Predictive Performance
  5. Simulation Study
  6. Simulation Design
  7. Internal Validation
  8. Successful Model Performance Across Simulated Scenarios with Internal Validation
  9. External Validation
  10. Correlated Covariates
  11. Best-Performing Models Across External Validation Scenarios
  12. Interactions between covariates
  13. Worst-Case Model Performance with Covariate Interactions
  14. Best-Case Predictive Performance with Covariate Interactions
  15. Illustrative Example: Model-Specific Performance Across Individual Cases Complexity
  16. ...and 18 more sections

Key Result

Proposition 1

Assume that $\hat{f}_t(\cdot)$ and $\hat{f}_c(\cdot)$ are predictors for which an expected value and variance can be well defined. Then the PITE Mean Squared Error ($\operatorname{MSE}_{\mathrm{PITE}}$) can be decomposed as where $\operatorname{MSE}_{\operatorname{t}} = \mathrm{Var}[\hat{f}_t(X)] + \mathrm{bias}_t^2$ and $\operatorname{MSE}_{\operatorname{c}} = \mathrm{Var}[\hat{f}_c(X)] + \mathr

Figures (8)

  • Figure 1: Internal validation: Relationship between predictive performance Root Mean Squared Error (RMSE) and Directional Accuracy (DIR) across models and Treatment Effect impact and correlation value between covariates. Each point represents a specific model-parameter configuration, labeled by model name, sample size (n), and number of predictors (p). Darkness gray areas reflect undesirable regions
  • Figure 2: Internal Validation: Models Achieving High PITE Accuracy ($\operatorname{RMSE} < 1$ and $\operatorname{DIR} > 0.95$) Across External Validation Scenarios with Covariate Interactions
  • Figure 3: External validation (Correlated covariates): Relationship between predictive performance Root Mean Squared Error (RMSE) and Directional Accuracy (DIR) across models and treatment effect impact and correlation value between covariates. Each point represents a specific model-parameter configuration, labeled by model name, sample size (n), and number of predictors (p). Darkness gray areas reflect undesirable regions
  • Figure 4: External validation (Correlated covariates): Models with lowest $\operatorname{RMSE}<2$ and High $\operatorname{DIR}>0.95$. Across Simulation Conditions [A--I] and dimension $p=45$.
  • Figure 5: External validation (Interaction between covariates): Relationship between predictive performance Root Mean Squared Error (RMSE) and Directional Accuracy (DIR) across models and treatment effect impact and correlation value between covariates. Each point represents a specific model-parameter configuration, labeled by model name, sample size (n), and number of interactions. Darkness gray areas reflect undesirable regions
  • ...and 3 more figures

Theorems & Definitions (5)

  • Proposition 1
  • proof
  • proof
  • proof
  • proof