Division of Pharmacokinetics and Drug Therapy Department of Pharmaceutical Biosciences Optimizing Dosing Strategies for Defined Therapeutic Targets Mats

Division of Pharmacokinetics and Drug TherapyDepartment of Pharmaceutical Biosciences

Optimizing Dosing Strategies for Defined Therapeutic Targets

Mats O. Karlsson and Siv Jönsson

Dept. of Pharmaceutical Biosciences

Uppsala University

Sweden


Overview

• Target definition and dose finding• Application to real drugs

– Posterior definition of utility function– Dose optimization based on

• Responder criteria• Utility functions• Concentration

• Simulations– A priori individualization based on concentration– A posteriori individualization based on biomarker


Dosing strategy alternatives

• The single, one-size-fits-all-always, dose• A priori individualization, based on

• Patient characteristics

• A posteriori individualization, based on – Effects– Side-effects– Biomarker– Drug concentration– A mixture of the above

• Combination of a priori and a posteriori


Target

• The selection of any dosing strategy requires a target concept

• The target could be based on– The weighted balance between beneficial effect(s) and side-

effects (utility)– Beneficial clinical endpoint(s)– Side-effect(s) – Drug concentration– Biomarker(s)

• Target can differ between subjects based on patient characteristics


Seriousness of devation from the target

• All-or-none criteria– Therapeutic window

• All values within the window are equally desireable

• All values outside of the window are equally undesirable

– Responder/non-responder concepts

• Penalty (loss) gradually increasing with increasing deviation from target, e.g.– Quadratic loss ( (observedi-targeti)2)

– Absolute loss ( |observedi-targeti|)

– Non-symmetric loss

• Seriousness of target deviation may vary between patients


Scenario 1

• A dose (dosing strategy) is selected based on some implicit criteria

• Stop


Scenario 2

1. A dose (dosing strategy) is selected based on some implicit criteria

2. Population model for dose – target variable

3. Estimation of the target and penalty function based on model and selected dose (dosing strategy)

4. Assessment of whether target and penalty function are appropriate1. If they are, stop

2. If they are not, revise dosing strategy in light of a more appropriate target/penalty function


Exposure

Drug side-effect

Frequency

Target Specification

Drug effect


Optimal dose versus weighting of events

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6 7

Weight (Adverse event / Beneficial event)

Do

se

All subjects

Sub-diagnosis 1

Sub-diagnosis 2

Renal impairment


Define target and penalty functions

• Ask a clinician • Consult preclinical and phase I data on drug• Consult literature• Consult marketing• Develop a few alternative targets / penalty functions• Apply to historical data, if available• Ask a few (many) clinicians• Revise• Include inter-clinician (-patient) variability in target

definition


Scenario 3

1. Formal target and penalty functions are defined

2. Population model for dose – target variable

3. Estimate the best dosing strategies given different constraints1. One-dose-fits-all

2. Two-dose individualization based on covariate

3. Two-dose individualization based on feedback

4. Etc

4. Select dosing strategy based on target fulfillment and practical considerations


Optimizing one-size-fits-all dose

• Define– Target and penalty function– Population PK and PD models

• Only partial models may be needed

• Covariate models essentially superfluous

• PK and PD parameters are simulated for a large number (>1000) of patients

• Obtain a prediction of each individual’s deviation from the target for a certain dose

• Obtain the optimal dose by minimising overall loss– Repeated simulations– Estimation


Target = individual’s prediction + deviation from target

8

9

10

11

12

0 20 40 60 80 100

Patient number

Tar

ge

t v

aria

ble

0

0.5

1

1.5

2

8 10 12

Predicted eff/conc

Lo

ss fu

nct

ion

Approach


Optimal a posteriori dosing strategies

1. Questions1. What dose strengths should be made available?

2. When should an observation for individualization be made?

3. At what value(s) should a dose change be made?

4. What is the best starting dose?

5. ...


Example: a posteriori optimal dosing

• Question: Is allowing individualization by two doses better than one-dose-fits-all?

