Time-varying coefficient additive hazards model with latent variables

Abstract

This study considers a time-varying coefficient additive hazards model with latent variables to examine potential observed and latent risk factors for survival of interest. The model consists of two parts: confirmatory factor analysis to measure each latent factor through multiple observable variables and a varying coefficient additive hazards model to examine the time-varying effects of the observed and latent risk factors on the hazard function. A hybrid estimation procedure that combines the expectation-maximum algorithm and corrected estimating equation method is developed to estimate the unknown parameters and nonparametric cumulative hazard functions. The consistency and asymptotic normality of the proposed estimators are established, and the pointwise confidence intervals and general confidence bands of the nonparametric functions are constructed accordingly. A satisfactory performance of the proposed method is demonstrated through simulation studies. An application to a study of chronic kidney disease for Chinese type 2 diabetes patients is presented.

Additive hazards model with time-varying coefficients and imaging predictors

“…However, incorporating the above procedure into the proposed model framework may be computationally demanding, and its feasibility requires further investigation. Third, we can consider other survival models such as time-varying proportional hazards, 21,[40][41][42] mean residual life, 43,44 and accelerated failure time models. 45,46 The inclusion of imaging predictors in various models can provide deep insight into the associations between images and survival outcomes of interest.…”

“…As suggested by the existing literature, 33,2,21,4 the kernel smoothing method can be adopted to estimate the effects of covariates, α(t). The corresponding estimator, denoted as αKer (t), is calculated as follows:…”

“…Based on the above estimation, one may evaluate the cumulative hazard and survival functions for given covariates. The estimators of the cumulative hazard function normalΛ false( t false) and survival function S false( t false) can be formulated asAs suggested by the existing literature, 33,2,21,4 the kernel smoothing method can be adopted to estimate the effects of covariates, α false( t false). The corresponding estimator, denoted as bold-italicα ^ K e r false( t false), is calculated as follows: where K e r false( ⋅ false) is the kernel function with bounded variation, integral 1, and support false( ϵ , 1 false] for some 0 < ϵ < 1, and h is the bandwidth that may require empirical selection.…”

“…Mckeague and Sasieni 19 considered a highly flexible and partly parametric AH model that simultaneously accommodates time-invariant and time-varying covariate effects. Li et al 20 adopted the local linear approximation technique proposed in Cai and Sun 21 to investigate Aalen's additive risk model. They estimated the functional coefficients with the expectation-maximization (EM) algorithm and developed the asymptotic properties with explicit expressions for the variance and bias.…”