model dose-response

This study addresses bias in dose–response estimation in randomized trials arising from measurement error in drug exposure or unobserved confounding. We propose a robust causal inference method leveraging dose itself as a natural instrumental variable (IV), integrating control-function and ANCOVA-based adjustment. Unlike conventional approaches, our method does not require correct specification of the exposure–outcome model and remains consistent and asymptotically normal even under model misspecification. Theoretical analysis establishes its robustness to unobserved confounding, while simulations demonstrate excellent finite-sample performance. Applied to a CAR-T cell therapy clinical trial, it significantly improves accuracy in identifying the optimal dose. Our key contribution is the first formalization of dose as a built-in IV, enabling a model-agnostic, misspecification-robust framework for causal dose–response estimation—balancing interpretability with statistical rigor.

This study addresses bias in dose–response (DR) estimation arising from unobserved confounding in randomized dose-finding trials. We propose and validate a dose–exposure–response (DER) modeling framework that integrates pharmacokinetic (PK) exposure data. Using a control function approach as an instrumental variable strategy, the method corrects for endogeneity in exposure measurement and unobserved confounding, with theoretical derivation and simulation studies conducted under nonlinear (particularly sigmoidal) exposure–response relationships. Results demonstrate that DER modeling substantially improves estimation efficiency of the DR curve and predictive accuracy of responses at specific dose levels—especially in low- and high-dose regions—compared to conventional DR models ignoring PK data. The performance gain intensifies with greater nonlinearity in the exposure–response relationship. Thus, DER modeling provides a more robust and efficient statistical framework for precision dose optimization.

Current pediatric drug development lacks a holistic, curve-wide perspective for assessing adult–pediatric exposure–response (E–R) curve equivalence, relying instead on discrete-point comparisons. Method: This paper proposes the first Bayesian extrapolation framework for full-curve similarity evaluation, innovatively employing the Maximum Curve Distance (MCD) as an integrated similarity metric. The framework combines Bayesian logistic regression modeling, adaptive threshold selection, sample size optimization, and joint frequentist control of Type I and Type II errors. Results: Simulation studies demonstrate robust error-rate control, enhanced statistical rigor, and improved regulatory acceptability. By transcending conventional pointwise equivalence assessments, this work establishes a verifiable, regulator-friendly paradigm for full-curve E–R equivalence evaluation in pediatric extrapolation.

This paper addresses the causal inference problem of extrapolating long-term dose–response curves under continuous interventions from short-term experimental data—particularly for evaluating long-horizon consequences of continuous actions in AI. We propose a nonparametric estimator based on kernel embeddings and kernel ridge regression, capable of modeling continuous actions/rewards in arbitrary domains, nonlinear responses, and individual heterogeneity. To our knowledge, this is the first method to establish a finite-sample, dimension-dependent uniform convergence bound for such extrapolation. The theoretical analysis integrates weak convergence theory with out-of-distribution extrapolation to ensure statistical reliability of counterfactual distribution estimation. Empirically, we successfully replicate and extend the long-term class-size effect curve using data from the Project STAR randomized education experiment, demonstrating both effectiveness and robustness of the proposed approach.

This paper addresses nonparametric estimation and valid inference for causal dose–response curves under continuous interventions: it seeks to avoid bias from parametric model misspecification while overcoming the slow convergence rates of conventional nonparametric methods caused by pathwise non-differentiability. To this end, we propose the first plug-in estimator that embeds the highly adaptive lasso (HAL) maximum likelihood estimator within a marginal structural framework, augmented with undersmoothing and smoothness-adaptive fitting. The resulting estimator for the marginal dose–response curve is consistent and semiparametrically efficient. It imposes no differentiability or linearity assumptions on the dose–response function and permits robust standard error construction. Simulation studies demonstrate that the proposed method achieves substantially higher estimation accuracy and nominal coverage of confidence intervals compared to existing approaches, with excellent finite-sample performance.

This study addresses the challenge of disentangling sources of inter-laboratory variability—specifically baseline offsets versus differences in sensitivity—in multi-laboratory assessments of linear dose–response relationships. To this end, the authors propose a precision evaluation framework based on linear mixed-effects models, integrating analysis of variance, F-tests, and ISO 5725 standards to define and estimate repeatability and between-laboratory variance components. Overall measurement precision is quantified via average dose-specific variance. Under a fully balanced design, the framework yields an exact decomposition of total sum of squares and closed-form ANOVA estimators, overcoming the limitation of conventional fixed-effects models that detect only the presence of differences without identifying their origin. The approach was successfully applied to bronchoalveolar lavage fluid data from a rat intratracheal instillation study involving nanomaterials, effectively distinguishing the sources of observed variability.

This study addresses the challenges of tuning and evaluation ambiguity in semiparametric and high-dimensional models arising from redundant components introduced by kernel smoothing or basis expansions. The authors propose an induced replication framework that leverages the principle of parametric inference, transforming model assessment into an in-sample prediction error problem by exploiting known replication mechanisms embedded within the model. Building upon Fisher’s concepts of sufficiency and conditional sufficiency, this approach replaces conventional out-of-sample prediction and is applicable to proportional hazards models, time-varying Poisson processes, and confidence set construction for sparse regression. Both theoretical analysis and numerical experiments demonstrate that the method accurately controls nominal error rates under correct model specification and exhibits high sensitivity to semiparametric misspecification.

This study addresses the challenge of estimating effect thresholds—such as ED50—in multivariate settings like time–dose–response relationships, where direct observations are often unavailable for many covariate combinations. The authors propose a parametric framework based on Generalized Additive Models for Location, Scale, and Shape (GAMLSS) to flexibly fit multidimensional response surfaces, enabling estimation and extrapolation of effect thresholds across arbitrary covariate configurations. This work represents the first systematic application of GAMLSS to multidimensional threshold modeling, supporting the construction of two-dimensional confidence bands or three-dimensional confidence planes. By coherently integrating information across dimensions, the approach enhances the reliability of extrapolations. Simulations and analyses of primary human hepatocyte cytotoxicity data demonstrate that the method accurately captures the joint effects of exposure duration and dose on toxicity.

This study addresses causal dose–response function estimation under continuous treatment in the presence of unobserved confounding, assuming only a proxy variable for the latent confounder is observed. It proposes the first proximal doubly robust estimator by constructing a novel proximal doubly robust pseudo-outcome, which, combined with local linear regression, quadratic bias correction, and cross-fitting, yields debiased estimates at the mean squared error–optimal bandwidth—without requiring undersmoothing or entropy conditions on function classes. Theoretically, the estimator achieves pointwise and finite-dimensional asymptotic normality as well as uniform Gaussian approximation. Empirical results demonstrate its strong performance in settings with latent confounding.

Existing methods primarily focus on estimating conditional means or medians, failing to fully characterize the uncertainty of individual dose–response curves under continuous treatments. Method: We propose a personalized causal inference framework for continuous exposures, framing causal effect estimation as a covariate shift problem. Our approach innovatively integrates weighted conformal prediction with quantile regression to construct statistically valid, individualized prediction bands—without requiring strong modeling assumptions. Contribution/Results: The method robustly handles covariate shift and provides rigorous uncertainty quantification for individual-level dose–response curves. Through simulations and real-world analysis of smoking behavior and healthcare expenditures, we successfully estimate the additional medical costs attributable to sustained smoking per individual, along with valid confidence intervals. This work bridges a critical theoretical and methodological gap in uncertainty quantification for personalized causal inference under continuous treatments.