Individualizing  Dosage  Regimens:  Learning  about  our  pa8ents  op8mally  while  trea8ng  them  at  the  same  8me,  achieving  maximum  

precision  throughout.    Roger W. Jelliffe, M.D.

Professor of Medicine Emeritus, Founder and Director Emeritus,

Laboratory of Applied Pharmacokinetics, USC Keck School of Medicine

Children’s Hospital of Los Angeles Los Angeles, CA, USA

jelliffe@usc.edu www.lapk.org

Our  Lab  

Fearless  Founder   Alan  Schumitzky  

Mike  Van  Guilder  Aida  Bustad   Dave  Bayard  

Michael  Neely  –  Hot  new  blood!  

Supported in part by NIH grants EB005803, GM 068968, and HD070886

Tasks  to  be  done  for  each  pa8ent    

•  1  –  First,  learn  op8mally  about  the  drug  •  2  –  Then,  op8mize  the  ini8al  dosage  regimen  •  3  –  Then,  learn  about  the  drug  in  that

 pa8ent  op8mally  while  you  must  treat    him/her  at  the  same  8me  

•  4  –  Con8nue  learning  and  trea8ng  op8mally    throughout  the  course  of  treatment.  

•  5  –  There  are  tools  for  each  part  of  this  task.  

Tool #1 - Nonparametric (NP-UPD) PK/PD models  

•  The  most  likely  (ML)  popula8on  parameter  distribu8ons,  given  the  data,  “CAN  BE  FOUND”  in  a  discrete  collec8on  of  support  points,  up  to  1  point  per  subject.  

•  Each  NP  model  parameter  support  point  contains  an  es8mate  of  each  model  parameter  value,  and  of  the  probability  of  that  collec8on  of  values  in  the  popula8on.  

•  No  assump8ons  need  to  be  made  about  the  shape  of  the  distribu8ons  in  the  popula8on.  They  use  UNCONSTRAINED  parameter  distribu8ons  (UPD).  

What  is  the  IDEAL  Popula8on  Model?  

•  The  correct  structural  PK/PD  Model.  •  The  collec8on  of  each  subject’s  exactly  known  parameter  values  for  that  model.  

•  Therefore,  mul8ple  discrete  individual  models,  one  model  from  each  subject.  

•  Usual  con8nuous  sta8s8cal  summaries  can  also  be  obtained,  but  usually  will  lose  info.  

•  NP  -­‐  UPD  models  best  approach  this  una_ainable  ideal.  

An  NP-­‐UPD  Popula8on    Model,  made  by  Mallet  

                 Tool  #  2 - Multiple Model (MM) dosage design  

Select  your  pa8ent’s  specific  therapeu8c  target  goal  –  not  a  window.  

Use  all  mul8ple  models  in  NP  pop  model  (the  blue  slide).  Give  a  candidate  dosage  regimen  to  each  model.  Predict  future  results  from  each  model,  each  predic8on  weighted  by  its  probability.  

Compute  WEIGHTED  SQUARED  ERROR  of  the  predic8ons  overall  failure  to  hit  the  target.  

Find  the  regimen  having  LEAST  weighted  squared  error  in  target  goal  achievement.  The  most  precise  regimen.  

It  uses  the  en8re  distribu8on  of  each  parameter,  not  just  a  single  value  summary  of  some  assumed  distribu8on.  

5/1/15   8  

Con8nuous  IV  Vanco.  Predic8ons  when  regimen  based  on  CPD  parameter  means  is  given  to  all  support  points  

5/1/15   9  

Vanco,  con8nuous  IV.  Predic8ons  when  MM  regimen  is  given  to  all  support  points  

No8ce  that…      The  dose  itself  is  a  most  important  tool  to  minimize  pa8ent  variability  in  response.  

   This  is  at  least  as  important  as  having  addi8onal  covariate  informa8on.    

   With  parametric  models  you  will  never  be  aware  of  this  issue,  and  never  be  able  to  do  it.  

