The structural error-in-equation model to evaluate individual bioequivalence

Individual bioequivalence is assessed using an extension of the classical structural equation model, known as the error-in-equation model. This procedure estimates the relationship between individual means, as well as the variance-covariance parameters, of the bioavailabilities measurement model, by considering individual means related through a straight line with a random term, whereas the classical structural equation considers a deterministic linear relationship. We discuss the implications of this approach in terms of the bioavailabilities measurement model and how to test the overall hypothesis of individual bioequivalence. Both models are compared in a simulation study and a case example is presented.     

First Passage Time Models for Prediction of Developmental Stages

The problem of predicting the date of a developmental stage for plants or animals is formulated as a first passage time problem for a random process, e.g. accumulated degree-days. By a suitable embedding in a continuous time model the likelihood becomes a smooth function of the parameters, which may be estimated by use of the maximum likelihood method. A set of data on waiting times from sowing to heading for spring barley is analysed. For data of this type we suggest models with variance components corresponding to stations and years. Modifications to take into account variables in addition to temperature, e.g. day length, soil properties and variety effects are briefly discussed. The transform both sides technique of CARROLL and RUPPERT (1984) is used to stabilize the variance and to achieve approximate normality of the residuals.     

Cultivar x environment interactions in sorghum,Sorghum bicolor (L.) moench

Summary The most significant and important interactions in 2, and 3-year sorghum zonal trials were location x year, cultivar x location and cultivar x location x year. Cultivar x year interaction was significant in one out of four ecologic zones used in the trials. The variance components were relatively small with the second order interaction variance component larger than the first order types involving cultivars. Environmental variance was the largest in all four zones.Computations on theoretical standard error of cultivar means suggest that six replications, eight locations and four years is an ideal testing procedure in the Northern Guinea Savanna, while in the Sudan Savanna, the combination is better with four replications, eight locations and three years. The true value or performance of a variety is most effectively obtained by increasing the number of years, while increasing number of replications is the least effective.     

Development of a sensitive high-performance thin-layer chromatography method for estimation of ranitidine in urine and its application for bioequivalence decision for ranitidine tablet formulations

A sensitive and simple HPTLC method was developed for estimation of ranitidine in human urine. The drug was extracted from urine after basification using dichloromethane. Dichloromethane extract was spotted on silica gel 60 F254 TLC plate and was developed in a mixture of ethyl acetate-methanol-ammonia (35:10:5 v/v) as the mobile phase and scanned at 320 nm. The RF value obtained for the drug was 0.67 +/- 0.03. The method was validated in terms of linearity (50-400 ng/spot), precision and accuracy. The average recovery of ranitidine from urine was 89.35%. The proposed method was applied to evaluate bioequivalence of two marketed ranitidine tablet formulations (150 mg, Formulation I and Formulation 2) using a crossover design by comparing urinary excretion data for unchanged ranitidine in six healthy volunteers. Various pharmacokinetic parameters like peak excretion rate [(dAU/dt)max], time for peak excretion rate (tmax), AUC0-24, AUC0-infinity, cumulative amount excreted were calculated for both formulations and subjected to statistical analysis. The relative bioavailability of Formulation 2 with respect to Formulation 1 was 93.76 and 95.31% on the basis of AUC0-24 and cumulative amount excreted, respectively. Statistical comparison of various pharmacokinetic parameters indicated that the two ranitidine tablet formulations are bioequivalent.     

Robustified maximum likelihood estimation in generalized partial linear mixed model for longitudinal data

Summary .  In this article, we study the robust estimation of both mean and variance components in generalized partial linear mixed models based on the construction of robustified likelihood function. Under some regularity conditions, the asymptotic properties of the proposed robust estimators are shown. Some simulations are carried out to investigate the performance of the proposed robust estimators. Just as expected, the proposed robust estimators perform better than those resulting from robust estimating equations involving conditional expectation like Sinha (2004, Journal of the American Statistical Association 99, 451–460) and Qin and Zhu (2007, Journal of Multivariate Analysis 98, 1658–1683). In the end, the proposed robust method is illustrated by the analysis of a real data set.     

Permutation tests for random effects in linear mixed models

Inference regarding the inclusion or exclusion of random effects in linear mixed models is challenging because the variance components are located on the boundary of their parameter space under the usual null hypothesis. As a result, the asymptotic null distribution of the Wald, score, and likelihood ratio tests will not have the typical χ(2) distribution. Although it has been proved that the correct asymptotic distribution is a mixture of χ(2) distributions, the appropriate mixture distribution is rather cumbersome and nonintuitive when the null and alternative hypotheses differ by more than one random effect. As alternatives, we present two permutation tests, one that is based on the best linear unbiased predictors and one that is based on the restricted likelihood ratio test statistic. Both methods involve weighted residuals, with the weights determined by the among- and within-subject variance components. The null permutation distributions of our statistics are computed by permuting the residuals both within and among subjects and are valid both asymptotically and in small samples. We examine the size and power of our tests via simulation under a variety of settings and apply our test to a published data set of chronic myelogenous leukemia patients.     

