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Ken Kowalski, Ann Arbor Pharmacometrics Group (A2PG)

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A General Framework for Model-Based Drug Development Using Probability Metrics for Quantitative Decision Making

Ken Kowalski, Ann Arbor Pharmacometrics Group (A2PG)

- Population Models
- Basic Notation and Key Concepts

- Basic Probabilistic Concepts
- General Framework for Model-Based Drug Development (MBDD)
- Examples
- Final Remarks/Discussion
- Bibliography

PaSiPhIC 2012

- General Form of a Two-Level Hierarchical Mixed Effects Model:
- Definitions:

PaSiPhIC 2012

- Typical Individual Prediction:
- Easy to compute, same functional form as f

- Integral is often intractable when f is nonlinear
- Typically requires Monte-Carlo integration (simulation)

- Cannot observe a ‘typical individual’
- Can observe a sample mean

PaSiPhIC 2012

- Statistical intervals (i.e., confidence and prediction intervals)
- Statistical power
- Probability of achieving the target value (PTV)
- Probability of success (POS)
- Probability of correct decision (POCD)

PaSiPhIC 2012

- A confidenceinterval (CI) is used to make inference about the true (unknown) quantity (e.g., population mean)
- Reflects uncertainty in the parameter estimates
- Typically used to summarize the current state of knowledge regarding the quantity of interest based on all available data used in the estimation of the quantity

- A predictioninterval (PI) is used to make inference for a future observation (or summary statistic of future observations)
- Reflects both uncertainty in the parameter estimates as well as the sampling variation for the future observation

PaSiPhIC 2012

Prediction Limits Recognizing Uncertainty in E( )

Prediction Limits if

E( ) Located Here

Distribution of sampling variation

Confidence Limits for

Note: Prediction intervals are always wider than confidence intervals.

PaSiPhIC 2012

Sample mean (parameter estimate)

Standard error of the mean (parameter uncertainty)

PaSiPhIC 2012

Sample variance of a future observation (sampling variation)

Sample mean (parameter estimate)

Sample variance of the mean (parameter uncertainty)

Note: The sample mean based on N previous observations is the best estimate for a single future observation.

PaSiPhIC 2012

Sample variance of the mean of M future observations (sampling variation)

Sample mean (parameter estimate)

Sample variance of the mean (parameter uncertainty)

Note 1: The sample mean based on N previous observations is the best estimate for the mean of M future observations.

Note 2:A prediction interval for M=∞ future observations is equivalent to a confidence interval (see Slide 8). This will also be referred to as ‘averagingout’ the sampling variation.

PaSiPhIC 2012

*Note for the simple mean model the standard error of the mean does not take into account uncertainty in the sampling variation (s) whereas in population models we typically take into account the uncertainty in Ω and .

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- Randomly sample with replacement subject data vectors to preserve within-subject correlations to construct bootstrap datasets
- Re-estimate model parameters for each bootstrap dataset to obtain an empirical (posterior) distribution of the parameter estimates (, Ω, )
- May require stratified-resampling procedure (by design covariates) for a pooled-analysis with very heterogeneous study designs
- E.g., limited data at a high dose in one study may be critical to estimation of Emax

PaSiPhIC 2012

- Draw random samples from multivariate normal distribution with
- Mean vector = [ ]
- Covariance matrix = Cov( )
- Obtained from Hessian or other procedure (e.g., COV step in NONMEM)

- Based on Fisher’s theory (Efron, 1982)

- Assumes asymptotic theory (large sample size) that maximum likelihood estimates converge to a MVN distribution
- See Vonesh and Chinchilli (1997)

- Based on Wald’s approximation that likelihood surface can be approximated by a quadratic model locally around the maximum likelihood estimates
- Approximations are dependent on parameterization
- Improved approximations may occur by estimating the natural logarithm of the parameter for parameters that must be positive

PaSiPhIC 2012

- The non-parametric bootstrap procedure is widely used in pharmacometrics
- Often used as a back-up procedure to quantify parameter uncertainty when difficulties arise in estimating the covariance matrix (eg., NONMEM COV step failure)
- In this setting issues with a large number of convergence failures in the bootstrap runs may call into question the validity of the confidence intervals (i.e., Do they have the right coverage probabilities?)

