Dose Response Analysis

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Dose Response Analysis in Clinical Trials
Boston Chapter ASA April 10th, 2006 Jim
MacDougall Bristol-Myers Squibb Medical Imaging
Division Billerica MA james.macdougall_at_bms.com
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Talk Outline

• Review Concepts of Dose Response Analysis in
  Clinical Trials
• Review Dose Response Tests
• Multiplicity Issues
• Dose Response Models
• Hybrid Approach

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Dose Response Analysis in Clinical Trials ICH E4
E9

• Assessment of the dose response should an
  integral part of establishing the safety and
  efficacy of the drug.
• When available, dose concentration data are
  useful and should be incorporated into the
  doseresponse analysis.
• Regulatory agencies and sponsors should be open
  to new approaches and receptive to reasoned
  exploratory data analysis in analyzing and
  describing dose response data.
• A well-controlled doseresponse study is also a
  study that can serve as primary evidence of
  effectiveness.
• Depending on the objective, the use of confidence
  intervals and graphical methods may be as
  important as the use of statistical tests.
• The PtC on Multiplicity in Clinical Trials
  provides useful detailed information

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New Regulatory Document from EMeA CHMP

• Reflection Paper on Methodological Issues in
  Confirmatory Clinical Trials with Flexible Design
  and Analysis Plan
• Released for consultation 31Mar06.
• http//www.emea.eu.int/pdfs/human/ewp/245902en.pdf

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Objectives in Dose-Response Analysis

• Practical Consideration
• The analysis of the data should be driven by the
  Design and Objectives of the study.
• Understanding the dose-response type questions
• Is there any drug effect?
• What is the Maximum Tolerated Dose (MTD)
• Maximum Effective Dose (MaxED)
• Minimum Effective Dose (MinED)?
• What is the nature of the dose response
  relationship?
• What is the optimal dose?
• Practical question
• Is the p-value for the comparison of placebo
  versus the move-forward dose lt 0.05.

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Question Is There Any Drug Effect?

• Linear Trend Tests
• Regression methods to determine if there is a
  linear dose response.
• Overall F-test
• In an ANOVA or linear modeling setting, testing
  that all means are equal. Bartholomews test an
  order restricted modification to F-test.
• Highest vs. Control
• The estimate of the highest group mean is
  compared to the control group.
• Contrasts
• In an ANOVA or linear modeling setting, using
  linear contrasts can provide additional power to
  detect dose response
• Jonckheeres Test
• Rank based method utilizing an ordered
  alternative comparing the number of times an obs.
  from a higher dose-group is larger than an obs.
  from a lower dose-group.

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Three Dose Response Scenarios1) Sigmoid
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Doses at 0, 10, 25, 50 and 100
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Three Dose Response Scenarios2) Step
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Doses at 0, 10, 25, 50 and 100
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Three Dose Response Scenarios3) Quadratic
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Doses at 0, 10, 25, 50 and 100
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Is there a Drug Effect? Compare Methods Relative
to 3 Different Dose Responses
n 20/group Max. effect size (?/?) 1
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Sigmoid
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Step
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Quad
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N10,000 simulations
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Tests for MinED/ NOSTASOT

• NOSTASOT dose No Statistical Significance of
  Trend dose.
• The maximal dose which is not significantly
  different from control
• Generally NOSTASOT higher than the true no-effect
  dose (due to lack of power).

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Three Tests for MED/ NOSTASOT
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Three Tests for MED/ NOSTASOT

• Rom, Costello, and Connell Test
• Based on applying the Closure Principle to
  Tukeys trend test.
• Provides additional testing beyond NOSTATSOT
  dose, (e.g. is highest dose statistically higher
  than others)
• SAS macro makes use straight-forward.

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Multiplicity Issues in Clinical Trials Dose
Response Analysis

• Testing multiple doses versus placebo inherently
  raises the issue of multiplicity
• It is anticipated by regulatory agencies that any
  aspects of multiplicity in a confirmatory trial
  will be addressed and documented (ICH-E9).
• One method of addressing multiplicity is the use
  of multiple comparison procedures which control
  the family-wise error rate at a predefined level
  (e.g. 0.05)

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Multiplicity Issues Strong vs. Weak Control of
the FWE

• Strong versus Weak control of the family-wise
  error rate
• Weak Control protects the FWE under the complete
  null
• Strong Control protects under any
  Null/Alternative configuration.
• In many situations only strong control is
  considered controlling the family-wise error rate
• Further on multiplicity discussion of closed
  procedures.