Lower Confidence Limits for the Positive Linear Combination of two Variances

An alternative method for determining the approximate lower confidence limits for the positive linear combination of two variances based on an approach similar to BULMER (1957) has been proposed. The probability coverage of the proposed alternative limits has been compared with the other existing methods.     

A Measure to Evaluate the Closeness of Satterthwaite's Approximation

Satterthwaite's approximation of the distribution of a nonnegative linear combination of independent mean squares is addressed in this article. A measure is developed to quantify the closeness of this approximation by using certain optimization results given by THIBAUDEAU and STYAN (1985). The main advantage of the proposed measure is to provide a theoretical framework for determining conditions under which Satterthwaite's approximation may be inadequate. This is demonstrated in three examples portraying frequently encountered problems in analysis of variance.     

A likelihood approach for quantitative-trait-locus mapping with selected pedigrees

Selective sampling is a cost-effective design for mapping quantitative trait loci (QTLs). A unified framework, which naturally combines two complementary sources of linkage information in the data, is proposed for the mapping of QTLs using selected pedigrees. Score statistics for detecting linkage are introduced for single-locus models (univariate or bivariate phenotypes) and two-locus epistasis models. A computer implementation of the methods for single-locus univariate-phenotype models is provided for nuclear families with arbitrary number of sibs and is freely available.     

How Large is the Probability for the Estimate of a Variance Component to be Negative?

For a balanced one-way classification, where the normally distributed observations obey a random model y_ij=μ+b_i+c_ij with two variance components var (b_i) = δ and var (c_ij) = δ, the probability is given that the analysis of variance estimate of δ will be negative. This probability depends on δ/δ and the degrees of freedom in the ANOVA table. Tables for this probability are given. If the normally distributed observations obey an intra-class correlation model, the probability that the Mean Square between groups is smaller than the Mean Square within groups can also be evaluated from the given tables.     

Genetic parameters affecting 180-days standardised milk yield, test-day milk yield and lactation length in Spanish Assaf (Assaf.E) dairy sheep

A total of 42,197 records of test-day milk yield (TDY) and 7654 lactations from 3854 individuals belonging to the Spanish Assaf (Assaf.E) breed were analysed using univariate and multivariate models to estimate genetic parameters affecting TDY, total milk yield standardised to 180 days (MY₁₈₀) and lactation length (LL) in order to asses their possibilities of use in the selection scheme of the Assaf.E population. Estimates of h² were, in general, on the lower limit of those usually reported for the three analysed traits. Estimates of heritability for MY₁₈₀ varied from 0.131 to 0.177. Estimates of h² for LL and TDY were consistent regardless the estimation model being of, roughly, 5% and 10%, respectively. The estimates for the permanent environmental effect (c²) of TDY were consistently the same (0.27–0.28) regardless the fitted model whilst they showed large differences for LL and MY₁₈₀. Genetic correlations were always positive and high ranging from 0.792 for the pair LL-TDY to 0.999 for the pair MY₁₈₀-TDY. Correlations between permanent environmental effects were even higher ranging from 0.932 for the pair LL-MY₁₈₀ and 0.999 for the pair MY₁₈₀-TDY. The advantages of using TDY as selection criterion in the Assaf.E improvement scheme are discussed.     

Testing random effects in the linear mixed model using approximate bayes factors

Summary .  Deciding which predictor effects may vary across subjects is a difficult issue. Standard model selection criteria and test procedures are often inappropriate for comparing models with different numbers of random effects due to constraints on the parameter space of the variance components. Testing on the boundary of the parameter space changes the asymptotic distribution of some classical test statistics and causes problems in approximating Bayes factors. We propose a simple approach for testing random effects in the linear mixed model using Bayes factors. We scale each random effect to the residual variance and introduce a parameter that controls the relative contribution of each random effect free of the scale of the data. We integrate out the random effects and the variance components using closed-form solutions. The resulting integrals needed to calculate the Bayes factor are low-dimensional integrals lacking variance components and can be efficiently approximated with Laplace's method. We propose a default prior distribution on the parameter controlling the contribution of each random effect and conduct simulations to show that our method has good properties for model selection problems. Finally, we illustrate our methods on data from a clinical trial of patients with bipolar disorder and on data from an environmental study of water disinfection by-products and male reproductive outcomes.     

Bayesian Inference for Smoking Cessation with a Latent Cure State

Summary .  We present a Bayesian approach to modeling dynamic smoking addiction behavior processes when cure is not directly observed due to censoring. Subject-specific probabilities model the stochastic transitions among three behavioral states: smoking, transient quitting, and permanent quitting (absorbent state). A multivariate normal distribution for random effects is used to account for the potential correlation among the subject-specific transition probabilities. Inference is conducted using a Bayesian framework via Markov chain Monte Carlo simulation. This framework provides various measures of subject-specific predictions, which are useful for policy-making, intervention development, and evaluation. Simulations are used to validate our Bayesian methodology and assess its frequentist properties. Our methods are motivated by, and applied to, the Alpha-Tocopherol, Beta-Carotene Lung Cancer Prevention study, a large (29,133 individuals) longitudinal cohort study of smokers from Finland.     

