Re: Error models and weighting

From: Nick Holford <n.holford@auckland.ac.nz> Subject: Re: Error models and weighting Date: Thu, 24 May 2001 20:40:30 +1200 The THETA(.) estimates the constant component not the proportional part. You are using a trick to make NONMEM do something it wasn't designed to do. Look at it this way -- the usual mixed proportional and constant error model: Y=F*(1+EPS(1) + EPS(2) or Y=F + F*EPS(1) + EPS(2) or Y=F + (F*EPS(1) + EPS(2))*1 or Y=F + standard_deviation*1 The trick is to use a FIXED EPS of 1 instead of the "*1" at the end and replace (F*EPS(1) + EPS(2)) with the equivalent standard_deviation. The total variance is: (F*THETA(CV))**2 + THETA(SD)**2 and it's square root, the standard_devation for that particular prediction is: SQRT((F*THETA(CV))**2 + THETA(SD)**2) where THETA(CV) is the THETA that estimates the proportional component and THETA(SD) is a THETA that estimates the constant component. So I suggest you use $SIGMA 1 FIX and add a THETA for THETA(CV) and use THETA(.) as THETA(SD) then write this: W=SQRT((F*THETA(CV))**2 + THETA(SD)**2) ; proportional + constant You can estimate EPS(1) instead of FIXing it to 1 (as suggested in the Xpose manual) but IMHO its clearer with two THETAs and the estimates are immediately interpretable as the approx. CV (THETA(CV) and the SD (THETA(SD)) of the residual unidentified variability (RUV) model. If you use the Xpose method then SQRT(SIGMA(1)) is the same as THETA(CV) and SQRT(SIGMA(1))*THETA(.) is the same as THETA(SD). > In a previous message via nmusers, Leonid Gibiansky suggested that I use > a simplier model - e.g. Y = F*(1+EPS(1))+EPS(2). If this model is > used, I do not know how to get IWRES for using Xpose. Why do you want to get IWRES? As far as I know Xpose only uses it for a residual plot. Like almost all residual plots the IWRES is practically worthless as a diagnostic. Just assign IWRES=1 to keep Xpose happy and use the much simpler and more elegant method that Leonid recommends to describe the RUV. You won't have to worry about F being zero either (provided THETA(SD) is > 0). -- Nick Holford, Divn Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556 http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm