Hazards Ratio Estimates and Confidence Limits

The PHREG Procedure

Hazards Ratio Estimates and Confidence Limits

Let $\beta_i$ and $\hat{\beta}_i$ denote the ith component of ${\beta}$ and $\hat{{\beta}}$ , respectively. The hazards ratio (also known as risk ratio) for the explanatory variable with regression coefficient $\beta_i$ is defined as ${\rm exp}(\beta_i)$ .The hazards ratio is estimated by ${\rm exp}(\hat{\beta}_i)$ . The $100(1-{\alpha})\%$ confidence limits for the hazards ratio are calculated as

${\rm exp} ( \hat{\beta}_{i} +- z_{\alpha /2} \sqrt{\hat{V}_{ii}(\hat{{\beta}})} )$

where $\hat{V}_{ii}(\hat{{\beta}})$ is the ith diagonal element of $\hat{V}(\hat{{\beta}})$ , and $z_{\alpha /2}$ is the $100(1-{\alpha}/2)$ percentile point of the standard normal distribution.

The hazards ratio is the ratio of the hazards functions that correspond to a change of one unit of the given variable and conditional on fixed values of all other variables.

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