Application of the Weibull Distribution with a Non-Constant Shape Parameter for Identifying Risk Factors in Pharyngeal Cancer Patients

Abstract

<br /> <strong><span style="font-size: small;">Background: </span></strong><span style="font-family: Times New Roman,Times New Roman; font-size: small;"><span style="font-family: Times New Roman,Times New Roman; font-size: small;">In its standard form, the parametric survival model assumes that the shape parameter is constant and the scaling parameter is not. This article focuses on how a model with a non-constant shape parameter could make differences in oncology studies and lead to more precise results. </span></span><strong><span style="font-size: small;">Materials and Methods: </span></strong><span style="font-family: Times New Roman,Times New Roman; font-size: small;"><span style="font-family: Times New Roman,Times New Roman; font-size: small;">Online data for part of a large clinical trial conducted by the Radiation Oncology Group in the United States available online on UMass </span></span><span style="font-family: Times New Roman,Times New Roman; font-size: small;"><span style="font-family: Times New Roman,Times New Roman; font-size: small;">Amherst`s website were employed. The full study included patients with squamous cell carcinoma from fifteen sites in </span></span><span style="font-family: Times New Roman,Times New Roman; font-size: small;"><span style="font-family: Times New Roman,Times New Roman; font-size: small;">the mouth and throat, although only data on three sites in the oropharynx reported by the six largest institutions were considered here. To identify clinical, pathological and biological characteristics of patients which might have had an effect on their survival, we compared Weibull distributions once with a constant shape parameter and again with a </span></span><span style="font-family: Times New Roman,Times New Roman; font-size: small;"><span style="font-family: Times New Roman,Times New Roman; font-size: small;">non-constant shape parameter. Analyzes were performed using SAS university edition. The level of significance was set at P ≤ 0.05. </span></span><strong><span style="font-size: small;">Results: </span></strong><span style="font-family: Times New Roman,Times New Roman; font-size: small;"><span style="font-family: Times New Roman,Times New Roman; font-size: small;">Based on the model with a constant shape parameter only the patient status was identified as a risk factor and the AIC of this model was 2152.4, but based on the model with a non-constant shape parameter, sex, patient status, stage of the tumor and the institute at which the patient had been treated were significant, with an AIC of 2150.1. </span></span><strong><span style="font-size: small;">Conclusion: </span></strong><span style="font-family: Times New Roman,Times New Roman; font-size: small;"><span style="font-family: Times New Roman,Times New Roman; font-size: small;">On the basis of the AIC, the second model with a non-constant shape parameter was suggested to be more accurate for identifying risk factors, leading to more precise results. </span></span>