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Weak Control of the FWE Fishers LSD

• Fishers LSD method
• Overall F-test
• If overall F-test is rejected, test individual
  doses vs. control at 0.05.
• Example 4 active doses vs. control (? 0.05)
• Assume the highest dose works so well that the
  overall F-test is almost surely rejected. Assume
  the other 3 lower doses are not effective.
• This leads to the probability of falsely
  rejecting at least one of the three lower doses
  12 (gt0.05).

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MCPs Common in Active vs. Control

• Bonferroni
• Standard adjustment tests each of k hypotheses at
  level ?/k.
• Fishers LSD
• Performs first an overall test first (e.g.
  F-test) followed by tests of individual doses
  versus placebo.
• Bonferroni-Holm Sequential Procedure
• A step-down sequential version of the
  Bonferroni method. P-values are tested from
  smallest to largest.
• Hochbergs Sequential Procedure
• A step-up procedure. P-values tested from
  largest to smallest.
• Dunnetts Test
• An MCP testing multiple treatments versus a
  control incorporating the correlation structure.
  Can be a step-down or step-up procedure
• Fixed Sequential Test
• Predefined sequence of hypothesis tests all
  tested at level ?.

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MCP Comparisons Relative 3 Different Dose
Responses 4 Active Doses vs. Placebo
Probability of Rejecting at Least 1 of the 4
Active Doses vs. Placebo (Ave )
n 20/group Max. effect size 1 (?/?)
N10,000 simulations
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MCP Dunnetts Method

• Dunnetts Step-Down Method
• Takes into account
• Testing multiple treatments against a control
• The distribution/correlation structure
  (multivariate t)
• Incorporates advantages of stepwise testing
• Note From a statistical point of view, when
  using Dunnetts test, placing a higher proportion
  of patients in the Control group is beneficial in
  that increases power.

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Dose-Response Analysis Modeling

• A model-based approach to dose-response assumes a
  functional relationship between the response and
  the dose following a pre-specified parametric
  model.
• A fitted model is used to test if a dose-response
  relationship is present and estimate other
  parameters of interest (MinED, MaxED, MTD).
• Modeling the dose-response relationship generally
  requires additional assumptions as opposed to
  using Multiple Comparison Procedures (MCPs) but
  can provide additional information.
• There are many different models used to
  characterize a dose-response linear, quadratic,
  orthogonal polynomials, exponential, linear in
  log-dose, EMAX.

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EMAX Model Introduction
The EMAX model Where R Response D
Dose E0 Baseline Response EMAX Maximum
effect attributable to the drug. ED50 Dose
which produces half of EMAX. N Slope factor
(Hill Factor)
4 Parameters
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EMAX Model Illustration
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Why/When Use the EMAX Model

• A useful model for characterizing dose-response
• A common descriptor of dose-response
  relationships
• Dose response of drug is monotonic and can be
  modeled as continuous
• A range of different dose levels
• Can be a useful tool in determining the optimal
  dose and the minimally effective dose
• Straight-forward to implement S-plus, SAS Proc
  NLIN, NONMEM

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EMAX Model N(Slope Factor) Parameter Sensitivity
The EMAX model N Slope factor (Hill
Factor) The slope factor determines the steepness
of the dose response curve. As N increases, the
dose range (i.e. ) tightens. When the
N set 1 EMAX model is used, the dose range is
set to be 81.
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Parameter Sensitivities N(Slope Factor)
E0 EMAX
N (Slope) 1
Dose Range ED90/ED10 81
E0
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Parameter Sensitivities N(Slope Factor)
E0 EMAX
Shallower slope
N (Slope) 0.5
Dose Range ED90/ED10 6561
E0
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Parameter Sensitivities N(Slope Factor)
E0 EMAX
Steeper slope
N (Slope) 5
Dose Range ED90/ED10 2.4
E0
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Dose Range vs. N (Slope Factor)
Dose Range N (Hill Factor) 6561 0.5
350 0.75 81 1.0 34 1.25
19 1.5 9 2 4 3 3 4
2.4 5 2.1 6 1.7 8
1.6 10 1.4 12
(ED90/ED10)
N ? 1.91 / log10(range) range ED90 / ED10
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EMAX Model A Caveat

