Statistical inference for self-designing clinical trials with a one-sided hypothesis

In the process of monitoring clinical trials, it seems appealing to use the interim findings to determine whether the sample size originally planned will provide adequate power when the alternative hypothesis is true, and to adjust the sample size if necessary. In the present paper, we propose a flexible sequential monitoring method following the work of Fisher (1998), in which the maximum sample size does not have to be specified in advance. The final test statistic is constructed based on a weighted average of the sequentially collected data, where the weight function at each stage is determined by the observed data prior to that stage. Such a weight function is used to maintain the integrity of the variance of the final test statistic so that the overall type I error rate is preserved. Moreover, the weight function plays an implicit role in termination of a trial when a treatment difference exists. Finally, the design allows the trial to be stopped early when the efficacy result is sufficiently negative. Simulation studies confirm the performance of the method.     

Two-stage design of quantal response studies

In a quantal response study, there may be insufficient knowledge of the response relationship for the stimulus (or dose) levels to be chosen properly. Information from such a study can be scanty or even unreliable. A two-stage design is proposed for such studies, which can determine whether and how a follow-up (i.e., second-stage) study should be conducted to select additional stimulus levels to compensate for the scarcity of information in the initial study. These levels are determined by using optimal design theory and are based on the fitted model from the data in the initial study. Its advantages are demonstrated using a fishery study.     

Valid inference in random effects meta-analysis

The standard approach to inference for random effects meta-analysis relies on approximating the null distribution of a test statistic by a standard normal distribution. This approximation is asymptotic on k, the number of studies, and can be substantially in error in medical meta-analyses, which often have only a few studies. This paper proposes permutation and ad hoc methods for testing with the random effects model. Under the group permutation method, we randomly switch the treatment and control group labels in each trial. This idea is similar to using a permutation distribution for a community intervention trial where communities are randomized in pairs. The permutation method theoretically controls the type I error rate for typical meta-analyses scenarios. We also suggest two ad hoc procedures. Our first suggestion is to use a t-reference distribution with k-1 degrees of freedom rather than a standard normal distribution for the usual random effects test statistic. We also investigate the use of a simple t-statistic on the reported treatment effects.     

Efficiency of estimating vaccine efficacy for susceptibility and infectiousness: randomization by individual versus household

In designing vaccine efficacy studies based on the secondary attack rate (SAR) or transmission probability in which both vaccine efficacy for susceptibility, VE(S), and vaccine efficacy for infectiousness, VE(I), are estimated, the allocation of vaccine and placebo within transmission units has an important influence on the efficiency of the study. We compared the following randomization schemes that result in different allocations of vaccine and placebo within two-member households: (1) randomization by individual for a mixed allocation, (2) randomization by transmission unit for concordant allocation, and (3) randomization of only one individual in each transmission unit to either vaccine or placebo. There is a complex interaction among the VE(S), VE(I), and the SAR that determines which allocation of vaccine and placebo within households provides the most information. In general, individual randomization with a mixed allocation of vaccine and placebo is better for estimating both VE(S) and VE(I) than is randomizing by household. However, for estimation of VE(I), at very low SARs and low VE(S), randomization by household is slightly more efficient than randomization by individual.     

Statistical quality control of variety trial data

I propose detection criteria for identifying an abnormal or erroneous data vector provided by a single variety trial in a longer series of variety trials. The test criteria are based on the linear effects estimated separately for each studied trial using global variance components estimated from the whole series of variety trials. The criteria comprise three mutually independent test statistics. The first one is a quadratic form in the estimated fixed effects, the second one is a quadratic form in the estimated realized linear random effects not including the residual effects, and the third one is a quadratic form in the estimated realized residual effects. Under the null hypothesis defining a valid data vector, the three quadratics have independent chi2 distributions. Under natural alternative hypotheses, they have noncentral chi2 distributions. Decomposing the total variation of the data vector studied into quadratic forms due to different types of the realized linear effects intuitively justifies the resulting test criteria. The decomposition may also be used to show that the resulting tests are likelihood ratio tests. I further present computational procedures that allow us to dispense with the need for prior estimation of the linear effects.     

Anti‐atherosclerotic effects of vitamin E – myth or reality?

