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Re: st: RE: clogit or logistic for matched pairs


From   Jay Kaufman <Jay_Kaufman@unc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: clogit or logistic for matched pairs
Date   Thu, 06 Nov 2003 14:58:22 -0500

> VISINTAINER PAUL wrote:
> 
> You might want to try -xtlogit- which will take into account the 
> clustering of your independent exposure variable. This will satisfy 
> your need for a conditional approach.   Depending on your data and 
> the covariates you include, you may actually get an outcome that is
> quite close to -logit- with a robust option.

For whatever its worth, here are the results of the proposed
solutions using the three methods suggested in the e-mails
from this afternoon, on the example in Hosmer & Lemshow 2000 
textbook, chapter 7 on matched-data. 

. use http://www.ats.ucla.edu/stat/stata/examples/alr2/lowbwt11

. clogit low smoke, group(pair) 

Conditional (fixed-effects) logistic regression   Number of obs   =        112
------------------------------------------------------------------------------
         low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       smoke |   1.011601   .4128614     2.45   0.014     .2024075    1.820794
------------------------------------------------------------------------------

. xtlogit low smoke, i(pair) 

Random-effects logistic regression              Number of obs      =       112
Group variable (i): pair                        Number of groups   =        56
------------------------------------------------------------------------------
         low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       smoke |   1.059392   .3991177     2.65   0.008     .2771353    1.841648
-------------+----------------------------------------------------------------

. logit low smoke, cluster(pair) 

Logit estimates                                   Number of obs   =        112
                             (standard errors adjusted for clustering on pair)
------------------------------------------------------------------------------
             |               Robust
         low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       smoke |   1.059392   .4117006     2.57   0.010     .2524732     1.86631
------------------------------------------------------------------------------

The estimate from the conditional logistic regression (shown first) matches
exactly the tabular analysis (mhodds low smoke pair) if one exponentiates the 
parameter estimate and confidence limits to get an OR from the original beta. 

So my impression, if I can generalize from this one example, is that -xtlogit- 
and -logit- with robust variance don't reproduce exactly the correct values 
from -clogit-, but that they are reasonably close.

Stata appears to have no built-in functions for matched COHORT data (as opposed
to matched case-control data) but the relevant formulas ar shown in Rothman & 
Greenland "Modern Epidemiology 2nd Edition, p. 283 (i.e. for the Mantel-Haenszel
RR instead of M-H OR as provided in Stata's -mhodds- command). 

However, the M-H RR is equal to the crude RR exactly because matching in a 
COHORT study (as opposed to a case-control study) adjusts for confounding 
by the matching factor.  See discussion in R & G 1998 pp. 283-285.  

- JK

-- 
Jay S. Kaufman, Ph.D         
-----------------------------
email: Jay_Kaufman@unc.edu
-----------------------------
Department of Epidemiology   
UNC School of Public Health  
2104C McGavran-Greenberg Hall
Pittsboro Road, CB#7435   
Chapel Hill, NC 27599-7435  
phone:  919-966-7435         
fax:    919-966-2089         
-----------------------------
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