- Often used as a back-up procedure to quantify parameter uncertainty when difficulties arise in estimating the covariance matrix (eg., NONMEM COV step failure)
- This form of parametric bootstrap procedure is less computationally intensive than other bootstrap procedures that require re-estimation
- Requires successful estimation of the covariance matrix (NONMEM COV step) but can lead to random draws outside the feasible range of the parameters unless appropriate transformations are applied

PaSiPhIC 2012

- Developing stable models that avoid extremely high pairwise correlations (>0.95) between parameter estimates and have low condition numbers (<1000) can help
- Ensure successful covariance matrix estimation
- Reduce convergence failures in non-parametric bootstrap runs

- Choice of bootstrap procedure should focus on the adequacy of the parametric assumption
- Random draws from MVN versus the more computationally intensive re-estimation approaches (e.g., non-parametric bootstrap)

PaSiPhIC 2012

Obtain random draw of , Ω, from bootstrap procedure for kth trial

Simulate subject level data

Yi | , Ω,

for M subjects

Summarize predictions (e.g., mean)

stratified by design (dose ,time, etc.)

Use percentile method to obtain statistical interval from K predictions

k<K

Repeat for

k=1,…,K trials

Note 1:To construct confidence interval consider sufficiently large M (e.g., ≥2000 subjects) to average out sampling variation in Ω and .

Note 2:For prediction intervals, M is chosen based on observed or planned sample size.

k=K

PaSiPhIC 2012

- True (unknown) treatment effect or quantity ()
- Target value (TV)
- A reference value for

- Data-analytic decision rule (e.g., Go/No-Go criteria)
- Based on an observed treatment effect or quantity (T)

PaSiPhIC 2012

- is the true (unknown) treatment effect
- Models provide a prediction of
- Uncertainty in the parameter estimates of the model provides uncertainty in the prediction of
- P( ) denotes the distribution of predictions of

PaSiPhIC 2012

- Semi-mechanistic model of inhibition of glucose production

Mean Model Fit of FPG Versus Dose(integrates data across dose and time)

Model-Predicted Placebo-Corrected FPG Versus Dose at Week 12

Week 0

Week2

Week 4

Week 6

Delta FPG (mg/dL)

Placebo-Corrected Delta FPG (mg/dL)

Week8

Week 12

Dose (mg)

Dose (mg)

Population Mean Prediction

PaSiPhIC 2012

Observed Mean

5th Percentile (90% LCL)

Typical Individual Prediction (PRED)

95th Percentile (90% UCL)

- Suppose we desire to develop a compound if the true unknown treatment effect () is greater than or equal to some target value (TV)
- TV may be chosen based on:
- Target marketing profile
- Clinically important difference
- Competitor’s performance

- TV may be chosen based on:
- If we knew truth we would make a Go/No-Go decision to develop the compound based on:
- Go: ≥ TV
- No-Go: < TV

PaSiPhIC 2012

- But we don’t know truth…
- So we conduct trials and collect data to obtain an estimate of the treatment effect (T)
- T can be a point estimate or confidence limit on the estimate or prediction of (e.g., placebo-corrected change from baseline FPG)

- So we conduct trials and collect data to obtain an estimate of the treatment effect (T)
- We might make a data-analytic Go/No-Go decision to advance the development of the compound if:
- Go:T ≥ TV
- No-Go:T < TV

PaSiPhIC 2012

- Power is a conditional probability based on an assumed fixed value of the treatment effect ()
- Power = P(T ≥ TV | ) where P(T ≥ TV | = TV) = (false positive)
- TV=0 for statistical tests of a treatment effect

- Power is an operating characteristic of the design based on a likely value of
- No formal assessment that the compound can achieve the assumed value of

PaSiPhIC 2012

Use the same final estimates (, Ω, )

for each

simulated trial

Simulate subject level data

Yi | , Ω,

for M subjects

Analyze simulated data as per SAP

to test

Ho: = TV

Ha: TV

Power is calculated as the fraction of the K trials in which

Ho is rejected

k<K

Repeat for

k=1,…,K trials

Note 1:Typically TV=0 when assessing whether the compound has an overall treatment effect.

