Age adjusted mortality rate

[Svetlana Bondar]

Hello! There are three variables in my database: pneumonia (yes / no), death (yes / no) and age (various categories). I need to show that patients with pneumonia die more often than without pneumonia adjusted for age (age adjusted mortality rate). How can I do it?

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(age death pneumonia)
0 0 0
0 0 0
0 0 0
1 0 0
1 0 0
1 0 0
1 0 0
2 1 1
2 0 0
2 0 0
2 0 0
5 0 0
5 0 0
5 0 0
5 1 1
5 1 1
6 1 1
6 1 1
6 1 1
6 0 0
7 0 0
7 1 0
7 1 1
7 1 0
7 1 1
8 1 0
8 1 1
8 1 1
8 1 1
8 1 1
3 0 1
3 0 1
3 0 0
3 0 0
3 1 1
4 0 1
4 0 0
4 1 1
4 1 1
4 0 1
end
label values age age
label def age 0 "20-29", modify
label def age 1 "30-39", modify
label def age 2 "40-49", modify
label def age 3 "50-59", modify
label def age 4 "60-69", modify
label def age 5 "70-79", modify
label def age 6 "80-89", modify
label def age 7 "90-99", modify
label def age 8 "100-109", modify
label values death death
label def death 0 "no", modify
label def death 1 "yes", modify
label values pneumonia pneumonia
label def pneumonia 0 "no", modify
label def pneumonia 1 "yes", modify

[Carlo Lazzaro]

Svetlana:
as per your data structure, you should add a -timevar- in order to exploit a, say, semi-parametric survival analysis regression model (eg, -stcox) and interact -i-age- with -i.pneumonia- to try to investigate the evidence (not to show) that -i.pneumonia-, when adjusted for -age- (by the way, see http://citeseerx.ist.psu.edu/viewdoc...=rep1&type=pdf about categorizing a continuous predictor like age) is an informative predictor of death (or not).
A very unsatisfactory toy-example could be:

g timevar=1
. stcox i.age##i.pneumonia

         failure _d:  death
   analysis time _t:  timevar

note: 0.age#1.pneumonia identifies no observations in the sample
note: 1.age#1.pneumonia identifies no observations in the sample
note: 8.age#1.pneumonia omitted because of collinearity
Iteration 0:   log likelihood =  -66.39983
Iteration 1:   log likelihood = -57.481066
Iteration 2:   log likelihood =  -55.97714
Iteration 3:   log likelihood = -55.551738
Iteration 4:   log likelihood = -55.406113
Iteration 5:   log likelihood =  -55.35318
Iteration 6:   log likelihood = -55.333791
Iteration 7:   log likelihood =  -55.32667
Iteration 8:   log likelihood = -55.324052
Iteration 9:   log likelihood = -55.323089
Iteration 10:  log likelihood = -55.322735
Iteration 11:  log likelihood = -55.322604
Iteration 12:  log likelihood = -55.322556
Iteration 13:  log likelihood = -55.322539
Iteration 14:  log likelihood = -55.322532
Iteration 15:  log likelihood =  -55.32253
Iteration 16:  log likelihood = -55.322529
Iteration 17:  log likelihood = -55.322529
Iteration 18:  log likelihood = -55.322529
Iteration 19:  log likelihood = -55.322529
Iteration 20:  log likelihood = -55.322529
Iteration 21:  log likelihood = -55.322529
Iteration 22:  log likelihood = -55.322529
Iteration 23:  log likelihood = -55.322529
Iteration 24:  log likelihood = -55.322529
Iteration 25:  log likelihood = -55.322529
Iteration 26:  log likelihood = -55.322529
Iteration 27:  log likelihood = -55.322529
Iteration 28:  log likelihood = -55.322529
Iteration 29:  log likelihood = -55.322529
Iteration 30:  log likelihood = -55.322529
Iteration 31:  log likelihood = -55.322529
Iteration 32:  log likelihood = -55.322529
Iteration 33:  log likelihood = -55.322529
Iteration 34:  log likelihood = -55.322529
Iteration 35:  log likelihood = -55.322529
Iteration 36:  log likelihood = -55.322529
Iteration 37:  log likelihood = -55.322529
Iteration 38:  log likelihood = -55.322529
Iteration 39:  log likelihood = -55.322529
Refining estimates:
Iteration 0:   log likelihood = -55.322529
Iteration 1:   log likelihood = -55.322529
Iteration 2:   log likelihood = -55.322529
Iteration 3:   log likelihood = -55.322529

Cox regression -- Breslow method for ties

No. of subjects =           40                  Number of obs    =          40
No. of failures =           18
Time at risk    =           40
                                                LR chi2(9)       =       22.15
Log likelihood  =   -55.322529                  Prob > chi2      =      0.0084

-------------------------------------------------------------------------------
           _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
          age |
       30-39  |   1.52e-08   19.43198    -0.00   1.000            0           .
       40-49  |   2.718279          .        .       .            .           .
       50-59  |   2.718281    3.84423     0.71   0.480     .1700253    43.45854
       60-69  |   20.08549   24.59961     2.45   0.014     1.821285    221.5069
       70-79  |   7.389048   9.049698     1.63   0.102     .6700138    81.48791
       80-89  |   148.4128   171.3723     4.33   0.000     15.43791    1426.771
       90-99  |   6.61e+10   1.10e+11    15.02   0.000     2.56e+09    1.71e+12
     100-109  |   9.92e+10   1.11e+11    22.65   0.000     1.11e+10    8.87e+11
              |
    pneumonia |
         yes  |          1   1.118034     0.00   1.000     .1117706    8.946893
              |
age#pneumonia |
   20-29#yes  |          1  (empty)
   30-39#yes  |          1  (empty)
   40-49#yes  |   3.65e+10          .        .       .            .           .
   50-59#yes  |   1.22e+10          .        .       .            .           .
   60-69#yes  |   2.47e+09          .        .       .            .           .
   70-79#yes  |   1.34e+10          .        .       .            .           .
   80-89#yes  |   6.68e+08          .        .       .            .           .
   90-99#yes  |        1.5       2.25     0.27   0.787     .0793029    28.37224
 100-109#yes  |          1  (omitted)
-------------------------------------------------------------------------------

.

Had you the number of deaths, you could consider -poisson-.