Sample size determination in step-down and step-up multiple tests for comparing treatments with a control

Optimal multiple testing and design in clinical trials

A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal procedures become more complex. In this paper, we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the procedures. This leads us to an explicit optimization problem with objective and constraints that describe its specific desiderata. We present a complete solution for deriving optimal procedures for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal procedures that are identical to existing procedures, such as Hommel's procedure or the procedure of Bittman et al. (2009), while for other cases it yields completely novel and more powerful procedures than existing ones. We demonstrate the nature of our novel procedures and their improved power extensively in a simulation and on the APEX study (Cohen et al., 2016).

Dose sparing and the lack of a dose-response relationship with an influenza vaccine in adult and elderly patients - a randomized, double-blind clinical trial

AIMS

The currently licensed seasonal trivalent influenza vaccines contain 15 μg haemagglutinin per strain for adult, and up to 60 μg for elderly patients. However, due to recent shortages, dose sparing to increase production capacity would be highly desirable. In the present study, we attempted to find a dose-response relationship for immunogenicity and, thus, the optimal dose for seasonal influenza vaccines in adult and elderly patients.

METHODS

A total of 256 subjects, including adult (aged 18-60 years) and elderly (aged over 60 years) individuals, were enrolled. Subjects were randomly assigned in a 1:1:1:1 ratio to receive a whole-virion, aluminium-adjuvanted trivalent influenza vaccine containing 3.5, 6, 9 or 15 μg haemagglutinin of seasonal A/H1N1, A/H3N2 and B influenza antigens manufactured by Omninvest Ltd., Hungary. Serum antibody titres against the vaccine virus strains were measured by haemagglutination inhibition.

RESULT

All vaccines were well tolerated. All four vaccines fulfilled all three immunogenicity licensing criteria, as determined by the European Committee for Proprietary Medicinal Products (CPMP)/Biotechnology Working Party (BWP)/214/96 guideline for all three virus strains and both age groups. The 3.5 μg vaccine showed 28% less seroconversion compared to the 15 μg dose in terms of influenza AH3N2 in the adult group (95% confidence interval -51, -3; P < 0.05). All other doses showed no significant difference in immunogenicity compared with the licensed vaccine containing 15 μg haemagglutinin.

CONCLUSIONS

Our data suggested that significant dose sparing is possible with the use of whole-virion vaccines and aluminium adjuvants, without compromising safety. This could have significant economic and public health impacts.

Sample size determination with familywise control of both type I and type II errors in clinical trials

The concept of controlling familywise type I and type II errors at the same time is essentially an integrated process to deal with multiplicity issues in clinical trials. The process will select a multiple testing procedure (MTP) which controls the familywise type I error and calculate the per hypothesis sample size such that the "studywise power" is maintained at desired level. The power of a study can be defined in several ways and it depends on the objective. In this article, we provide general guidance on how to make the selection of MTPs and calculate sample size simultaneously. We introduce the concept of strong and weak control of the familywise type II error and generalized familywise type II error. We also proposed the novel Bonferroni+ and optimal Bonferroni+ procedures to allocate per hypothesis type II error. We demonstrated the value of the proposed work as it cannot be replaced by simple simulations. A real clinical trial is discussed throughout the article as an example.

Sample size determination in two-sided distribution-free treatment versus control multiple comparisons

The problem of power and sample size determination for distribution-free multiple comparison tests of K treatments versus a control group is addressed. We define the power as the probability of correctly rejecting one specified or all K hypotheses, corresponding to the per-pair and all-pairs power, respectively. The power formulas are derived for both joint ranking and pairwise ranking mechanism for general multiple comparison problems, followed by explicit form of these formulas when the single-step, step-down, or step-up adjustments are applied. The proposed power and sample size calculation methods apply to scenarios both when the underlying distributions are known and when they are unknown but a pilot study is available. Numerical methods via quasi-Monte Carlo integration and Monte Carlo integration are assessed. Our simulation studies show the accuracy of the power and sample size calculation formulas. We recommend the Monte Carlo integration as the calculation algorithm. An example from a mouse peritoneal cavity study is used to demonstrate the application of the methods.

Qualitative differences between C57BL/6J and DBA/2J mice in morphine potentiation of brain stimulation reward and intravenous self-administration

RATIONALE

The C57BL/6J (C57) and DBA/2J (DBA) mice are the most common genotypes used to identify chromosomal regions and neurochemical mechanisms of interest in opioid addiction. Unfortunately, outside of the oral two-bottle choice procedure, limited and sometimes controversial evidence is available for determining their relative sensitivity to the rewarding effects of morphine.

OBJECTIVES

The purpose of this study was to utilize classically accepted models of drug abuse liability to determine relative susceptibility to the rewarding effects of morphine.

METHODS

The ability of morphine or amphetamine to potentiate lateral hypothalamic brain stimulation and intravenous morphine self-administration (across three doses in a fixed ratio schedule and at the highest dose in progressive ratio schedules) was investigated in both genotypes.

RESULTS

In both measures, C57 and DBA mice differed dramatically in their response to morphine. Morphine potentiated rewarding stimulation in the C57 mice but antagonized it in the DBA mice. Consistent with these findings, intravenous morphine did not serve as a positive reinforcer in DBA mice under conditions that were effective in the C57 mice using a fixed ratio schedule and failed to sustain levels of responding sufficient to maintain a constant rate of drug intake under a progressive ratio schedule. In contrast, amphetamine potentiated the rewarding effects of brain stimulation similarly in the two genotypes.

CONCLUSIONS

These findings provide strong evidence that morphine is rewarding in the C57 genotype and not in the DBA genotype. Understanding their relative susceptibility is important given the prominence of these genotypes in candidate gene identification and gene mapping.

Step down procedure for comparing several treatments with a control based on multivariate normal response

In this study we consider a multiple comparison of several treatments with a control based on multivariate normal response in clinical trials. Specifically we construct a step down procedure by referring to Dunnett and Tamhane (1991). Furthermore we formulate the all-pairs power by using the recursive formula derived by Hayter and Tamhane (1991) and Dunnett, Horn and Vollandt (2001). Finally we compare the step down procedure with the single step procedure proposed by Nakamura and Imada (2005) in terms of some numerical examples regarding the power of the test.

FDR Control by the BH Procedure for Two-Sided Correlated Tests with Implications to Gene Expression Data Analysis

The multiple testing problem attributed to gene expression analysis is challenging not only by its size, but also by possible dependence between the expression levels of different genes resulting from coregulations of the genes. Furthermore, the measurement errors of these expression levels may be dependent as well since they are subjected to several technical factors. Multiple testing of such data faces the challenge of correlated test statistics. In such a case, the control of the False Discovery Rate (FDR) is not straightforward, and thus demands new approaches and solutions that will address multiplicity while accounting for this dependency. This paper investigates the effects of dependency between bormal test statistics on FDR control in two-sided testing, using the linear step-up procedure (BH) of Benjamini and Hochberg (1995). The case of two multiple hypotheses is examined first. A simulation study offers primary insight into the behavior of the FDR subjected to different levels of correlation and distance between null and alternative means. A theoretical analysis follows in order to obtain explicit upper bounds to the FDR. These results are then extended to more than two multiple tests, thereby offering a better perspective on the effect of the proportion of false null hypotheses, as well as the structure of the test statistics correlation matrix. An example from gene expression data analysis is presented.