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From: Paolo Denti <paolo.denti_at_uct.ac.za>

Date: Fri, 20 May 2016 17:14:48 +0200

Dear Bob and Alison,

thank you for the prompt responses.

So it seems like the same TOL is used both for the precision of the differe=

ntial equations and the stopping criterion of SS, correct?

Bob

I am not sure I feel brave/bold enough to recode my own version of NONMEM, =

but I can try.

The question is, would this also decrease the TOL of the DE solver while ca=

lculating SS? Because that may have other consequences, while all I would l=

ike to do is to make the SS routine less picky, without decreasing the prec=

ision of the whole run.

Alison,

to get the values in the compartments, I have just asked NONMEM to print ou=

t the values while executing the $DES block.

NONMEM spits out a huge table here, so I filtered out only the values at ti=

me 0, after each cycle of repeated dosing. It is true that at time 0 NONMEM=

puts the dose back in, but when looking at the tail of the curve (at aroun=

d II hours) all the values in the absorption compartments are super small o=

r also negative. If one uses transit compartments absorption, that's even w=

orse. I have pasted code and dataset below, but I will also send you a sepa=

rate email with attachments.

Thanks to both for looking into this. I really think it would help to speed=

this up, as I have spoken to other people with the same problem.

Ciao,

Paolo

Dataset:

#ID TIME EVID AMT DV MDV SS II

1 0 1 450 . 1 1 24

1 1 0 . . 0 0 .

1 4 0 . . 0 0 .

1 11 0 . . 0 0 .

1 24 0 . . 0 0 .

Model file:

$PROBLEM SS investigation - normal 1st order NO LAG

$INPUT ID TIME EVID AMT DV MDV SS II

$DATA Sim_SS.csv IGNORE=#

$SUBROUTINE ADVAN13 TRANS1 TOL=9 ; TOL=3

$MODEL NCOMPARTMENTS=2

COMP=(DEPOT,DEFDOSE)

COMP=(CENTRAL)

$THETA (0,8) ; 1. TVCL [L/h]

$THETA (0,40) ; 2. TVV [L]

$THETA (0,2) ; 3. TVKA [1/h]

$THETA (0,0.15) ; 4. Sigma_prop

$THETA (0,0.5) ; 5. Sigma_add [mg/L]

$THETA (0,0,2) FIX ; 6. DUMMY

$THETA (0,0,15) FIX ; 7. DUMMY

$OMEGA 0 FIX ; 1. BSV_CL

$OMEGA 0 FIX ; 2. BSV_Vd

$OMEGA 0 FIX ; 3. BSV_Ka

$OMEGA 0 FIX ; 4. BSV_BIO

$OMEGA 0 FIX ; 5. BSV_MTT

$SIGMA 1 FIX ; RESIDUAL

$PK

BSVCL= ETA(1) ; BSV_CL

BSVV = ETA(2) ; BSV_V

BSVKA= ETA(3) ; BSV_KA

BSVBIO=ETA(4) ; BSV_BIO

BSVMTT=ETA(5) ; BSV_MTT

TVCL =THETA(1) ; Pop CL

TVV =THETA(2) ; Pop V

TVKA =THETA(3) ; Pop KA

TVBIO=1 ; Pop BIO

SIG_PROP=THETA(4) ; Sigma PROP

SIG_ADD=THETA(5) ; Sigma ADD

;ALAG1 = THETA(6)

CL=TVCL * EXP(BSVCL)

V =TVV *EXP(BSVV)

KA=TVKA*EXP(BSVKA)

BIO=TVBIO*EXP(BSVBIO)

K=CL/V

F1 = BIO

WRITE(50,2) 1, ID,TIME,A(1),A(2) ; TO OUTPUT INTERGRATION STEPS IN TEXTFIL=

E

$DES

DADT(1) = -KA*A(1)

DADT(2) = KA*A(1) -K*A(2)