 Jelliffe  R:  Goal-­‐Oriented,  Model-­‐Based  Drug  Regimens:  SePng  Individualized  Goals  for  

each  PaTent.  Therap.  Drug  Monit.  22:  325-­‐329,  2000.  Jelliffe  R,  Bayard  D,  Milman  M,  Van  Guilder  M,  and  Schumitzky  A:  Achieving  Target  

Goals  most  Precisely  using  Nonparametric  Compartmental  Models  and  "MulTple  Model"  Design  of  Dosage  Regimens.  Therap.  Drug  Monit.    22:  346-­‐353,  2000.  

Bustad  A,  Terziivanov  D,  Leary  R,  Port  R,  Schumitzky  A,  and  Jelliffe  R:  Parametric  and  Nonparametric  PopulaTon  Methods:  Their  ComparaTve  Performance  in  Analysing  a  Clinical  Data  Set  and  Two  Monte  Carlo  SimulaTon  Studies.  Clin.  Pharmacokinet.,  45:  365-­‐383,  2006.  

Tool # 3 - Correct description of assay errors Describe  Assay  Errors  by  1/variance,  NOT  CV%.  

•  Get  es8mate  of  SD  for  every  TDM  serum  level  going  through  the  lab  assay  system.  

•  Variance  =  SD2  

•  1/Variance  =  correct  Weight.  •  Assay  Error  Polynomial  (AEP):  

     SD  =  A0C0  +  A1C1  +  A2C2  +  A3C3  •  Store  it  in  the  solware.  •  No  need  to  censor  low  data  any  more  •  No  LLOQ!  This  is  an  illusion  from  using  CV%.  Jelliffe  RW,  Schumitzky  A,  Van  Guilder  M,  Liu  M,  Hu  L,  Maire  P,  Gomis  P,  Barbaut  X,  and  Tahani  B:  Individualizing  Drug  Dosage  Regimens:  Roles  of  PopulaTon  PharmacokineTc  and  Dynamic  Models,  Bayesian  FiPng,  and  AdapTve  Control.  TherapeuTc  Drug  Monitoring,  15:  380-­‐393,  1993.  

21.15

10.33 9.9663

14.323

0.56708

0.423024 0.413376

0.7973

1.7188

0

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1.2

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1.8

2

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Concentration (ug/ml)

SD

5

10

15

20

25

CV

%

CV%

SD

Tool # 4 – Estimate CCr from changing SCr  

0.4W(C2  –  C1)  =  P  –  Cavg  x  CCr  x  1440  (Daily  change  =  Produc8on  –  Excre8on)  

•  Where  P  is  daily  crea8nine  produc8on  (see  ar8cle)  C1  and  C2  are  SCr  in  mg/100ml,  W  is  weight  (in  hundreds  of  grams),  and  CCr  is  crea8nine  clearance  (in  hundreds  of    ml/min).  

Then  adjust  for  1.73  M2  BSA    Jelliffe  R:  Es8ma8on  of  Crea8nine  Clearance  in  Pa8ents  with  Unstable  

Renal  Func8on,  without  a  Urine  Specimen.  Am.  J.  Nephrology,  22:  3200-­‐3204,  2002.  

   

Es8ma8on  errors  in  CCr  

CV  of  serum  crea8nine  =  ±  5%  CV  of  urine  crea8nine  =  ±  8%  

Then  if  collect  24  hr  urine  with  CV  =  ±  5%,  52=25  twice  =  50,  plus  82=64,  =  114.  

SQRT  114  ~  11  So  the  classical  CCr  has  a  CV  =  ±  11%,    

or  95%  conf  limits  of  ±  22%  

Es8mated  vs  Measured  CCr  

Tool # 5 - MM Optimal TDM protocols  

Do  NOT  wait,  and  do  not  get  only  steady  state  trough  levels!  Start  right  with  the  very  first  dose!  Consider  1  sample  for  each  model  parameter  to  be  es8mated.  Use,  for  example,  D-­‐op8mal  design  strategies.  There  is  an  

op8mal  8me  to  sample  for  each  model  parameter  value,  given  a  certain  dosage  regimen  format.  

