Help with age-adjusted mortality rates

[Morgan Wang]

Hi Stata community!

I have a dataset of around 500 patients, and looking at long-term outcomes. I have mortality outcome (named Dead- 0 or 1) and time to event in years (named PersonTime). I want to express mortality rate per 100-person years by subgroups of patients by Gender (0,1) and by Disease status (FNcategory- 0, 1, 2). BUT I want to also adjust for age as age would be a confounder when it comes to mortality.

I started with stset PersonTime, failure(Dead)


I then fit a Cox proportional hazards model to adjust for Age, stratified by Gender and Disease status
stcox i.Gender i.FNcategory Age, robust


------------------------------------------------------------------------------
| Robust
_t | Haz. ratio std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
1.Gender | 1.928237 .3191884 3.97 0.000 1.393984 2.667246
|
FNcategory |
1 | 1.266628 .3227276 0.93 0.354 .768722 2.087032
2 | 1.730459 .4978788 1.91 0.057 .9845954 3.041337
|
Age | 1.113583 .0096699 12.39 0.000 1.094791 1.132698
------------------------------------------------------------------------------

I've been told that I then need to do:
predict hazard, xb
gen AdjustedHazard = exp(hazard)

and gen MortalityRateAdjusted = (AdjustedHazard * PersonTime * 100)
to get an adjusted mortality rate based on an adjusted hazard which accounts for age?

But the numbers I get are completely nonsensical and way too large per 100 person-years.

What should I do?? I'm not sure if this is the right way.

I'm going crazy with this and not sure if missing something here. Any help is greatly appreciated!

[Carlo Lazzaro]

Morgan:
welcome to this forum.
You may want to consider -poisson- as in the following toy-example, which is supported by a dataset that comes with An Introduction to Stata for Health Researchers, Fifth Edition, Stata Press, 2021:

. use "C:\Professione\Statistiche\Stata\ishr\compliance3.dta"
(Compliance data stset with age as time axis)


. gen event=_d

. gen pyr=( _t - _t0 )


. poisson event b0.particip i.particip i.ranagr , exposure(pyr) ir

Iteration 0:  Log likelihood = -338.41165  
Iteration 1:  Log likelihood = -338.40638  
Iteration 2:  Log likelihood = -338.40638  

Poisson regression                                      Number of obs =    555
                                                        LR chi2(5)    =  32.23
                                                        Prob > chi2   = 0.0000
Log likelihood = -338.40638                             Pseudo R2     = 0.0454

------------------------------------------------------------------------------
       event |        IRR   Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    particip |
     1. Yes  |   .4889068   .0989234    -3.54   0.000     .3288496    .7268666
             |
      ranagr |
      66-67  |   1.447485    .599327     0.89   0.372     .6429489    3.258754
      68-69  |   2.679351   .9941403     2.66   0.008     1.294797    5.544438
      70-71  |   1.663297   .6732149     1.26   0.209     .7523993     3.67698
      72-73  |   3.238091   1.161152     3.28   0.001     1.603449    6.539172
             |
       _cons |   .0314407   .0108945    -9.98   0.000      .015942    .0620073
     ln(pyr) |          1  (exposure)
------------------------------------------------------------------------------
Note: _cons estimates baseline incidence rate.

. mat list e(b)

e(b)[1,8]
         event:      event:      event:      event:      event:      event:      event:      event:
            0b.          1.        64b.         66.         68.         70.         72.            
      particip    particip      ranagr      ranagr      ranagr      ranagr      ranagr       _cons
y1           0  -.71558348           0   .36982745   .98557463   .50880188   1.1749839  -3.4596509

. lincom _cons+1.particip , eform

 ( 1)  [event]1.particip + [event]_cons = 0

------------------------------------------------------------------------------
       event |     exp(b)   Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |   .0153716   .0049496   -12.97   0.000     .0081778    .0288936
------------------------------------------------------------------------------

.

The mortality rate for a study participant aged 64-65 approximates 15 deaths/1000 person-year.