Note 2:When using simulations to evaluate power it is good practice to also simulate data under the null (e.g., no treatment effect or placebo model) to verify that the Type 1 error () is maintained.

k=K

PaSiPhIC 2012

- Probability of achieving the target value is defined as the proportion of trials where the true ≥ TV
- PTV = P( ≥ TV)
- Does not depend on design or sample size
- Based only on prior information through the model(s) and its assumptions

- PTV = P( ≥ TV)
- PTV is a measure of confidence in the compound at a given stage of development
- Can change as compound progresses through development

- PTV can be calculated from the same set of simulations used to construct confidence intervals of the predicted treatment effect ()

PaSiPhIC 2012

Obtain random draw of , Ω, from bootstrap procedure for kth trial

Simulate subject-level data Yi | , Ω,

for arbitrarily

large M

Summarize simulated data to obtain population mean predictions of

Calculate PTV as proportion of K trials in which

≥ TV

k<K

Repeat for

k=1,…,K trials

Note:To calculate PTV use anarbitrarily large M (e.g., ≥2000 subjects) to average out sampling variation in Ω and . PTV should only reflect the parameter uncertainty based on all available data used in the model estimation.

k=K

PaSiPhIC 2012

- Probability of success is defined as the proportion of trials where a data-analytic Go decision is made
- POS = P(Go) = P(T ≥ TV)

- POS is an operating characteristic that evaluates both the performance of the compound and the design
- In contrast to Power = P(T ≥ TV | ) which is an operating characteristic of the performance of the design for a likely value of

- POS is sometimes referred to as ‘average power’ where a Go decision is based on a statistical hypothesis test

PaSiPhIC 2012

Obtain random draw of , Ω, from bootstrap procedure for kth trial

Simulate subject-level data Yi | , Ω,

for planned sample size (M)

Summarize simulated data to obtain estimate of (T) and perform hypothesis test

Calculate POS as proportion of K trials in which

T ≥ TV

k<K

Repeat for

k=1,…,K trials

Note:POS integrates the conditional probability of a significant result over the distribution of plausible values of reflected through the uncertainty in the parameter estimates for , Ω, and .

k=K

PaSiPhIC 2012

- A correct data-analytic Go decision is made when
- T ≥ TV and ≥ TV

- A correct data-analytic No-Go decision is made when
- T < TV and < TV

- Probability of a correct decision is calculated as the proportion of trials where correct decisions are made
- POCD = P(T ≥ TV and ≥ TV) + P(T < TV and < TV)

- POCD can only be evaluated through simulation where the underlying truth () is known based on the data-generation model used to simulate the data

PaSiPhIC 2012

Classify

Go: ≥TV

No Go: <TV Under Truth

Obtain random draw of , Ω, from bootstrap procedure for kth trial

Classify

Go: T≥TV

No Go: T<TV

Under Trial Data

Compare Truth Versus

Data-Analytic Decision

Classify

Go: ≥TV

No Go: <TV Under Truth

Simulate subject-level data Yi | , Ω,

for planned sample size (M)

Summarize simulated data to obtain estimate of

(T)

Calculate POS as proportion of K trials in which

T ≥ TV

Repeat for

k=1,…,K trials

k<K

k=K

Note:Classification of trial under truth is obtained from the PTV simulations.