WRITE(50,2) 2, ID,T,A(1),A(2) ; TO OUTPUT INTERGRATION STEPS IN TEXTFILE

$ERROR

IPRED = A(2)/V

IRES = DV - IPRED

W=SQRT((SIG_PROP*IPRED)**2+SIG_ADD**2) ; Residual SD

IWRES=IRES/W

Y=IPRED+W*EPS(1)

AA1=A(1)

AA2=A(2)

WRITE(50,2) 3, ID,TIME,A(1),A(2) ; TO OUTPUT INTERGRATION STEPS IN TEXTFIL=

E

$SIMULATION (123) ONLYSIM

;$ESTIMATION METHOD=1 INTER MAXEVAL=9999 PRINT=1 NOABORT NSIG=3; c=

alculation method

On 2016/05/19 16:23, Alison Boeckmann wrote:

Dear Paolo,

As Bob explained, ZSPOW uses the TOL defined by the user in the $SUBROUTIN=

ES record to determine precision. ADVAN9 and ADVAN13 also use a separate a=

bsolute tolerance ATOL, which is by default set to 12, but you can modify i=

t with $EST … ATOL= , and see if it affects the precision of the =

SS evaluation.

You could also try using ADVAN6/SS6.

I can't understand why the SS option is taking so long with ADVAN13/SS13. =

The table of results you report do not correspond to the way SS is computed=

in PREDPP, and I can't understand where you got the numbers in the table.

You say "the amount in the absorption compartment AA1 is literally numerica=

l noise after II hours". But PREDPP never reports this amount, because SS a=

mounts are reported *after* a dose has been administered.

The way SS with multiple dosing is computed is described in the May 2015 ve=

rsion of Guide VI PREDPP. This is supplied with the latest alpha versions =

of NONMEM7.4. See Chapter V. Event Records, Section F.4 Implementation of =

Steady State. There are three calls to ADVAN with TIME=0 to obtain the i=

nitial estimate. After that, the root finder ZSPOW makes as many calls as =

it needs, but they are not necessarily sequential in TIME.

Can you please send me your control stream and a fragment of the data so I =

can figure out what is going on?

Alison

PS. In case you don't have the May 2015 version of guide VI PREDPP, here is=

an extract:

(The guide still needs to be updated for ADVAN13, but the same process is u=

sed.)

=========================

When the model is defined by differential equations (SS6, SS8, SS9), PREDPP=

cannot use an ana- lytic solution, even if one happens to exist. Instead, =

the solutions are found by a numerical technique using ZSPOW, a root-findin=

g subroutine from IMSL.

With multiple dosing, ZSPOW searches for a vector of compartment amounts an=

d their eta deriva- tives such that the initial and final (end of dosing in=

terval) vector is the same. ADVAN6, ADVAN8, and ADVAN9 perform a numerical =

integration of the differential equations (and in the case of ADVAN9, algeb=

raic equations). The ADVAN routine is used to advance (integrate) the state=

vector A from time 0 to time II with the appropriate dose pattern. Let AII=

represent the state vector after advance to time II with the appropriate d=

ose. A search is made for Ass such that Ass - AII = 0

If SS=3, the state vector A contains user-supplied initial estimates. Oth=

erwise, the SS routines sets A=0 and makes three calls to ADVAN. Each cal=

l advances the state vector from t=0 to t=II with the appropriate dosin=

g pattern. The result is the initial estimate.

Once the SS solution is found, the SS routine adds the final bolus dose to =

the state vector, or starts the final infusion.

===================

Paolo:

From what I can tell in scanning the code of ..\pr\SS13.f90, the TOL settin=

g on the $SUBROUTINES record appears to determine the precision of the stea=

dy state condition. You can change the TOL value, or, if you wish the SS p=

recision to differ from the ODE evaluation precision, you can modify SS13.f=

90, as it is open source to users, by replacing the NRD argument (which con=

tains the TOL value submitted by the $SUBROUTINES record) to all calls to Z=

SPOW1 with an alternative value of your choosing. Recompile SS13.f90, then=

execute NONMEM with nmfe73 script as usual.

