Koon Shing Kwong

Calculation of critical values for Dunnett and Tamhane's step-up multiple test procedure

Dunnett and Tamhane (1992, J. Amer. Statist. Assoc. 87, 162–170; 1993, Statist. Probab. Lett. 16 (1), 55–58; 1995, Biometrics 51, 217–227) proposed a step-up testing procedure for comparing k treatments with a control and showed that it is often more powerful than its competitors, the single-step (Dunnett, 1955, J. Amer. Statist. Assoc. 50, 1096–1121) and the step-down (Miller, 1966, Simultaneous Statistical Inference, McGraw-Hill, New York; Dunnett and Tamhane, 1991, Statist Med. 10 (6), 939–947) procedures. However, the applications of the step-up procedure may be hindered by the lengthy time for computing the required critical values, especially when the design of experiment is unbalanced or the value of k is large. In this paper we propose some more efficient approaches to the computation of the critical values to make the step-up test more applicable.

A modified Benjamini–Hochberg multiple comparisons procedure for controlling the false discovery rate

When performing simultaneous statistical tests, the Type I error concept most commonly controlled by analysts is the familywise error rate, i.e., the probability of committing at least one Type I error. However, this criterion is unduly stringent for some practical situations and therefore may not be appropriate. An alternative concept of error control was provided by Benjamini and Hochberg (J. Roy. Statist. Soc. B 57 (1995) 289) who advocate control of the expected proportion of falsely rejected hypotheses which they term the false discovery rate or FDR. These authors devised a step-up procedure for controlling the FDR. In this article, when the joint distribution of test statistics is known, continuous, and positive regression dependent on each one from a subset of true null hypotheses, we derive and discuss a modification of their procedure which affords increased power. An example is provided to illustrate our proposed method.

Extension of three‐arm non‐inferiority studies to trials with multiple new treatments

Non-inferiority (NI) trials are becoming increasingly popular. The main purpose of NI trials is to assert the efficacy of a new treatment compared with an active control by demonstrating that the new treatment maintains a substantial fraction of the treatment effect of the control. Most of the statistical testing procedures in this area have been developed for three-arm NI trials in which a new treatment is compared with an active control in the presence of a placebo. However, NI trials frequently involve comparisons of several new treatments with a control, such as in studies involving different doses of a new drug or different combinations of several new drugs. In seeking an adequate testing procedure for such cases, we use a new approach that modifies existing testing procedures to cover circumstances in which several new treatments are present. We also give methods and algorithms to produce the optimal sample size configuration. In addition, we also discuss the advantages of using different margins for the assay sensitivity test between the active control and the placebo and the NI test between the new treatments and the active control. We illustrate the new approach by using data from a clinical trial.

A more powerful step-up procedure for controlling the false discovery rate under independence

Recently, Benjamini and Hochberg (J. Roy. Statist. Soc. B 57 (1995) 289) and Benjamini and Liu (J. Statist. Plann. Inference 82 (1999) 163) proposed step-up and step-down multiple hypotheses testing procedures, respectively, for controlling the false discovery rate (FDR) when all the test statistics are independent. In this paper, we propose another step-up procedure such that the FDR is still controlled at a specified significance level. Based on a simulation study, the new procedure is more powerful than both existing step-up and step-down procedures, especially when most of the hypotheses are false.

Sample size determination in step‐up testing procedures for multiple comparisons with a control

Step-up procedures have been shown to be powerful testing methods in clinical trials for comparisons of several treatments with a control. In this paper, a determination of the optimal sample size for a step-up procedure that allows a pre-specified power level to be attained is discussed. Various definitions of power, such as all-pairs power, any-pair power, per-pair power and average power, in one- and two-sided tests are considered. An extensive numerical study confirms that square root allocation of sample size among treatments provides a better approximation of the optimal sample size relative to equal allocation. Based on square root allocation, tables are constructed, and users can conveniently obtain the approximate required sample size for the selected configurations of parameters and power. For clinical studies with difficulties in recruiting patients or when additional subjects lead to a significant increase in cost, a more precise computation of the required sample size is recommended. In such circumstances, our proposed procedure may be adopted to obtain the optimal sample size. It is also found that, contrary to conventional belief, the optimal allocation may considerably reduce the total sample size requirement in certain cases. The determination of the required sample sizes using both allocation rules are illustrated with two examples in clinical studies.