PaSiPhIC 2012

- Basic assumptions of MBDD
- Six components of MBDD
- Clinical trial simulations (CTS) as a tool to integrate MBDD activities
- Table of trial performance metrics
- Improving POCD
- Setting performance targets
- Comparing performance targets between early and late stage clinical drug development

PaSiPhIC 2012

- Predicated on the assumptions:
- That we can and should develop predictive models
- That these models can be used in CTS to predict trial outcomes

- Think of MBDD as a series of learn-predict-confirm cycles
- Update models based on new data (learn)
- Conduct CTS to predict trial outcomes (predict)
- Conduct trial to obtain actual outcomes and evaluate predictions (confirm)

Learn

Predict

Confirm

PaSiPhIC 2012

Quantitative Decision Criteria

PK/PD &

Disease Models

Trial Performance Metrics

Evaluate probability of achieving

target value (PTV),

success (POS),

correct decisions (POCD)

Leverage understanding of pharmacology/disease – useful for extrapolation

Implement SAP,

evaluate alternative analysis methods – ANCOVA, MMRM, regression, NLME

Evaluate designs and dose selection; incorporate trial execution models such as dropout models

Understand competitive landscape from a dose-response perspective

Explicitly and quantitatively defined criteria

“draw line in the sand”

MBDD

Meta-Analytic Models (Meta-Data from Public Domain)

Data-Analytic Models

Design & Trial Execution Models

PaSiPhIC 2012

- Just as a clinical trial is the basic building block of a clinical drug development program, clinical trial simulations should be the cornerstone of an MBDD program
- CTS allows us to assume (know) truth for a hypothetical trial
- Based on simulation model we know
- Mimic all relevant design features of a proposed clinical trial
- Sample size, treatments (doses), covariate distributions, drop out rates, etc.

- Analyze simulated data based on the proposed statistical analysis plan (SAP)
- Calculate T (test statistic for treatment effect) and apply data-analytic decision rule

- CTS should be distinguished from other forms of stochastic simulations
- E.g., CIs for dose predictions, PTV calculations, etc.

- CTS can be used to integrate the components of MBDD and the various probabilistic concepts (including POS and POCD)

PaSiPhIC 2012

Trial No Go

Trial Go

Total

Correct No Go

Incorrect Go

P(True No Go)

“True” No Go

Incorrect No Go

Correct Go

P(True Go)

“True” Go

P(Trial No Go)

P(Trial Go)

1.0

Total

POCD

POS

PTV

PaSiPhIC 2012

- Change the design
- n/group
- Regression-based designs ( # of dose groups, n/group)
- Consider other design constraints (cross-over, titration, etc.)

- Change the data-analytic model
- Regression versus ANOVA
- Longitudinal versus landmark analysis

- Change the data-analytic decision rule
- Alternative choices for T
- Point estimate, confidence limit, etc.

- Alternative choices for T
- All of the above can be evaluated in a CTS

PaSiPhIC 2012

- PTV will change over time as model is refined and new data emerge
- Bring forward compounds/treatments with higher PTV as compound moves through development
- PTV may be low in early development

- Industry average Phase 3 failure rate is approximately 50%
- It is difficult to improve on this average unless we can routinely quantify PTV
- Strive to achieve PTV>50% before entering Phase 3

- Bring forward compounds/treatments with higher PTV as compound moves through development
- Strive to achieve high POCD in decision-making throughout development

PaSiPhIC 2012

Trial No Go

Trial No Go

Trial Go

Trial Go

Total

Total

True

No Go

True

No Go

True Go

True Go

Total

Total

Late Development

POCD should be high

PTV should be high

Advance good compounds / treatments to registration

Early Development

POCD should be high

PTV may be low

Kill poor compounds /

treatments early

PaSiPhIC 2012

- Rheumatoid Arthritis Example
- Phase 3 development decision

- Urinary Incontinence Example
- Potency-scaling for back-up to by-pass Phase 2a POC trial and proceed to a Phase 2b dose-ranging trial

- Acute Pain Differentiation Case Study
- Decision to change development strategy to pursue acute pain differentiation hypothesis

