Download Pharmacometrics - About POP

Pharmacometric Tools in The
Pharmaceutical Industry: Concepts
and Application in Drug
Development
Serge Guzy; PhD
President, CEO, POP-PHARM; Inc.
Pharmacokinetics
• What the body does to the drug
– Distribute in circulation
– Distribute in tissue
– Eliminate drug by chemical degradation or filtering via
kidneys
Pharmacodynamics
• What the drug does to the body
– Interact with target protein in circulation or on a cell
surface
– Reduce or enhance activity of circulating protein or cell
– Mitigate disease condition
Definition of Half-Life
• The time required for the concentration of drug to
decline by ½
• Example:
–
–
–
–
–
Drug is 20 ug/mL at 1 hour after dosing
Drug is 10 ug/mL at 5 hours after dosing
Drug is 5 ug/mL at 9 hours after dosing
½ drug cleared every 4 hours.
Half-life is therefore 4 hours
Pharmacometrics
• Pharmacometrics
– analysis and interpretation of data produced in
pre-clinical and clinical trials.
– Inter-disciplinary field
• Biostatistics
• Computational methods
• Pharmacokinetic/Pharmacodynamic modeling.
Pharmacometric components
• Population pharmacokinetic and pharmacodynamic
modeling
• Disease progression modeling
• Clinical trial simulation
Population pharmacokinetic and
pharmacodynamic modeling
• Population modeling involves the analysis of
data from a group (population) of individuals,
with all their data analyzed simultaneously to
provide information about the variability of
the model's parameters.
Disease progression modeling
• Mathematical models to describe, explain,
investigate and predict the changes in disease
status as a function of time. It incorporates
– functions of natural disease progression
– Drug action which reflects the effect of a drug on
disease status
Clinical Trial Simulation
• Simulation of a clinical trial can provide a data set
that will resemble the results of an actual trial.
• Multiple replications of a clinical trial simulation can
be used to make statistical inferences
– Estimate the power of the trial
– Predicting p-value
– Estimate the expected % of the population that should fall
within a predefined therapeutic range
Impact of Pharmacometrics on Drug
Approval and Labeling Decisions: Example 1
•
•
•
Drug nesiritide for the treatment of acute decompensated congestive heart failure
– Acute decompensated heart failure (ADHF) is a common and potentially
serious cause of acute respiratory distress.
– PD marker used to measure severity of the disease: The Pulmonary wedge
pressure (PWP) is the pressure measured in a pulmonary artery distal to an
occlusion of that artery
• High in the presence of ADHF
• Drug for ADHF should decrease PWP
– Side effect: Hypotension
In April 1999, the FDA issued a nonapprovable letter to the sponsor.
A subsequent Pharmacometric analysis was performed to optimize dosing regimen
of nesiritide to achieve a faster decrease in PCWP (benefit) and minimize
undesired hypotension (risk)?
– Exposure (PK) and response (PD) data from the original submission were
modeled. The developed model was used to explore various alternative dosing
scenarios.
– Evidently, 2 µg/kg followed by 0.01 µg/min/kg infusion seems to offer a
reasonable benefit-risk profile.
– The sponsor submitted the results in support of a revised dosing regimen.
– The FDA approved nesiritide for acute CHF in May 2001.
Impact of Pharmacometrics on Drug Approval
and Labeling Decisions: Example 2
•
The sponsor sought approval of apomorphine (Apokyn), subcutaneous injection)
for acute use in patients with Parkinson’s disease.
– Along with the registration studies, the sponsor submitted results from a dose-finding (2 to 10
mg) study with a suggested maximum recommended dose.
•
•
•
In the renal-impaired apomorphine demonstrated a 50% increase in exposure.
The FDA conducted exposure-response analysis to aid in evaluating the appropriate dosing
instructions for labeling.
Regulatory Questions
– Is the maximum recommended dose and the titration strategy proposed by the sponsor
appropriate?
– Is there a need for adjusting dose in the renal impaired?
•
Role of Pharmacometric Analysis
– The data from the dose-finding study indicated a concentration-dependent effect on Unified
Parkinson’s Disease Rating Scale, which is desired, and blood pressure, which is undesired.
•
•
•
Simulations using the exposure-response model suggested only minor additional benefits beyond 6
mg.
The starting dose for patients with renal impairment was recommended to be 1 mg.
Regulatory Action
– The dosing recommendations suggested by the Pharmacometric exposure-response analysis
were incorporated in the labeling after discussions with the sponsor.
Detailed Case Study: TV1102 Phase 2a
Study Design
•
Objective of the study
–
–
•
Study Design
–
–
•
16 weeks, 8 weeks treatment period (first week induction phase followed by seven weeks
maintenance period) followed by 8 weeks without treatment.
