**CHAPTER 4**

**Interpretation of a Fitted Proportional Hazards Regression Model**

**4.1 INTRODUCTION**

The interpretation of a fitted proportional hazards model requires that we be able to draw practical inferences from the estimated coefficients in the model. We begin by discussing the interpretation of the coefficients for nominal (Section 4.2) and continuous (Section 4.3) scale covariates. In Section 4.4 we discuss the issues of statistical adjustment and the interpretation of estimated coefficients in the presence of statistical interaction. The chapter concludes with a discussion of the interpretation of fitted values from the model and covariate adjusted survivorship functions.

In any regression model, the estimated coefficient for a covariate represents the rate of change of a function of the dependent variable per-unit change in the covariate. Thus, to provide a correct interpretation of the coefficients, we must determine the functional relationship between the independent and dependent variables and we must define the unit change in the covariate likely to be of interest.

In Chapters 2 and 3 we recommended that the hazard function be used in regression analysis to study the effect of one or more covariates on survival time. We must first determine what transformation of the hazard function is linear in the coefficients. In the family of generalized linear models (i.e., linear, logistic, Poisson, and other regression models) this linearizing transformation is known as the *link function ...*