PaSiPhIC 2012

- Endpoints:
- DAS28 remission (DAS28 < 2.6)
- ACR20 response (20% improvement in ACR score)

- Models developed based on Phase 2a study:
- Continuous DAS28 longitudinal PK/PD model with Emax direct-effect drug model
- ACR20 logistic regression PK/PD model with Emax drug model
- Both direct and indirect-response models evaluated

- Conducted clinical trial simulations for a 24-week Phase 2b placebo-controlled dose-ranging study (placebo, low, medium and high doses)
- At Week 12 non-responders assigned to open label extension at medium dose level
- Primary analysis at Week 24; Week 12 responses for non-responders carried forward to Week 24

- Evaluated No-Go/Hold/Go criteria for Phase 3 development

PaSiPhIC 2012

- No Go:Stop development
- Hold: Wait for results of separate Phase 2b active comparator trial
- Go: Proceed with Phase 3 development without waiting for results from comparator trial

PaSiPhIC 2012

- CTS results suggest a high probability that the team will have to wait for results from the Phase 2b active comparator trial before making a decision to proceed to Phase 3. Very low probability of taking low dose into Phase 3.

PaSiPhIC 2012

- Endpoint:
- Daily micturition (MIC) counts

- Models developed:
- Longitudinal Poisson-Normal model developed for daily MIC counts for lead compound
- Time-dependent Emax drug model using AUC0-24 as measure of exposure

- Potency scaling for back-up based on:
- In vitro potency estimates for lead and back-up (back-up more potent than lead)
- Equipotency assumption between lead and back-up

- Longitudinal Poisson-Normal model developed for daily MIC counts for lead compound
- Conducted CTS to evaluate Phase 2b study designs for back-up compound (placebo and four active dose levels)
- Evaluated various dose scenarios of low (L), medium #1 (M1), medium #2 (M2) and high (H) doses levels
- Implemented SAP (constrained MMRM analysis with step down trend tests)
- Quantified POS for the L, M1, M2 and H doses for the various dose scenarios and potency assumptions

PaSiPhIC 2012

Note: Low (L) dose was selected to be a sub-therapeutic response. Design was not powered to detect a significant treatment effect at this dose.

PaSiPhIC 2012

- CTS results:
- High POS (>95%) demonstrating statistical significance at the H dose for all 6 dose scenarios
- Insensitive to potency assumptions

- High POS (>88%) demonstrating statistical significance at the M2 dose for all 6 dose scenarios
- Insensitive to potency assumptions

- POS varied substantially for demonstrating statistical significance of the M1 dose
- Depending on dose scenario and potency assumption

- POS < 60% for demonstrating statistical significance at the L dose
- Except for dose scenarios 4 – 6 for the in vitro potency assumption

- High POS (>95%) demonstrating statistical significance at the H dose for all 6 dose scenarios

CTS results provided guidance to the team to select a range of doses that would have a high probability of demonstrating dose-response while being robust to the uncertainty in the relative potency between the back-up and lead compounds. Provided confidence to bypass POC and move directly to a Phase 2b trial for the back-up.

PaSiPhIC 2012

- SC-75416 is a selective COX-2 inhibitor
- Capsule dental pain study conducted
- Poor pain response relative to active control (50 mg rofecoxib)
- Lower than expected SC-75416 exposure with capsule relative to oral solution evaluated in Phase 1 PK studies

- PK/PD models developed to assess whether greater efficacy would have been obtained if exposures were more like that observed for the oral solution
- Pain relief scores (PR) modeled as an ordered-categorical logistic normal model
- Dropouts due to rescue therapy modeled as a discrete survival endpoint dependent on the patient’s last observed PR
- Assumes a missing at random (MAR) dropout mechanism

PaSiPhIC 2012

- PK/PD modeling predicted greater efficacy with oral solution relative to capsules
- A 6-fold higher SC-75416 dose (360 mg) than previously studied predicted to have clinically relevant improvement in pain relief relative to active control (400 mg ibuprofen)
- Model extrapolates from capsules to oral solution and leverages in-house data from other COX-2s and NSAIDs