Robert J. Bauer, Ph.D.

Vice President, Pharmacometrics R&D

ICON Early Phase

820 W. Diamond Avenue

Suite 100

Gaithersburg, MD 20878

Office: (215) 616-6428

Mobile: (925) 286-0769

<mailto:Robert.Bauer_at_iconplc.com>Robert.Bauer_at_iconplc.com<mailto:Robert.Bau=

er_at_iconplc.com>

<http://www.iconplc.com/>www.iconplc.com<http://www.iconplc.com>

On Wed, May 18, 2016, at 03:15 AM, Paolo Denti wrote:

Dear NMUsers (and developers),

I am trying to speed up our run times when using SS in ADVAN13 models (user=

defined differential equations), and I would like to share some thoughts t=

o get some feedback.

We work on steady-state PK data, so ideally we would like to use the SS opt=

ion, but the run times whenever we use ADVAN13 become unfeasibly long (even=

20 times more), and this even for models that should reach steady state in=

2-3 doses.

As an alternative we end up using ad-hoc "patch-up" solutions, like initial=

ising compartments, or just adding 4-5 doses "manually" in the dataset, but=

this is a bit tedious/tricky.

I am writing to see if there is a way to speed up the SS feature.

I decided to look into what was going on by asking NONMEM to simulate a SS =

PK profile and print out all the temporary iterations.

It seems like NONMEM first opens a separate "SS session" used to work out t=

he SS amounts in each compartment. The model is taken to SS by repeatedly g=

iving doses every II, until the system is deemed to have reached steady-sta=

te. At this point, NONMEM goes back to the "main session", initialises all =

compartments to the amounts found in the "SS session", gives the final dose=

, and moves on with the analysis.

Nothing surprising here, and it's understandable that things take longer wi=

th SS, cuz the calculation of these SS amounts implies solving the differen=

tial equations for all the extra time of the "SS session". What I found odd=

though, is that the number of doses that NONMEM uses to reach steady-state=

seems to me much higher than needed. In my test I used a simple 1-cmpt KA =

model coded in ADVAN13 and a drug with a half-life of 3.5 hours, so I was e=

xpecting 2 dosing intervals (48 hours) to be more than enough to get to ste=

ady state, as maths says the amounts should be 99.993% there. NONMEM instea=

d used 13 doses in the example below.

The amounts are reported in the table below. After iteration 3 the amount i=

n AA2 just changes by tiny values, arguably comparable to numerical noise.

#DOSE T TOT_TIME AA2

0 0 0 0

1 0 24 4.114874

2 0 48 4.148738

3 0 72 4.149017

4 0 96 4.149017

5 0 120 4.149017

6 0 144 4.149019

7 0 168 4.149019

8 0 192 4.149019

9 0 216 4.149019

10 0 240 4.149019

11 0 264 4.149019

12 0 288 4.149019

13 0 312 4.149019

Does anyone know what stopping criterion NONMEM uses to call it SS and move=

on? Is there a way to relax it? I think 0.1% would be fine in most practic=

al cases - at least for preliminary runs - and in this example it would sav=

e 80% of the run time. Plus if one keeps in mind that this is a numerical s=

olver, it is not clear how "real" the wee digits are, obviously depending o=

n TOL.

The other tricky thing I found is that the amount in the absorption compart=

ment AA1 is literally numerical noise after II hours, meaning that for some=

entries it is even negative (e.g. -2.08038E-15) and jumps between positive=

and negative. Could it be that this is what is tricking NONMEM's stopping =

criterion to detect SS? Maybe if the stopping criterion only asks for a rel=

ative change <TOL, it will struggle to achieve that with values that change=

sign.

Any settings that may help speed things up? Something like tinkering with T=

OL and ATOL?

Or maybe is it possible to set a maximum to the number of doses that NONMEM=

tests to reach steady-state?

Sorry for the nerdy topic, and thanks for any advice!

