# st: Why don't my IRs and Cox HRs echo each other?

 From "Polis, Chelsea B." To "statalist@hsphsun2.harvard.edu" Subject st: Why don't my IRs and Cox HRs echo each other? Date Wed, 6 May 2009 19:29:05 -0400

```Dear statalisters,

I am doing survival analysis on time to death with time-varying covariates on an open, population
-based cohort study.  The base sample is essentially a census of individuals in 56 villages, and
I am utilizing information from all female incident HIV seroconverters.

I computed incidence rates based on the raw data ((number of deaths/person-time at risk)*100 - I obtained
time at risk using the stdes command), but the IRs don't seem to echo trends in the univariate Cox HRs.

In the sample data below, things appear reasonable for HC use (deaths per 100 person years is lower
if HC=yes, and the HR reflects this).  But for current age, deaths are higher in the 25-34 category
than in the 15-24 category, but the HR trends suggests that being 25-34 is protective (though not
significantly).  Also, the magnitude seems off, for example, in the variable "Sex partners in past
year" - having two or more seems to more than triple the hazard in the Cox regression, but merely
increases from 7.46 to 9.10 in the deaths per 100 p-y.

Am I missing something in expecting these numbers to echo trends in each other?  Is this just a
matter of non-significance within individual categories?  Or a difference in time-to-event versus
person-time analysis?  Or because I am doing an analysis with time-varying covariates?  Should I not
expect these to align? Any help is appreciated!

Variable        Deaths  PY at risk      Deaths per      HR      95% CI  p-value
100 p-y
HC use                                                                          0.07
No             91              1262.7  7.21            1.00
Yes            13              293.0           4.44            0.58    0.32-1.04
Current age                                                                             0.38
15-24  20              394.0           5.08            1.00
25-34  49              711.8           6.88            0.73    0.43-1.24
35+            35              449.9           7.78            0.68    0.38-1.20
Sex partners in past year                                                       0.01
None           18              241.2           7.46            1.00
One            76              1204.6  6.31            1.31    0.78-2.21
Two+           10              109.9           9.10            3.40    1.54-7.54

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```