- Project team considers change in development strategy to pursue a high-dose efficacy differentiation hypothesis
- Original strategy was to determine an acute pain dose that was equivalent to an active control and then scale down the dose for chronic pain (osteoarthritis)
- Based on well established relationships that chronic pain doses for NSAIDs tend to be about half of the acute pain dose

- Original strategy was to determine an acute pain dose that was equivalent to an active control and then scale down the dose for chronic pain (osteoarthritis)

PaSiPhIC 2012

- Proposed conducting a proof of concept oral solution dental pain study
- Demonstrate improvement in pain relief for 360 mg SC relative to 400 mg ibuprofen
- Primary endpoint is TOTPAR6 (SC vs. ibuprofen)
- TOTPAR6 = 3 (TV) is considered clinically relevant

- Perform ANOVA on observed LOCF-imputed TOTPAR6 response and calculate LS mean differences
- T = LS mean (SC) – LS mean (ibuprofen)
- LCL95 = 2-sided lower 95% confidence limit on T

- Demonstrate improvement in pain relief for 360 mg SC relative to 400 mg ibuprofen
- Compound and data-analytic decision rule:
- Truth: Go if ≥3, No-Go if <3
- Data:Go if T≥3 and LCL95>0, No-Go if T<3 or LCL95≤0

PaSiPhIC 2012

Simulate PR Model Parameters

(PR,2) ~ MVN

Simulate PR Scores

M=2,000 patients

per treatment

Perform LOCF Imputation and Calculate TOTPAR6

Simulate Dropout Times

M=2,000 patients

per treatment

Simulate Dropout Model Parameters

DO ~ MVN

Calculate Population Mean TOTPAR6 & TOTPAR6

Across M=2,000 pts

k<K

Determine

True Decision

Go: 3

No Go: <3

k=K

Repeat for

k = 1,…,K=10,000 trials

Summarize Distribution of TOTPAR6 ()

PaSiPhIC 2012

PTV = P( 3) = 67.2%

Mean Prediction = 3.2

PTV = 67.2% sufficiently high to warrant recommendation to conduct oral solution dental pain study to test efficacy differentiation hypothesis.

PaSiPhIC 2012

Simulate PR Scores for k-th Trial

n pts / treatment

Calculate Mean TOTPAR6 (T), SEM & 95% LCL

Perform LOCF Imputation & Calculate TOTPAR6

Simulate Dropout Times for k-th Trial

n pts / treatment

Apply Decision Rule

Go: LCL>0 and T3

No Go: LCL0 or T<3

Compare Truth vs. Data-Analytic Decision

Repeat for

k=1,…,K=10,000 trials

Calculate Metrics

POS

POCD

k<K

k=K

PaSiPhIC 2012

POCD = 70.72%

POS = 61.90%

PTV = 67.20%

A sufficiently high POCD and POS supported the recommendation and approval to proceed with the oral solution dental pain study.

PaSiPhIC 2012

Obs = -1.8

Pred = -7.0

Pred = -0.9

Obs = -9.6

Pred = 3.2

Pred = 2.0

Obs = 3.3

Obs = 2.6

PaSiPhIC 2012

- 360 mg SC-75416 met pre-defined Go decision criteria
- Confirmed model predictions
- Demonstrated statistically significant improvement relative to 400 mg ibuprofen

- MBDD approach provided rationale to pursue acute pain differentiation strategy that might not have been pursued otherwise
- Allowed progress to be made while reformulation of solid dosage form was done in parallel
- Validation of model predictions provided confidence to pursue alternative pain settings for new formulations without repeating dental pain study
- Model could be used to provide predictions for new formulations

PaSiPhIC 2012

- Some thoughts on implementing MBDD
- Challenges to implementing MBDD

PaSiPhIC 2012

- We need to clearly define objectives
- What questions are we trying to address with our models?

