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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