Abstract

The conventional Cox proportional hazards (PH) model typically assumes fully observed predictors and constant regression coefficients. However, some predictors are latent variables, each of which must be characterized by multiple observed indicators from various perspectives. Moreover, the predictor effects may vary with time in practice. Accommodating such latent variables and identifying temporal covariate effects are frequently of primary interest. This study proposes a generalized structural equation model to investigate the temporal effects of observed and latent risk factors on the hazards of interest. The proposed model comprises a confirmatory factor analysis model as the measurement equation and a varying-coefficient PH model with observed and latent predictors as the structural equation. A hybrid procedure that combines the expectation-maximization (EM) algorithm and the corrected estimating equation approach is developed to estimate unknown parameters and coefficient functions. Simulation studies demonstrate the satisfactory performance of the proposed method. An application to a health survey study reveals insights into risk factors for elders’ life expectancy.

摘要

传统的 Cox 比例风险 (PH) 模型通常假设完全观察到的预测变量和常数回归系数。然而，一些预测变量是潜在变量，每个变量都必须由多个从不同角度观察到的指标来表征。此外，预测效果在实践中可能会随时间变化。容纳此类潜在变量和识别时间协变量效应通常是主要兴趣所在。本研究提出了一个广义结构方程模型来研究观察到的和潜在的风险因素对感兴趣的危害的时间影响。所提出的模型包括作为测量方程的验证性因素分析模型和作为结构方程的具有观察和潜在预测因子的变系数 PH 模型。开发了一种结合期望最大化 (EM) 算法和修正估计方程方法的混合程序来估计未知参数和系数函数。仿真研究证明了所提出方法的令人满意的性能。一项健康调查研究的应用揭示了对影响老年人预期寿命的风险因素的见解。