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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
[email protected]
Talk Outline
Review 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 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 < 0.05.
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.
Bartholomew’s 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
Jonckheere’s 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.
Three Dose Response Scenarios
1) Sigmoid


 

Doses at: 0, 10, 25, 50 and 100
Three Dose Response Scenarios
2) Step





Doses at: 0, 10, 25, 50 and 100
Three Dose Response Scenarios
3) Quadratic





Doses at: 0, 10, 25, 50 and 100
Is there a Drug Effect? Compare Methods
Relative to 3 Different Dose Responses
n = 20/group
Max. effect size (/) =1
Linear F-test H v. C Jonck



Sigmoid


96%
88% 86%
92%
98%
98% 86%
98%
30%
75% 33%
60%

Step
 




Quad

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/ NOSTASOT
Tukey’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 Ftest 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. Control
Bonferroni
Standard adjustment tests each of k hypotheses at level /k.
Fisher’s 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.
Hochberg’s Sequential Procedure
A “step-up” procedure. P-values tested from largest to smallest.
Dunnett’s 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 .
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
(/)
LSD
Holm
Hoch
Dunn
Fixed
85%
(1.3)
75% 75%
(1.0) (1.0)
77%
(1.1)
88%
(1.3)
96%
(1.8)
86% 87%
(1.5) (1.5)
88%
(1.6)
88%
(1.7)
74%
(1.7)
77% 78%
(1.5) (1.6)
79%
(1.6)
35%
(1.1)



Sigmoid



Step
 




Quad

N=10,000 simulations
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 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.
EMAX Model Introduction
The EMAX model:
R = E0 +
DN  EMAX
DN
+
N
ED50
Where:
R
= Response
D
= Dose
E0
= Baseline Response
4 Parameters
EMAX = Maximum effect attributable to the drug.
ED50 = Dose which produces half of EMAX.
N
= Slope factor (Hill Factor)
EMAX Model Illustration
E0 + EMAX
N (Slope)
Response
EMAX
E0
ED50
Dose
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
EMAX Model: N(Slope Factor)
Parameter Sensitivity
The EMAX model:
R = E0 
DN  EMAX
DN
+
N
ED50
N = Slope factor (Hill Factor)
The slope factor determines the steepness of the
dose response curve.
ED90
As N increases, the dose range (i.e.
) tightens.
ED10
When the N set =1 EMAX model is used, the dose
range is set to be 81.
Parameter Sensitivities: N(Slope Factor)
E0 + EMAX
Response
N (Slope) = 1
Dose Range
ED90/ED10 = 81
E0
0.01
0.1
1
10
Dose
100
1000
Parameter Sensitivities: N(Slope Factor)
Response
E0 + EMAX
Shallower slope
N (Slope) = 0.5
Dose Range
ED90/ED10 = 6561
E0
0.01
0.1
1
10
Dose
100
1000
Parameter Sensitivities: N(Slope Factor)
E0 + EMAX
Response
Steeper slope
N (Slope) = 5
Dose Range
ED90/ED10 = 2.4
E0
0.01
0.1
1
10
Dose
100
1000
Dose Range: (ED90/ED10)
Dose Range vs. N (Slope Factor)
10000
1000
100
10
Dose Range
6561
350
81
34
19
9
4
3
2.4
2.1
1.7
1.6
1.4
N (Hill Factor)
0.5
0.75
1.0
1.25
1.5
2
3
N  1.91 / log10(range)
4
5
range = ED90 / ED10
6
8
10
12
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
N (Slope Factor)
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.
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 Approach
Pinheiro, 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 Approach
Thomas (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 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
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 2002
http://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.
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; 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 1017, 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
SAS
SAS/STAT User’s Guide Version 8 Volumes 1-3. SAS Publishing 1999.
NONMEM (UCSF) PK/PD software
http://www.globomaxservice.com/products