• In situations where the study design does not
  include dose values that produce close to a
  maximal effect, the resulting parameter estimates
  may be poorly estimated.
• Dutta, Matsumoto and Ebling (1996) demonstrated
  that when the highest dose in the study was less
  than ED95 the parameter estimates for EMAX, ED50,
  and N are poorly estimated with a high
  coefficient of variation and bias.
• However, within the range for which the data were
  available, the fit of the EMAX model to the data
  was quite good.
• Hence, care should be taken in the interpretation
  of the parameter estimates when an EMAX model is
  applied in to a study where the design may not
  include maximal dose levels.

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Hybrid Modeling Approach

• Dose response analysis has been divided into two
  major approaches
• Multiple comparison approaches
• want to demonstrate that a particular dose is
  effective vs. placebo, limited number of doses
• Model-based approaches
• assumes a functional relationship between
  response and dose, more doses (study logistics
  and manufacturing issues)
• Pinheiro, Bretz, and Branson (2006) suggest a
  hybrid approach
• Tukey et. Al. (1985) Bretz et. al. (2005)
  Abeslon and Tukey (1963)

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Hybrid Modeling ApproachPinheiro, Bertz, and
Branson (2006)

• Determine a set of candidate dose response
  models (e.g. emax, logistic, linear, quadratic,
  )
• For each candidate model, determine the
  corresponding contrast test, a linear combination
  of the means that best reflects the assumed dose
  response curves.
• Under an ANOVA model, the joint distribution of
  these contrasts are multivariate t. Correlation
  structure of contrasts can be estimated and used
  in the MCP method.
• The model corresponding to the contrast with the
  lowest adjusted p-value (or other criteria) is
  chosen and used in further dose analysis (e.g.
  estimate the MinED).
• Method has the advantage of pre-specification
  while still being suitable for various
  dose-response scenarios.

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Hybrid Modeling ApproachThomas (2006) in press

• Thomas extended the approach given in Brentz et.
  al. (2005)
• Looked at the Emax (with Hill parameter) model
  only, and showed that this model closely matched
  the monotonic basis functions in Bretz (2005),
  logistic, linear, linear in-log-dose,
  exponential,
• Bayesian estimation methods are applied to
  address sparse dosing and poor parameter
  estimation.