• Responder / non-responder concept• Obtain optimal one dose

– Estimate a single dose size

• Obtain optimal a posteriori two dose strategy– Estimate simultaneously

• lower dose size

• higher dose size

• fraction of patients that preferentially should be treated by the lower (higher) dose

– Use $MIXTURE function in NONMEM


Satisfactory effect +

Acceptable side-effects =

Responder

Prob(Unacceptable side-effect)

0.0E+00

2.0E-01

4.0E-01

6.0E-01

8.0E-01

1.0E+00

1.2E+00

0 10 20 30 40 50 60 70

Dose

Pro

babi

lity

Prob(Satisfactory effect)

0.0E+00

2.0E-01

4.0E-01

6.0E-01

8.0E-01

1.0E+00

1.2E+00

0 10 20 30 40 50 60 70

Dose

Pro

babi

lity


Estimation of optimal individualised dosing strategy

Dose 10 4 18

63%

Acceptable side-effect RespondersSatisfactory effect

47%

74%

61%


Simulation Studies - Comments

• Robustness of dosing strategy to variation in utility definition between clinicians/patients desireable

• All-or-none type responder definitions favour individualization to a higher degree than gradual utility functions


Optimal a priori dosing strategies

1. Questions1. What is the best covariate

to base dosing on?

2. Number of doses sizes (subpopulations)?

3. What covariate intervals should each dose size be applied to?

2 dose groups:Cut-off valueHigher doseLower dose

= 3 parameters

3 dose groups:= 5 parameters

Covariate

CL


Optimizing covariate-based dosing

• Define– Target and penalty function– Population PK and PD models

• Covariate models essential

• Population distribution of covariate(s) simulated or obtained from empirical data base

• PK and PD parameters are simulated for a large number of patients

• Obtain a prediction of each individual’s deviation from the target for a certain dose

• Obtain the optimal dosing strategy by estimation of dose sizes and cut-off value(s)


Individualisation based on a covariateNXY-059

• Drug for usage during acute hospitalisation following stroke

• Two-step infusion (1-h loading, 71-h maintenance)

Time

Con

cent

ratio

n

CL ~ CLCRVc ~ WT



• Target: Cu = 100 M• Penalty: Quadratic loss in log domain• Pop PK model

– CL ~CLCR– V ~WT

• Empirical CLCR and WT distributions• Loading infusion: 1-2 dose groups, CLCR or WT• Maintenance: 2-4 dose groups, CLCR• Selection of dosing strategy

– >90% of patients above 70 M– <5% of patients above 150 M


• One loading dose 2400 units/h

• Three maintenance infusion levels– CLCR > 80 ml/min 1110 units/h– CLCR 50 - 80 ml/min 681 units/h– CLCR 30 - 50 ml/min 426 units/h


0 50 100 150CLCR (mL/min)

0

50

100

150

200

250

300

C1h

, u

nb

ou

nd

0 50 100 150CLCR (mL/min)

0

50

100

150

200

250

300

Cs

s,

un

bo

un

d


Target fulfillment in prospective study

• 92% > lower limit• 7% > upper limit


Simulations I – A priori dosing

• Dosing based on CRCL– Standard approach often uses

• Predetermined cut-off values

• Large dose decrements (often a factor 2 or higher)

– Optimal approach depending on• Drug characteristics

– Fraction excreted unchanged (fe)

– Interindividual variability in CLR and CLNR

• Penalty function shape

• CRCL distribution in target population– Parametric simulation– Empirical databases


Individualisation based on a covariateSimulations – main results

40 50 60 70 80 90 100 110Median CLCR in population (mL/min)

40

50

60

70

80

90

100

110

Op

tim

al C

LC

R c

ut-

off

(m

L/m

in)

fe = 1fe = 0.5

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Median fe (CLR/CL ratio) in population

1.0

1.2

1.4

1.6

1.8

Do

se r

atio

2nd/1st of 2 doses2nd/1st of 3 doses3rd/2nd of 3 doses


Relative change in AUC variability

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.2 0.4 0.6 0.8 1.0

Fraction excreted unchanged (fe)

Change in A

UC

variability

2 dose levels

3 dose levels4 dose levels


0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200

CLcr (ml/min)

AUC

AUC variability before dose adjustment 29.3%

AUC variability after dose adjustment 28.7%


Target definition

• Target definition– To aid data collection– To guide modeling efforts– To improve communication within project team – To appropriately value the drug compared to competitors– To assess (or claim) whether the dose is right


Dosing strategy estimation

• Dosing strategy estimation– To motivate choice of dose– To obtain conditions for optimal individualization– To assess maximal potential value of individualization– To justify individualization (or lack thereof)– Simplicity in dosing can be directly offset against decrease in

target fulfillment– Is easy!

Documents

Division of Pharmacokinetics and Drug Therapy Department of Pharmaceutical Biosciences Optimizing Dosing Strategies for Defined Therapeutic Targets Mats