Re: st: stptime command issue

[weddings@stata.com (Wesley D. Eddings, StataCorp)]

Elisabetta Petracci <elisabetta.petracci@gmail.com> asked how to reproduce the
person-time calculations of -stptime-:

> I am running the example 2 (page 338) of the st.pdf Stata 11 manual to
> calculate age-specific incidence rates.
...
> Then I run:*

> stptime, per(1000) at(40(10)70) trim

(output inserted below)

         failure _d:  fail == 1 3 13
   analysis time _t:  (dox-origin)/365.25
             origin:  time dob
  enter on or after:  time doe
                 id:  id
               note:  _group<=40 trimmed

Cohort     |  person-time   failures        rate   [95% Conf. Interval]
-----------+-----------------------------------------------------------
(40  -  50]|    907.00616          6   6.6151701   2.971936    14.72457
(50  -  60]|    2107.0418         18   8.5427828   5.382317    13.55906
(60  -  70]|    1493.2923         22   14.732548   9.700656    22.37457
-----------+-----------------------------------------------------------
     total |    4507.3402         46   10.205575   7.644246    13.62512

> At this point I wanted to check by hand the calculation of person-time at
> least for the first age group.

> I don't get 907 person-time for the first age-group. Shouldn't I take those
> subjects who have _t<=50 and then sum over the _t within this interval?*

The -stptime- estimate of 907 cannot be reproduced by summing the values of _t.
(The _t variable was created by -stset- and records analysis time.)  Let's look
at the observations that satisfy _t <= 50:

. sort _t 

. 
. list _st _d _t _t0 if _t<=50

     +----------------------------------+
     | _st   _d          _t         _t0 |
     |----------------------------------|
  1. |   1    1    42.57358     31.4141 |
  2. |   1    0   46.201232   30.075291 |
  3. |   1    0   46.373717   30.332649 |
  4. |   1    0    46.86653    36.15332 |
  5. |   1    0    47.26078   31.134839 |
     |----------------------------------|
  6. |   1    0   47.753593    36.87885 |
  7. |   1    0    47.86037   37.314168 |
  8. |   1    1     47.8987    45.46475 |
  9. |   1    0   47.915127   32.125941 |
 10. |   1    1   47.964408    43.59206 |
     |----------------------------------|
 11. |   1    1   48.041068   46.546201 |
 12. |   1    0   48.741958   48.180698 |
 13. |   1    1   49.062286   45.442847 |
 14. |   1    1   49.062286     44.5859 |
 15. |   1    0     49.1718   38.297057 |
     |----------------------------------|
 16. |   1    0   49.976728    46.89117 |
     +----------------------------------+

(The variable _t0 tells when each record begins.)  Summing the sixteen values of
_t gives 762.7, which doesn't match the 907 reported by -stptime-.  The
calculations don't match because _t records the ending time for each record, not
the person-time contribution.  The contribution for the first record, for
example, is not 42.57358---it's 42.57358 - 40 = 2.57358.  And the contribution
for the tenth observation is only 47.964408 - 43.59206 = 4.372348, because the
record does not begin until time _t0 = 43.59206.

We've listed only the sixteen smallest values of _t, but other records will have
person-time contributions too.  Here's how to create a variable "pt4050"
containing the contributions:

. generate pt4050 = min(50 - 40, _t - 40) if _t0 <= 40
(311 missing values generated)

. 
. replace pt4050 = min(50 - _t0, _t - _t0) if _t0 > 40 & _t0 <= 50
(170 real changes made)

The observations with missing values of "pt4050" do not contribute person-time
for the (40, 50] cohort.  The sum of the values of "pt4050" is the estimate we
need:

. summarize pt4050

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
      pt4050 |       196    4.627582    3.057497   .1327858         10

. 
. display r(sum)
907.00616

-- Wes                  
weddings@stata.com      
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