Bioequivalence trials with the incomplete 3 x 3 crossover design

In bioequivalence trials, one often considers two or more generic products with the original one. The 3 x 3 crossover design can be adopted to evaluate the two generic candidates with a brand name drug, rather than conducting two separate 2 x 2 crossover trials. Dropouts, however, are more likely to occur due to various administrative reasons when we consider a higher order crossover design. A modified method, which was originally given by Chow and Shao (1997), is extended to compare two generic products with a reference in the incomplete 3 x 3 crossover design. A simulation study and discussion are also presented.     

Genotype x environment interaction of crossover type: detecting its presence and estimating the crossover point

Genotype-environment interaction (GEI) introduces inconsistency in the relative rating of genotypes across environments and plays a key role in formulating strategies for crop improvement. GEI can be either qualitative (i.e., crossover type) or only quantitative (i.e., non-crossover type). Since the presence of crossover-type interaction has a strong implication for breeding for specific adaptation, it is important to assess the frequency of crossover interactions. This paper presents a test for detecting the presence of crossover-type interaction using the response-environment relationship and enumerates the frequency of crossovers and estimation of the crossover point (CP) on the environment axis, which serves as a cut-off point for the two environments groups where different/specific selections can be made. Sixty-four barley lines with various selection histories were grown in northern Syria and Lebanon giving a total of 21 environments (location-year combinations). Linear regression of the genotypic response on the environmental index represented a satisfactory model, and heterogeneity among regressions was significant. At a 5% level of significance, 38% and 19% of the pairs showed crossover interactions when the error variances were considered heterogeneous and homogeneous, respectively, implying that an appreciable number of crossovers took place in the case of barley lines responding to their environments. The CP of 1.64 t/ha, obtained as the CP of regression lines between the genotype numbers 19 and 31, provided maximum genotype x environment-group interaction. Across all environments, genotype nos. 59 and 12 stood first and second for high yield, respectively. The changes in the ranks of genotypes under the groups of environments can be used for selecting specifically adapted genotypes. Received: 25 January 1999 / Accepted: 16 March 1999     

Matrix-based concordance correlation coefficient for repeated measures

Summary In many clinical studies, Lin's concordance correlation coefficient (CCC) is a common tool to assess the agreement of a continuous response measured by two raters or methods. However, the need for measures of agreement may arise for more complex situations, such as when the responses are measured on more than one occasion by each rater or method. In this work, we propose a new CCC in the presence of repeated measurements, called the matrix‐based concordance correlation coefficient (MCCC) based on a matrix norm that possesses the properties needed to characterize the level of agreement between two p× 1 vectors of random variables. It can be shown that the MCCC reduces to Lin's CCC when p= 1. For inference, we propose an estimator for the MCCC based on U‐statistics. Furthermore, we derive the asymptotic distribution of the estimator of the MCCC, which is proven to be normal. The simulation studies confirm that overall in terms of accuracy, precision, and coverage probability, the estimator of the MCCC works very well in general cases especially when n is greater than 40. Finally, we use real data from an Asthma Clinical Research Network (ACRN) study and the Penn State Young Women's Health Study for demonstration.     

Behavioral testing of antidepressant compounds: an analysis of crossover design for correlated binary data

The differential reinforcement of low-rate 72 seconds schedule (DRL-72) is a standard behavioral test procedure for screening potential antidepressant compounds. The protocol for the DRL-72 experiment, proposed by Evenden et al. (1993), consists of using a crossover design for the experiment and one-way ANOVA for the statistical analysis. In this paper we discuss the choice of several crossover designs for the DRL-72 experiment and propose to estimate the treatment effects using either generalized linear mixed models (GLMM) or generalized estimating equation (GEE) models for clustered binary data.     

Tests of significance for point-biserial rank correlation coefficients in the presence of ties

This paper deals with exact and asymptotic tests of significance of the point-biserial rank correlations of the KENDALL and SPEARMAN tests when ties are present and mid-ranks are assigned to tied values.     

On the relationship between cumulative correlation coefficients and the quality of crystallographic data sets

In 2012, Karplus and Diederichs demonstrated that the Pearson correlation coefficient CC_1/2 is a far better indicator of the quality and resolution of crystallographic data sets than more traditional measures like merging R‐factor or signal‐to‐noise ratio. More specifically, they proposed that CC_1/2 be computed for data sets in thin shells of increasing resolution so that the resolution dependence of that quantity can be examined. Recently, however, the CC_1/2 values of entire data sets, i.e., cumulative correlation coefficients, have been used as a measure of data quality. Here, we show that the difference in cumulative CC_1/2 value between a data set that has been accurately measured and a data set that has not is likely to be small. Furthermore, structures obtained by molecular replacement from poorly measured data sets are likely to suffer from extreme model bias.     

A Bayesian analysis of the two-period crossover design for clinical trials

Statisticians have been critical of the use of the two-period crossover designs for clinical trials because the estimate of the treatment difference is biased when the carryover effects of the two treatments are not equal. In the standard approach, if the null hypothesis of equal carryover effects is not rejected, data from both periods are used to estimate and test for treatment differences; if the null hypothesis is rejected, data from the first period alone are used. A Bayesian analysis based on the Bayes factor against unequal carryover effects is given. Although this Bayesian approach avoids the "all-or-nothing" decision inherent in the standard approach, it recognizes that with small trials it is difficult to provide unequivocal evidence that the carryover effects of the two treatments are equal, and thus that the interpretation of the difference between treatment effects is highly dependent on a subjective assessment of the reality or not of equal carryover effects.     

Review fluorescence correlation spectroscopy for probing the kinetics and mechanisms of DNA hairpin formation

This article reviews the application of fluorescence correlation spectroscopy (FCS) and related techniques to the study of nucleic acid hairpin conformational fluctuations in free aqueous solutions. Complimentary results obtained using laser-induced temperature jump spectroscopy, single-molecule fluorescence spectroscopy, optical trapping, and biophysical theory are also discussed. The studies cited reveal that DNA and RNA hairpin folding occurs by way of a complicated reaction mechanism involving long- and short-lived reaction intermediates. Reactions occurring on the subnanoseconds to seconds time scale have been observed, pointing out the need for experimental techniques capable of probing a broad range of reaction times in the study of such complex, multistate reactions.     

A Note on Two‐Sample Tests for Comparing Intra‐Individual Genetic Sequence Diversity between Populations

Summary Gilbert, Rossini, and Shankarappa (2005 , Biometrics 61 , 106‐117) present four U‐statistic based tests to compare genetic diversity between different samples. The proposed tests improved upon previously used methods by accounting for the correlations in the data. We find, however, that the same correlations introduce an unacceptable bias in the sample estimators used for the variance and covariance of the inter‐sequence genetic distances for modest sample sizes. Here, we compute unbiased estimators for these and test the resulting improvement using simulated data. We also show that, contrary to the claims in Gilbert et al., it is not always possible to apply the Welch–Satterthwaite approximate t‐test, and we provide explicit formulas for the degrees of freedom to be used when, on the other hand, such approximation is indeed possible.