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RE: st: Comparing change in rates - frustrating problem, please help


From   "Kieran McCaul" <[email protected]>
To   <[email protected]>
Subject   RE: st: Comparing change in rates - frustrating problem, please help
Date   Sun, 1 Feb 2004 09:38:54 +0800

OK Joseph and Ricardo, see what you think of this.


Here's some real data I have.

People have been recruited into a RCT to evaluate an intervention that is
designed to encourage them to implement smoking bans in their home.

So there is a baseline measure BAN1 (Do you ban smoking in the home (Y/N)?)
and the same measure repeated at the end of the trial BAN2

In the intervention group the results look like this:

.
. mcc ban2 ban1 if intervention==1

                 | Controls               |
Cases            |   Exposed   Unexposed  |     Total
-----------------+------------------------+----------
         Exposed |        47          16  |        63
       Unexposed |         6          59  |        65
-----------------+------------------------+----------
           Total |        53          75  |       128

McNemar's chi2(1) =      4.55    Prob > chi2 = 0.0330
Exact McNemar significance probability       = 0.0525

Proportion with factor
        Cases       .4921875
        Controls    .4140625     [95% Conf. Interval]
                   ---------     --------------------
        difference   .078125     -.0002214   .1564714
        ratio       1.188679      1.013845   1.393663
        rel. diff.  .1333333      .0192232   .2474435

        odds ratio  2.666667      .9911545   8.320598   (exact)



If I reshape the data, I create a new variable 'period' which identifies the
post-period (case) from the pre-period or baseline (control). I can do a
conditional logistic regression on the these data:

. xi:clogit period i.ban if intervention==1, group(id) or
i.ban             _Iban_0-1           (naturally coded; _Iban_0 omitted)

Conditional (fixed-effects) logistic regression   Number of obs   =
256
                                                  LR chi2(1)      =
4.72
                                                  Prob > chi2     =
0.0299
Log likelihood = -86.364559                       Pseudo R2       =
0.0266

----------------------------------------------------------------------------
--
      period | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
     _Iban_1 |   2.666667   1.276569     2.05   0.040     1.043487
6.814758
----------------------------------------------------------------------------
--

Now I get the same OR, but different 95%CIs because mcc is using an exact
method.

In the non-intervention arm, the results look like this:

. mcc ban2 ban1 if intervention==0

                 | Controls               |
Cases            |   Exposed   Unexposed  |     Total
-----------------+------------------------+----------
         Exposed |        47          10  |        57
       Unexposed |         7          72  |        79
-----------------+------------------------+----------
           Total |        54          82  |       136

McNemar's chi2(1) =      0.53    Prob > chi2 = 0.4669
Exact McNemar significance probability       = 0.6291

Proportion with factor
        Cases       .4191176
        Controls    .3970588     [95% Conf. Interval]
                   ---------     --------------------
        difference  .0220588     -.0445985   .0887161
        ratio       1.055556      .9124773   1.221069
        rel. diff.  .0365854     -.0601456   .1333163

        odds ratio  1.428571      .4908621   4.421907   (exact)


and reshaping and repeating this analysis, I get the following.  Same OR,
but different 95%CIs.

. xi:clogit period i.ban if intervention==0, group(id) or
i.ban             _Iban_0-1           (naturally coded; _Iban_0 omitted)

Conditional (fixed-effects) logistic regression   Number of obs   =
272
                                                  LR chi2(1)      =
0.53
                                                  Prob > chi2     =
0.4657
Log likelihood = -94.001919                       Pseudo R2       =
0.0028

----------------------------------------------------------------------------
--
      period | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
     _Iban_1 |   1.428571   .7040076     0.72   0.469     .5437826
3.753
---------------------------------------------------------


Now if I put the two arms of the trial together, introducing a variable
'intervention' to identify which arm of the trial each person is in, I can
fit the model:


. xi:clogit period i.ban*i.intervention, group(id) or
i.ban             _Iban_0-1           (naturally coded; _Iban_0 omitted)
i.intervention    _Iintervent_0-1     (naturally coded; _Iintervent_0
omitted)
i.ban*i.inter~n   _IbanXint_#_#       (coded as above)

note: _Iintervent_1 omitted due to no within-group variance.

Conditional (fixed-effects) logistic regression   Number of obs   =
528
                                                  LR chi2(2)      =
5.25
                                                  Prob > chi2     =
0.0725
Log likelihood = -180.36648                       Pseudo R2       =
0.0143

----------------------------------------------------------------------------
--
      period | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
     _Iban_1 |   1.428571   .7040077     0.72   0.469     .5437825
3.753001
_IbanXint_~1 |   1.866667   1.282474     0.91   0.364     .4855762
7.175897
----------------------------------------------------------------------------
--

The effect if 'ban' in this model is simply the effect in the
non-intervention arm:


. lincom  _Iban_1,or

 ( 1)  _Iban_1 = 0

----------------------------------------------------------------------------
--
      period | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
         (1) |   1.428571   .7040077     0.72   0.469     .5437825
3.753001
----------------------------------------------------------------------------
--

. lincom  _Iban_1+ _IbanXint_1_1,or


The effect of 'ban' in the intervention arm is given by:

 ( 1)  _Iban_1 + _IbanXint_1_1 = 0

----------------------------------------------------------------------------
--
      period | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
         (1) |   2.666667   1.276569     2.05   0.040     1.043487
6.814758
----------------------------------------------------------------------------
--

Are these two significantly different?  That's given by the p-value for the
interaction term:0.364.

I think that this is valid.  The variable 'intervention' is "omitted due to
no within-group variance" - it has a beta of zero by design, so you could
regard it as being in the model, it just doesn't appear because the design
matches it out.

The difference in the p-values that you obtain using exact methods is
another problem entirely - if I had something that would do "exact
conditional logistic regression" I would have obtained results that matched
those pproduced by mcc.

Kieran










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