Ciao,

Paolo

PS And big thanks to our PhD student Maxwell who ran all the tedious simula=

tions!

--

------------------------------------------------

Paolo Denti, PhD

Pharmacometrics Group

Division of Clinical Pharmacology

Department of Medicine

University of Cape Town

K45 Old Main Building

Groote Schuur Hospital

Observatory, Cape Town

7925 South Africa

phone: +27 21 404 7719

fax: +27 21 448 1989

email: paolo.denti_at_uct.ac.za<mailto:paolo.denti_at_uct.ac.za>

------------------------------------------------

Disclaimer - University of Cape Town This e-mail is subject to UCT policies=

and e-mail disclaimer published on our website at http://www.uct.ac.za/abo=

ut/policies/emaildisclaimer/ or obtainable from +27 21 650 9111. If this e-=

mail is not related to the business of UCT, it is sent by the sender in an =

individual capacity. Please report security incidents or abuse via csirt_at_uc=

t.ac.za<mailto:csirt_at_uct.ac.za>

--

Alison Boeckmann

alisonboeckmann_at_fastmail.fm<mailto:alisonboeckmann_at_fastmail.fm>

--

------------------------------------------------

Paolo Denti, PhD

Pharmacometrics Group

Division of Clinical Pharmacology

Department of Medicine

University of Cape Town

K45 Old Main Building

Groote Schuur Hospital

Observatory, Cape Town

7925 South Africa

phone: +27 21 404 7719

fax: +27 21 448 1989

email: paolo.denti_at_uct.ac.za<mailto:paolo.denti_at_uct.ac.za>

------------------------------------------------

Disclaimer - University of Cape Town This e-mail is subject to UCT policies=

and e-mail disclaimer published on our website at http://www.uct.ac.za/abo=

ut/policies/emaildisclaimer/ or obtainable from +27 21 650 9111. If this e-=

mail is not related to the business of UCT, it is sent by the sender in an =

individual capacity. Please report security incidents or abuse via csirt_at_uc=

t.ac.za

Received on Fri May 20 2016 - 11:14:48 EDT

Date: Fri, 20 May 2016 17:14:48 +0200

Dear Bob and Alison,

thank you for the prompt responses.

So it seems like the same TOL is used both for the precision of the differe=

ntial equations and the stopping criterion of SS, correct?

Bob

I am not sure I feel brave/bold enough to recode my own version of NONMEM, =

but I can try.

The question is, would this also decrease the TOL of the DE solver while ca=

lculating SS? Because that may have other consequences, while all I would l=

ike to do is to make the SS routine less picky, without decreasing the prec=

ision of the whole run.

Alison,

to get the values in the compartments, I have just asked NONMEM to print ou=

t the values while executing the $DES block.

NONMEM spits out a huge table here, so I filtered out only the values at ti=

me 0, after each cycle of repeated dosing. It is true that at time 0 NONMEM=

puts the dose back in, but when looking at the tail of the curve (at aroun=

d II hours) all the values in the absorption compartments are super small o=

r also negative. If one uses transit compartments absorption, that's even w=

orse. I have pasted code and dataset below, but I will also send you a sepa=

rate email with attachments.

Thanks to both for looking into this. I really think it would help to speed=

this up, as I have spoken to other people with the same problem.

Ciao,

Paolo

Dataset:

#ID TIME EVID AMT DV MDV SS II

1 0 1 450 . 1 1 24

1 1 0 . . 0 0 .

1 4 0 . . 0 0 .

1 11 0 . . 0 0 .

1 24 0 . . 0 0 .

