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Re: error message-Hessian of posterior density is non positive definite during search

From: Gastonguay, Marc <marcg>
Date: Fri, 26 Feb 2010 12:34:16 -0500

Vincenzo / Amit:
A quick inspection of your code reveals a typo in the denominator of
your probability expression.

P = EXP(A)/1+EXP(A)
  should be:
P = EXP(A)/ (1+EXP(A))

Due to FORTRAN order of operation, you need the parentheses around the
entire term (1+EXP(A)).

Hope this helps.

Marc

Marc R. Gastonguay, Ph.D.
President & CEO, Metrum Research Group LLC < metrumrg.com >
Scientific Director, Metrum Institute < metruminstitute.org >
2 Tunxis Rd, Suite 112, Tariffville, CT 06081 Direct:
+1.860.670.0744 Main: +1.860.735.7043 Fax: +1.860.760.6014



On Feb 26, 2010, at 11:35 AM, Vincenzo Di Iorio wrote:

>
> On behalf of Amit Taneja:
>
> Dear Nonmem users,
>
> I have been trying to fit a linear logistic model to a set of binary
> response data in nonmem6. However, nonmem terminates and gives the
> following
> message. My dataset has 36 subjects and 5 pd sample points per
> subject. On
> the other hand, a logistic emax model fits the data well and
> consistently. I
> even get the covariance step. One would expect a linear model to fit
> more
> easily than an emax model?
>
> My control stream is provided below as is a sample of the dataset,
> and the
> output file is enclosed. I would appreciate your inputs on resolving
> this
> vexing issue.
>
> Thanks
> Amit Taneja
>
> Pharmacology
> Leiden Amsterdam Center for Drug Research
> Leiden
> Netherlands
>
> ------------------
>
> Relevant part of output file (Error message)=
>
> MONITORING OF SEARCH:
>
> 0HESSIAN OF POSTERIOR DENSITY IS NON-POSITIVE-DEFINITE DURING SEARCH
>
> ----------------------------------
>
> $PROB
> $INPUT ID TIME PDB=DV PD CAUC MDV EVID DGRP
> $DATA GpdV_od.csv IGNORE=
>
> $PRED
> ;in this model we fit a linear model in the logit space
>
> ; Baseline Probabilities
> PLAC = THETA(1)
>
> ; Drug Conc effect Emax model, assuming gamma = 1
> SLOP = THETA(2)
> ;EC50 = THETA(3)
> DRUG = SLOP*CAUC
>
> ; Logit
> A = DRUG + PLAC + ETA(1) ;
>
> ; the term exp(drug+plac+eta) is expressed as A
> P = EXP(A)/1+EXP(A)
>
> ;PB0 = P0/(1+P0) ; Probability of parameter=0 ; e**x/1+e**x; x=logit
> function
> ;PB1 = 1-PB0 ; probability of parameter=1
> ;IF (DV.EQ.0) PB = PB0
> ;IF (DV.EQ.1) PB = PB1
>
> Y = -2*PDB*A-2*LOG(1-P)
>
> $THETA
> (1,157.9) ; PLAC Theta(1)
> (1,10) ; SLOP Theta(2)
> ; EC50 EPER 1 Theta(3)
> ;15.85 ; L0 Theta(4)
>
> $OMEGA
> 1
>
> $ESTIM METHOD=COND LAPLACIAN -2LL
> $COV MAT=R
>
> $TABLE ID TIME P PD CAUC PLAC SLOP MDV EVID DGRP NOPRINT ONEHEADER
> FILE=Gp_lin15.tab
>
>
> # SAMPLE OF THE INPUT DATASET
>
> ID TIME PDB PD CAUC MDV EVID DGRP CONC
> 1 0 0 5.328576 0 0 0 0 0
> 1 1 0 0.499059 0 0 0 0 0
> 1 2 1 22.8096 0 0 0 0 0
> 1 3 0 0.299475 0 0 0 0 0
> 1 4 0 0.333036 0 0 0 0 0
> 8 0 0 2.168496 0 0 0 100 0
> 8 1 1 111.4464 1131.1 0 0 100 359.43
> 8 2 1 54.94748 3638.7 0 0 100 541.01
> 8 3 1 222.75 6887.6 0 0 100 636.91
> 8 4 1 222.75 10529.2 0 0 100 688.48
> 15 0 0 17.21501 0 0 0 100 0
> 15 1 1 65.75828 1131.1 0 0 100 356.33
> 15 2 1 222.75 3638.7 0 0 100 541
>
>
> -----------------------------------------------------------------------------------
> Vincenzo Luca Di Iorio
> Consultant PME User support - GSK R&D Limited
> -----------------------------------------------------------------------------------
>
>
> -----------------------------------------------------------
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>


Received on Fri Feb 26 2010 - 12:34:16 EST

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