Why or when is the hazard ratio more than the range of the confidence interval? As I understood it, the hazard ratio must fall with in the range of the confidence interval.
The Confidence Intervals (CI) is interpreted in a similar manner to odds ratio CI. Since the true value of the coefficient in the population cannot be exactly determined based on any sample, even with high significance levels, CI's lower and upper values give a range in which the true population value lies - usually with 95% certainty.
For example, in this mock
coef exp(coef) se(coef) z Pr(>|z|) Working 0.6370 1.8908 0.2362 2.697 0.00699 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 exp(coef) exp(-coef) lower .95 upper .95 Working 1.891 0.5289 1.19 3.004
Having a job (
Working) increases the hazard ratio of getting a girlfriend by ~81%, with the population value being between an increase of 19% to 300% (with a 95% probability).