Testing Equivalence Simultaneously for Location and Dispersion of two Normally Distributed Populations

In clinical trials with an active control usually therapeutical equivalence of a new treatment is investigated by looking at a location parameter of the distributions of the primary efficacy variable. But even if the location parameters are close to each other existing differences in variability may be connected with different risks for under or over treatment in an individual patient. Assuming normally distributed responses a multiple test procedure applying two shifted one-sided t-tests for the mean and accordingly two one-sided F-tests for the variances is proposed. Equivalence in location and variability is established if all four tests lead to a rejection at the (one-sided) level α. A conservative procedure “correcting” the t-tests for heteroscedasticity is derived. The choice of a design in terms of the global level α, the global power, the relevant deviations in the population means and variances, as well as the sample size is outlined. Numerical calculations of the actual level and power for the proposed designs show, that for balanced sample sizes the classical uncorrected one-sided t-tests can be used safely without exaggerating the global type I error probability. Finally an example is given.     

Impact of Chiral Bioanalytical Methods on the Bioequivalence of Ibuprofen Products Containing Ibuprofen Lysinate and Ibuprofen Base

The purpose was to assess the impact of the use of a chiral bioanalytical method on the conclusions of a bioequivalence study that compared two ibuprofen suspensions with different rates of absorption. A comparison of the conclusion of bioequivalence between a chiral method and an achiral approach was made. Plasma concentrations of R‐ibuprofen and S‐ibuprofen were determined using a chiral bioanalytical method; bioequivalence was tested for R‐ibuprofen and for S‐ibuprofen separately and for the sum of both enantiomers as an approach for an achiral bioanalytical method. The 90% confidence interval (90% CI) that would have been obtained with an achiral bioanalytical method (90% CI: C_max: 117.69–134.46; AUC₀^t: 104.75–114.45) would have precluded the conclusion of bioequivalence. This conclusion cannot be generalized to the active enantiomer (90% CI: C_max: 103.36–118.38; AUC₀^t: 96.52–103.12), for which bioequivalence can be concluded, and/or the distomer (90% CI: C_max: 132.97–151.33; AUC₀^t: 115.91–135.77) for which a larger difference was observed. Chiral bioanalytical methods should be required when 1) the enantiomers exhibit different pharmacodynamics and 2) the exposure (AUC or C_max) ratio of enantiomers is modified by a difference in the rate of absorption. Furthermore, the bioequivalence conclusion should be based on all enantiomers, since the distomer(s) might not be completely inert, in contrast to what is required in the current regulatory guidelines. In those cases where it is unknown if the ratio between enantiomers is modified by changing the rate of absorption, chiral bioanalytical methods should be employed unless enantiomers exhibit the same pharmacodynamics. Chirality 28:429–433, 2016. © 2016 Wiley Periodicals, Inc.     

Cross sectional study on cytokine production (TNF-α, IL-8) in German coalminers with progressive massive fibrosis and in control miners using a rapid wholeblood assay

Whole-blood release of tumour necrosis factor (TNF-α) and interleukin 8 (IL-8) was studied in 26 German ex-coalminers with progressive massive fibrosis (≥A, ILO 1980; cases) and 26 ex-miners free of pneumoconiosis (≤ 0/1; controls) using a simple wholeblood assay. Cases and controls were matched individually by age and duration of coalmine dust exposure (5-year window). Whole-blood cytokine release was determined (blinded to case control status) in incubations without additions (spontaneous) and with endotoxin (LPS, 3 ng ml^-1) or with coalmine dust (CMD; 5 mg ml^-1). CMD-stimulated TNF-α release was significantly increased and LPS-induced IL-8 release was significantly decreased in cases (matched t-tests: p < 0.01). No effect of duration of exposure was detectable in an unmatched analysis. No clear relationship with lung function parameters independent from case/control-status was observed, although a possible positive association with central airway resistance was indicated by multiple regression for both CMD stimulated TNF-α and LPS-stimulated IL-8. This study on individually matched coalminers validates previous findings on monocyte TNF release as a marker for pneumoconiosis using a method (whole-blood assay) that is more feasible for epidemiological studies. The different response of TNF-α and IL-8 may be useful in studying the occurrence of different endpoints like pneumoconiosis and lung function decrease.     

