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# st: SV: RE: risk ratio

 From "Tomas Lind" To Subject st: SV: RE: risk ratio Date Mon, 22 Mar 2010 16:36:16 +0100

```Hi Joseph,

I am working with Stata v10 (but we are going to upgrade to v11 soon). You
find my code below to generate data according to a logit model.

In the first example I generate data with an odds-model. The
beta-coefficient used to generate data is 0.49.

When analyzing these data with logistic regression I get my beta-coefficient
(0.50 in this run). When analyzing data with a Poisson-model, beta is
estimated to 0.069. I suppose this is because a Poisson-model is measuring
RR not OR.

clear *
set obs 100000
* Expo is logNf  mean=16,2 sd=8,2
gen pm10 = exp(2.66 + 0.49 * invnorm(uniform()))
generate z=(-11.2 + (0.5*(pm10) ))

generate p_case=(1/(1+exp(-z)))		// p_case=0.2

generate case=0
replace case=1 if(uniform()<p_case & p_case !=.)

glm fall pm10 , link(logit) fam(bin)		// beta = 0.50
glm fall pm10 , link(log)   fam(poi)  robust	// beta = 0,069

In example 2 I generate data with the -genbinomial- with a log link to
generate data where exposure is proportional to risk. In this case Poisson
regression gives me the correct beta but the logistic regression does not.

clear *
set obs 200000
gen x1 = invnorm(uniform())
gen x2 = invnorm(uniform())
gen xb = -1 + 0.5*x1 + 1.5*x2

rename y  case
// genbinomial might give values outside 0, 1.

drop  if case==.				// p(case)=0.3

glm case x1 x2 , link(log) fam(po) vce(robust) // OK beta1=0,50   beta2=1,51
glm case x1 x2 , link(logit) fam(bin) 	// Wrong beta1=0,82   beta2=2,44

Yours

Tomas

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[mailto:owner-statalist@hsphsun2.harvard.edu] För jhilbe@aol.com
Skickat: den 21 mars 2010 15:52
Till: statalist@hsphsun2.harvard.edu
Ämne: st: RE: risk ratio

response model that
can be used to estimate a relative risk ratio:

I have an article coming out in the next Stata Journal that details how
to create synthetic models for a wide  variety
of discrete response regression models. For your problem though, I
think that the best approach is to create a synthetic
binary logistic model with a single predictor - as you specified. Then
model the otherwise logistic data as
Poisson with a robust variance estimator. And the coefficient must be
exponentiated. It can be interpreted as a relative
risk ratio.

Below is code to create a simple binary logistic model. Then model as
mentioned above. You asked for a
continuous pseudo-random variate, so I generated it from a normal
distribution. I normally like to use pseudo-random
uniform variates rather normal variates when creating these types of
models, but it usually makes little difference.
Recall that without a seed the model results will differ each time run.
If you want the same results, pick a seed. I used my birthday.

I hope that this is what you were looking for.

Joseph Hilbe

*  intercept = 2;  Beta for X1=0.75
clear
set obs 50000
set seed 1230
gen x1 = invnorm(runiform())
gen xb = 2 + 0.75*x1
gen exb = 1/(1+exp(-xb))
gen by = rbinomial(1, exb)
glm by x1, nolog fam(bin 1)
glm by x1, nolog fam(poi) eform robust

. glm by x1, nolog fam(bin 1)
Generalized linear models                          No. of obs      =
50000
Optimization     : ML                              Residual df      =
49998
Scale parameter = 1
Deviance         =  37672.75548                    (1/df) Deviance =
.7534852
Pearson          =  49970.46961                    (1/df) Pearson  =
.9994494
Variance function: V(u) = u*(1-u)                  [Bernoulli]
Link function    : g(u) = ln(u/(1-u))              [Logit]
AIC             =
.7535351
Log likelihood   = -18836.37774                    BIC             =
-503294.5
-------------------------------------------------------------------------
-----
|                 OIM
by |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+-----------------------------------------------------------
-----
x1 |   .7534291   .0143134    52.64   0.000     .7253754
.7814828
_cons |   1.993125   .0149177   133.61   0.000     1.963887
2.022363
-------------------------------------------------------------------------
-----

. glm by x1, nolog fam(poi) eform robust
Generalized linear models                          No. of obs
=50000
Optimization     : ML                              Residual df     =
49998
Scale parameter = 1
Deviance         =  12673.60491                    (1/df) Deviance =
.2534822
Pearson          =   7059.65518                    (1/df) Pearson  =
.1411988
Variance function: V(u) = u                        [Poisson]
Link function    : g(u) = ln(u)                    [Log]
AIC             =
1.970592
Log pseudolikelihood = -49262.80246                BIC             =
-528293.7
-------------------------------------------------------------------------
-----
|               Robust
by |        IRR   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+-----------------------------------------------------------
-----
x1 |   1.104476   .0021613    50.78   0.000     1.100248
1.10872
-------------------------------------------------------------------------
-----
.
Tomas Lind wrote:
Does anyone know how to generate fake data for a dichotomous outcome
(0, 1)
that is dependent on a continuous exposure variable in an
epidemiological
relative risk context. I know how to use the logit transformation but in
that case exposure is proportional to log(ods) and not to risk.

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```