constant CV

From: Thierry Buclin <Thierry.Buclin@chuv.hospvd.ch> Subject: constant CV Date: Fri, 27 Apr 2001 09:39:41 +0200 Brian Thank you for the light-clear explanation about Clement's question. I have a perplexing interrogation about the intuitive meaning of the coefficient ov variation estimated in the "constant CV" error model (e.g. CL=TVCL*EXP(ETA(1)). You state that the mean and variance of a log normal distribution are exp(log(TVCL) + 0.5*omegasquared) and exp(omegasquared) - 1)*exp(2*log(TVCL) + omegasquared) respectively, implying that the coefficient of variation is sqrt(exp(omegasqrared) - 1). Consider a "constant" error model giving three individual estimates of CL, say 2, 4 and 6 L/h. The omegasquared is 4 and the SD is 2 L/h : this value describes the typical variation among individual estimates, this is intuitively convincing, OK ? Now consider a "constant CV" error model giving individual CL estimates of 2, 4 and 8 L/h. Intuitively, I would consider that the Logs display a typical variation of Log(2), and therefore the CL estimates a variation by a factor of 2, hence a CV of 100%. However, the calculation you mention gives a CV of 78.5%. I am convinced that it is statistically founded, but how could you reconcile this result with common sense intuition ? In other words, if I fit a model assuming constant CV error, is it better to report CV values calculated according to sqrt(exp(omegasqrared) - 1) or to exp(sqrt(omegasquared)) -1 ? Thierry BUCLIN, MD Lecturer, consulting physician and clinical researcher Division of Clinical Pharmacology University Hospital CHUV - Beaumont 633 CH 1011 Lausanne - SWITZERLAND Tel: +41 21 314 42 61 - Fax: +41 21 314 42 66