Comparison of sample size formulae for 2x2 cross-over designs applied to bioequivalence studies

We consider the comparison of two formulations in terms of average bioequivalence using the 2 × 2 cross-over design. In a bioequivalence study, the primary outcome is a pharmacokinetic measure, such as the area under the plasma concentration by time curve, which is usually assumed to have a lognormal distribution. The criterion typically used for claiming bioequivalence is that the 90% confidence interval for the ratio of the means should lie within the interval (0.80, 1.25), or equivalently the 90% confidence interval for the differences in the means on the natural log scale should be within the interval (-0.2231, 0.2231). We compare the gold standard method for calculation of the sample size based on the non-central t distribution with those based on the central t and normal distributions. In practice, the differences between the various approaches are likely to be small. Further approximations to the power function are sometimes used to simplify the calculations. These approximations should be used with caution, because the sample size required for a desirable level of power might be under- or overestimated compared to the gold standard method. However, in some situations the approximate methods produce very similar sample sizes to the gold standard method. Copyright © 2005 John Wiley & Sons, Ltd.

Effects of bovine alpha-lactalbumin and casein glycomacropeptide-enriched infant formulae on faecal microbiota in healthy term infants

Objective: Certain milk factors may promote the growth of a host-friendly gastrointestinal microbiota, for example, one that is predominated by bifidobacteria, a perceived healthpromoting genus. This may explain why breast-fed infants experience fewer intestinal infections than their formula-fed counterparts who are believed to have a more diverse microbiota, which is similar to that of adults. The effects of formulas supplemented with 2 such ingredients from bovine milk, a-lactalbumin (alpha-lac) and casein glycomacropeptide (GMP), on gut flora were investigated in this study. Patients and Methods: Six-week-old (4-8 wk), healthy term infants were randomised to a standard infant formula or 1 of 2 test formulae enriched in alpha-Jac with higher or lower GMP until 6 months. Faecal bacteriology was determined by the culture-independent procedure fluorescence in situ hybridisation. Results: There was a large fluctuation of bacterial counts within groups with no statistically significant differences between groups. Although all groups showed a. predominance of bifidobacteria, breast-fed infants had a small temporary increase in counts. Other bacterial levels varied in formula-fed groups, which overall showed an adult-like faecal microflora. Conclusions: It can be speculated that a prebiotic effect for alpha-lac and GMP is achieved only with low starting populations of beneficial microbiota (eg, infants not initially breast-fed.

Physiological and bifidogenic effects of prebiotic supplements in infant formulae

This randomized controlled trial involving 110 healthy neonates studied physiological and bifidogenic effects of galactooligosaccharides (GOS), oligofructose and long-chain inulin (FOS) in formula. Subjects were randomized to Orafti Synergy1 (50 oligofructose: 50 FOS) 0.4g/dl or 0.8g/dl, GOS:FOS (90:10) 0.8g/dl or a standard formula according to Good Clinical Practise (GCP) guidelines. A breast-fed group was included for comparison. Outcome parameters were weight, length, intake, stool characteristics, crying, regurgitation, vomiting, adverse events and fecal bacterial population counts. Statistical analyses used non-parametric tests. During the first month of life weight, length, intake and crying increased significantly in all groups. Regurgitation and vomiting scores were low and similar. Stool frequency decreased significantly and similarly in all formula groups but was lower than in the breast-fed. All prebiotic groups maintained soft stools, only slightly harder than those of breast-fed infants. The standard group had significantly harder stools at wks 2 and 4 compared to 1 (P<0.001 & P=0.0279). The total number of fecal bacteria increased in all prebiotic groups (9.82, 9.73 and 9.91 to 10.34, 10.38 and 10.37, respectively, log10 cells/g feces, P=0.2298) and resembled more the breast-fed pattern. Numbers of lactic acid bacteria, bacteroides and clostridia were comparable. In the SYN1 0.8 g/dl and GOS:FOS groups Bifidobacterium counts were significantly higher at D14 & 28 compared to D3 and comparable to the breast-fed group. Tolerance and growth were normal. In conclusion, stool consistency and bacterial composition of infants taking SYN1 0.8 g/dl or GOS:FOS supplemented formula was closer to the breast-fed pattern. There was no risk for dehydration.

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

The acoustic signature of fluid flow in complex porous media

Effective medium approximations for the frequency-dependent and complex-valued effective stiffness tensors of cracked/ porous rocks with multiple solid constituents are developed on the basis of the T-matrix approach (based on integral equation methods for quasi-static composites), the elastic - viscoelastic correspondence principle, and a unified treatment of the local and global flow mechanisms, which is consistent with the principle of fluid mass conservation. The main advantage of using the T-matrix approach, rather than the first-order approach of Eshelby or the second-order approach of Hudson, is that it produces physically plausible results even when the volume concentrations of inclusions or cavities are no longer small. The new formulae, which operates with an arbitrary homogeneous (anisotropic) reference medium and contains terms of all order in the volume concentrations of solid particles and communicating cavities, take explicitly account of inclusion shape and spatial distribution independently. We show analytically that an expansion of the T-matrix formulae to first order in the volume concentration of cavities (in agreement with the dilute estimate of Eshelby) has the correct dependence on the properties of the saturating fluid, in the sense that it is consistent with the Brown-Korringa relation, when the frequency is sufficiently low. We present numerical results for the (anisotropic) effective viscoelastic properties of a cracked permeable medium with finite storage porosity, indicating that the complete T-matrix formulae (including the higher-order terms) are generally consistent with the Brown-Korringa relation, at least if we assume the spatial distribution of cavities to be the same for all cavity pairs. We have found an efficient way to treat statistical correlations in the shapes and orientations of the communicating cavities, and also obtained a reasonable match between theoretical predictions (based on a dual porosity model for quartz-clay mixtures, involving relatively flat clay-related pores and more rounded quartz-related pores) and laboratory results for the ultrasonic velocity and attenuation spectra of a suite of typical reservoir rocks. (C) 2003 Elsevier B.V. All rights reserved.