**CHAPTER 1**

**Introduction to Regression Modeling of Survival Data**

**1.1 INTRODUCTION**

Regression modeling of the relationship between an outcome variable and one or more independent (predictor) variable(s) is commonly employed in virtually all fields. The popularity of this approach is due to the fact that plausible models may be easily fit, evaluated, and interpreted. Statistically, the specification of a model requires choosing both systematic and error components. The choice of the systematic component involves an assessment of the relationship among the “average” of the outcome variable relative to specific levels of the independent variable(s). This may be guided by an exploratory analysis of the current data and/or past experience. The choice of an error component involves specifying the statistical distribution of what remains to be explained after the model is fit.

In an applied setting, the task of model selection is, to a large extent, based on the goals of the analysis and on the measurement scale of the outcome variable. For example, a clinician may wish to model the relationship among body mass index (BMI, kg/m^{2}) and caloric intake and gender among teenagers seen in the clinics of a large health maintenance organization (HMO). A good place to start would be to use a model with a linear systematic component and normally distributed errors (i.e., the usual linear regression model). Suppose, instead, that the clinician decides to convert BMI into a 0 – 1 dichotomous variable ...