From: "Hutmacher, Matt" - mhutmach@amgen.com Subject: [NMusers] Fitting Data Below the Quantification Limit Date: 1/6/2004 6:23 PM Hello all, I was wondering if anyone has experience fitting PK Models where some data are below the quantification limit. Specifically, if anyone has attempted to fit the censored likelihoods that are described in Stuart Beal's JPP manuscript, JPP 2001; 28 481-504. If you have any NONMEM code or implementation suggestions it would be greatly appreciated. Thanks, Matt _______________________________________________________ From: Lewis B. Sheiner - lbs@lewisbsheiner.net Subject: RE: [NMusers] Fitting Data Below the Quantification Limit Date: 1/10/2004 5:21 PM All - As I understand it, NM6 should have built-in code to do the necessary integrations in a conveneint way. In the mean-time, here (below and attached) is some code that Russ Wada, Bill Poland, and I came up with that works at least on a very simple test problem. That's all the testing I've done. The code assumes Y|eta is normally distributed with expected value = MN and standard deviation = SD, so it will not work for time-to-event Y, logisticY, etc. LBS. ========================================================== $ERROR [or $PRED] MN= ... ; Your model for E(DV); often just F SD= ... ; Your model for SD(DV) QL= ... ; The QL -- A fixed value X=(QL-MN)/SD ABSX=X IF (X.LT.0) ABSX=-X ; compute -2LL contrib l2pi=1.837877 ; log 2*pi IF (DV .GT. QL) THEN ; >QL case: L=N(MN,SD2) Y = l2pi + 2*LOG(SD)+((DV-MN)/SD)**2 ENDIF IF (DV .LE. QL) THEN; >QL case: L=N(MN,SD2), need CUM NL ; Compute NN = Std CUM NL (STDNCDF) at X -- from Abramovitz & Stegun, ; Handbook of Mathematical Functions b1=0.31938153 b2=-0.356563782 b3=1.781477937 b4=-1.821255978 b5=1.330274429 pp=0.2316419 c2=0.3989423 tt=1/(1+ABSX*pp) b=c2*EXP(-1/2*ABSX**2) n1=((((b5*tt+b4)*tt+b3)*tt+b2)*tt+b1)*tt n2=1-b*n1 ENDIF IF(DV .LE. QL.AND.X.LT.0) THEN ; belongs in above 'IF' but can't nest NN=1-n2 ELSE NN = n2 ENDIF IF (DV.LT.QL.AND.ABSX.LT.6) THEN Y = -2*LOG(NN) ENDIF IF(DV .LE. QL .AND. X .GE. 6.0) THEN ; X > +6SD, STDNCDF~ 1 Y = 0 ENDIF IF(DV .LE. QL .AND. X .LE. -6.0) THEN ; X < -6SD, trunc to -2*log(1-STDNCDF(6)) Y = -37.8379 ; ENDIF $EST METHOD=COND LAPLACE -2LL $THETA ... $OMEGA ... ==================================================================== _______________________________________________________