[Paper Review] A marginalizable frailty model for correlated right-censored data

Rui Zhang Kwun Chuen Gary Chan|arXiv (Cornell University)|Mar 26, 2014

Statistical Methods and Inference3 citations

TL;DR

This paper proposes a marginalizable frailty model for correlated right-censored data that enables direct interpretation of covariate effects as log failure odds ratios. By using multivariate Gaussian random variables to construct multivariate exponential frailties, the model allows flexible correlation structures and consistent estimation via a hybrid expectation-maximization algorithm, with asymptotically valid inference and application to real data demonstrated in simulations and the Rats study.

ABSTRACT

We introduce a flexible individual frailty model for clustered right-censored data, in which covariate effects can be marginally interpreted as log failure odds ratios. Flexible correlation structures can be imposed by introducing multivariate exponential distributed frailties, constructed from a set of multivariate Gaussian random variables. Finite and infinite dimensional parameters are consistently estimated by maximizing a composite contributing marginal likelihood and a consistent estimate for their asymptotic covariance is proposed. Parameter estimation is implemented through a hybrid expectation-maximum algorithm. Simulations and an analysis of the Rats study were carried out to demonstrate our method.

Motivation & Objective

• To develop a frailty model that allows marginally interpretable covariate effects as log failure odds ratios in clustered survival data.
• To enable flexible modeling of diverse correlation structures in multivariate survival data beyond exchangeable correlations.
• To provide consistent estimation of both finite- and infinite-dimensional parameters using a composite marginal likelihood approach.
• To develop a hybrid EM algorithm for efficient parameter estimation in the presence of high-dimensional frailties.
• To ensure asymptotic theory holds, including consistency and asymptotic normality, under regularity conditions.

Proposed method

• Constructs multivariate exponential frailties from multivariate Gaussian random variables to allow flexible dependence structures in clustered survival data.
• Uses a complementary log-log link to connect the baseline log failure odds to covariates and frailties, enabling marginal interpretation of regression coefficients.
• Employs a composite marginal likelihood approach to estimate finite-dimensional parameters (e.g., regression coefficients) and infinite-dimensional parameters (e.g., baseline cumulative hazard).
• Proposes a hybrid expectation-maximization algorithm that alternates between estimating frailties and updating model parameters, with closed-form updates in the E-step.
• Derives a consistent estimator for the asymptotic covariance matrix of the parameter estimates to support inference.
• Implements non-parametric maximum likelihood estimation for the baseline cumulative hazard function, treating it as a step function with increasing jumps.

Experimental results

Research questions

• RQ1 Can a frailty model be constructed such that covariate effects are marginally interpretable as log failure odds ratios?
• RQ2 How can flexible correlation structures be modeled in multivariate right-censored data beyond shared frailty assumptions?
• RQ3 What estimation strategy ensures consistency and asymptotic normality when both finite- and infinite-dimensional parameters are present?
• RQ4 Can a hybrid EM algorithm efficiently handle high-dimensional frailties without requiring full likelihood computation?
• RQ5 How does the proposed model perform in finite samples compared to existing methods in terms of bias, efficiency, and coverage?

Key findings

• The proposed model successfully enables marginally interpretable covariate effects as log failure odds ratios, facilitating public health interpretation.
• The use of multivariate Gaussian-based frailties allows for flexible, non-exchangeable correlation structures, improving model fit over standard shared frailty models.
• The hybrid EM algorithm achieves consistent estimation of both regression coefficients and baseline cumulative hazard, with computational efficiency due to closed-form E-step updates.
• The method provides a consistent estimator for the asymptotic covariance matrix, supporting valid inference and hypothesis testing.
• Simulations and the Rats study demonstrate good finite-sample performance, with accurate coverage and low bias in parameter estimates.
• The model maintains the full likelihood framework, ensuring existence of parameters of interest even under model misspecification, unlike some semi-parametric alternatives.