M. Brent McHenry
Department of Biostatistics, Bioinformatics and Epidemiology
Medical University of South Carolina
Charleston, South Carolina
A Novel Approach of Estimation for Additive Rate Regression Models with
Parametric Underlying Failure Time Distributions
For failure time outcomes, modeling the hazard rate as an exponential
function of covariates is by far the most popular. However, in the last few
decades, additive hazard rate regression models have received some
attention, in which the hazard rate is modeled as a linear function of the
covariates. Popular fully parametric distributions include the exponential
and piecewise exponential. In this paper, for an additive rate regression
model in which the distribution of the failure time is exponential or
piecewise exponential, we show that the maximum likelihood estimates (MLE)
can be obtained using a Poisson linear model, without any additional
programming or iteration loops. As a result, the MLEs can be obtained in
any generalized linear models program.
Therefore, in this paper we emphasis not to develop new methodologies, but
instead to present new uses and interpretations for already familiar
methods. In addition, we propose goodness of fit statistics for the overall
model fit and to test the functional form of covariates. The selection from
Box-Tidwell transformations of the power family are based on assessing the
likelihood. We apply the proposed methods in two examples in which the
additive hazard rate regression model appears more appropriate.
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