Hazard Ratios

The hazard ratio for a quantitative effect with regression coefficient is defined as exp, where denotes the jth unit vector. In general, a log-hazard ratio can be written as , a linear combination of the regression coefficients, and the hazard ratio exp is obtained by replacing with .

The confidence intervals for hazard ratios are obtained by exponentiating the confidence limits of the corresponding linear combination. Thus, the confidence limits are

where is the percentile point of the t distribution with df degrees of freedom. See the section Degrees of Freedom for more information about df. If you use the DF=NONE option in the MODEL statement, then the procedure uses the percentile point of the standard normal distribution.