Model file:

$PROBLEM SS investigation - normal 1st order NO LAG

$INPUT ID TIME EVID AMT DV MDV SS II

$DATA Sim_SS.csv IGNORE=#

$SUBROUTINE ADVAN13 TRANS1 TOL=9 ; TOL=3

$MODEL NCOMPARTMENTS=2

COMP=(DEPOT,DEFDOSE)

COMP=(CENTRAL)

$THETA (0,8) ; 1. TVCL [L/h]

$THETA (0,40) ; 2. TVV [L]

$THETA (0,2) ; 3. TVKA [1/h]

$THETA (0,0.15) ; 4. Sigma_prop

$THETA (0,0.5) ; 5. Sigma_add [mg/L]

$THETA (0,0,2) FIX ; 6. DUMMY

$THETA (0,0,15) FIX ; 7. DUMMY

$OMEGA 0 FIX ; 1. BSV_CL

$OMEGA 0 FIX ; 2. BSV_Vd

$OMEGA 0 FIX ; 3. BSV_Ka

$OMEGA 0 FIX ; 4. BSV_BIO

$OMEGA 0 FIX ; 5. BSV_MTT

$SIGMA 1 FIX ; RESIDUAL

$PK

BSVCL= ETA(1) ; BSV_CL

BSVV = ETA(2) ; BSV_V

BSVKA= ETA(3) ; BSV_KA

BSVBIO=ETA(4) ; BSV_BIO

BSVMTT=ETA(5) ; BSV_MTT

TVCL =THETA(1) ; Pop CL

TVV =THETA(2) ; Pop V

TVKA =THETA(3) ; Pop KA

TVBIO=1 ; Pop BIO

SIG_PROP=THETA(4) ; Sigma PROP

SIG_ADD=THETA(5) ; Sigma ADD

;ALAG1 = THETA(6)

CL=TVCL * EXP(BSVCL)

V =TVV *EXP(BSVV)

KA=TVKA*EXP(BSVKA)

BIO=TVBIO*EXP(BSVBIO)

K=CL/V

F1 = BIO

WRITE(50,2) 1, ID,TIME,A(1),A(2) ; TO OUTPUT INTERGRATION STEPS IN TEXTFIL=

E

$DES

DADT(1) = -KA*A(1)

DADT(2) = KA*A(1) -K*A(2)

WRITE(50,2) 2, ID,T,A(1),A(2) ; TO OUTPUT INTERGRATION STEPS IN TEXTFILE

$ERROR

IPRED = A(2)/V

IRES = DV - IPRED

W=SQRT((SIG_PROP*IPRED)**2+SIG_ADD**2) ; Residual SD

IWRES=IRES/W

Y=IPRED+W*EPS(1)

AA1=A(1)

AA2=A(2)

WRITE(50,2) 3, ID,TIME,A(1),A(2) ; TO OUTPUT INTERGRATION STEPS IN TEXTFIL=

E

$SIMULATION (123) ONLYSIM

;$ESTIMATION METHOD=1 INTER MAXEVAL=9999 PRINT=1 NOABORT NSIG=3; c=

alculation method

On 2016/05/19 16:23, Alison Boeckmann wrote:

Dear Paolo,

As Bob explained, ZSPOW uses the TOL defined by the user in the $SUBROUTIN=

ES record to determine precision. ADVAN9 and ADVAN13 also use a separate a=

bsolute tolerance ATOL, which is by default set to 12, but you can modify i=

t with $EST … ATOL= , and see if it affects the precision of the =

SS evaluation.

You could also try using ADVAN6/SS6.

I can't understand why the SS option is taking so long with ADVAN13/SS13. =

The table of results you report do not correspond to the way SS is computed=

in PREDPP, and I can't understand where you got the numbers in the table.

You say "the amount in the absorption compartment AA1 is literally numerica=

l noise after II hours". But PREDPP never reports this amount, because SS a=

mounts are reported *after* a dose has been administered.

The way SS with multiple dosing is computed is described in the May 2015 ve=

rsion of Guide VI PREDPP. This is supplied with the latest alpha versions =

of NONMEM7.4. See Chapter V. Event Records, Section F.4 Implementation of =

Steady State. There are three calls to ADVAN with TIME=0 to obtain the i=

nitial estimate. After that, the root finder ZSPOW makes as many calls as =

it needs, but they are not necessarily sequential in TIME.