Efficacy variable modeled
–
•
Cohort 1 – 40 patients to be s.c administered three ‘induction’ doses of 200 mg ATL 1102 each on
days 1, 4, and 7 of study and then a ‘maintenance’ dose regimen of 200 mg twice a week (days 4 and
7 of the week) for seven weeks.
Cohort 2 – 40 patients to be administered placebo injections s.c. according to the schedule of Cohort
1
Duration
–
•
prove the therapeutic concept and to determine the pharmacokinetic profile of ATL 1102 by
subcutaneous injections in patients with multiple sclerosis
Develop a PK/PD/Efficacy model that will allow optimally designing the next Phase 2 b study
Cumulative Number of T1 Gd-Enhancing Lesions
PK measurements
–
6 samples on Day 1, 28, 56 and 112 as follows:
•
•
1 sample before administration of medication and after 1, 2, 3, 4 and 6 hours
MRI measurements
–
Day 28,56,84 and 112
Population PK/T1 Modeling
• The observed T1 lesions data suggest a significant
difference between the Placebo and Treated group
(see next slide)
• We modeled the average T1 lesion time profile using
a Poisson (response is categorical) regression (T1
lesion changes with time) model and linked it to the
PK model. This model can therefore simulate Placebo
T1 time profile as well as treated T1 time profile.
– The model accounts also for the patients that did not show
any active lesions during the course of the Phase 2a trial
Observed T1 enhancing lesions over time:
Placebo vs. Treated Group
PK/T1 Modeling: Processes
SC
Dose
Poisson (C)
Extravascular
Compartment
ka
k12
ka
k21
T1
c
k31
k10
Linear Clearance
Kmet,i
(i=1,7)
Vm,Km
k13
Tissue 2
Kout,i
PK/T1 Modeling: Mathematical Model
SC compartment
dA(1)
 - K 01. A(1)
dt
Plasma compartment
dA(2)
 K 01. A(1).F - K10. A(2) - K12. A(2)  K 21. A(3) - K13. A(2)  K 31. A(4)
dt
-VMAX . A(2) / ( A(2)  KM .V 2)
Peripheral Tissue 1
dA(3)
 K12. A(2) - K 21. A(3)
dt
Peripheral Tissue 2
dA(4)
 K13. A(2) - K 31. A(4)
dt
Mass balance for the number of T1 lesions: A(5) is the logarithm of the Poisson mean.
The rate of change of A(5) is assumed to be a constant ( ) for Placebo (constant slope) while the slope
is affected by the drug through a Michael Menten equation type.
dA(5)
  .(1- e max.( A(2) / ( A(2)  EC 50.V 2))
dt
t  t0 , A(5)   .t0  int ercept
t0 is the first recorded time for each patient
int ercept is the value of A(5) at t=0
)
Fitting Results
Parameter
Value
Meaning
slope (placebo) 0.000218611 change in the log(average number of T1 lesions) per unit of time
intercept
-0.372133322 log(average number of T1 lesions) at t =t0
emax
3.601925822 maximum change relative to Placebo in the log(average number of T1 lesions)
ec50
0.095389776 drug concentration at which the log(average number of T1 lesions) is half emax
Knowing the Efficacy parameters will help predicting the efficacy
time profile for the upcoming Phase 2b Trial
Population PK/Platelet Modeling
• An indirect response model was linked to the
PK model in order to quantify the correlation
between Platelet and PK time profile
PK/PD Modeling: Processes
SC
Dose
kin(1-C/(C+ED50))
Extravascular
Compartment
ka
k12
ka
k21
Platelets
c
k31
k10
kout
Linear Clearance
Kmet,i
(i=1,7)
Vm,Km
k13
Tissue 2
Kout,i
PK/Platelet Modeling: Mathematical Model
SC compartment
dA(1)
 - K 01. A(1)
dt
Plasma compartment
dA(2)
 K 01. A(1).F - K10. A(2) - K12. A(2)  K 21. A(3) - K13. A(2)  K 31. A(4)
dt
-VMAX . A(2) / ( A(2)  KM .V 2)
Peripheral Tissue 1
dA(3)
 K12. A(2) - K 21. A(3)
dt
Peripheral Tissue 2
dA(4)
 K13. A(2) - K 31. A(4)
dt
Mass balance for Platelets: A(5) is the platelet number.
dA(5)
A(2)
 kin.(1  E max.
