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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). Outline. Population Models Basic Notation and Key Concepts Basic Probabilistic Concepts

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Ken kowalski ann arbor pharmacometrics group a2pg

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

Ken Kowalski, Ann Arbor Pharmacometrics Group (A2PG)


Outline

Outline

  • 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


Population models basic notation

Population ModelsBasic Notation

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

    • Definitions:

PaSiPhIC 2012


Population models key concepts

Population ModelsKey Concepts

  • Typical Individual Prediction:

    • Easy to compute, same functional form as f

  • Population Mean Prediction:

    • Integral is often intractable when f is nonlinear

    • Typically requires Monte-Carlo integration (simulation)

  • The typical individual and population mean predictions are not the same when f is nonlinear

    • Cannot observe a ‘typical individual’

    • Can observe a sample mean

  • PaSiPhIC 2012


    Basic probabilistic concepts

    Basic Probabilistic Concepts

    • 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


    What s the difference between a confidence interval and prediction interval

    What’s the difference between a confidence interval and prediction interval?

    • 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


    Relationship between cis and pis

    Relationship Between CIs and PIs

    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


    Confidence interval for the mean based on a sample of n observations

    Confidence interval for the mean based on a sample of N observations

    Sample mean (parameter estimate)

    Standard error of the mean (parameter uncertainty)

    PaSiPhIC 2012


    Prediction interval for a single future observation

    Prediction interval for a single future observation

    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


    Prediction interval for the mean of m future observations

    Prediction interval for the mean of M future observations

    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


    A conceptual extension of confidence and prediction intervals to population modeling

    A Conceptual Extension of Confidence and Prediction Intervals to Population Modeling

    *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 .

    PaSiPhIC 2012


    Quantifying parameter uncertainty in population models nonparametric bootstrap

    Quantifying Parameter Uncertainty in Population Models – Nonparametric Bootstrap

    • 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


    Quantifying parameter uncertainty in population models parametric bootstrap

    Quantifying Parameter Uncertainty in Population Models – Parametric Bootstrap

    • 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


    Non parametric versus parametric bootstrap procedures

    Non-parametric Versus Parametric Bootstrap Procedures

    • 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?)

    • 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


    Non parametric versus parametric bootstrap procedures 2

    Non-parametric Versus Parametric Bootstrap Procedures (2)

    • 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


    Simulation procedure to construct statistical intervals for population model predictions

    Simulation Procedure to Construct Statistical Intervals for Population Model Predictions

    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


    To describe other probabilistic concepts we need to define some additional quantities

    To describe other probabilistic concepts we need to define some additional quantities

    • 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


    Treatment effect

    Treatment Effect ()

    •  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


    Example of model predicted dose response model for fasted plasma glucose fpg

    Example of Model-Predicted Dose-Response Model for Fasted Plasma Glucose (FPG)

    • 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)


    Target value tv

    Target Value (TV)

    • 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

    • 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


    Data analytic decision rule

    Data-Analytic Decision Rule

    • 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)

    • 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


    Statistical power

    Statistical Power

    • 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


    Simulation procedure to calculate power based on a population model predicted

    Simulation Procedure to Calculate Power Based on a Population Model-Predicted 

    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 ptv

    Probability of Achieving the Target Value (PTV)

    • 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 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


    Simulation procedure to calculate ptv based on population model predictions

    Simulation Procedure to Calculate PTV Based on Population Model Predictions

    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 pos

    Probability of Success (POS)

    • 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


    Simulation procedure to calculate pos based on a population model predicted

    Simulation Procedure to Calculate POS Based on a Population Model-Predicted 

    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


    Probability of correct decision pocd

    Probability of Correct Decision (POCD)

    • 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


    Simulation procedure to calculate pocd based on a population model predicted

    Simulation Procedure to Calculate POCD Based on a Population Model-Predicted 

    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


    General framework for mbdd

    General Framework for MBDD

    • 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


    Basic assumptions of mbdd

    Basic Assumptions of MBDD

    • 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


    Six components of mbdd

    Six Components of MBDD

    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


    Clinical trial simulations cts

    Clinical Trial Simulations (CTS)

    • 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


    Table of trial performance metrics

    Table of Trial Performance Metrics

    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


    Improving the probability of making correct decisions

    Improving the probability of making correct decisions

    • 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.

