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A Bayesian Critique of Rank-Based Methods for Surrogate Marker Evaluation

Pietro Carlotti, Layla Parast

Abstract

Surrogate markers are often employed in clinical trials to replace primary outcomes that may be difficult, expensive, or time-consuming to measure directly. These markers can accelerate the evaluation of new treatments, provided they reliably capture the causal relationship between treatment and true clinical benefit. Parast et al. (2024) recently proposed a rank-based approach for evaluating surrogate markers, characterized by its nonparametric nature and minimal assumptions. While this method is useful in small-sample model-agnostic settings, it has several limitations, including a lack of clear causal interpretation, low statistical power, and insufficient robustness to different data-generating mechanisms. In this paper, we propose a Bayesian approach that addresses these shortcomings by focusing on causal treatment effect estimands and, in doing so, improves power through covariate adjustment. We demonstrate the advantages of our proposed method through a simulation study designed to highlight gains in both accuracy and power.

A Bayesian Critique of Rank-Based Methods for Surrogate Marker Evaluation

Abstract

Surrogate markers are often employed in clinical trials to replace primary outcomes that may be difficult, expensive, or time-consuming to measure directly. These markers can accelerate the evaluation of new treatments, provided they reliably capture the causal relationship between treatment and true clinical benefit. Parast et al. (2024) recently proposed a rank-based approach for evaluating surrogate markers, characterized by its nonparametric nature and minimal assumptions. While this method is useful in small-sample model-agnostic settings, it has several limitations, including a lack of clear causal interpretation, low statistical power, and insufficient robustness to different data-generating mechanisms. In this paper, we propose a Bayesian approach that addresses these shortcomings by focusing on causal treatment effect estimands and, in doing so, improves power through covariate adjustment. We demonstrate the advantages of our proposed method through a simulation study designed to highlight gains in both accuracy and power.
Paper Structure (12 sections, 2 theorems, 54 equations, 1 figure, 1 algorithm)

This paper contains 12 sections, 2 theorems, 54 equations, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. Notation
  4. Existing Frequentist Rank-Based Approach
  5. Limitations of the Existing Approach
  6. Comparison between Discrepancy Parameters
  7. Proposed Bayesian Imputation-Based Approach
  8. Parametric Models for the Data Generating Mechanism
  9. Identifiability and Interpretation of the Posterior
  10. Selection Procedure for the Validation Threshold
  11. Simulation Study
  12. Discussion

Key Result

Theorem 1

Let the true data-generating process be defined as where $D_{i}$ is the observed data for unit $i$ and $f_{\phi^{*}}$ is the true distribution of the data, parametrized by $\phi^{*}$. Let the Bayesian model be defined as where $\pi$ is a prior distribution over the parameter $\phi$. Then, if the Bayesian model is regular according to Definition def:regularity, the posterior distribution of $\phi

Figures (1)

  • Figure 1: Heatmap of $|\theta - \delta|$ as a function of $d_S$ and $d_Y$ with $\Delta = 5$.

Theorems & Definitions (3)

  • Definition 1: Regularity of a Bayesian model
  • Theorem 1: Schwartz's theorem
  • Theorem 2