Variance in animal longevity: contributions of heterogeneity and stochasticity

Variance in longevity among individuals may arise as an effect of heterogeneity (differences in mortality rates experienced at the same age or stage) or as an effect of individual stochasticity (the outcome of random demographic events during the life cycle). Decomposing the variance into components due to heterogeneity and stochasticity is crucial for evolutionary analyses.In this study, we analyze longevity from ten studies of invertebrates in the laboratory, and use the results to partition the variance in longevity into its components. To do so, we fit finite mixtures of Weibull survival functions to each data set by maximum likelihood, using the EM algorithm. We used the Bayesian Information Criterion to select the most well supported model. The results of the mixture analysis were used to construct an age × stage-classified matrix model, with heterogeneity groups as stages, from which we calculated the variance in longevity and its components. Almost all data sets revealed evidence of some degree of heterogeneity. The median contribution of unobserved heterogeneity to the total variance was 35%, with the remaining 65% due to stochasticity. The differences among groups in mean longevity were typically on the order of 30% of the overall life expectancy. There was considerable variation among data sets in both the magnitude of heterogeneity and the proportion of variance due to heterogeneity, but no clear patterns were apparent in relation to sex, taxon, or environmental conditions.     

Robust estimation of multivariate covariance components

In many settings, such as interlaboratory testing, small area estimation in sample surveys, and heritability studies, investigators are interested in estimating covariance components for multivariate measurements. However, the presence of outliers can seriously distort estimates obtained using standard procedures such as maximum likelihood. We propose a procedure based on M-estimation for robustly estimating multivariate covariance components in the presence of outliers; the procedure applies to balanced and unbalanced data. We present an algorithm for computing the robust estimates and examine the performance of the estimator through a simulation study. The estimator is used to find covariance components and identify outliers in a study of variability of egg length and breadth measurements of American coots.     

Using X-ray CT based tree-ring width data for tree growth trend analysis

Changes in the environment influence the growth of tree species in Europe. Understanding the drivers of these growth changes is important to predict further growth and adapt forest management. To disentangle the different drivers of growth changes, it is common practice to apply mixed modeling techniques to tree-ring width series. Mixed modeling requires precise, replicated and well cross-dated tree-ring width series. The goal of this study was to compare a recently developed ring width measuring method based on X-ray Computed Tomography images (CT scan) with the standard LINTAB measuring method and to examine whether the same growth trends are detected with both methods using common beech (Fagus sylvatica) and sessile oak trees (Quercus petraea) as a case study. Although the CT scan method has a lower resolution than LINTAB measurements, it is of interest since it measures wood density in addition to ring width and it is less laborious in comparison to standard ring width measuring methods. No significant differences in ring width were found between the two measuring methods. The small non-significant difference between the two methods could largely be explained by the drying of cores needed for CT scanning. The same growth trends were detected with both methods: for common beech and sessile oak in Southern Belgium. These findings suggest that ring widths measured on CT scan images can be used as input for long-term modeling of tree growth changes for the targeted tree species.     

The effects of selection for gain in mice on the direct-maternal genetic correlation

Components of genetic variation for postweaning growth traits were estimated for both control and growth stocks of mice. The effect of phenotypic selection for gain, which genetically combines selection for additive direct and maternal effects, on additive genetic variance components, heritability, and additive genetic correlationsis discussed. Quantitative genetic theory predicts that simultaneous selection for two metric traits in the same direction will cause the genetic correlation between the two traits to become more negative. The results presented in this paper conflict with this theory. The direct-maternal additive genetic correlation was more negative in the control line (with 356 mice) than in the growth-selected line (with 320 mice) for the three traits analyzed (0.310 vs 0.999 for 21-day weight, 0.316 vs 1.000 for 42-day weight, and 0.506 vs 1.000 for gain from 21–42 days). Estimates were obtained by restricted maximum likelihood (REML) computed under a derivative free algorithm (DFREML).     

Confidence Intervals on Ratios of Variance Components for the Unbalanced Two Factor Nested Model

The model considered in this article is the two-factor nested unbalanced variance component model: for p = 1, 2, …, P; q = 1, 2, …, Q_p; and r = 1, 2, …, R_pq. The random variables Y_pqr are observable. The constant μ is an unknown parameter, and A_p, B_pq and C_pqr are (unobservable) normal and independently distributed random variables with zero means and finite variances σ²_A, σ²_B, and σ²_C, respectively. Approximate confidence intervals on ?_A and ?_B using unweighted means are derived, where The performance of these approximate confidence intervals are evaluated using computer simulation. The simulated results indicate that these proposed confidence intervals perform satisfactorily and can be used in applied problems.