Atherosclerosis and its complications such as coronary heart disease, myocardial infarction and stroke are the leading causes of death in the developed world. High blood pressure, diabetes, smoking and a diet high in cholesterol and lipids clearly increase the likelihood of premature atherosclerosis, albeit other factors, such as the individual genetic makeup, may play an additional role. Several epidemiological studies and intervention trials have been performed with vitamin E, and some of them showed that it prevents atherosclerosis. For a long time, vitamin E was assumed to act by decreasing the oxidation of LDL, a key step in atherosclerosis initiation. However, at the cellular level, vitamin E acts by inhibition of smooth muscle cell proliferation, platelet aggregation, monocyte adhesion, oxLDL uptake and cytokine production, all reactions implied in the progression of atherosclerosis. Recent research revealed that these effects are not the result of the antioxidant activity of vitamin E, but rather of precise molecular actions of this compound. It is assumed that specific interactions of vitamin E with enzymes and proteins are at the basis of its non-antioxidant effects. Vitamin E influences the activity of several enzymes (e.g. PKC, PP2A, COX-2, 5-lipooxygenase, nitric oxide synthase, NADPH-oxidase, superoxide dismutase, phopholipase A2) and modulates the expression of genes that are involved in atherosclerosis (e.g. scavenger receptors, integrins, selectins, cytokines, cyclins). These interactions promise to reveal the biological properties of vitamin E and allow designing better strategies for the protection against atherosclerosis progression.     

Use of Ψ<Superscript>α</Superscript>-ETOs in the unified treatment of electronic attraction,electric field and electric field gradient multicenter integrals of screened Coulomb potentials over Slater orbitals

In this study, using complete orthonormal sets of -ETOs (where =1, 0, –1, –2, ...)introduced by the author, a large number of series expansion formulae for the multicenter electronic attraction (EA), electric field (EF) and electric field gradient (EFG) integrals of the Yukawa-like screened Coulomb potentials (SCPs) is presented through the new central and noncentral potentials and the overlap integrals with the same screening constants. The final results obtained are valid for arbitrary locations of STOs and their parameters.An erratum to this article can be found at     

Oxidative stress in cardiovascular disease: myth or fact?

Oxidative stress is a mechanism with a central role in the pathogenesis of atherosclerosis, cancer, and other chronic diseases. It also plays a major role in the aging process. Ischemic heart disease is perhaps the human condition in which the role of oxidative stress has been investigated in more detail: reactive oxygen species and consequent expression of oxidative damage have been demonstrated during post-ischemic reperfusion in humans and the protective role of antioxidants has been validated in several experimental studies addressing the pathophysiology of acute ischemia. Although an impressive bulk of experimental studies substantiate the role of oxidative stress in the progression of the damage induced by acute ischemia, not a single pathophysiologic achievement has had a significant impact on the treatment of patients and randomized, controlled clinical trials, both in primary and secondary prevention, have failed to prove the efficacy of antioxidants in the treatment of ischemic cardiovascular disease. This dichotomy, between the experimental data and the lack of impact in the clinical setting, needs to be deeply investigated: certainly, the pathophysiologic grounds of oxidative stress do maintain their validity but the concepts of the determinants of oxidative damage should be critically revised. In this regard, the role of intermediate metabolism during myocardial ischemia together with the cellular redox state might represent a promising interpretative key.     

Statistical analysis of noninferiority trials with a rate ratio in small-sample matched-pair designs

Testing of noninferiority has become increasingly important in modern medicine as a means of comparing a new test procedure to a currently available test procedure. Asymptotic methods have recently been developed for analyzing noninferiority trials using rate ratios under the matched-pair design. In small samples, however, the performance of these asymptotic methods may not be reliable, and they are not recommended. In this article, we investigate alternative methods that are desirable for assessing noninferiority trials, using the rate ratio measure under small-sample matched-pair designs. In particular, we propose an exact and an approximate exact unconditional test, along with the corresponding confidence intervals based on the score statistic. The exact unconditional method guarantees the type I error rate will not exceed the nominal level. It is recommended for when strict control of type I error (protection against any inflated risk of accepting inferior treatments) is required. However, the exact method tends to be overly conservative (thus, less powerful) and computationally demanding. Via empirical studies, we demonstrate that the approximate exact score method, which is computationally simple to implement, controls the type I error rate reasonably well and has high power for hypothesis testing. On balance, the approximate exact method offers a very good alternative for analyzing correlated binary data from matched-pair designs with small sample sizes. We illustrate these methods using two real examples taken from a crossover study of soft lenses and a Pneumocystis carinii pneumonia study. We contrast the methods with a hypothetical example.     

Rethinking historical controls

Inference from traditional historical controls, i.e. comparing a new treatment in a current series of patients with an old treatment in a previous series of patients, may be subject to a strong selection bias. To avoid this bias, Baker and Lindeman (1994) proposed the paired availability design. By applying this methodology to estimate the effect of epidural analgesia on the probability of Cesarean section, we made two important contributions with the current study. First, we generalized the methodology to include different types of availability and multiple time periods. Second, we investigated how well the paired availability design reduced selection bias by comparing results to those from a meta-analysis of randomized trials and a multivariate analysis of concurrent controls. The confidence interval from the paired availability approach differed considerably from that of the multivariate analysis of concurrent controls but was similar to that from the meta-analysis of randomized trials. Because we believe the multivariate analysis of concurrent controls omitted an important predictor and the meta-analysis of randomized trials was the gold standard for inference, we concluded that the paired availability design did, in fact, reduce selection bias.