Cancel first part of question re Logistic

From: Doug Oman <oman@stat.berkeley.edu> Subject: Cancel first part of question re Logistic Date: 23 Jan 1998 12:57:54 -0500 Oops, how embarrassing, cancel first question (the model is properly identified - exponents are multiplied, not added). I'd still be interested in answers to other questions - what is sigmoid emax model?; should my simple PRED code work; Apologies for the clutter and thanks for your help -D. Oman -- >From Douglas W. Oman Department of Biostatistics, U.C. Berkeley oman@stat.berkeley.edu (forwards to Home below) Home dougoman@wco.com (707) 878-2573

From: Doug Oman <oman@stat.berkeley.edu> Subject: Logistic Mixed models with NONMEM Date: 23 Jan 1998 12:58:09 -0500 Some questions about using NONMEM for mixed logistic modelling: 1. It seems that in the example PRED record (copied below) from the logistic modelling section in the NONMEM user's archives, that THETA(1) and THETA(3) only appear together, ie, as THETA(1)*EXP(THETA(3)). Therefore the model should not be identifiable (ie, there would be an infinite number of solutions; the way to generate other solutions from one solution would be to add K to THETA(3) and divide THETA(1) by EXP(K)). Surely this can't be correct? 2. I've created a very simple PRED record (also below) for calculation of a global mean in a mixed logistic model (ie, the covariate DOSE is no longer present). Should it work? $SUBROUTINES CONTR=contr CCONTR=ccontr $PRED ; NEXT LINE IS VERBATIM CODE " CALL GETETA(ETA) A = THETA(1)+ETA(1) B = EXP(A) P = B/(1+B) Y = P**DV*(1-P)**(1-DV) 3. The documentation for the PRED record from the NONMEM user's archives (copied below) says that it implements a 'sigmoid emax model'. I know little pharmacology so I don't know what that model is. How can I find out (Online resources, if any, would be especially helpful)? Thank you -Doug Oman ================ EXAMPLE PRED RECORD FROM NONMEM ARCHIVES ============ $PROB POP [>1 OBS/INDIVID] $DATA <your_data_file> $INPUT ID=L1 DOSE DV $SUBROUTINES CONTR=contr CCONTR=ccontr $PRED ; NEXT LINE IS VERBATIM CODE " CALL GETETA(ETA) GAMMA=THETA(1)*EXP(THETA(3)*ETA(1)) IF(GAMMA.GT.10) EXIT D50 = THETA(2)*EXP(ETA(1)) IF(D50.LT..00001) EXIT LDOS= LOG(DOSE) A = GAMMA*LDOS - GAMMA*LOG(D50) B = EXP(A) P = B/(1+B) Y = P**DV*(1-P)**(1-DV) ;$THETA, $OMEGA, as necessary/desired. ;be sure to use METH=1 LAPLACE on $EST -- >From Douglas W. Oman Department of Biostatistics, U.C. Berkeley oman@stat.berkeley.edu (forwards to Home below) Home dougoman@wco.com (707) 878-2573

From: lewis@c255.ucsf.EDU (LSheiner) Subject: Logistic Mixed models with NONMEM Date: 23 Jan 1998 19:44:58 -0500 To reply to Doug's comments - I'm not saying there wouldn't be problems, but Doug's concern is not entirely justified ... THETA(3) multiplies ETA(1), so that, equivalently, GAMMA=THETA(1)*EXP(ETA(1))**THETA(3), or GAMMA = a*RV**b, Where RV = log-normally distributed random variable. The two constants, a and b, are not, in principle, unidentifiable. In fact, the model I used arose in a particular problem because the more general model (below) showed that ETA(1) and ETA(2) had a correlation of 1 in the particular data set I was analysing. Here is the more general case (which I will now put in the repository to avoid further confusion): $PRED ; NEXT LINE IS VERBATIM CODE " CALL GETETA(ETA) GAMMA=THETA(1)*EXP(ETA(1)) IF(GAMMA.GT.10) EXIT D50 = THETA(2)*EXP(ETA(2)) IF(D50.LT..00001) EXIT LDOS= LOG(DOSE) A = GAMMA*LDOS - GAMMA*LOG(D50) B = EXP(A) P = B/(1+B) Y = P**DV*(1-P)**(1-DV) ..... $OMEGA BLOCK (2) .2 .1 .2 > > 2. I've created a very simple PRED record (also below) > for calculation of a global mean in a mixed logistic model > (ie, the covariate DOSE is no longer present). Should it work? > $SUBROUTINES CONTR=contr CCONTR=ccontr > $PRED > ; NEXT LINE IS VERBATIM CODE > " CALL GETETA(ETA) > A = THETA(1)+ETA(1) > B = EXP(A) > P = B/(1+B) > Y = P**DV*(1-P)**(1-DV) > Looks fine to me. > > 3. The documentation for the PRED record from the NONMEM > user's archives (copied below) says that it > implements a 'sigmoid emax model' . > I know little pharmacology so I don't know > what that model is. How can I find out (Online > resources, if any, would be especially helpful)? > See the README.009 file in the same directory. Also, you can read about the various types of PD models, for example (and among many other places) in: Black JW, Leff P: Operational models of pharmacological antagonism. Proc Roy Soc B, 220:141-162, 1983, or Holford NHG, Sheiner LB: (a) Pharmacokinetic and Pharmacodynamic modelling in vivo. CRC-Critical Reviews in Bioengineering, 5:273, 1981; (b) Understanding the Dose-Effect Relationship: Clinical application of pharmacokinetic-pharmacodynamic models. Clinical Pharmacokinetics 6: 429, 1981; (c) Kinetics of pharmacologic Response. Pharmac. Ther. 16:143, 1982, and in Rowland, M & Tucker, G (eds), Pharmacokinetics: Theory and Methodology, Pergammon Press, Oxford, 1986.