[Paper Review] A Latent Gaussian Process Model with Application to Monitoring Clinical Trials

Yanxun Xu, Yuan Ji|arXiv (Cornell University)|Mar 31, 2014

Gaussian Processes and Bayesian Inference33 references3 citations

TL;DR

This paper proposes a Bayesian latent Gaussian process (LGP) model to monitor clinical trials with repeated, cyclic binary outcomes—such as disease relapse and remission—by modeling the underlying continuous disease progression. The method enables early trial termination for futility, forecasts individual patient responses, and compares treatment effects using hybrid Monte Carlo inference and posterior consistency guarantees.

ABSTRACT

In many clinical trials treatments need to be repeatedly applied as diseases relapse frequently after remission over a long period of time (e.g., 35 weeks). Most research in statistics focuses on the overall trial design, such as sample size and power calculation, or on the data analysis after trials are completed. Little is done to improve the efficiency of trial monitoring, such as early termination of trials due to futility. The challenge faced in such trial monitoring is mostly caused by the need to properly model repeated outcomes from patients. We propose a Bayesian trial monitoring scheme for clinical trials with repeated and potentially cyclic binary outcomes. We construct a latent Gaussian process (LGP) to model discrete longitudinal data in those trials. LGP describes the underlying latent process that gives rise to the observed longitudinal binary outcomes. The posterior consistency property of the proposed model is studied. Posterior inference is conducted with a hybrid Monte Carlo algorithm. Simulation studies are conducted under various clinical scenarios, and a case study is reported based on a real-life trial.

Motivation & Objective

• Address the lack of adaptive monitoring methods for clinical trials with repeated, cyclic binary outcomes such as disease relapse and remission.
• Model the underlying continuous disease progression process that gives rise to discrete, binary longitudinal observations.
• Develop a Bayesian framework for interim monitoring that allows early termination due to futility or lack of efficacy.
• Enable individualized prediction of future patient responses based on observed cyclic patterns.
• Compare treatment effects by modeling both population-level trends and subject-specific cyclic dynamics.

Proposed method

• Model the observed binary outcomes as realizations of a latent continuous Gaussian process, with the binary response determined by a threshold on the latent variable.
• Decompose the latent process into a population-level treatment effect $\mu(t)$ and a subject-specific cyclic component $\tau_j(t)$, modeled as a Gaussian process.
• Use a hierarchical Bayesian model with non-informative priors on hyperparameters to allow flexible, data-driven inference.
• Implement posterior inference using a hybrid Monte Carlo (HMC) algorithm to efficiently explore the high-dimensional parameter space.
• Incorporate posterior consistency theory to ensure the model converges to the true underlying process as sample size increases.
• Construct a test statistic based on the discrepancy between observed and predicted outcomes to evaluate model fit and support futility monitoring.

Experimental results

Research questions

• RQ1 Can a latent Gaussian process model effectively capture the cyclic and repeated nature of binary outcomes in long-term clinical trials?
• RQ2 How can posterior consistency be established for a latent Gaussian process model applied to discrete longitudinal binary data?
• RQ3 To what extent can the model forecast future patient responses based on early-stage observations?
• RQ4 Can the model support an adaptive monitoring scheme that allows early termination due to futility?
• RQ5 How do the treatment effect and subject-specific cyclic patterns compare across different treatment arms?

Key findings

• The proposed latent Gaussian process model demonstrates posterior consistency, ensuring that the estimated latent process converges to the true underlying process as the number of observations increases.
• Simulation studies show the model accurately captures cyclic patterns in binary outcomes and provides reliable individualized forecasts of future responses.
• The model enables effective futility monitoring by detecting lack of treatment benefit earlier than traditional methods, reducing unnecessary trial duration.
• The hybrid Monte Carlo algorithm ensures efficient posterior sampling and stable convergence in high-dimensional parameter spaces.
• The case study based on a real clinical trial confirms the model's practical utility in monitoring treatment response over extended follow-up periods.
• The model outperforms standard logistic regression and linear state-space models in capturing nonlinear and cyclic disease progression patterns.