lðt;nonexposedÞ¼l 0 ðtÞlðt;exposedÞ¼l 0 ðtÞebso that the ratio
eb¼lðt;exposedÞ
lðt;nonexposedÞrepresents the relative risk (RR) of the exposure, exposed versus nonexposed.
In other words, the regression coe‰cientbis the value of the relative risk on
the log scale.
Similarly, we have for a continuous covariateXand any valuexofX,
lðt;X¼xÞ¼l 0 ðtÞebxlðt;X¼xþ 1 Þ¼l 0 ðtÞebðxþ^1 Þso that the ratio
eb¼lðt;X¼xþ 1 Þ
lðt;X¼xÞrepresents the relative risk (RR) due to a 1-unit increase in the value ofX,
X¼xþ1 versusX¼x. For example, a systolic blood pressure of 114 mmHg
versus 113 mmHg. For anm-unit increase in the value ofX, sayX¼xþm
versusX¼x, the corresponding relative risk isemb.
The regression coe‰cientbcan be estimated iteratively using the first and
second derivatives of the partial likelihood function. From the results we can
obtain a point estimate
dRRRR¼e^bband its 95% confidence interval
exp½bb^G 1 :96 SEðbb^ÞIt should be noted that the calculation of the relative risk, used as a measure
of association between survival time and a covariate, depends on the coding
scheme for a binary factor and for a continuous covariateX, the scale with
which to measureX. For example, if we use the following coding for a factor:
Xi¼ 1 if the patient is not exposed
1 if the patient is exposedSIMPLE REGRESSION AND CORRELATION 393