    • All of the above can be evaluated in a CTS

    PaSiPhIC 2012


    Setting performance targets

    Setting Performance Targets

    • 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

    • Strive to achieve high POCD in decision-making throughout development

    PaSiPhIC 2012


    Comparing performance targets between early and late stage clinical drug development

    Comparing performance targets between early and late stage clinical drug development

    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


    Examples

    Examples

    • 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


    Example rheumatoid arthritis

    Example – Rheumatoid Arthritis

    • 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


    Example rheumatoid arthritis 2

    Example – Rheumatoid Arthritis (2)

    • 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


    Example rheumatoid arthritis 3

    Example – Rheumatoid Arthritis (3)

    • 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


    Example urinary incontinence

    Example – Urinary Incontinence

    • 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

    • 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


    Example urinary incontinence 2

    Example – Urinary Incontinence (2)

    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


    Example urinary incontinence 3

    Example – Urinary Incontinence (3)

    • 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

    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


    Case study acute pain differentiation background

    Case Study – Acute Pain DifferentiationBackground

    • 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


    Case study acute pain differentiation background 2

    Case Study – Acute Pain DifferentiationBackground (2)

    • 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

    PaSiPhIC 2012


    Case study acute pain differentiation proposed poc dental pain trial

    Case Study – Acute Pain DifferentiationProposed POC Dental Pain Trial

    • 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

    • 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


    Case study acute pain differentiation simulation procedure to calculate ptv

    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 ()

    Case Study – Acute Pain DifferentiationSimulation Procedure to Calculate PTV

    PaSiPhIC 2012


    Case study acute pain differentiation posterior distribution of totpar6

    PTV = P(  3) = 67.2%

    Mean Prediction = 3.2

    Case Study – Acute Pain DifferentiationPosterior Distribution of TOTPAR6

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

    PaSiPhIC 2012


    Case study acute pain differentiation cts procedure to evaluate poc trial designs

    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 T3

    No Go: LCL0 or T<3

    Compare Truth vs. Data-Analytic Decision

    Repeat for

    k=1,…,K=10,000 trials

    Calculate Metrics

    POS

    POCD

    Case Study – Acute Pain DifferentiationCTS Procedure to Evaluate POC Trial Designs

    k<K

    k=K

    PaSiPhIC 2012


    Case study acute pain differentiation cts trial performance metrics

    Case Study – Acute Pain DifferentiationCTS Trial Performance Metrics

    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


    Case study acute pain differentiation comparison of observed and predicted about 9 months later

    Obs = -1.8

    Pred = -7.0

    Pred = -0.9

    Obs = -9.6

    Pred = 3.2

    Pred = 2.0

    Obs = 3.3

    Obs = 2.6

    Case Study – Acute Pain DifferentiationComparison of Observed and Predicted (About 9 months later…)

    PaSiPhIC 2012


    Case study acute pain differentiation summary of results

    Case Study – Acute Pain DifferentiationSummary of Results

    • 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


    Final remarks discussion

    Final Remarks/Discussion

    • Some thoughts on implementing MBDD

    • Challenges to implementing MBDD

    PaSiPhIC 2012


    Final remarks discussion some thoughts on implementing mbdd

    Final Remarks/DiscussionSome thoughts on implementing MBDD

    • 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


    Final remarks discussion some thoughts on implementing mbdd 2

    Final Remarks/DiscussionSome thoughts on implementing MBDD (2)

    • 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


    Final remarks discussion challenges to implementing mbdd

    Final Remarks/DiscussionChallenges to implementing MBDD

    • 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


    Final remarks discussion challenges to implementing mbdd 2

    Final Remarks/DiscussionChallenges to implementing MBDD (2)

    • 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


    Bibliography

    Bibliography

    • 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


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