Diminished Confidence Levels in the Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y=β₀ + β₁ x + e (model I of linear regression) in the literature confidence estimators of an unknown position x₀ are given at which either the expectation of y is given (see FIELLER, 1944; FINNEY, 1952), or realizations of y are given (see GRAYBILL, 1961). These confidence regions with level 1—α need not be intervals. The occurrence of interval shape is a random event. Its probability is equal to the power of the t test for the examination of the hypothesis H: β₁ = 0. The papers mentioned above claim to provide confidence intervals with level 1 ? α. But because of the restriction of (1 —α)—confidence regions to intervals the true confidence probability is the conditional probability W_c: W_c = P (the confidence region covers x₀| the region has interval shape). Here this conditional probability is shown to be less than 1 —α. Evidence on the possible deviations from 1 —α has been obtained by simulations.     

An Alternative Approach for the Assessment of Bioequivalence Between Two Formulations of a Drug

The problem of the assessment of bioequivalence between a test formulation (T) and a reference formulation (R) of a drug using a two-way crossover experiment is considered. To claim bioequivalence between two formulations, it is required by the United States Food and Drug Administration (FDA) to demonstrate that the true ratio of means μT/μR of pharmacokinetic parameters of concern falls within some reasonable limits (e.g., (80%, 120%)) with certain assurance. A commonly used approach is to construct an approximate 90% confidence interval for μT/μR and compare it with (80%, 120%). In this paper, an exact approach according to the FDA's criteria is proposed. The proposed procedure is derived by constructing an exact confidence region (an ellipse) for (μR, μT) and comparing it with the region bounded by μT = 0.8 μR and μT = 1.2 μR. Bioequivalence is concluded if the ellipse is within the critical region.     

Unconditional Confidence Interval for the Difference between Two Proportions

In applied statistics it is customary to have to obtain a one‐ or two‐tail confidence interval for the difference d = p₂ – p₁ between two independent binomial proportions. Traditionally, one is looking for a classic and non‐symmetric interval (with respect to zero) of the type d ∈ [δ_L;δ_U], d ≤ δ₀ or d ≥ δ₀. However, in clinical trials, equivalence studies, vaccination efficacy studies, etc., and even after performing the classic homogeneity test, intervals of the type |d| ≤ Δ₀ or |d| ≥ Δ₀, where Δ₀ > 0, may be necessary. In all these cases it is advisable to obtain the interval by inverting the appropriate test. The advantage of this procedure is that the conclusions obtained using the test are compatible with those obtained using the interval. The article shows how this is done using the new exact and asymptotic unconditional tests published. The programs for performing these tests may be obtained at URL http://www.ugr.es/~bioest/software.htm.     

Mixed Moment Estimation in Hermite Distribution and its Comparison with Other Estimation Procedures from Sample Size Considerations

In this paper (1) expressions (correct to n^?2 terms) for biases, variances, and covariances of the estimators a and b of Hermite distribution with probability generating function Exp[a(t–1) + b(t–1)] are obtained for two mixed moment estimates; (2) for the biases and variance-covariances, approximate regions of the parameter space (a>0, b>0) have been outlined where a sample of size 100 can be considered as “safe” in the sense that contribution of second order terms in them is 5% of that from the first order term; (3) comparison of the biases and variance-covariances of these two sets of estimators are made with those for the moment estimators, maximum likelihood estimates and the even point estimators for a sample of size 100 using the terms up to order n^?2; (4) the comparisons based on n^?2 terms in (3) have not only provided information on the estimation procedures included in the Hermite distribution, but also demonstrated the importance of higher order terms in the sampling properties of the various alternative techniques for the Hermite distribution.     