Olen,  get  a  peak  and  a  sample  at  about  1/3  the  peak.  Be_er,  consider  the  new  MM-­‐op8mal  design,  op8mizing  the  

8mes  to  maximize  precision  of  dosing  to  desired  target  conc,  or  AUC,  for  example.  

Do  NOT  waste  money,  effort,  and  pa8ent  care  with  poor  designs.  The  TDM  community  can  do  a  MUCH  BETTER  job  here.    

5/1/15 USC LAPK 17

Best  8me    to  sample  

For  a  constant  assay  error,  the  greatest  change  in  serum  conc  when  volume  of  dist  changes  is  at  the  true  peak,  not  later.  Samples  near  the  peak  are  most  informa8ve  about  Vd.  

Example  of  D-­‐OpTmal  Design:    Finding  Volume  Vd  from  a  First-­‐Order  Response  

5/1/15 USC LAPK 18

The  greatest  change  in  serum  conc  from  a  change  in  the  Kel  is  when  the  serum  conc  is  36%  of  the  original  peak  value.  Samples  near  1.44  half-­‐8mes  are  most  informa8ve  about  Kel.  

Example  of  D-­‐OpTmal  Design:    Finding  Kel  from  First-­‐Order  Response  

Best  8me    to  sample  

Mul8ple  Model  Op8mal  Design  

–  Optimizing experimental design this way is fundamentally different from optimizing experimental design to estimate patient’s parameters, as in D-optimal design, etc.

0.020.04

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VK

1 - Randomly sample a population model support point. 2 - Give it a simulated dose and some simulated observations, at a specific set of candidate sampling times, with assay noise. 3 - Get the MAP Bayesian posterior estimate. 4 – See if that MAP estimate corresponds to the original point (correct classification) or some other point (incorrect). 5 – Repeat steps 1-4 many times. See the percent of times the classification is correct. 6 – Do this for many candidate designs. 7 - Find the sampling design that minimizes the percent incorrect classification.

20

•  Model Response Separation r(t) is the separation between two model responses at a given time t

• Defines natural statistic for discriminating between two models •  Bayes Risk of mis-classification is shown in gray area

Model Response Separation r(t)

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1Model Responses

Time

Model 1 ReponseModel 2 Response

r(t) = response separation

-1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2Two-Model Classification Problem

r(t)=response separation

Bayes Risk

•  Bayes Risk (gray area) decreases as response separation r(t) increases

•  Models are best discriminated by sampling at a time t that maximizes r(t)

Pull Gaussians apart to minimize gray area

21 21

ED EID API MMOpt Invariant under regular linear reparametrization*

Yes Yes

Yes

Yes

Invariant under regular nonlinear reparametrization*

No No

Yes Yes

Allows taking fewer than p samples, p= # of parameters

No

No

No

Yes

Can handle heterogeneous model structures

No

No

No

Yes

Gives known optimal solution to 2-model example*

No

No

No

Yes

Captures main elements of minimizing Bayes risk

No

No

No

Yes

Comparison Table

*Proved in Bayard et. al., PODE 2013 [23]

22

Weighted  MMOpt  

Optimal Dosing

Parameter Estimation

Metric Estimation

23 23

Model Parameters # K V

1 0.090088 113.7451

2 0.111611 93.4326

3 0.066074 90.2832

4 0.108604 89.2334

5 0.103047 112.1093

6 0.033965 94.3847

7 0.100859 109.8633

8 0.023174 111.7920

9 0.087041 108.6670

10 0.095996 100.3418

PK Population Model with 10 Multiple Model Points - First-Order PK Model

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Time (hr)

Conc

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0 5 10 15 200

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100

150

200

250

300

350

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Time (hr)

Units

Dose input = 300 units for 1 hour, starting at time 0

Model Responses •  Grid points 15 min apart •  MMOpt optimized over time grid

24

Unweighted  MMOpt  for  PK  Es8ma8on  •  Summary of optimal 1,2 and 3 sample designs applied to PK Estimation

•  1 Sample Design: MMOpt performance equals Bayesian optimal design (both have Bayes Risk of 0.5474).

