Time-dependent Covariate Effects Research Articles

An objective method for detecting time-dependent effects in graft survival.

The proportional hazards model has become increasingly important in the analysis of censored survival data after transplantation. Neverthless, in clinical transplantation it is still undefined how the influence of covariates changes over time. The additive regression model is an alternative (or extension) to the Cox model. It results in plots (Aalen plots) that may give information on the effect of covariates over time by way of the cumulative regression function plots. A total of 386 primary cadaveric kidney transplants performed between 1984 and 1996 were included in our analysis. The follow-up period ranged from 24 to 156 months. According to Aalen, an additive regression model was used and plots for the detection of time-dependent effects of covariates were determined. Patients dying with functioning grafts were classed as graft failures. Factors potentially affecting graft outcome, such as sex, donor and recipient's age, HLA A-B match, cold ischaemia time (CIT), delayed graft function (DGF), serum creatinine at 1 month (Cr1), rejection episodes within 3 months (R3), and type of brain death (BD), were considered. The slopes of the plots by donor age, DGF, HLA A-B match, R3, Cr1 and BD appear to have a significant influence throughout the observation period, with different time-dependent effects on graft survival. Slopes for DGF, Cr1, and age of donor are positive (increased hazard), while slopes for HLA match and BD are negative (decreased hazard). Estimated regression functions for DGF, donor age and Cr1 show a prompt slope (within 3 months); the covariate R3 has a clear influence for about 5 years, and then seems to disappear; and BD appears to have a consistent effect over the entire period. The additive regression model with Aalen plots represents a useful technique in the analysis of survival data after kidney transplantation. Some covariates, such as R3, may often lose their effects on graft survival, with a relevant clinical impact. Others have a clear and additive influence over the entire period (BD), while the effects of donor age, DGF and CR1 each appear to have a prompt effect in the outcome.

Flexible Bayesian modelling for survival data.

The analysis of failure time data often involves two strong assumptions. The proportional hazards assumption postulates that hazard rates corresponding to different levels of explanatory variables are proportional. The additive effects assumption specifies that the effect associated with a particular explanatory variable does not depend on the levels of other explanatory variables. A hierarchical Bayes model is presented, under which both assumptions are relaxed. In particular, time-dependent covariate effects are explicitly modelled, and the additivity of effects is relaxed through the use of a modified neural network structure. The hierarchical nature of the model is useful in that it parsimoniously penalizes violations of the two assumptions, with the strength of the penalty being determined by the data.

Aalen Plots Under Proportional Hazards

SUMMARY Mau's graphical method for the detection of time-dependent effects of covariates in survival data is based on a linear model for the hazard function suggested by Aalen. The performance of the technique under the more common Cox proportional hazards model is considered and a modification designed to aid interpretation is suggested.

Nonparametric Survival Analysis with Time-Dependent Covariate Effects: A Penalized Partial Likelihood Approach

Techniques are developed for nonparametric analysis of data under a Cox-regression-like model permitting time-dependent covariate effects determined by a regression function $\beta_0(t)$. Estimators resulting from maximization of an appropriate penalized partial likelihood are shown to exist and a computational approach is outlined. Weak uniform consistency (with a rate of convergence) and pointwise asymptotic normality of the estimators are established under regularity conditions. A consistent estimator of a common baseline hazard function is presented and used to construct a consistent estimator of the asymptotic variance of the estimator of the regression function. Extensions to multiple covariates, general relative risk functions and time-dependent covariates are discussed.

On a Graphical Method for the Detection of Time-Dependent Effects of Covariates in Survival Data

On compare l'information visuelle issue des traces des fonctions de regression d'Aalen aux coefficients de regression d'un modele recent de Cox