Inversion of 310-helix screw sense in a (D-αMe)Leu homotetrapeptide induced by a guest D-(αMe)val residue

The terminally blocked tetrapeptide pBrBz-[D -(αMe)Leu]₂-D -(αMe)Val-D -(αMe)Leu-OtBu is folded in the crystal state in a left-handed 3₁₀-helical structure stabilized by two consecutive 1 ← 4 C?O ?H? N intramolecular H-bonds, as determined by X-ray diffraction analysis. A CD study strongly supports the view that this conformation is also that largely prevailing in MeOH solution. A comparison with the published conformation of pBrBz-[D -(αMe)Leu]₄-OtBu indicates that incorporation of a single internal β-branched (αMe)Val guest residue into the host homo-tetrapeptide from the γ-branched (αMe)Leu residue is responsible for a dramatic structural perturbation, i.e. an inversion of the 3₁₀ screw sense from right to left-handed.     

Functional analysis of a t complex responder locus transgene in mice

Transmission ratio distortion (TRD) of mouse t haplotypes occurs through the interaction of multiple distorter loci with the t complex responder (Tcr) locus. Males heterozygous for a t haplotype will transmit the t-bearing chromosome to nearly all of their offspring. This process is mediated by the production of functionally inequivalent gametes: wildtype meiotic partners of t spermatozoa are rendered functionally inactive. The Tcr locus, which is required for TRD to occur, is thought to somehow protect its host spermatid from the sperm-inactivating effects of linked distorter genes (Lyon 1984). In previous work, Tcr was mapped to a small genetic interval in t haplotypes, and a candidate gene from this region was isolated (Tcp-10b ^t). In this work, we further localize Tcr to a 40-kb region that contains the 21-kb Tcp-10b ^t gene. A cloned genomic copy of Tcp-10b ^t was used to generate transgenic mice. The transgene was bred into a variety of genetic backgrounds to test for non-Mendelian segregation. Abberrant segregation was observed in some mice carrying either a complete t haplotype or a combination of certain partial t haplotypes. These observations, coupled with those of Snyder and colleagues (in this issue), provide genetic and functional evidence that the Tcp-10b ^t gene is Tcr. However, other genotypes that were predicted to produce distortion did not. The unexpected data from a variety of crosses in this work and those of our colleagues suggest that elements to the TRD system and the Tcr locus remain to be identified.     

Convenient Synthesis of 2′-Deoxy-2-fluoroadenosine from 2-Fluoroadenine

Abstract

A convenient synthesis of 2′-deoxy-2-fluoroadenosine from commercially available 2-fluoroadenine is described. The coupling reaction of silylated 2-fluoroadenine with phenyl 3,5-bis[O-(t-butyldimethylsilyl)]-2-deoxy-1-thio-D-erythro-pentofuranoside gave the corresponding 2-fluoro-2′-deoxyadenosine derivative (α/β =1:1) in good yield. The α- and β-anomers were separated by chromatography, and then desilylated to give compounds 1a and 1b.     

On Confidence Interval Construction for Establishing Equivalence of Two Binary-Outcome Treatments in Matched-Pair Studies in the Presence of Incomplete Data

Matched-pair design is often adopted in equivalence or non-inferiority trials to increase the efficiency of binary-outcome treatment comparison. Briefly, subjects are required to participate in two binary-outcome treatments (e.g., old and new treatments via crossover design) under study. To establish the equivalence between the two treatments at the α significance level, a (1−α)100% confidence interval for the correlated proportion difference is constructed and determined if it is entirely lying in the interval (−δ ₀,δ ₀) for some clinically acceptable threshold δ ₀ (e.g., 0.05). Nonetheless, some subjects may not be able to go through both treatments in practice and incomplete data thus arise. In this article, a hybrid method for confidence interval construction for correlated rate difference is proposed to establish equivalence between two treatments in matched-pair studies in the presence of incomplete data. The basic idea is to recover variance estimates from readily available confidence limits for single parameters. We compare the hybrid Agresti–Coull, Wilson score and Jeffreys confidence intervals with the asymptotic Wald and score confidence intervals with respect to their empirical coverage probabilities, expected confidence widths, ratios of left non-coverage probability, and total non-coverage probability. Our simulation studies suggest that the Agresti–Coull hybrid confidence intervals is better than the score-test-based and likelihood-ratio-based confidence interval in small to moderate sample sizes in the sense that the hybrid confidence interval controls its true coverage probabilities around the pre-assigned coverage level well and yield shorter expected confidence widths. A real medical equivalence trial with incomplete data is used to illustrate the proposed methodologies.     