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Useful References
Dose Response Ting, Naitee (Editor). Dose
Finding in Drug Development, 2006
Springer. Ruberg, S.J. Doseresponse studies.
II. Analysis and interpretation. J. Biopharm.
Stat. 1995, 5 (1), 1542. Ruberg, S.J.
Doseresponse studies. I. Some design
considerations. J. Biopharm. Stat. 1995, 5 (1),
114. Ting, N. Dose Response Study Designs. In
Encyclopedia of Biopharmaceutical Statistics
Chow, S., Ed. Marcel Dekker, 2003 Sheiner,
L.B. Beal, S.L. Sambol, N.C. Study designs for
dose-ranging. Clin. Pharmacol. Ther. 1989, 46,
6377. ICH-E4 E9 Guidelines
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Useful References
MCPs Westfall, P. Tobias, R. Rom, D.
Wolfinger, R. Hochberg, Y. Multiple Comparisons
and Multiple Tests using the SAS System SAS
Institute Cary, NC, 1999. Where to download the
SAS macros referenced in the Westfall SAS MCP
book ftp//ftp.sas.com/pub/publications/A56648 Hs
u, M. Multiple Comparisons Chapman and Hall
London, 1996. Yosef Hochberg, Ajit C. Tamhane
Multiple Comparison Procedures Wiley
1987 Miller, R. Simultaneous Statistical
Inference Springer-Verlag New York,
1981. Tamhane, A.C. Dunnett, C. Stepwise
multiple test procedures with biometric
applications. J. Stat. Plan. Inference 1999, 82,
5568. Lakshminarayanan, M. Multiple
Comparisons. In Encyclopedia of Biopharmaceutical
Statistics Chow, S., Ed. Marcel Dekker,
2000. CPMP Points to Consider on Multiplicity
issues in Clinical Trials September
2002 http//www.emea.eu.int/pdfs/human/ewp/090899e
n.pdf
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Useful References
Reference and introduction to EMAX model Holford
N., and Sheiner, L., Understanding the
Dose-Effect Relationship Clinical Application of
Pharamacokinetic-Pharmacodynamic Models.
Clinical Pharmacokinetics 6 429-435 (1981)
Tallarida, R., Drug Synergism and Dose-Effect
Data Analysis. Chapman Hall/CRC
2000 Boroujerdi, M., Pharmacokinetics
Principles and Applications. McGraw Hill 2001.
Presentation of PK/PD from a Statistical
Viewpoint Davidian, M., "What's in Between Dose
and Response? Pharmacokinetics, Pharmacodynamics,
and Statistics" in PDF (Myrto Lefkopoulou
Lecture, Harvard School of Public Health,
September 2003). http//www4.stat.ncsu.edu/davidi
an
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Useful References
Examples of the EMAX model being used Angus BJ.
Thaiaporn I. Chanthapadith K. Suputtamongkol Y.
White NJ. Oral artesunate dose-response
relationship in acute falciparum malaria.
Antimicrobial Agents Chemotherapy.
46(3)778-82, 2002 Mar. Graves, D., Muir, K.,
Richards W., Steiger B., Chang, I., Patel, B.,
Hydralazine Dose-Response Curve Analysis,
Journal of Pharmacokinetics and Biopharmaceutics,
Vol 18, No. 4, 1990. Demana P., Smith E.,
Walker, R., Haigh J., Kanfer, I., Evaluation of
the Proposed FDA Pilot Dose-Response Methodology
for Topical Corticosteroid Bioequivalence
Testing, Pharmaceutical Research Vol 14, No. 3,
1997. Staab, A., Tillmann, C., Forgue, S.,
Mackie, A., Allerheiligen, S., Rapado J.,
Troconiz, I., Population Dose-Response Model for
Tadalafil in the Treatment of Male Erectile
Dysfunction, Pharmaceutical Research, Vol 21,
No. 8. August 2004.
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Useful References
Non-Linear Mixed Models Davidian, M. and
Giltinan, D.M. (2003) Nonlinear models for
repeated measurements An overview and update.
Editor's Invited paper, Journal of Agricultural,
Biological, and Environmental Statstics 8,
387-419. http//www4.stat.ncsu.edu/davidian Dav
idian, M., and Giltinan, D. M., Nonlinear Models
for Repeated Measurement Data, New York Chapman
and Hall, 1995. Vonesh, E. F., and Chinchilli,V.
M., Linear and Nonlinear Models for the Analysis
of Repeated Measurements, New York Marcel
Dekker, 1997.
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Useful References
Discussions on Study Designs for Dose
Ranging Sheiner, L.B., Beal, S. L., and Sambol,
N.C. Study Designs for Dose-Ranging Clin.
Pharmacol. Thera. 1989 4663-77. Sheiner, L.B.,
Hashimoto Y., and Beal, S.L. A Simulation Study
Comparing Designs for Dose Ranging Girard P.,
Laporte-Simitsidis S., Mismetti P., Decousus H.,
and Boissel J. Influence of Confounding Factors
on Designs for Dose-Effect Relationships
Estimates Statistics in Medicine 995, Vol 14,
987 1005. Senn, S., Statistical Issues in Drug
Development, John Wiley Sons, 1997 Temple, R.
Government Viewpoint of Clinical Trials Drug
Information Journal 16 10-17, 1982 Temple, R., .
Where Protocol Design Has Been a Critical
Factor in Success or Failure, DIA Annual Meeting
June 14, 2004. .PPT slides http//www.fda.gov/cde
r/present/DIA2004/default.htm
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SAS SAS/STAT Users Guide Version 8 Volumes 1-3.
SAS Publishing 1999. NONMEM (UCSF) PK/PD
software http//www.globomaxservice.com/products