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RE: st: different age effect between groups


From   "Svend Juul" <SJ@SOCI.AU.DK>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: different age effect between groups
Date   Tue, 31 Oct 2006 11:40:29 +0100

Enzo wrote:

I have a Cox model where women invited to test screening (mammography)
are compared for cause specific mortality with women not invited. The
age ranges from 50 to 69.

I checked the functional form of the variable age using gam.
The age effect is linear in not invited cases.

In invited the age effect rises until 55 and then flattens or even
decreases as shown in the strate output:

. strate inv agegroup,per(1000)

failure _d: status2004
analysis time _t: (exit-origin)/365.25
origin: time datainc
id: ID

Estimated rates (per 1000) and lower/upper bounds of 95% confidence
intervals
(9251 records included in the analysis)

+---------------------------------------------------------------------+
| inv agegroup D Y Rate Lower Upper |
|---------------------------------------------------------------------|
| 0. Not Invited 50- 132 5.5111 23.952 20.195 28.407 |
| 0. Not Invited 55- 131 4.7708 27.458 23.137 32.587 |
| 0. Not Invited 60- 182 5.8115 31.317 27.083 36.214 |
| 0. Not Invited 65- 234 6.5993 35.458 31.194 40.305 |
|---------------------------------------------------------------------|
| 1. All Invited 50- 90 5.9692 15.077 12.263 18.537 |
| 1. All Invited 55- 153 7.5791 20.187 17.229 23.653 |
| 1. All Invited 60- 142 7.6450 18.574 15.757 21.895 |
| 1. All Invited 65- 124 8.0587 15.387 12.904 18.348 |
+---------------------------------------------------------------------+

My question is how to model this different age effect in invited and not
invited women.
Probably I need some interaction term.
---------------------------------------------------------------

Enzo,

I would describe the main findings a bit differently: The effect of the
intervention (invitation to screening) seems to increase with age.

The most direct way to study the interaction (effect modification) is by
a Mantel-Haenszel stratified analysis; you gave the necessary
information:

  clear
  input inv agegroup D Y Rate Lower Upper
  0 50 132 5.5111 23.952 20.195 28.407 
  0 55 131 4.7708 27.458 23.137 32.587 
  0 60 182 5.8115 31.317 27.083 36.214 
  0 65 234 6.5993 35.458 31.194 40.305 
  1 50 90 5.9692 15.077 12.263 18.537 
  1 55 153 7.5791 20.187 17.229 23.653 
  1 60 142 7.6450 18.574 15.757 21.895 
  1 65 124 8.0587 15.387 12.904 18.348 
  end

  ir D inv Y, by(agegroup)

          agegroup |      IRR       [95% Conf. Interval]   M-H Weight
  -----------------+-------------------------------------------------
                50 |   .6294927      .4760889   .8291503     68.63361
(exact)
                55 |     .73518      .5783773   .9355852     80.39434
(exact)
                60 |   .5930997      .4728399   .7427298     103.3991
(exact)
                65 |    .433949      .3461902   .5417813     128.6489
(exact)
  -----------------+-------------------------------------------------
             Crude |   .5815387      .5173876    .653321
(exact)
      M-H combined |   .5759002      .5130383   .6464644
  -------------------------------------------------------------------
   Test of homogeneity (M-H)    chi2(3) =     11.19  Pr>chi2 = 0.0107

The test of homogeneity tells that the IRRs are significantly different
- a test for trend would be nice here; see later.

With the information you give, -poisson- is another possibility. I first
expand the dataset to the number of deaths (that may be unnecessary; I
am not sure). Here you can make an interaction term:

  gen t=Y/D
  gen d=1
  expand D
  xi: poisson d i.inv i.agegroup , exposure(t) irr
  xi: poisson d i.inv*i.agegroup , exposure(t) irr     // Interaction

If we still want a test for trend, this could be done:

  gen invage=inv*agegroup
  poisson d inv agegroup , exposure(t) irr
  poisson d inv agegroup invage , exposure(t) irr      // Interaction

Hope this helps,

Svend

__________________________________________

Svend Juul
Institut for Folkesundhed, Afdeling for Epidemiologi
(Institute of Public Health, Department of Epidemiology)
Vennelyst Boulevard 6
DK-8000  Aarhus C, Denmark
Phone: +45 8942 6090
Home:  +45 8693 7796
Email: sj@soci.au.dk
__________________________________________ 

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