Dose Response Analysis in Clinical Trials

Boston Chapter ASA Boston Chapter ASA April 10April 10thth, 2006, 2006

Jim MacDougallJim MacDougall

Bristol-Myers SquibbBristol-Myers Squibb

Medical Imaging DivisionMedical Imaging Division

Billerica MABillerica MAjames.macdougall@bms.com

Talk OutlineReview Concepts of Dose Response Analysis in Clinical Trials

Review Dose Response Tests

Multiplicity Issues

Dose Response Models

Hybrid Approach

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 dose–response 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 dose–response 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

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

Objectives in Dose-Response AnalysisPractical 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 < 0.05.

Question: Is There Any Drug Effect?Linear Trend TestsRegression 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. Bartholomew’s test: an order restricted modification to F-test.

Highest vs. ControlThe estimate of the highest group mean is compared to the control group.

ContrastsIn an ANOVA or linear modeling setting, using linear contrasts can provide additional power to detect dose response

Jonckheere’s TestRank 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.

Three Dose Response Scenarios1) Sigmoid

Doses at: 0, 10, 25, 50 and 100

Three Dose Response Scenarios2) Step

Doses at: 0, 10, 25, 50 and 100

Three Dose Response Scenarios3) Quadratic

Doses at: 0, 10, 25, 50 and 100

Is there a Drug Effect? Compare Methods Relative to 3 Different Dose Responses

Linear F-test H v. C Jonck

96% 88% 86% 92%

98% 98% 86% 98%

30% 75% 33% 60%

Sigmoid

Step

Quad

n = 20/group Max. effect size (/) =1

N=10,000 simulations

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).

Three Tests for MED/ NOSTASOTTukey’s Trend Test

1. Test global H0: 0 = 1 = … = g at (if reject continue)

2. Test H0: 0 = 1 = … = g-1 at (if reject continue)

3. Continue in this manner

– Last dose where H0 test is rejected is NOSTASOT dose

William’s MinED Test

– Similar to Tukey’s trend test in the three steps, but different in that

Uses t-type test statistics

If the doses are not ordered monotonically from control, those results are pooled (e.g. if y0 > y1) then use (y0 + y1) )/2 as the estimate for both 0 and 1

– There is a SAS macro out there for this._ _ _ _

Three Tests for MED/ NOSTASOT

Rom, Costello, and Connell Test

– Based on applying the Closure Principle to Tukey’s trend test.

– Provides additional testing beyond NOSTATSOT dose, (e.g. is highest dose statistically higher than others)

– SAS macro makes use straight-forward.

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)

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.

Weak Control of the FWE: Fisher’s LSD

Fisher’s 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% (>0.05).

MCPs Common in Active vs. ControlBonferroniStandard adjustment tests each of k hypotheses at level /k.

Fisher’s LSDPerforms first an overall test first (e.g. F-test) followed by tests of individual doses versus placebo.

Bonferroni-Holm Sequential ProcedureA “step-down” sequential version of the Bonferroni method. P-values are tested from smallest to largest.

Hochberg’s Sequential ProcedureA “step-up” procedure. P-values tested from largest to smallest.

Dunnett’s TestAn MCP testing multiple treatments versus a control incorporating the correlation structure. Can be a “step-down” or “step-up” procedure

Fixed Sequential TestPredefined sequence of hypothesis tests all tested at level .

MCP Comparisons Relative 3 Different Dose Responses; 4 Active Doses vs. Placebo

LSD Holm Hoch Dunn Fixed

85%(1.3)

75%(1.0)

75%(1.0)

77%(1.1)

88%(1.3)

96%(1.8)

86%(1.5)

87%(1.5)

88%(1.6)

88%(1.7)

74%(1.7)

77%(1.5)

78%(1.6)

79%(1.6)

35%(1.1)

Sigmoid

Step

Quad

Probability of Rejecting at Least 1 of the 4 Active Doses vs. Placebo (Ave #)

N=10,000 simulations

n = 20/group Max. effect size =1(/)

MCP: Dunnett’s Method

Dunnett’s Step-Down Method

Takes into account:

1. Testing multiple treatments against a control

2. The distribution/correlation structure (multivariate t)

3. Incorporates advantages of stepwise testing

Note: From a statistical point of view, when using Dunnett’s test, placing a higher proportion of patients in the Control group is beneficial in that increases power.

Dose-Response Analysis ModelingA 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.

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)

R = E0 +DN EMAX

DN + ED50N

4 Parameters

EMAX Model Illustration

ED50

N (Slope)

Res

pons

e

Dose

E0 + EMAX

E0

EMAX

Why/When Use the EMAX ModelA 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

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.

R = E0 DN EMAX

DN + ED50N

ED90

ED10

Parameter Sensitivities: N(Slope Factor)

Res

pons

e

Dose0.01 0.1 1 10 100 1000

E0 + EMAX

E0

N (Slope) = 1

Dose Range ED90/ED10 = 81

Parameter Sensitivities: N(Slope Factor)

Res

pons

e

Dose0.01 0.1 1 10 100 1000

N (Slope) = 0.5

E0 + EMAX

E0

Shallower slope

Dose Range ED90/ED10 = 6561

Parameter Sensitivities: N(Slope Factor)

Res

pons

e

Dose0.01 0.1 1 10 100 1000

E0 + EMAX

E0

N (Slope) = 5Steeper slope

Dose Range ED90/ED10 = 2.4

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

(ED

90/E

D10)

N 1.91 / log10(range)

range = ED90 / ED10

Dos

e R

ange

:

1

10

100

1000

10000

N (Slope Factor)0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

EMAX Model: A CaveatIn 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.

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)

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.

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.

Useful References

Dose Response

Ting, Naitee (Editor). Dose Finding in Drug Development, 2006 Springer.

Ruberg, S.J. Dose–response studies. II. Analysis and interpretation. J. Biopharm. Stat. 1995, 5 (1), 15–42.

Ruberg, S.J. Dose–response studies. I. Some design considerations. J. Biopharm. Stat. 1995, 5 (1), 1–14.

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, 63–77.

ICH-E4 & E9 Guidelines

Useful ReferencesMCPs

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 bookftp://ftp.sas.com/pub/publications/A56648

Hsu, 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, 55–68.

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 2002http://www.emea.eu.int/pdfs/human/ewp/090899en.pdf

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/~davidian

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.

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

Davidian, 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.

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; 46:63-77.

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/cder/present/DIA2004/default.htm

Useful References

SAS

SAS/STAT User’s Guide Version 8 Volumes 1-3. SAS Publishing 1999.

NONMEM (UCSF) PK/PD software

http://www.globomaxservice.com/products