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

2. Talk Outline
Review Concepts of Dose Response Analysis in Clinical Trials
Review Dose Response Tests
Multiplicity Issues
Dose Response Models
Hybrid Approach

3. 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

4. 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.

5. 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.

6. 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.

7. Three Dose Response Scenarios 1) Sigmoid    
Doses at: 0, 10, 25, 50 and 100

8. Three Dose Response Scenarios 2) Step    
Doses at: 0, 10, 25, 50 and 100

9. Three Dose Response Scenarios 3) Quadratic    
Doses at: 0, 10, 25, 50 and 100

10. 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%
30%
75%
33%
60%
n = 20/group
Max. effect size (/) =1  
Sigmoid     
Step       
Quad 
N=10,000 simulations

11. 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).

12. Three Tests for MED/ NOSTASOT
Tukey’s Trend Test
Test global H0: 0 = 1 = … = g at  (if reject continue)
Test H0: 0 = 1 = … = g-1 at  (if reject continue)
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. _

13. 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.

14. 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)

15. 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.

16. 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).

17. 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 .

18. MCP Comparisons Relative 3 Different Dose Responses; 4 Active Doses vs
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%
(1.0)
77%
(1.1)
88%
96%
(1.8)
86%
(1.5)
87%
(1.6)
(1.7)
74%
78%
79%
35%
Sigmoid 
Step 
Quad 
N=10,000 simulations

19. MCP: Dunnett’s Method Dunnett’s 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 Dunnett’s test, placing a higher proportion of patients in the Control group is beneficial in that increases power.

20. 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.

21. 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 + ED50 N
4 Parameters

22. EMAX Model Illustration
E0 + EMAX E0
EMAX
N (Slope)
ED50
C:\JimMac\EMAX Chapter\figures\emax_f01a.cgm

23. 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

24. 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 + ED50 N
ED90
ED10

25. Parameter Sensitivities: N(Slope Factor)
E0 + EMAX
N (Slope) = 1
Dose Range
ED90/ED10 = 81 E0

26. Parameter Sensitivities: N(Slope Factor)
E0 + EMAX
Shallower slope
N (Slope) = 0.5
C:\JimMac\EMAX Chapter\figures\emax_f02c.cgm
Dose Range
ED90/ED10 = 6561 E0

27. Parameter Sensitivities: N(Slope Factor)
E0 + EMAX
Steeper slope
N (Slope) = 5
C:\JimMac\EMAX Chapter\figures\emax_f02e.cgm
Dose Range
ED90/ED10 = 2.4 E0

28. Dose Range vs. N (Slope Factor)
Dose Range N (Hill Factor)
9 2
4 3
3 4
2.4 5
(ED90/ED10)
N  1.91 / log10(range)
range = ED90 / ED10
C:\JimMac\EMAX Chapter\figures\emax_f12a.cgm

29. 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.

30. 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)

31. 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.

32. 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.

33. 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

34. 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

35. 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: (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).

36. 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.

37. 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,
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.

38. 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 ; 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 , 1982
Temple, R., . “Where Protocol Design Has Been a Critical Factor in Success or Failure”, DIA Annual Meeting June 14, PPT slides

39. SAS NONMEM (UCSF) PK/PD software
SAS/STAT User’s Guide Version 8 Volumes 1-3. SAS Publishing 1999.
NONMEM (UCSF) PK/PD software