•  MMOpt performance improves on EDopt design for 2 and 3 sample designs –  2 Sample Design: Bayes Risk of 0.29 versus 0.33 –  3 Sample Design: Bayes Risk of 0.23 versus 0.26

•  All results are statistically significant to p<0.0001

25

Weighted  MMOpt  for  AUC  Control  

26

Weighted  MMOpt  for  AUC  Control  (Cont’d)  •  Summary of optimal 1,2 and 3 sample designs applied to AUC control

•  1 Sample Design: weighted MMOpt performance approximates that of the weighted Bayesian optimal design (RMS error of 3.62 versus 3.77 AUC units)

•  MMOpt performance improves on EDopt design for 2 and 3 sample designs –  2 Sample Design: RMS error of 2.11 versus 2.62 (units of AUC) –  3 Sample Design: RMS error of 1.70 versus 2.42 (units of AUC)

•  All results are statistically significant to p<0.0001

Tool # 6 - NP Bayesian adaptive control tools

Previous  data  =  past  experience  =  popula8on  model.    1  –  Pop  model  is  the  Bayesian  Prior  (prior  to  now)  –  

 es8mates  probability  of  model  parameters  based  on  past  experience.  

2  -­‐  New  data  from  pa8ent.  Recompute  param      distribu8ons  based  on  past  +  new.  

3  -­‐  This  is  the  Bayesian  posterior  –  the  individualized    pt  model.    

An  Ini8al  Gentamicin  Predic8on  based  on  popula8on  model  prior:  goal  =  12  ug/ml  

95 Percentile Distance

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Gevng  Individualized  Bayesian  Models  in  Pa8ents  –  4  ways  

 

1.  MM  Bayesian  posteriors  2.  MAP  Bayesian  Posteriors  3.   Hybrid  Bayesian  posteriors.  4.   Interac8ng  MM  (IMM)  Sequen8al  

 Bayesian  Posteriors.    

     

Es8mates  with  MM  posterior  

Hybrid  Bayesian  posterior  •  Start  with  MAP  Bayesian.  It  reaches  out,  but  not  fully  (shrinkage).  Pop  prior  holds  it  back.  

•  Add  new  support  points  nearby,  inside  and  mostly  outside,  to  AUGMENT  the  pop  model  for  the  coming  new  pa8ent  data.  

•  Then  do  MM  Bayesian  on  ALL  the  support  points.  

•  Can  also  use  for  pa8ents  without  a  popula8on  model.  

 

Pa8ent  on  digoxin  and  quinidine  -­‐  Hybrid  Bayesian  posterior  plot  

Pa8ent  on  digoxin  and  quinidine  -­‐  Hybrid  Bayesian  Posterior  Joint  Density  

Interac8ng  Mul8ple  Model  (IMM)  Sequen8al  Bayesian  analysis.  

•  All  other  fivng  methods  assume  fixed  parameter  values  throughout  the  data  analysis.  

•  IMM  lets  param  distribu8ons  change  with  each  new  data  point  to  get  sequen8al  Bayesian  posterior  distribu8ons.    

•  IMM  tracks  Gent  and  Vanco  behavior  best  in  ICU  pa8ents.  

•  Bayard  D,  and  Jelliffe  R:  A  Bayesian  Approach  to  Tracking  PaTents  having  Changing  PharmacokineTc  Parameters.  J.  Pharmacokin.  Pharmacodyn.  31  (1):  75-­‐107,  2004.  

•  Macdonald  I,    Staatz  C,  Jelliffe  R,  and  Thomson  A:  EvaluaTon  and  Comparison  of  Simple  MulTple  Model,  Richer  Data  MulTple  Model,  and  SequenTal  InteracTng  MulTple  Model  (IMM)  Bayesian  Analyses  of  Gentamicin  and  Vancomycin  Data  Collected  From  PaTents  Undergoing  Cardiothoracic  Surgery.  Ther.  Drug  Monit.  30:67–74,  2008.  

