Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

D. E. Clark; M. El-Taha

doi:10.1055/s-0038-1634534

Methods of Information in Medicine, Table of Contents

Methods Inf Med 1998; 37(03): 235-238
DOI: 10.1055/s-0038-1634534

Original Article

Schattauer GmbH

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

D. E. Clark

¹Department of Surgery, Maine Medical Center, Portland, ME

,

M. El-Taha

²Department of Mathematics and Statistics, University of Southern Maine, Portland, ME, USA

› Author Affiliations

Abstract

A Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (e^x)/(1 + e^x). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

Keywords

Decision Tree - Probabilistic - Monte Carlo - Correlation - LogisticNormal

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References

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