- We need explicit and quantitatively defined decision criteria
- It’s difficult to know how to apply the models if decision criteria are ambiguous or ill-defined

- We need complete transparency in communicating model assumptions
- Entertain different sets of plausible model assumptions
- Evaluate designs for robustness to competing assumptions

- We need to routinely evaluate the predictive performance of the models on independent data
- Modeling results should be presented as ‘hypothesis generating’ requiring confirmation in subsequent independent studies

PaSiPhIC 2012

- Conduct CTS integrating information across disciplines
- Implement key features of the design and trial execution (e.g., dropout)
- Implement statistical analysis plan (SAP)

- Provide graphical summaries of CTS results for recommended design prior to the release of the actual trial results
- Perform quick assessment of predictive performance when actual trial reads out

- Update models and quantification of PTV after actual trial reads out
- i.e., Begin new learn-predict-confirm cycle

PaSiPhIC 2012

- Focus on timelines of individual studies and a ‘go-fast-at-risk’ strategy (i.e., minimizing gaps between studies) can be counter-productive to a MBDD implementation
- M&S (learning phase) is a time-consuming effort

- Integration of MBDD activities in project timelines will require focus on integration of information across studies
- Not just tracking of individual studies

- May need processes to allow modelers to be un-blinded to interim results to begin modeling activities earlier to meet aggressive timelines
- Insufficient scientific staff with programming skills to perform CTS
- Pharmacometricians and statisticians with such skills should be identified
- CTS implementation often requires considerable customization to address the project’s needs (i.e., no two projects are alike)

PaSiPhIC 2012

- Insufficient modeling and simulation resources to implement MBDD on all projects
- Reluctance to be explicit in defining decision rules (i.e., reluctance to ‘draw line in the sand’)
- Due to complexities and tradeoffs in making decisions
- Can be difficult to achieve consensus
- http://www.ascpt.org/Portals/8/docs/Meetings/2012%20Annual%20Meeting/2012%20speaker%20presentations/ASOP%20TUE%20CHERRY%20BLOS%20SESSION%201.pdf

- Reluctance to use assumption rich models
- We make numerous assumptions now when we make decisions…we’re just not very explicit about them
- MBDD can facilitate open debate about explicit assumptions

PaSiPhIC 2012

- Neter, J., and Wasserman, W. Applied Linear Statistical Models, Irwin Inc., IL, 1974, pp. 71-73.
- Efron, B. The Jackknife, the Bootstrap, and Other Resampling Plans, Society for Industrial and Applied Mathematics, PA, 1982, pp. 29-30.
- Vonesh, E.F., and Chinchilli, V.M. Linear and Nonlinear Models for the Analysis of Repeated Measurements, Marcel Dekker, Inc., NY, 1997, pp. 245-246.
- Kowalski, K.G., Ewy, W., Hutmacher, M.M., Miller, R., and Krishnaswami, S. “Model-Based Drug Development – A New Paradigm for Efficient Drug Development”. Biopharmaceutical Report 2007;15:2-22.
- Lalonde, R.L., et al. “Model-Based Drug Development”. Clin Pharm Ther 2007;82:21-32.
- Chuang-Stein, C.J., et al. “A Quantitative Approach to Making Go/No Go Decisions in Drug Development”. DIJ2011;45:187-202.
- Smith, M.K., et al. “Decision-Making in Drug Development – Application of a Model-Based Framework for Assessing Trial Performance”. Book chapter in Clinical Trial Simulations: Applications and Trends, KimkoH.C. and Peck C.C. eds. , Springer Inc., NY, 2011, pp. 61-83.
- Kowalski, K.G., Olson, S., Remmers, A.E., and Hutmacher, M.M. “Modeling and Simulation to Support Dose Selection and Clinical Development of SC-75416, a Selective COX-2 Inhibitor for the Treatment of Acute and Chronic Pain”. Clin Pharm Ther, 2008; 83: 857-866.

PaSiPhIC 2012