Adaptive Clinical Trial Methods

• The Future of Drug Development: Advancing Clinical Trial Design

“Declining pharmaceutical industry productivity is well recognized by drug developers, regulatory authorities and patient groups. A key part of the problem is that clinical studies are increasingly expensive, driven by the rising costs of conducting phase 2 and 3 trials. It is therefore crucial to ensure that these phases are conducted more efficiently, and that attrition rates are reduced. We argue that moving from the traditional clinical development approach based on sequential, distinct phases towards a more integrated view that uses adaptive design tools to increase flexibility and maximize the use of accumulated knowledge could have an important role in achieving these goals. Applications and examples of these tools — such as Bayesian methodologies — in early- and late-stage development are discussed, as well as the advantages and barriers to widespread implementation.“

Cyrus Mehta, Nitin Patel with fellow industry and academia co-authors, including PhRMA Adaptive Trial Working Group members
Nature Reviews Drug Discovery | AOP, published online 9, October 2009

• Simulation: A Critical Tool in Adaptive Trials

“In recent years there has been increased industry interest and utilization of adaptive clinical trials. Although the term “adaptive” covers a large range of study features and designs, much of the current excitement is around designs that enable treatment groups to be dropped during the trial to enable more doses to be investigated and/or to reduce time between development phases using seamless designs.“

Nitin Patel, w/ Bill Byrom and Graham Nicholls of Perceptive Informatics
Applied Clinical Trials Magazine, an Advanstar publication, July, 2009

• Exact Confidence Bounds Following Adaptive Group Sequential Tests

“We provide a method for obtaining confidence intervals, point estimates, and p-values for the primary effect size parameter at the end of a two-arm group sequential clinical trial in which adaptive changes have been implemented along the way. The method is based on applying the adaptive hypothesis testing procedure of Müller and Schåfer (2001, Biometrics 57, 886–891) to a sequence of dual tests derived from the stage-wise adjusted confidence interval of Tsiatis, Rosner, and Mehta (1984, Biometrics 40, 797–803). In the nonadaptive setting this confidence interval is known to provide exact coverage. In the adaptive setting exact coverage is guaranteed provided the adaptation takes place at the penultimate stage. In general, however, all that can be claimed theoretically is that the coverage is guaranteed to be conservative. Nevertheless, extensive simulation experiments, supported by an empirical characterization of the conditional error function, demonstrate convincingly that for all practical purposes the coverage is exact and the point estimate is median unbiased. No procedure has previously been available for producing confidence intervals and point estimates with these desirable properties in an adaptive group sequential setting.“

Cyrus Mehta, w/ Werner Brannath and Martin Posch
Biometrics, The International Biometric Society, June, 2009

• Adaptive Design for Confirmatory Clinical Trials

“This paper discusses the benefits and limitations of adaptive sample size re-estimation for late stage confirmatory clinical trials. Comparisons are made with more traditional fixed sample and group sequential designs. It is seen that the real benefit of the adaptive approach arises through the ability to invest sample size resources into the trial in stages. The trial starts with a small up-front sample size commitment. Additional sample size resources are committed to the trial only if promising results are obtained at an interim analysis. This strategy is more advantageous than the fixed sample or group sequential approaches in certain settings.“

Cyrus R. Mehta
Good Clinical Practice, an Informa UK Ltd. publication, 2009

• Optimizing Trial Design: Sequential, Adaptive, and Enrichment Strategies

“Because the clinical development process is enormously expensive and time consuming, there is considerable interest in statistical methods that use accumulating data from a clinical trial to inform and modify its design. Such redesign might include changes in target sample size and even changes in the target population. This article discusses developments in adaptive design of interest to cardiovascular research.“

Ping Gao, Cyrus R. Mehta and James H. Ware
Circulation, a Taylor & Francis Group publication, 2008

• Sample Size Re-estimation for Adaptive Sequential Design in Clinical Trials

“We describe a method for sample size re-estimation at the penultimate stage of a group sequential design that achieves specified power against an alternative hypothesis corresponding to the current point estimate of the treatment effect.“

Ping Gao, Cyrus R. Mehta and James H. Ware
Journal of Biopharmaceutical Statistics, a Taylor & Francis Group publication, 2008

• Exact Confidence Bounds Following Adaptive Group Sequential Tests

“A method for obtaining confidence intervals, point estimates and p-values for the primary effect size parameter at the end of a two-arm group sequential clinical trial in which adaptive changes have been implemented along the way.“

Werner Brannath, Cyrus R. Mehta and Martin Posch
Biometrics, Blackwell Publishing, 2008

• Repeated Confidence Intervals for Adaptive Group Sequential Trials

"Proposing a method for computing conservative confidence intervals for a group sequential test in which an adaptive design change is made one or more times over the course of the trial."
Cyrus R. Mehta, Peter Bauer, Martin Posch and Werner Brannath
Statistics in Medicine, a Wiley InterScience publication, 2007

• Adaptive, Group Sequential and Decision Theoretic Approaches to Sample Size Determination

"Three adaptive methods for sample size re-estimation within a group sequential framework."