Sequence of the t complex Tcp-10a t gene and examination of the Tcp-10 t gene family

Transmission ratio distortion (TRD) is a property of complete t haplotypes which results in the preferential transmission of the t haplotype chromosome from heterozygous t/+ males to the majority of the offspring. A candidate gene for one of the primary genetic elements in TRD, the t complex responder locus has recently been suggested to be Tcp-10b ^t. There are multiple, functional Tcp-10 ^t genes, but genetic data suggest the presence of the Tcp-10a ^t gene alone is compatible with normal transmission ratios. Here we present the complete sequence and genomic structure of the Tcp-10a ^t gene which is compared with sequence data from a number of cDNAs and genomic subclones representing all active Tcp-10 ^t family genes. A detailed table of all sequence variants discovered in the course of our investigation is presented, and we have clarified the extent of 5 untranslated alternative splicing patterns exhibited by this gene family. A 60 base pair (bp) in-frame deletion from the 5 end of exon 3 of the Tcp-10a ^t gene is also presented and compared with the equivalent region of Tcp-10b ^t and Tcp-10c ^t. A search of the University of Edinburgh database has revealed a significant homology between the Tcp-10b ^t open reading frame and several cytosolic filament proteins. Interestingly, the region of homology is involved in the deletion from the Tcp-10a ^t gene.     

Crystal structure of Boc-Ala-Aib-Ala-Aib-Aib-methyl ester,a pentapeptide fragment of the channel-forming ionophore suzukacillin

t-Buthyoxycarbonyl-L -alanyl-α-aminiosobutyryl-L -alanyl-α-aminoisobutyryl-α-aminoisobutyric acid methyl ester (t-Boc-L -Ala-Aib-L -Ala-Aib-Aib-OMe), C₂₄H₄₃N₅O₈, an end-protected pentapeptide with a sequence corresponding to the 6th through the 10th residues in suzukacillin, crystallizes in the orthorhombic space group P2₁2₁2₁ with a = 11.671, b = 14.534, c = 17.906 Å and z = 4. The molecule exists as a right-handed 3₁₀-helix with a pitch of 6.026 Å. The helix is stabilized by three 4 → 1 hydrogen bonds with the NH groups of Ala(3), Aib(4), and Aib(5) hydrogen bonding to the carbonyl oxygens of t-Boc, Ala(1), and Aib(2), respectively. The helical molecules arrange themselves in a head-to-tail fashion along the a direction in such a way that the NH groups of Ala(1) and Aib(2) hydrogen bond to the carbonyl oxygens of Aib(4) and Aib(5), respectively, of a translationally related molecule. The helical columns thus formed close-pack nearly hexagonally to form the crystal.     

Effects of the Mode of Competition on Stationary Size Distribution in Plant Populations

