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st: RE: ODDSRISK - odds ratios to risk ratios


From   Jhilbe@aol.com
To   statalist@hsphsun2.harvard.edu
Subject   st: RE: ODDSRISK - odds ratios to risk ratios
Date   Sun, 23 Dec 2007 17:59:46 EST

I just took a brief look at the Digest while on vacation. There are a  couple 
of good questions asked about the oddsrisk program that I posted to  SSC.  
The method as indeed been rather popular in medical journals, so I  thought 
having the program available for Stata users was worthwhile. But like  most 
statistical procedures, one must take care of assumptions, and  criteria of best 
application. There has been considerable discussion regarding  the relationship 
of odds, risk, incidence, and prevalence ratios. In some cases  they may be 
closely identical, in others they are not close at all. 
 
The test of Zhang and Yu (oddsrisk) was designed for cohort studies, but  
they seem to imply that the test can be used for case control and observational  
studies as well. The test certainly has been used in some published articles 
for  C-C and observational type studies. 
 
With respect to the CIs - yes, there has been a criticism that with a  number 
of confounders that the CI's may be biased. I have made comparisons  of 
oddsrisk results, poisson with robust SEs, and log-binomial regression - and  with 
log-geometric regression, and did not find the oddsrisk SEs to be much  
different from these other methods. The SE's of the various "estimations"  of risk 
ratio all overlap to a considerable degree, even at the alpha=.01 level.  
Actually, the log-geometric regression may produce better estimates than the  other 
methods. I plan to do simulation studies to determine the preferable  method.
 
I have also used King's relogit method, setting the incidence rate at that  
of the response, not the unexposed group of the risk factor. You cannot obtain  
OR with this method, so I converted the coefficients and SEs to their 
respective  OR and CI's. I show each of the results below. 
 
I must get back to family stuff - holidays. However, I can perhaps  respond 
more after Christmas. 
 
Joseph Hilbe
 
 
 
. use heart01
 
. logit death anterior hcabg, nolog or
 
Logistic  regression                                Number of obs   =        
4696
LR chi2(2)      =       33.08
Prob > chi2     =     0.0000
Log  likelihood =  -769.45359                        Pseudo R2       =      
0.0210
------------------------------------------------------------------------------
death | Odds Ratio   Std. Err.       z    P>|z|     [95% Conf.  Interval]
-------------+----------------------------------------------------------------
anterior |   2.270016   .3536024      5.26   0.000      1.67277     3.080501
hcabg |     2.21646    .720926     2.45    0.014      1.17165      4.19297
------------------------------------------------------------------------------
 

. oddsrisk death anterior hcabg
 
---------------------------------------------------------------------
Incidence  for unexposed risk group =      0.0261
---------------------------------------------------------------------
Predictor     Odds Ratio   Risk Ratio     [95% Conf.  Interval]
---------------------------------------------------------------------
anterior         2.2700        2.1973        1.6439        2.9221
hcabg            2.2165        2.1484        1.1664        3.8709
---------------------------------------------------------------------
 
. poisson death anterior hcabg, nolog irr robust
 
Poisson  regression                                 Number of obs   =        
4696
Wald chi2(2)    =       31.75
Prob > chi2     =     0.0000
Log  pseudolikelihood =    -773.925                  Pseudo R2       =      
0.0201
------------------------------------------------------------------------------
|                Robust
death  |        IRR   Std.  Err.      z     P>|z|     [95% Conf.  Interval]
-------------+----------------------------------------------------------------
anterior |   2.195271   .3293879      5.24   0.000     1.635951     2.945819
hcabg |    2.110155   .6257602     2.52    0.012      1.18003     3.773424
------------------------------------------------------------------------------
 

binreg death anterior hcabg, nolog rr n(1)
 
Generalized linear  models                           No. of obs      =       
4696
Optimization     : MQL Fisher  scoring               Residual df     =       
4693
(IRLS  EIM)                       Scale parameter =          1
Deviance         =   1538.830113                     (1/df) Deviance =    
.327899
Pearson          =   4708.103575                     (1/df) Pearson  =  
1.003218
 
Variance function: V(u) =  u*(1-u)                   [Bernoulli]
Link function    : g(u) =  ln(u)                     [Log]
 
                                                    BIC             =  
-38137.98
------------------------------------------------------------------------------
|                  EIM
death | Risk Ratio   Std.  Err.      z     P>|z|     [95% Conf.  Interval]
-------------+----------------------------------------------------------------
anterior |   2.197761   .3290377      5.26   0.000     1.638864     2.947257
hcabg |    2.123596   .6296464     2.54    0.011     1.187656      3.79711
------------------------------------------------------------------------------
 

. georeg death anterior hcabg, irr nolog
 
Geometric  Estimates                                  Number of obs    =     
4696
Model chi2(2)    =    30.35
Prob > chi2      =  0.0000
Log Likelihood  =    -778.2667486                      Pseudo R2        =   
0.0191
------------------------------------------------------------------------------
death |        IRR   Std.  Err.      z     P>|z|     [95% Conf.  Interval]
-------------+----------------------------------------------------------------
anterior |   2.193189   .3411827      5.05   0.000     1.616811     2.975041
hcabg |    2.098832   .6799387     2.29    0.022     1.112301     3.960348
------------------------------------------------------------------------------
(LR test against Poisson, chi2(1) = -8.683506 P =  1.0000)
 
 
 
. tab death
 
      Death |
within 48 |
hrs  onset |      Freq.      Percent         Cum.
------------+-----------------------------------
0 |      5,146        95.51        95.51
1  |         242        4.49       100.00
------------+-----------------------------------
Total |      5,388       100.00
 

. relogit death anterior hcabg, wc(.0449)
 
Corrected logit  estimates                              Number of obs =      
4696
------------------------------------------------------------------------------
|                Robust
death  |      Coef.   Std.  Err.      z     P>|z|     [95% Conf.  Interval]
-------------+----------------------------------------------------------------
anterior |   .8158849   .1560863      5.23   0.000     .5099615     1.121808
hcabg |    .8330481   .3237294     2.57    0.010     .1985502     1.467546
_cons |   -3.530083   .1269887   -27.80    0.000    -3.778976     -3.28119
------------------------------------------------------------------------------
 
RR - ANTERIOR
. di exp(_b[anterior])
2.2611757
 
RR - HCABG
. di exp(_b[hcabg])
2.3003197
 

CI - ANTERIOR
. di    exp(_b[anterior]-invnorm(0.975)*_se[anterior])
1.665227
 
. di    exp(_b[anterior]+invnorm(0.975)*_se[anterior])
3.0704016
 
CI - HCABG
. di    exp(_b[hcabg]-invnorm(0.975)*_se[hcabg])
1.2196333
 
. di    exp(_b[hcabg]+invnorm(0.975)*_se[hcabg])
4.3385754
 
 



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