Cyrus R. Mehta and Nitin R. Patel
Statistics in Medicine, a Wiley InterScience publication, 2006

Group Sequential Trial Methods

• Planning for an Adaptive Design: a Case Study in COPD (Chronic Obstructive Pulmonary Disease)

"Use of East software to evaluate properties of study designs with one or more interim analyses for futility."

Byron Jones, Pfizer Global Development, with G. Atkinson, J. Ward, E. Tan and T. Kerbusch
Pharmaceutical Statistics, a Wiley InterScience publication, 2006

• On the Inefficiency of the Adaptive Design for Monitoring Clinical Trials

"Adaptive designs have been advocated recently for monitoring clinical trials. We show that that one can improve uniformly on such adaptive designs using standard group-sequential tests based on the sequentially computed likelihood ratio test statistic."
Anastasios Tsiatis, North Carolina State Univ. and Cyrus Mehta, Cytel Software Corp.
Biometrika, (2003), 90, 2, pp. 367–378

• Symposium on Group Sequential Inference

Cyrus R. Mehta, Harvard University & Cytel Software Corporation
Presentated at The ASA-NJ's Spring Symposium, June 2002

• Flexible Sample Size Considerations Using Information Based Interim Monitoring

Cyrus R. Mehta, Harvard University & Cytel Software Corp., Anastasios A. Tsiatis, North Carolina State University
Drug Information Journal, December 2001

• Interim Monitoring of Group Sequential Trials Using Spending Functions for the Type I and Type II Error Probabilities

Sandro Pampallona, ForMed, Statistics for Medicine; Anastasios A. Tsiatis, North Carolina State University; and Kyungmann Kim, University of Wisconsin
Drug Information Journal, December 2001

Exact Inference Methods

• Confidence Interval of the Difference of Two Independent Binomial Proportions Using Weighted Profile Likelihood

“We propose a method based on profile likelihood, where the likelihood is weighted by noninformative Jeffrey' prior. By doing extensive simulations, we find that the proposed method performs well compared to Wilson's method.”
Vivek Pradhan and Tathagata Banerjee
Communications in Statistics - Simulation and Computation, a Taylor & Francis publication, 2008

• Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions

Thomas J. Santner, Vivek Pradhan, Pralay Senchaudhuri, Cyrus R. Mehta, and Ajit Tamhane Computational Statistics & Data Analysis 51 (2007) 5791 – 5799, August, 2007

• Choice of test for association in small sample unordered r × c tables

S. Lydersen, V. Pradhan, P. Senchaudhuri and P. Laake
Statistics in Medicine 2007; 26:4328–4343, February, 2007

• Aspirin Prophylaxis in Patients at Low Risk for Cardiovascular disease: a systematic review of all-cause mortality

(Original Research)
John M. Boltri, Mark R. Akerson, Robert L. Vogel; Journal of Family Practice, August, 2002

• Association and Haplotype Analysis of the Insulin-Degrading Enzyme (IDE) Gene, a Strong Positional and Biological Candidate for Type 2 Diabetes Susceptibility. (Brief Genetics Report)

Christopher J. Groves, Steven Wiltshire, Damian Smedley, Katherine R. Owen, Timothy M. Frayling, Mark Walker, Graham A. Hitman, Jonathan C. Levy, Stephen O'Rahilly, Stephan Menzel, Andrew T. Hattersley, Mark I McCarthy; Diabetes, May, 2003

• Porphyrin Status in Aluminum Foundry Workers Exposed to Hexachlorobenzene and Octachlorostyrene.

Anders I Selden, Ylva Floderus, Lennart S. Bodin, H Kan B. Westberg, Stig Thunell
Archives of Environmental Health, July, 1999

• Exact Inference for Categorical Data PDF 231KB

Cyrus R. Mehta and Nitin R. Patel
Harvard University and Cytel Software Corporation
January 1, 1997

• Exact Level and Power of Permutation, Bootstrap and Asymptotic Tests of Trend PDF 172KB

Christopher D.Corcoran, Utah State University; and
Cyrus R.Mehta, Harvard University and Cytel Software Corporation
Journal of Modern Statistical Methods, 2001

• Statistical Techniques for Comparing Measurers and Methods of Measurement: A Critical Review PDF 1,544KB

John Ludbrook, Univ. of Melbourne, Parkville, Victoria, Australia.
Clinical and Experimental Pharmacology and Physiology (2002) 29, pp 527-536 + addendum.

Logistic Regression

• Bias Reduction and a Solution for Separation of Logistic Regression with Missing Covariates

Tapabrata Maiti and Vivek Pradhan
Biometrics (2008) December publication pending

• Correspondence: Defibrotide for hepatic VOD in children: exact statistics can help

Dr. R.A. Ammann
Bone Marrow Transplantation (2004) 34, 277-278

• A Preliminary Investigation of Maximum Likelihood Logistic Regression versus Exact Logistic Regression

Elizabeth N. King and Thomas P. Ryan
The American Statistician, August 2002, Vol. 56, No. 3, pp 163-170
Excerpt: ". . . maximum likelihood can produce very poor, even nonsensical, results under certain conditions."

