Randomization tests for multiarmed randomized clinical trials

We examine the use of randomization-based inference for analyzing multiarmed randomized clinical trials, including the application of conditional randomization tests to multiple comparisons. The view is taken that the linkage of the statistical test to the experimental design (randomization procedure) should be recognized. A selected collection of randomization procedures generalized to multiarmed treatment allocation is summarized, and generalizations for two randomization procedures that heretofore were designed for only two treatments are developed. We explain the process of computing the randomization test and conditional randomization test via Monte Carlo simulation, developing an efficient algorithm that makes multiple comparisons possible that would not be possible using a standard algorithm, demonstrate the preservation of type I error rate, and explore the relationship of statistical power to the randomization procedure in the presence of a time trend and outliers. We distinguish between the interpretation of the p-value in the randomization test and in the population test and verify that the randomization test can be approximated by the population test on some occasions. Data from two multiarmed clinical trials from the literature are reanalyzed to illustrate the methodology.

[1]  William F Rosenberger,et al.  On the use of randomization tests following adaptive designs , 2016, Journal of biopharmaceutical statistics.

[2]  R. Hilgers,et al.  Chronological Bias in Randomized Clinical Trials Arising from Different Types of Unobserved Time Trends , 2014, Methods of Information in Medicine.

[3]  Paul H. Garthwaite,et al.  CONFIDENCE INTERVALS FROM RANDOMIZATION TESTS , 1996 .

[4]  D P Byar,et al.  The Veterans Administration Study of Chemoprophylaxis for Recurrent Stage I Bladder Tumours: Comparisons of Placebo, Pyridoxine and Topical Thiotepa , 1980 .

[5]  L. J. Wei,et al.  Nonparametric Estimation for a Scale-Change with Censored Observations , 1983 .

[6]  Guoqing Diao,et al.  Conditional Monte Carlo randomization tests for regression models , 2014, Statistics in medicine.

[7]  Diane Uschner,et al.  Randomization: The forgotten component of the randomized clinical trial , 2018, Statistics in medicine.

[8]  Michael A Proschan,et al.  Re‐randomization tests in clinical trials , 2019, Statistics in medicine.

[9]  J. Tukey.  Comparing individual means in the analysis of variance. , 1949, Biometrics.

[10]  J. Lachin,et al.  Chenodiol (chenodeoxycholic acid) for dissolution of gallstones: the National Cooperative Gallstone Study. A controlled trial of efficacy and safety. , 1981, Annals of internal medicine.

[11]  William F. Rosenberger,et al.  Sequential monitoring with conditional randomization tests , 2012 .

[12]  O. J. Dunn.  Multiple Comparisons among Means , 1961 .

[13]  William F. Rosenberger,et al.  Randomization in Clinical Trials: Rosenberger/Randomization in Clinical Trials , 2016 .

[14]  Nicolai Meinshausen,et al.  Asymptotic optimality of the Westfall--Young permutation procedure for multiple testing under dependence , 2011, 1106.2068.

[15]  W. Kruskal,et al.  Use of Ranks in One-Criterion Variance Analysis , 1952 .

[16]  C. F. Wu,et al.  Some Restricted randomization rules in sequential designs , 1983 .

[17]  F. J. Anscombe,et al.  The Validity of Comparative Experiments , 1948 .

[18]  S. Grundy,et al.  Design and methodological considerations in the National Cooperative Gallstone Study: a multicenter clinical trial. , 1981, Controlled Clinical Trials.

[19]  L. J. Wei,et al.  An Application of an Urn Model to the Design of Sequential Controlled Clinical Trials , 1978 .

[20]  William F. Rosenberger,et al.  Bias properties and nonparametric inference for truncated binomial randomization , 2003 .

[21]  B. Efron.  Forcing a sequential experiment to be balanced , 1971 .

[22]  D. Byar,et al.  Comparisons of placebo, pyridoxine, and topical thiotepa in preventing recurrence of stage I bladder cancer. , 1977, Urology.

[23]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .