The double triangular test in practice

The double triangular test was introduced twenty years ago, and the purpose of this paper is to review applications that have been made since then. In fact, take-up of the method was rather slow until the late 1990s, but in recent years several clinical trial reports have been published describing its use in a wide range of therapeutic areas. The core of this paper is a detailed account of five trials that have been published since 2000 in which the method was applied to studies of pancreatic cancer, breast cancer, myocardial infarction, epilepsy and bedsores. Before those accounts are given, the method is described and the history behind its evolution is presented. The future potential of the method for sequential case-control and equivalence trials is also discussed. Copyright © 2004 John Wiley & Sons, Ltd.

A jackknife variance estimator for unequal probability sampling

The jackknife method is often used for variance estimation in sample surveys but has only been developed for a limited class of sampling designs.We propose a jackknife variance estimator which is defined for any without-replacement unequal probability sampling design. We demonstrate design consistency of this estimator for a broad class of point estimators. A Monte Carlo study shows how the proposed estimator may improve on existing estimators.

Variance estimation with highly stratified sampling designs with unequal probabilities

It is common practice to design a survey with a large number of strata. However, in this case the usual techniques for variance estimation can be inaccurate. This paper proposes a variance estimator for estimators of totals. The method proposed can be implemented with standard statistical packages without any specific programming, as it involves simple techniques of estimation, such as regression fitting.

Variance estimation for systematic sampling from deliberately ordered populations

The systematic sampling (SYS) design (Madow and Madow, 1944) is widely used by statistical offices due to its simplicity and efficiency (e.g., Iachan, 1982). But it suffers from a serious defect, namely, that it is impossible to unbiasedly estimate the sampling variance (Iachan, 1982) and usual variance estimators (Yates and Grundy, 1953) are inadequate and can overestimate the variance significantly (Särndal et al., 1992). We propose a novel variance estimator which is less biased and that can be implemented with any given population order. We will justify this estimator theoretically and with a Monte Carlo simulation study.

Variance estimation with Chao's sampling scheme

We show that the Hájek (Ann. Math Statist. (1964) 1491) variance estimator can be used to estimate the variance of the Horvitz–Thompson estimator when the Chao sampling scheme (Chao, Biometrika 69 (1982) 653) is implemented. This estimator is simple and can be implemented with any statistical packages. We consider a numerical and an analytic method to show that this estimator can be used. A series of simulations supports our findings.

Adjusted jackknife for imputation under unequal probability sampling without replacement

Imputation is commonly used to compensate for item non-response in sample surveys. If we treat the imputed values as if they are true values, and then compute the variance estimates by using standard methods, such as the jackknife, we can seriously underestimate the true variances. We propose a modified jackknife variance estimator which is defined for any without-replacement unequal probability sampling design in the presence of imputation and non-negligible sampling fraction. Mean, ratio and random-imputation methods will be considered. The practical advantage of the method proposed is its breadth of applicability.

Using phylogeny to investigate the origins of the Cape flora: the importance of taxonomic, gene and genome sampling strategies

Phylogenetic methods hold great promise for the reconstruction of the transition from precursor to modern flora and the identification of underlying factors which drive the process. The phylogenetic methods presently used to address the question of the origin of the Cape flora of South Africa are considered here. The sampling requirements of each of these methods, which include dating of diversifications using calibrated molecular trees, sister pair comparisons, lineage through time plots and biogeographical optimizations are reviewed. Sampling of genes, genomes and species are considered. Although increased higher-level studies and increased sampling are required for robust interpretation, it is clear that much progress is already made. It is argued that despite the remarkable richness of the flora, the Cape flora is a valuable model system to demonstrate the utility of phylogenetic methods in determining the history of a modern flora.

Flavonoid supplement improves leg health and reduces fluid retention in pre-menopausal women in a double-blind, placebo-controlled study

Flavonoid extracts derived from plant foods have been shown to benefit certain types of fluid retention. However, no studies have investigated these compounds for use in premenstrual fluid retention, a complaint common among women with otherwise normal menstrual cycles. Therefore, we conducted a double-blind, placebo-controlled, pilot study into the effect of a daily flavonoid extract (Colladeen(R), 320 mg oligomeric procyanidins) on premenstrual fluid retention. Fluid retention was assessed at baseline and throughout 4 menstrual cycles of the intervention using validated questionnaires. Leg girth was also measured at baseline and at the end of the study. Thirty subjects completed the study (n = 18 active treatment; n = 12 placebo). Although no significant changes in leg girth measurements were noted, there was a significant improvement in subjective "leg health" scores after flavonoid treatment compared to placebo (p = 0.013). Furthermore, this was accompanied by an improvement in reported premenstrual fluid retention nearing significance (p = 0.066). We conclude that flavonoids supplements may provide a new therapeutic direction to counter premenstrual fluid retention and improve leg health. A larger study is now warranted.

The significance of "nonsignificance" in randomized controlled studies: a discussion inspired by a double-blinded study on St. John's Wort (Hypericum perforatum L.) for premenstrual symptoms

Objectives: This study aimed to investigate the efficacy of St. John's wort extract (SJW) as a treatment for premenstrual symptoms. Design: The study was a randomized, double-blinded, placebo-controlled trial, with two parallel treatment groups. After a no-treatment baseline cycle, volunteers were randomized to either SJW or placebo for a further two menstrual cycles. Settings/location: A postal trial conducted from The University of Reading, Berkshire, England. Subjects: One hundred and sixty-nine (169) normally menstruating women who experienced recurrent premenstrual symptoms were recruited onto the study. One hundred and twenty-five (125) completed the protocol and were included in the analysis. Interventions: Six hundred milligrams (600) mg of SJW (standardized to contain 1800 mug of hypericin) or placebo (containing lactose and cellulose). Outcome measure: A menstrual diary was used to assess changes in premenstrual symptoms. The anxiety-related subgroup of symptoms of this instrument was used as the primary outcome measure. Results: After averaging the effects of treatment over both treatment cycles it was found that there was a trend for SJW to be superior to placebo. However, this finding was not statistically significant. Conclusion: The possibility that this nonsignificant finding resulted from insufficient statistical power in the study, rather than a lack of efficacy of SJW, is discussed. Following this discussion the recommendation is made that, in future, similar studies should be powered to detect a minimum clinically relevant difference between treatments.

Supramolecular peptide helix from a novel double turn forming peptide containing a beta-amino acid

A single-crystal X-ray diffraction study of the terminally protected tetrapeptide Boc-beta-Ala-Aib-Leu-Aib-OMe 1 (Aib: alpha-aminoisobutyric acid; beta-Ala: beta-Alanine) reveals that it adopts a new type of double turn structure which self-associates to form a unique supramolecular helix through intermolecular hydrogen bonds. Scanning electron microscopic studies show that peptide 1 exhibits amyloid-like fibrillar morphology in the solid state. (C) 2003 Elsevier Science Ltd. All rights reserved.

Infrared intensities of furan, pyrrole and thiophene: beyond the double harmonic approximation

Infrared intensities of the fundamental, overtone and combination transitions in furan, pyrrole and thiophene have been calculated using the variational normal coordinate code MULTIMODE. We use pure vibrational wavefunctions, and quartic force fields and cubic dipole moment vector surfaces, generated by density functional theory. The results are compared graphically with second-order perturbation calculations and with relative intensities from experiment for furan and pyrrole.

Double coupling reactions of 3,4-bis(stannyl)furanone: facile preparation of diaryl- and dibenzylfuranones

The palladium-catalyzed cross-coupling reaction of 3,4-bis(tributylstannyl)furan-2(5H)-one using chelating ligand or polar solvent gives mixtures of single and double coupled products, even when one equivalent of halide coupling partner is used. After optimization, the double coupling reaction was shown to be general, with the use of two equivalents of aryl iodides giving 3,4-disubstituted furanones, The reaction using benzyl bromides proceeds at lower temperatures than the corresponding coupling using aryl iodides, giving dibenzylfuranones. The methodology has been exemplified in a synthesis of (+/-)-hinokinin.