Adaptive Clinical Trial Methods

• 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 (publication pending), 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."
By Anastasios Tsiatis, Dept. of Statistics, North Carolina State Univ. and Cyrus Mehta, Cytel Software Corp. President and Co-Founder
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 Corporation, and 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

by 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

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

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

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

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

by 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

by 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.
• McCullagh, P. and Nelder, J. A. (1989). “Generalized Linear Models.” Chapman and Hall.
• Mehta, C.R., Patel, N.R., and Gray, R. (1986). “Computing an Exact Confidence Interval for the Common Odds Ratio in Several 2×2 Contingency Tables.” Journal of the American Statistical Association 80:969–973.
• Moolgavkar, S.H. and Venzon, D.J. (1987). “Confidence Regions in Curved Exponential Families: Application to Matched Case-control and Survival Studies with General Relative Risk Functions.” Ann. Stat. 15(346):359.
• Morgan, B. J. T. (1992). “Analysis of Quantal Response Data.” Chapman and Hall.
• Nelder, J.A. and Mead, R. (1965). “A Simplex Method for Function Minimization.” Computer J. 7:308–313.
• Ochi,Y. (1983). “The Correlated Probit Regression of Binary Responses with Extra-binomial Variability.” Ph.D. thesis. Department of Biostatistics, University of Washington.
• Ochi,Y. and Prentice, R.L. (1983). “Regression Methods for Count Data with Extra-binomial Variation.” Pp. 127–139 in Atomic Bomb Survivor Data: Utilization and Analysis, edited by R. Prentice and D. Thompson. Philadelphia: SIAM.
• 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.
• Segreti, A.C. and Munson, A.E. (1981). “Estimation of the Median Lethal Dose when Responses within a Litter are Correlated.” Biometrics 37:153–156.
• 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.
• Shano, D.F. and Phua, K.H. (1976). “Algorithm 500, Minimization of Unconstrained Multivariate Functions [E4].” ACM Trans. on Math. Software 2(1):87–94.
• Shapiro, S., Sloan, D., et al. (1979) “Oral-Contraceptive Use in Relation to Myocardial Infarction.” Lancet, April 7, 1979, 743–746.
• 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.
• Stiratelli, R., Laird, N. andWare, J. H. (1984). “Random Effects Models for Serial Observations with Dichotomous Response.” Biometrics 40:961–971.
• 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.
• Storer, B.E.,Wacholder, S. and Breslow, N.E. (1983). “Maximum Likelihood Fitting of General Risk Models to Stratified Data.” Applied Statistics 32:172–181.
• 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.
• Van Ryzin, J. (1975). “Estimating the Mean of a Random Binomial Parameter with Trial Size Random.” Sankhya 37(1):10–27.
• Væth, M. (1985). “On the Use ofWald’s Test in Exponential Families.” Int’l. Stat. Rev. 53(2):199–214.
• Wacholder, S. (1986). “Binomial Regression in GLIM: Estimating Risk Ratios and Risk Differences.” Am. J. Epi. 123(1):174–184.
• Weil, C.S. (1970). “Selection of the Valid Number of Sampling Units and a Consideration of their Combination in Toxicological Studies Involving Reproduction, Teratogenesis or Carcinogenesis.” Fd. Cosmet. Toxicol. 8:177–182.
• Wichmann, B.A. and Hill, I.D. (1982). “An efficient and portable pseudo-random number generator.” Applied Statistics 31, 188-190.
• 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.