Hazard models with varying coefficients for multivariate failure time data

TL;DR

This paper introduces new estimation methods for multivariate failure time data using varying coefficient hazard models, improving efficiency and reducing computational costs with proven statistical properties and practical application.

Contribution

It proposes a local pseudo-partial likelihood approach, a weighted average estimator, and a one-step estimator, enhancing estimation efficiency and computational simplicity in survival analysis.

Findings

The one-step estimator reduces computational cost significantly.

The weighted average estimator outperforms the maximum local pseudo-partial likelihood estimator in efficiency.

Simulation studies confirm the theoretical properties and practical advantages of the proposed methods.

Abstract

Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudo-partial likelihood procedure is proposed for estimating the unknown coefficient functions. A weighted average estimator is also proposed in an attempt to improve the efficiency of the estimator. The consistency and asymptotic normality of the proposed estimators are established and standard error formulas for the estimated coefficients are derived and empirically tested. To reduce the computational burden of the maximum local pseudo-partial likelihood estimator, a simple and useful one-step estimator is proposed. Statistical properties of the one-step estimator are established and simulation studies are conducted to compare the performance of the one-step estimator to that of the maximum local pseudo-partial likelihood estimator. The results show that the one-step estimator can save computational cost without compromising performance both asymptotically and empirically and that an optimal weighted average estimator is more efficient than the maximum local pseudo-partial likelihood estimator. A data set from the Busselton Population Health Surveys is analyzed to illustrate our proposed methodology.