)  kout. A(5)
dt
A(2)  ED50.V
kin
t  0, A(5) 
kout
V is the Volume of distribution associated with the Plasma compartment
Average Population PD estimates
kin
kout
ED50
Value
units
1.284273 (platelet/hour)
0.005264 /hour
0.351775 ug/ml
Knowing the PD parameters will help predicting the PD time
profile for the upcoming Phase 2b Trial
Phase 2b Trial design and Goal
•
•
•
•
The Phase-2b tentative design is a 6 month treatment period, with 2-3 ATL dose
groups and placebo. MRI would be observed once a month with the primary
endpoint being the percent reduction in the average cumulative (starting on
Month 4 and cumulated every month until Month 7) number of T1 lesions, relative
to Placebo. The optimal regimen would have preferably the following
characteristics.
At least 60% reduction of cumulative T1 lesions compared to placebo
Platelets with not more than 10% of subjects <150 (10^9/L) at any time, 5% of
subjects <100 (10^9/L) at any time and no subject <50 (10^9/L) at any time
The dosing to be explored are 100 mg, 200 mg and 400 mg with dosage intervals
varying from weekly to every 4 weeks. The goal of the simulation exercise was to
have insight to the following issues:
– What dosing regimens can provide the required outcome based on the boundaries of
MRI and platelets?
– What is the outcome simulating the predefined regimens?
– Can drug loading provide any advantage?
Calculation of the Cumulative number of
T1 lesions
• The PK/PD model was used to predict on Month 4-5-6 and 7 the
expected average number of T1 lesions
• Therefore, the cumulative number of T1 lesions for the treated
group is simply calculated by just summing up the number of T1
lesions starting on month 4 until Month 7. We call it cum_T1_drug
• The same calculation proceeds for the Placebo group (same model
with a zero dose). We call it cum_T1_Placebo
– The % MRI improvement ( %MRI ) is directly computed using the following
formula
%MRI=(cum_T1_Placebo-cum_T1_drug)/cum_T1_Placebo x 100
Phase 2b Trial Simulation Results: Percent MRI improvement
vs.Total Dosing per 4 weeks for dosage intervals between 1
and 4 weeks: MRI cumulated on Month 4-5-6 and 7
Interval Week
MRI Improvement is better for small Dosage intervals, given a fixed total dose
Phase 2b Trial Simulation Results: Estimation of the percent
of Patients to reach platelet counts below a certain threshold
value
• The PK/PD model that was developed and fit to the Phase 2a data lead to
an estimate of both the PK/PD average parameters as well as the
parameters quantifying the variability across the population
– The average parameter values were used to simulate the average PK/PD
profile using the Phase 2b dosing conditions (shown next slide)
• Both average and variability information can be used to simulate
hypothetical patients that would behave similarly than the actual
population for any specific dosage regimen
• We simulated a large number of patients and recorded their platelet
counts for each of them at the expected measurements times (usually
predose), based on the potential Phase 2b Trial designs.
• Each patient that had at least one recorded platelet count less than X (X
being either 150,100 or 50) was considered as passing the threshold value
• The percent of patients passing at least once the specific threshold value
was then plotted versus the total dosing per 4 weeks for different dosage
intervals.
Example of simulation of both PK and Platelet average time
profile: 200 mg TV1102 given weekly
The predictions are predose up to the last dose, then every day for 30 days
after last dose. PK and Platelets are mirror projections (PK going down, PD
going up)
Phase 2b Trial Simulation Results: Percent subjects with
Platelet <150 versus total dose per 4 weeks and
dosage interval
Dosage interval
Phase 2b Trial Simulation Results: Percent subjects with
Platelet <100 versus total dose per 4 weeks and
dosage interval
Dosage Interval
Phase 2b Trial Simulation Results: Percent subjects with
Platelet <50 versus total dose per 4 weeks and
dosage interval
Conclusions
• PK and Platelet time profiles are highly correlated
• The only safety concerns are with the percent of Patients expected to have
platelet counts less than 150 which is larger than 10% for a total dose per
4 weeks exceeding 400 mg
• However, 200 mg every week (800 mg per 4 weeks) should not lead to
more than 5% of the population with platelet counts less than 100
• In Conclusion, for the tentative Phase2b Trial design, we have
– 200mg every week: safety concerns only for Platelet counts less than 150
(about 20% of the population) but
• less than 5% of the population will have platelet counts less than 100 for that
regimen
• MRI reduction is expected to be about 60%
– 200 mg every two weeks (no safety concerns)
• MRI reduction is expected to be about 45%
– 200 mg every three weeks (no safety concerns)
• MRI reduction is expected to be about 35%
Conclusions
• The proposed design of 200mg every week, two and three
weeks without a loading dose should lead to enough
separation in the MRI response (60,45 and 35% MRI
reduction) to model a dose response relationship
– Characterize a dose response relationship will lead to an optimal
design of Phase 3.
• The safety concern for a 200 mg Dose every week has been
addressed and quantified
– About 20% of the population is expected to have platelet counts less
than 150 for that dosage regimen but only 2% would have platelet
counts less than 100