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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: RE: risk ratio |

Date |
Sun, 21 Mar 2010 16:52:34 -0000 |

As a footnote to this, note a few equivalences: invlogit(x) <=> 1 / (1 + exp(-x)) rnormal() <=> invnorm(runiform()) An alternative to gen x1 = invnorm(runiform()) gen xb = 2 + 0.75*x1 gen exb = 1/(1+exp(-xb)) gen by = rbinomial(1, exb) is thus gen x1 = rnormal() gen by = rbinomial(1, invlogit(2 + 0.75*x1)) Nick n.j.cox@durham.ac.uk Joseph Hilbe 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. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: RE: risk ratio***From:*Joseph Hilbe <j.m.hilbe@gmail.com>

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