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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

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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 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

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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.

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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 < 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. 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.

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**Three Dose Response Scenarios 1) Sigmoid**

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

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**Three Dose Response Scenarios 2) Step**

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

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**Three Dose Response Scenarios 3) Quadratic**

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**

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

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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**

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. _

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**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.

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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: 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).

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**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 .

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**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

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**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.

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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) R = E0 + DN EMAX DN + ED50 N 4 Parameters

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**EMAX Model Illustration**

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

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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. R = E0 DN EMAX DN + ED50 N ED90 ED10

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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 C:\JimMac\EMAX Chapter\figures\emax_f02c.cgm Dose Range ED90/ED10 = 6561 E0

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**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

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**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

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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 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.

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**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.

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**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

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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 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

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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: (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).

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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, 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.

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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 ; 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

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**SAS NONMEM (UCSF) PK/PD software**

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

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