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st: RE: risk ratio
From
Joseph Hilbe <[email protected]>
To
[email protected]
Subject
st: RE: risk ratio
Date
Sat, 20 Mar 2010 13:01:47 -0700
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
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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