Accelerated Stability Modeling for Bioproducts

2013 MBSW, Muncie, IndianaMay 21, 2013

Kevin Guo

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 2

Examples of Bioproducts

Abbott Labs

GenentechAmgen/Pfizer

Eli Lilly

GenentechMerckGenentech

Eli Lilly

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 3

What is BioproductBioproducts are proteins produced from recombinant DNA and grown in an

expression system such as bacteria, yeast, or eukaryotic systems

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• One of the key objectives in developing bioproduct is to find a commercial formulation prototype that has an acceptable stability profile throughout a desired shelf-life of 18 months or more, under typical storage condition of 2-8°C

• To expedite the decision process of selecting the optimal formulation prototype, a short-term accelerated stability is usually conducted by subjecting the formulation candidates to elevated multi temperature exposures (typically 15°C and higher)

• Based on this short-term multi temperature stability study, a prediction model is then developed to estimate the long-term stability profile of the formulation candidates under the intended long-term storage condition

Background

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 5

Why Stability Testing

• Safety point of view from patient• Critical quality attribute (CQA)• Establish shelf life of the drug• Study the storage conditions• Study the container closure system• Provide evidence how the quality of the drug product changes over

time

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 6

What’s so Special about Bioproduct Stability?Common problems with stability of proteins

• Usually sensitive to light, heat, air, and trace metal impurities• Small or large stress factors can disrupt protein folding• Numerous physical degradation routes, including agitation, freezing,

interaction with surfaces and phase boundaries• Possible Non-Arrhenius behavior• One type of degradation can facilitate other types of degradation

leading to a cascading effect• Possibility of different degradation mechanisms appearing depending

on the age of the product• Limited formulation options

Reference: Handbook of Stability Testing in Pharmaceutical Development. Anthony Mazzeo and Patrick Carpenter, Ch17, Stability Studies for Biologics

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 7

• Why accelerated stability studies work despite the problems listed on the previous slide?– Degradation is often reasonably Arrhenius below 40°C– Information from pre-formulation studies and other one-off studies

Bioproduct Stability

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 8

Challenges in Accelerated Stability Modeling

• When developing the prediction model from the short-term accelerated stability study:– Bioproducts typically degrade in a nonlinear fashion, numerous

chemical degradation routes possible, much more so than the small molecule compounds

– The underlying degradation mechanism is often very complex and a characterization study to understand the degradation kinetic is prohibitively expensive

– Limited resources to execute the accelerated study that minimal number of temperatures and testing time-points can be incorporated in the study design

• This presentation describes a proposal on how to develop the prediction model. Some key features:– Leveraging Arrhenius principle of the temperature dependence of a

chemical reaction

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 9

Accelerated Stability Study Design

• Key features of the stability design– Short-term, should be completed in 3 months or less– Typically utilize 4 temperatures at minimum: long-term storage

condition of 5°C + 3 elevated temperatures (15 – 40°C)– Highest temperature is chosen such that it is representative of

lower temperature stability profiles (e.g. elevated temperature degrades in the same pathway as the lower ones)

– Utilize materials (e.g. Drug Substance) that are representative of those for commercial use

– May incorporate other factors of interests besides temperature (e.g. pH, concentration of drug substance, choice of excipient, etc)

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 10

A Typical Accelerated Stability Study Sampling Scheme

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 11

Fixed Time-points vs. Fixed Amt of Change

• Fixed Schedule• Advantages:

• platform-wide approach (doesn’t need to vary with molecule)

• requires little prior knowledge• provides stability profile

• Disadvantages:• labor intensive• different levels of degradation at

different storage conditions – can bias rate coefficient estimates

• Fixed Degradant• Advantages:

• efficient• same level of degradation (rate coefficient

bias does not depend on storage condition)• Disadvantages:

• requires Ea estimate to design correct storage temperature / time-point combinations

• target degradant level must be selected a-priori

Months Months

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 12

Arrhenius Equation

• Rate constant k of a chemical reaction depends on the temperature (Kelvin) and activation energy Ea according to the following equation:

)ln(1ln 0,Ra kTR

Ek

k = Reaction rate

Ea = Activation Energy (Kcal mol-1)

R = Gas constant (Kcal mol-1 K-1)

T = Temperature in Kelvin

kR,0 = Pre-exponential Factor

RTER

aekk 0,

ln (k)

1 / T

RESlope a

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 13

ln (k)

1 / T

RESlope a

Double Regression Analysis

• Step 1. Estimation of the k– Fit “Zero-order” regression of the concentration of an

analytical property vs. time, at each Temperature condition

• Step 2. Estimation of the Activation Energy– Fit Arrhenius Regression, using fitted k(T) values [i.e.,

slopes] from regression in Step 1 as Ys:

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 14

• High variability relative to degradation may lead to negative rate constant estimates that become truncated at the logarithm scale (e.g. increasing monomer ln(-x)=NA)

• Insufficient resolution (high degree of rounding) that results in the same value at each time-point can produce zero rate constant estimates (k=0) that become truncated (ln(0) -inf)

• Non-constant variance with the logarithmic form of Arrhenius

-6

-5

-4

-3

-2

-1

0

ln (k

)3.2 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6

1000/T

Double Regression Analysis

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 15

Therapeutic proteins are complex molecules that can degrade (aggregate) via a variety of different physical/chemical mechanisms.

For simplicity, consider only two broad categories: reactivenon-reactive

time Only the ‘reactive’ monomer aggregates

Use first-order Arrhenius kinetics to describe the system

,0 exptotal NR R RM t M M k t

,0 ,0exp expR R a R ak k E RT k E RT

Parameters:Mtotal – total monomer concentrationt – timeMNR – non-reactive monomer concentrationMR,0 – reactive monomer concentration at t = 0kR – first-order rate constantkR,0 – Arrhenius pre-exponential termEa – apparent activation energykR,0’ = ln( kR,0 ) – for numerical convergence

A good compromise between first-principles rigor and practical limitations

Non-Linear Model Description

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Non-Linear Model Fitting

time

Mto

tal

MNR

MNR + MR,0

Parameters:Mtotal – total monomer concentrationt – timeMNR – non-reactive monomer concentrationMR,0 – reactive monomer concentration at t = 0kR – first-order rate constantkR,0 – Arrhenius pre-exponential termEa – apparent activation energykR,0’ = ln( kR,0 ) – for numerical convergence

Model parameter is a function of…

Parameter

Analytical Property Formulationa Temperature

MNR yes yes no

MR,0 yes no no

kR yes yes yes

kR,0, kR,0’ yes yes no

Ea yes no noa Formulation = unique set of pH, ionic strength, excipients; replicates of a given formulation (different “runs”) were fit independently.

The nonlinear regression platform in JMP 8.0.2 was used to estimate unknown

parameters

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 17

Double Regression vs. Non-Linear

91

92

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98

99

Mon

omer

0 1 2 3Month

5253040

TempC

90

92

94

96

98

100

Mon

omer

0 1 2 3

Month

Nonlinear Model

91

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Mon

o me r

0 1 2 3Month

-2.5-2

-1.5-1

-0.50

0.51

Ln(K

)

0.00

32

0.00

33

0.00

34

0.00

35

0.00

36

1/T

Double Regression

Intercept1/T

Term25.849401-7798.273

EstimateEaK_r,0'M_r,0M_nr

Parameter19.96833256631.4011371399.184416511689.793893802

Estimate

Ea=15.486

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 18

Concluding Remarks

• Summary– An approach for modeling the accelerated stability data for

biomolecules are presented– The nonlinear model based on the interplay between of reactive

and non-reactive species shown to fit the data quite well when there is sufficient degradation

• Future work– Evaluate alternative loss functions for better model selection (i.e.

goodness-of-fit)– Evaluate alternative nonlinear models– Find potential patterns from existing biomolecules that may provide

clues on how to better design and analyze data for future studies

Company Confidential Copyright© 2013 Eli Lilly and CompanySlide 19

Acknowledgments

• Adam Rauk, inVentiv Health• Will Weiss• Suntara Cahya