• A Modified Score Function Estimator for Multinomial Logistic Regression in Small Samples

Shelley B. Bull, Carmen Mak, Celiea M.T. Greenwood
Computational Statistics and Data Analysis, 39 (2002) pp 57-74

• Efficient Monte Carlo Methods for Conditional Logistic Regression

by Cyrus R. Mehta, Nitin R. Patel and Pralay Senchaudhuri
Journal of the American Statistical Association, March 2000, Vol. 95, No. 449, Theory and Methods, pp 99-108

Epidemiology Related

• Mauritsen, R.H. (1984). “Logistic Regression With Random Effects.” Unpublished Ph.D. thesis, Department of Biostatistics, University of Washington.
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• Morgan, B. J. T. (1992). “Analysis of Quantal Response Data.” Chapman and Hall.
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• Ochi,Y. (1983). “The Correlated Probit Regression of Binary Responses with Extra-binomial Variability.” Ph.D. thesis. Department of Biostatistics, University of Washington.
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• Paul, S.R. (1982). “Analysis of Proportions of Affected Foetuses in Teratological Experiments.” Biometrics 38:361–370.
• Pendergast, J., Gange, S. J., Newton, M. A., Linstrom, M. J., Palta, M., and Fisher, M. R. (1996). “A Survey of Methods for Analyzing Clustered Binary Response Data.” International Statistical Review 64:89–118.
• Pierce, D.A. (1976). “A Random Effects Model for Matched Pairs of Binomial Data.” Tech. report no. 55, Dept. of Statistics, Oregon State University.
• Pierce, D.A. and Sands, B.R. (1975). “Extra-Bernoulli Variation in Binary Data.” Tech. report no. 46, Dept. of Statistics, Oregon State University.
• Pregibon, D. (1981). “Logistic Regression Diagnostics.” Ann. of Stat. 9(4):705–724
• Prentice, R.L. (1986). “Correlated Binary Regression Using an Extended Beta-Binomial Distribution, with Discussion of Correlation Included by Covariate Measurement Error.” Journal of the American Statistical Association 81:321–327.
• Prentice, R.L. and Mason, M.W. (1986). “On the Application of Linear Relative Risk Regression Models.” Biometrics 42:109–120.
• Press,W.H., et al. (1992). Numerical Recipes in FORTRAN. Cambridge University Press.
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• Self, S.G. and Liang, K. (1987). “Asymptotic Properties of Maximum Likelihood Estimator and Likelihood Ratio Tests under Nonstandard Conditions.” Journal of the American Statistical Association 82:605–610.
• Self, S.G. and Mauritsen, R.H. (1992). “Power Calculations for Likelihood Ratio Tests in Generalized Linear Models.” Biometrics 48:31–39.
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• Skellam, J.G. (1948). “A Probability Distribution Derived from the Binomial Distribution by Regarding the Probability of Success as Variable between the Sets of Trials.” J. Royal Statis. Soc. B 10(2):257–265.
• Southward, M.G. and Van Ryzin, J. (1972). “Estimating the Mean of a Random Binomial Parameter.” Proc. of the Sixth Berkeley Symposium on Math. Stat. and Prob. 4:249–263.
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• Storer, B.E. and Crowley, J. (1985). “A Diagnostic for Cox Regression and General Conditional Likelihoods.” Journal of the American Statistical Association 80:139–147.
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• Tarone, R.E. (1979). “Testing the Goodness of Fit of the Binomial Distribution.”
• Biometrika 66(3):585–590.
• Thomas, D.C. (1981). “General Relative Risk Functions for Survival Time and Matched Case-control Analysis.” Biometrics 37:673–686.
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• Williams, D. (1975). “The Analysis of Binary Responses from Toxicological Experiments Involving Reproduction and Teratogenicity.” Biometrics 31:949–952.

Toxicity Related

• Catalano PJ, and Ryan LM (1992). Bivariate latent variable models for clustered discrete and continuous outcomes. Journal of the American Statistical Association, 87:651-658.
• Catalano PJ, Scharfstein DO, Ryan LM, Kimmel CA, and Kimmel GL (1993). Statistical model for fetal death, fetal weight, and malformation in developmental toxicity studies. Teratology, 47:281-290.
• Catalano PJ, Scharfstein DO, Ryan LM (1994). Modeling fetal death and malformation in developmental toxicity. Risk Analysis, 14:611-619.
• Catalano PJ (1997). Bivariate modelling of clustered continuous and ordered categorical outcomes. Statistics in Medicine, 16: 883-900.
• Crump KS(1984), A new method for determining allowable daily intakes. Fundamental and Applied Toxicology, 4:854-871.
• Crump KS (1995). Use of the benchmark dose approach in health risk assessment, Risk Assessment Forum, US EPA.
• Kimmel CA, Gaylor DW (1988). Issues in Qualitative and Quantitative Risk Analysis for Developmental Toxicology. Risk Analysis, 8:15-20.
• Ryan LM (1992). Quantitative risk assessment for developmental toxicity. Biometrics, 48:163-174.