The effects of the mode of between-individual competition onthe stationary size distribution in uneven-aged and continuallyreproducing tree populations were investigated theoretically,based on the diffusion and continuity equation models. The B(t,x) function, which gives a measure proportional to total leafarea of individual trees larger than dbh (trunk diameter atbreast height) x at time t, expresses the effect of one-sidedcompetition on the subject individual of dbh x. The effect oftwo-sided competition on individuals of any size is equallygiven by B(t, x₀), i.e. total leaf area of the stand (or LAI),where x₀ is the minimum dbh. The following two points, whichwere shown by Kohyama (1991) from results of model simulation,were theoretically derived: (1) the effect of the diffusionterm [D(t, x) function] of the diffusion model on the stationarysize distribution is small for the range of parameter valuesobtained empirically for the warm-temperate and tropical rainforests; (2) the shape of the stationary size distribution underone-sided competition is less changed by a change in the seedlingsupply rate than under two-sided competition. The followingtwo points were further shown theoretically: (3) one-sided competitionis likely to lead to a monotonically decreasing size distributionof dbh with the peak at x = x₀, which is a characteristic ofthe rain forest; (4) the slope of size distribution of dbh steepensas one-sided competition intensifies. Relationships betweenthe mode of competition and the stability of population structure,and general functional forms of one-sided and two-sided competitionare discussed. Diffusion model, one-sided competition, stability of population structure, stationary size distribution, two-sided competition     

How to Use the Two Sample t-Test

This work discusses how two sample t-tests behave when applied to data that may violate the classical statistical assumptions of independence, heteroscedasticity and Gaussianity. The usual two sample t-statistic based on a pooled variance estimate and the Welch-Aspin statistic are treated in detail. Practical “rules-of-thumb” are given along with their applications to various examples so that readers will easily be able to use such tests on their own data sets.     

Separation of supercoiled and open-circular plasmid DNA by liquid-liquid counter-current chromatography

We report for the first time the use of liquid-liquid counter-current chromatography (CCC) for the preparative scale fractionation of plasmid DNA. Almost complete fractionation of supercoiled and open circular plasmid DNA (6.9 kb) could be achieved using a phase system comprising 12.5% (w/w) PEG 600 and 18% (w/w) K₂HPO₄. Experiments were carried out on a Brunel J-type CCC machine (100 ml PTFE coil) at a mobile phase flow rate of 0.5 ml min^{– 1} and a rotational speed of 600 rpm. Compared to conventional HPLC techniques the capacity of CCC is not limited by the surface area of resin available for adsorption. Symbols: C _b, Concentration of plasmid in lower phase (g ml^–1); C _t, Concentration of plasmid in upper phase (g ml^–1); CV, Total volume of mobile phase present in the coil and connecting leads (ml); K, Equilibrium solute partition coefficient (K=C _t/C _b); OC, Open circular plasmid; SC, Supercoiled plasmid; S _f, Percentage stationary phase retention (S _f=V _s/V _c); t _s, Time for phase separation (s); V _b, Volume of bottom phase (ml); V _c, Coil volume (ml); V _m, Volume of mobile phase present in coil at equilibrium (ml); V _r, Volume ratio of two phases (V _r=V _t/V _b); V _s, Volume stationary phase present in coil at equilibrium (ml); V _t, Volume of top phase (ml); V _tot, Total volume of phase system (ml).     

Structural versatility of peptides from Cα,α-disubstituted glycines: Preferred conformation of the chiral isovaline residue

The molecular structures of four protected isovaline- (Iva-) containing peptides to the pentamer level have been determined by x-ray diffraction. The peptides are t-Boc-Ala-(S)-Iva-Ala-OMe (t-Boc : tert-butyloxycarbonyl; OMe : methoxy) and its (R)-Iva diastereomer, and t-Boc-[Ala-(R)-Iva]₂-Ala-OH and its (S)-Iva diastereomeric methyl ester analogue. The two tripeptides are folded in an open type II β-bend conformation. The fully developed right-handed 3₁₀-helix formed by the (R)-Iva pentapeptide, which includes an unusual intramolecular (acid) O? H ?O?C(peptide) H bond, is partially unfolded (near the C-terminus) in the (S) -Iva pentapeptide. ¹H-nmr and Fourier transform ir absorption studies suggest that in CDCl₃ solution (a) the two tripeptides maintain a type II β-bend conformation of comparable stability and (b) both diastereomeric pentapeptide sequences adopt a fully developed 3₁₀-helix. A comparison with the preferred conformation of other extensively investigated C^α,α-disubstituted glycines is made and the implications for the use of the Iva residue in designing conformationally constrained analogues of bioactive peptides are briefly discussed.     