Can you please send me your control stream and a fragment of the data so I =

can figure out what is going on?

Alison

PS. In case you don't have the May 2015 version of guide VI PREDPP, here is=

an extract:

(The guide still needs to be updated for ADVAN13, but the same process is u=

sed.)

=========================

When the model is defined by differential equations (SS6, SS8, SS9), PREDPP=

cannot use an ana- lytic solution, even if one happens to exist. Instead, =

the solutions are found by a numerical technique using ZSPOW, a root-findin=

g subroutine from IMSL.

With multiple dosing, ZSPOW searches for a vector of compartment amounts an=

d their eta deriva- tives such that the initial and final (end of dosing in=

terval) vector is the same. ADVAN6, ADVAN8, and ADVAN9 perform a numerical =

integration of the differential equations (and in the case of ADVAN9, algeb=

raic equations). The ADVAN routine is used to advance (integrate) the state=

vector A from time 0 to time II with the appropriate dose pattern. Let AII=

represent the state vector after advance to time II with the appropriate d=

ose. A search is made for Ass such that Ass - AII = 0

If SS=3, the state vector A contains user-supplied initial estimates. Oth=

erwise, the SS routines sets A=0 and makes three calls to ADVAN. Each cal=

l advances the state vector from t=0 to t=II with the appropriate dosin=

g pattern. The result is the initial estimate.

Once the SS solution is found, the SS routine adds the final bolus dose to =

the state vector, or starts the final infusion.

===================

Paolo:

From what I can tell in scanning the code of ..\pr\SS13.f90, the TOL settin=

g on the $SUBROUTINES record appears to determine the precision of the stea=

dy state condition. You can change the TOL value, or, if you wish the SS p=

recision to differ from the ODE evaluation precision, you can modify SS13.f=

90, as it is open source to users, by replacing the NRD argument (which con=

tains the TOL value submitted by the $SUBROUTINES record) to all calls to Z=

SPOW1 with an alternative value of your choosing. Recompile SS13.f90, then=

execute NONMEM with nmfe73 script as usual.

Robert J. Bauer, Ph.D.

Vice President, Pharmacometrics R&D

ICON Early Phase

820 W. Diamond Avenue

Suite 100

Gaithersburg, MD 20878

Office: (215) 616-6428

Mobile: (925) 286-0769

<mailto:Robert.Bauer_at_iconplc.com>Robert.Bauer_at_iconplc.com<mailto:Robert.Bau=

er_at_iconplc.com>

<http://www.iconplc.com/>www.iconplc.com<http://www.iconplc.com>

On Wed, May 18, 2016, at 03:15 AM, Paolo Denti wrote:

Dear NMUsers (and developers),

I am trying to speed up our run times when using SS in ADVAN13 models (user=

defined differential equations), and I would like to share some thoughts t=

o get some feedback.

We work on steady-state PK data, so ideally we would like to use the SS opt=

ion, but the run times whenever we use ADVAN13 become unfeasibly long (even=

20 times more), and this even for models that should reach steady state in=

2-3 doses.

As an alternative we end up using ad-hoc "patch-up" solutions, like initial=

ising compartments, or just adding 4-5 doses "manually" in the dataset, but=

this is a bit tedious/tricky.

I am writing to see if there is a way to speed up the SS feature.

I decided to look into what was going on by asking NONMEM to simulate a SS =

PK profile and print out all the temporary iterations.

It seems like NONMEM first opens a separate "SS session" used to work out t=

he SS amounts in each compartment. The model is taken to SS by repeatedly g=

iving doses every II, until the system is deemed to have reached steady-sta=

te. At this point, NONMEM goes back to the "main session", initialises all =

compartments to the amounts found in the "SS session", gives the final dose=

, and moves on with the analysis.

