Fitting Lin & Ying's Additive Hazards Regression Model Using a Weighted Least Squares Estimator for Poisson Regression

• Activity Number: 466
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): M. Brent McHenry*+ and Stuart Lipsitz and Debajyoti Sinha
• Companies: Bristol-Myers Squibb and Brigham and Women's Hospital and Florida State University
• Keywords: Additive Hazards ; Survival Analysis ; Weighted Least Squares ; Computational ; Poisson Linear Model ; Method-of-moments

Abstract

For failure time outcomes, modeling the hazard rate as an exponential function of covariates is by far the most popular. However, additive hazard rate regression models, in which the hazard rate is modeled as a linear function of the covariates, have received attention in the last few decades. If the distribution of the failure time is exponential, Aitkin et al. (2005) showed that the maximum likelihood estimates (MLE) of the additive hazard rate regression model can be obtained using a Poisson linear model. Instead of maximum likelihood, here we propose a weighted least squares (WLS) method-of-moments estimator to consistently estimate the additive hazard regression parameters. The WLS estimates are obtained by a slight modification of the Poisson additive regression estimating equations. The approach can also be used for a piecewise exponential, and we show that, as the intervals widths for the piecewise exponential converge to 0, e.g., each interval contain only one failure, the WLS estimates will be identical to the Martingale based method of moments estimate proposed by Lin and Ying (1994).