QPRC 2016

Robustness of Weibull Regression when the Shape Parameter is Not Constant

Georgia Mueller and Steven E. Rigdon

Saint Louis University, St. Louis, MO, Department of Biostatistics
Southern Illinois University School of Medicine, Springfield, IL, Center for Clinical Research

The Weibull distribution is more appropriate than the exponential for analyzing survival data because it has two parameters. The parameters θ and κ of the Weibull distribution can be estimated from data arising from a factorial design. The concern when modeling survival data with the Weibull distribution is that researchers often assume that κ is constant across all treatments, which may not be a valid assumption. This study aims to explore the consequence of assuming a model with a constant κ when κ is nonconstant.  Simulated is used to estimate power in order to observe the robustness of the constant κ. Our model reflected the effect of both sample size and censoring.  We found the survival regression model with a Weibull distribution was fairly robust when sample sizes and parameters are large regardless censoring.  However, when sample sizes are small, power substantially reduces, and therefore, it is important to check for the assumption of nonconstant κ and take steps to adjust the statistical models to ensure valid results.