Genetic variation in oxytocin rs2740210 and early adversity associated with postpartum depression and breastfeeding duration

Mothers vary in duration of breastfeeding. These individual differences are related to a variety of demographic and individual maternal factors including maternal hormones, mood and early experiences. However, little is known about the role of genetic factors. We studied single‐nucleotide polymorphisms (SNPs) in the OXT peptide gene (rs2740210; rs4813627) and the OXT receptor gene (OXTR rs237885) in two samples of mothers from the Maternal adversity, Vulnerability and Neurodevelopment study (MAVAN), a multicenter (Hamilton and Montreal, Canada) study following mothers and their children from pregnancy until 7 years of age. Data from the Hamilton site was the primary sample (n = 201) and data from Montreal was the replication sample (n = 151). Breastfeeding duration, maternal mood (measured by the CES‐D scale) and early life adversity (measured by the CTQ scale) were established during 12 months postpartum. In our primary sample, polymorphisms in OXT rs2740210, but not the other SNPs, interacted with early life adversity to predict variation in breastfeeding duration (overall F_8,125 = 2.361, P = 0.021; interaction effect b = ?8.12, t = ?2.3, P = 0.023) and depression (overall F_8,118 = 5.751, P ≤ 0.001; interaction effect b = 6.06, t = 3.13, P = 0.002). A moderated mediation model showed that higher levels of depression mediated the inverse relation of high levels of early life adversity to breastfeeding duration, but only in women possessing the CC genotype [effect a′ = ?3.3401, 95% confidence interval (CI) = ?7.9466 to ?0.0015] of the OXT SNP and not in women with the AA/AC genotype (a′ = ?1.2942, ns). The latter findings (moderated mediation model) were replicated in our Montreal sample (a′ = ?0.277, 95% CI = ?0.7987 to ?0.0348 for CC; a′ = ?0.1820, ns for AA/AC) .     

Mapping and validation of quantitative trait loci for spikelets per panicle and 1,000-grain weight in rice (Oryza sativa L.)

This study identified four and five quantitative trait loci (QTLs) for 1,000-grain weight (TGW) and spikelets per panicle (SPP), respectively, using rice recombinant inbred lines. QTLs for the two traits (SPP3a and TGW3a, TGW3b and SPP3b) were simultaneously identified in the two intervals between RM3400 and RM3646 and RM3436 and RM5995 on chromosome 3. To validate QTLs in the interval between RM3436 and RM5995, a BC₃F₂ population was obtained, in which TGW3b and SPP3b were simultaneously mapped to a 2.6-cM interval between RM15885 and W3D16. TGW3b explained 50.4% of the phenotypic variance with an additive effect of 1.81 g. SPP3b explained 29.1% of the phenotypic variance with an additive effect of 11.89 spikelets. The interval had no effect on grain yield because it increased SPP but decreased TGW and vice versa. Grain shape was strongly associated with TGW and was used for QTL analysis in the BC₃F₂ population. Grain length, grain width, and grain thickness were also largely controlled by TGW3b. At present, it is not clear whether one pleiotropic QTL or two linked QTLs were located in the interval. However, the conclusion could be made ultimately by isolation of TGW3b. The strategy for TGW3b isolation is discussed.     

Confidence Intervals for the Risk Ratio in Cohort Studies under Inverse Sampling

Three simple interval estimates for the risk ratio in inverse sampling are considered. The first two interval estimates are derived on the basis of Fieller's Theorem and the delta method with the logarithmic transformation, respectively. The third interval estimate is derived on the basis of an F-test statistic proposed by BENNETT (1981) for testing equal probabilities of a disease between two comparison groups when the disease is rare. To evaluate the performance of these three methods, a Monte Carlo simulation is used to compare the actual coverage probability with the nominal confidence level for each method and to estimate the expected length of the corresponding confidence interval in a variety of situations. On the basis of the results found in the simulation, we have concluded that the method with the logarithmic transformation is either equivalent to or better than the other two methods for all situations considered here.