Nothing surprising here, and it's understandable that things take longer wi=

th SS, cuz the calculation of these SS amounts implies solving the differen=

tial equations for all the extra time of the "SS session". What I found odd=

though, is that the number of doses that NONMEM uses to reach steady-state=

seems to me much higher than needed. In my test I used a simple 1-cmpt KA =

model coded in ADVAN13 and a drug with a half-life of 3.5 hours, so I was e=

xpecting 2 dosing intervals (48 hours) to be more than enough to get to ste=

ady state, as maths says the amounts should be 99.993% there. NONMEM instea=

d used 13 doses in the example below.

The amounts are reported in the table below. After iteration 3 the amount i=

n AA2 just changes by tiny values, arguably comparable to numerical noise.

#DOSE T TOT_TIME AA2

0 0 0 0

1 0 24 4.114874

2 0 48 4.148738

3 0 72 4.149017

4 0 96 4.149017

5 0 120 4.149017

6 0 144 4.149019

7 0 168 4.149019

8 0 192 4.149019

9 0 216 4.149019

10 0 240 4.149019

11 0 264 4.149019

12 0 288 4.149019

13 0 312 4.149019

Does anyone know what stopping criterion NONMEM uses to call it SS and move=

on? Is there a way to relax it? I think 0.1% would be fine in most practic=

al cases - at least for preliminary runs - and in this example it would sav=

e 80% of the run time. Plus if one keeps in mind that this is a numerical s=

olver, it is not clear how "real" the wee digits are, obviously depending o=

n TOL.

The other tricky thing I found is that the amount in the absorption compart=

ment AA1 is literally numerical noise after II hours, meaning that for some=

entries it is even negative (e.g. -2.08038E-15) and jumps between positive=

and negative. Could it be that this is what is tricking NONMEM's stopping =

criterion to detect SS? Maybe if the stopping criterion only asks for a rel=

ative change <TOL, it will struggle to achieve that with values that change=

sign.

Any settings that may help speed things up? Something like tinkering with T=

OL and ATOL?

Or maybe is it possible to set a maximum to the number of doses that NONMEM=

tests to reach steady-state?

Sorry for the nerdy topic, and thanks for any advice!

Ciao,

Paolo

PS And big thanks to our PhD student Maxwell who ran all the tedious simula=

tions!

--

------------------------------------------------

Paolo Denti, PhD

Pharmacometrics Group

Division of Clinical Pharmacology

Department of Medicine

University of Cape Town

K45 Old Main Building

Groote Schuur Hospital

Observatory, Cape Town

7925 South Africa

phone: +27 21 404 7719

fax: +27 21 448 1989

email: paolo.denti_at_uct.ac.za<mailto:paolo.denti_at_uct.ac.za>

------------------------------------------------

Disclaimer - University of Cape Town This e-mail is subject to UCT policies=

and e-mail disclaimer published on our website at http://www.uct.ac.za/abo=

ut/policies/emaildisclaimer/ or obtainable from +27 21 650 9111. If this e-=

mail is not related to the business of UCT, it is sent by the sender in an =

individual capacity. Please report security incidents or abuse via csirt_at_uc=

t.ac.za<mailto:csirt_at_uct.ac.za>

--

Alison Boeckmann

alisonboeckmann_at_fastmail.fm<mailto:alisonboeckmann_at_fastmail.fm>

--

------------------------------------------------

Paolo Denti, PhD

Pharmacometrics Group

Division of Clinical Pharmacology

Department of Medicine

University of Cape Town

K45 Old Main Building

Groote Schuur Hospital

Observatory, Cape Town

7925 South Africa

phone: +27 21 404 7719

fax: +27 21 448 1989

email: paolo.denti_at_uct.ac.za<mailto:paolo.denti_at_uct.ac.za>

------------------------------------------------

Disclaimer - University of Cape Town This e-mail is subject to UCT policies=

and e-mail disclaimer published on our website at http://www.uct.ac.za/abo=

ut/policies/emaildisclaimer/ or obtainable from +27 21 650 9111. If this e-=

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Received on Fri May 20 2016 - 11:14:48 EDT

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