By  avoiding  clearance  and  using  Vs  and  Ks  instead,  the  2  separate  issues  of  fluid  balance  and  drug  eliminaTon  can  be  managed  best.  

TDM  up  to  now  has  been  mostly  for  achieving  general  serum  concentra8on  

guidelines.  •  But  now,  what  about  seeing  each  pa8ent  as  a  unique  individual?  

•  Pa8ents  vary  greatly  in  their  sensi8vity  to  serum  concentra8ons.  

•  Also,  digoxin  clinical  effect  does  not  correlate  with  serum  concentra8ons,  but  with  peripheral,  nonserum  compartment,  concentra8ons.  

 Serum digoxin concentrations in nontoxic and toxic patients found by Doherty [1]. Note great overlap between therapeutic and toxic concentrations, and the fact that approximately half the patients with serum levels of 3.0 ng/ml or more were NOT toxic. Also note that the incidence of toxicity is very low for levels up to 1.0 ng/ml, moderate (though significant) for levels of 1.0 to 2.0, more above 2.0, but still only about 50% for levels of 3.0 ng/ml or greater.

Management  of  digoxin  therapy  

•  Two  compartment  NP  pop  model.  •  Clinical  effect  correlates  with  peripheral  compartment  concentra8ons,  not  with  central  (serum)  concentra8ons.  

•  Plan  regimens  either  for  trough  serum  concentra8ons  (usually  0.7  ng/ml)  or  peak  peripheral  concentra8ons  (usually  7  ng/gm,  7  hrs  aler  an  oral  dose).  

•  But  pa8ents  with  aur  fib,  flu_er  olen  need  9-­‐18  ng/gm  to  convert  and  stay  converted.  

Bauman  et  al:  Am.J.Cardiovascular  Drugs  2006;  6:  

Literature  data  

•  Study                    Digoxin  /Placebo          Periph  conc.          P  •  Falk  et  al            9/18  v  8/18    8.0                  NS  •  DAAF                          60/117  v  56/122                    9.23                  NS  •  Jordaens  et  al            9/19  v  8/20                        11.25                      NS  

                         Conversion  to  RSR  •  Hou  et  al                                  17/24  (71%)                              9.0                  <0.05  •  Weiner  et  al            40/47  (85%)                      13.9      <<0.005  

 

(Clinical  PharmacokineTcs  (DOI)  10.1007/s40262-­‐014-­‐0141-­‐6)  

New  onset  AF  –    SCr  =  0.8,    Serum  concentra8ons  over  8me  

 

New  onset  AF  –    SCr  =  0.8,    Peripheral  concentra8ons  over  8me  

New  onset  AF  –  96  F    SCr  =  8,  CCr  =  3.7  Serum  concentra8ons  over  8me  

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WgtAvg

New  onset  AF  –  96  F    SCr  =  8,  CCr  =  3.7  Peripheral  concentra8ons  over  8me  

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Problems  with  educa8on  in  drug  therapy  

•  No  one  teaches  meaningful  PK  in  med  schools  anywhere  

•  No  one  knows  anything  about  dosage  individualiza8on  

•  Their  only  informa8on  comes  from  the  drug  companies  

•  Poor  illiterate  med  schools!  •  Poor  illiterate  docs!  •  Poor  poorly  treated  pa8ents!  •  Rich  and  richer  drug  companies!  •  Rich  and  richer  lawyers!  

                 Problems  with  drug  marke8ng  

Suppressing  their  own  science  for  marke8ng!  

•  They  have  the  data  for  each  pa8ent  -­‐  •  Outcome,  and  An8platelet  effect.  •  They  can  easily  find  the  an8platelet  effect  associated  with  best  outcome,  least  bleeding.  

•  They  can  set  a  target  an8platelet  effect,  •  And  dose  each  pa8ent  to  achieve  it!  •  Why  do  they  adver8se  that  this  is  NOT  NEEDED??  Why??  Think  about  it!  

•  WE  BADLY  NEED  INDIVIDUALIZED  DOSAGE.