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From |
"Daniel Waxman" <dan@amplecat.com> |

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

Subject |
st: RE: simulated data for logistic regression... remedial algebra help? |

Date |
Sun, 18 Nov 2007 23:56:34 -0500 |

Not sure if the lack of response reflects a lack of clarity in stating the problem, or just that the solution isn't obvious to anyone. In case it is the former, I'll restate the problem: The goal is to create a simulated data set. To do so, I would like to determine the probabilities of an outcome (death) given a positive or negative test result, when the overall mortality rate, the odds ratio for mortality as a function of that test and proportion of positive test results in the population are known. The problem reduces (I believe) to solving: p1/(1-p1)=2(p2/(1-p2) p2= k1-p1k2 where: p1 = mortality rate for a positive test p2 = mortality rate for a negative test k1 = constant = (overall mortality rate)/(proportion of population with a positive test) k2 = constant = (proportion negative test)/(proportion positive test) Does this problem look familiar to anyone? If my poor math skills are not failing me, I believe that I end up with p1^3 term. Does this sound right? Would it mean that there is no exact solution? Any other suggestions for creating simulated data with these properties? Dan -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Daniel Waxman Sent: Saturday, November 17, 2007 6:44 PM To: statalist@hsphsun2.harvard.edu Subject: st: simulated data for logistic regression... remedial algebra help? I am trying to create a series of simulated data sets for use in logistic regression with the following properties: Mortality (outcome) remains constant. There is a single dichotomous independent variable whose odds ratio (coefficient) and proportion of positives can vary between the sets. It all comes down to solving for the intercept (`b0'), given the following relationships: probability_negative=invlogit(`b0’) probability_positive=invlogit(log(`odds’)+`b0’) `proportion_positive’*probability_positive+(1-`proportion_positive’)*probabi lity_negative=`mortality’ Sad to admit, but I am bumping up against the limitations of my algebra skills. I'd imagine this is trivial for many of you... i.e.: ************** clear set obs 1000 local odds=2 local proportion_positive= .10 local mortality = .05 gen test=uniform()<`proportion_positive’ /* ************solve for `b0' here************ */ gen probability_negative=invlogit(`b0’) gen probability_positive=invlogit(log(`odds’)+`b0’) gen died=uniform() < cond(test==0,probability_negative,probability_positive) logistic died test ************************ Thanks. Dan No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.5.503 / Virus Database: 269.16.0/1136 - Release Date: 11/17/2007 2:55 PM * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: simulated data for logistic regression... remedial algebra help?***From:*Steven Joel Hirsch Samuels <sjhsamuels@earthlink.net>

**Re: st: RE: simulated data for logistic regression... remedial algebra help?***From:*Steven Joel Hirsch Samuels <sjhsamuels@earthlink.net>

**References**:**st: simulated data for logistic regression... remedial algebra help?***From:*"Daniel Waxman" <dan@amplecat.com>

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