Evaluation of One-Sided Percentage Points of the Singular Multivariate Normal Distribution

This paper presents a new theorem, as a substitute for existing results which are shown to have some errors, for evaluating the exact one-sided percentage points of the multivariate normal distribution with a singular negative product correlation structure. By extending the result from the multivariate normal distribution to the multivariate t-distribution with corresponding singular correlation structure, we tabulate the one-sided critical points for the Analysis of Means procedure.

A modified Dunnett and Tamhane step-up approach for establishing superiority/equivalence of a new treatment compared with k standard treatments

Abstract There are still some open questions whether the existing step-up procedures for establishing superiority and equivalence of a new treatment compared with several standard treatments can strongly control the type I familywise error rate (FWE) at the designated level. In this paper we modify one of the three step-up procedures suggested by Dunnett and Tamhane (16 (1997) Statist. Med. 2489–2506) and then prove that the modified procedure strongly controls the FWE. The method for evaluating the critical values of the modified procedure is also discussed. A simulation study reveals that the modified procedure is generally more powerful than the original procedure.

Step-up procedures for non-inferiority tests with multiple experimental treatments.

Non-inferiority (NI) trials are becoming more popular. The NI of a new treatment compared with a standard treatment is established when the new treatment maintains a substantial fraction of the treatment effect of the standard treatment. A valid NI trial is also required to show assay sensitivity, the demonstration of the standard treatment having the expected effect with a size comparable to those reported in previous placebo-controlled studies. A three-arm NI trial is a clinical study that includes a new treatment, a standard treatment and a placebo. Most of the statistical methods developed for three-arm NI trials are designed for the existence of only one new treatment. Recently, a single-step procedure was developed to deal with NI trials with multiple new treatments with the overall familywise error rate controlled at a specified level. In this article, we extend the single-step procedure to two new step-up procedures for NI trials with multiple new treatments. A comparative study of test power shows that both proposed step-up procedures provide a significant improvement of power when compared to the single-step procedure. One of the two proposed step-up procedures also allows the flexibility of allocating different error rates between the sensitivity hypothesis and the NI hypotheses so that the assignment of fewer patients to the placebo becomes possible when designing NI trials. We illustrate the new procedures using data from a clinical trial.

Step-up testing procedure for multiple comparisons with a control for a latent variable model with ordered categorical responses

In clinical studies, multiple comparisons of several treatments to a control with ordered categorical responses are often encountered. A popular statistical approach to analyzing the data is to use the logistic regression model with the proportional odds assumption. As discussed in several recent research papers, if the proportional odds assumption fails to hold, the undesirable consequence of an inflated familywise type I error rate may affect the validity of the clinical findings. To remedy the problem, a more flexible approach that uses the latent normal model with single-step and stepwise testing procedures has been recently proposed. In this paper, we introduce a step-up procedure that uses the correlation structure of test statistics under the latent normal model. A simulation study demonstrates the superiority of the proposed procedure to all existing testing procedures. Based on the proposed step-up procedure, we derive an algorithm that enables the determination of the total sample size and the sample size allocation scheme with a pre-determined level of test power before the onset of a clinical trial. A clinical example is presented to illustrate our proposed method.

On Sample Size and Quick Simultaneous Confidence Interval Estimations for Multinomial Proportions

Abstract Asymptotically, sample proportions from a multinomial distribution converge in distribution to a multivariate normal distribution with a singular negative product correlation structure. Based on this result, we propose a new approach to estimate the sample size requirement for constructing quick simultaneous confidence intervals (QSCI) for multinomial proportions. In addition, this new approach can be used to construct QSCI and provides a statistical justification to the reports of the opinion polling.