Optimal design of complex experiments with qualitative factors of influence

A complex experiment with qualirarive factors influencing the outcome of the experiment can be seen as a general ANOVA setup. A design of such an experiment will be the assignment at which of the possible levels of the factors the actual experiment should be performed. In this paper optimal designs of such experiments will be characterized with respect to three different optimality criteria including the so called uniform optimality of a design. The possible applications of the main optimization result providing these characterizations can be used to more general experiments. The particular results on these generalizations will be indicated at the end of this paper.     

Polynomial regression with errors in the variables

A polynomial functional relationship with errors in both variables can be consistently estimated by constructing an ordinary least squares estimator for the regression coefficients, assuming hypothetically the latent true regressor variable to be known, and then adjusting for the errors. If normality of the error variables can be assumed, the estimator can be simplified considerably. Only the variance of the errors in the regressor variable and its covariance with the errors of the response variable need to be known. If the variance of the errors in the dependent variable is also known, another estimator can be constructed.     

对生产帕累托最优条件充分性的质疑与改进

现有的理论中,生产帕累托最优条件不充分,其最优状态不是唯一的,使得理论自身及随后的应用上产生了一些矛盾。确定唯一最优状态的充分条件应该是：双方都满意的交换利益分割和边际技术替代率相等。前者保证交换实现,后者保证交换产生的利益被完全穷尽。只要遵循新交换原则,交换必能实现,但不一定是帕累托最优。信息不充分时,如果信息不对称者对对方所判断的生产函数改变了其真实生产函数的技术性质,交换虽能实现,但生产并没有达到帕累托最优。     

Insights into the appropriate level of disaggregation for efficient time series model forecasting

This paper provides a potentially valuable insight on how to assess if the forecasts from an autoregressive moving average model based on aggregated data could be substantially improved through disaggregation. It is argued that, theoretically, the absence of moving average (MA) terms indicates that no forecasting efficiency improvements can be achieved through disaggregation. In practice, it is found that there is a strong correlation between the statistical significance of the MA component in the aggregate model and the magnitude of the forecast mean square error (MSE) decreases that can be achieved through disaggregation. That is, if a model includes significant MA terms, the forecast MSE improvements that may be gained from disaggregation could be substantial. Otherwise, they are more likely to be relatively small or non-existent.     

Uniform robustness against nonnormality of the t and f tests

The size of the two-sample t test is generally thought to be robust against nonnormal distributions if the sample sizes are large. This belief is based on central limit theory, and asymptotic expansions of the moments of the t statistic suggest that robustness may be improved for moderate sample sizes if the variance, skewness, and kurtosis of the distributions are matched, particularly if the sample sizes are also equal.

It is shown that asymptotic arguments such as these can be misleading and that, in fact, the size of the t test can be as large as unity if the distributions are allowed to be completely arbitrary. Restricting the distributions to be identical or symmetric (but otherwise arbitrary) does not guarantee that the size can be controlled either, but controlling the tail-heaviness of the distributions does. The last result is proved more generally for the k-sample F test.     

Rank-Based Classification Using Robust Discriminant Functions

The Pareto distribution model assumption in the peaks over threshold method, will be tested by making using of the Kolmogorov–Smirnov goodness of fit method. Pareto distributed variables can be transformed to exponential, and the test will be for exponentiality. It was found that the statistic can be used as an indication of where to choose the threshold and to check the Pareto model assumption.     

A robust Parafac model for compositional data

Compositional data are characterized by values containing relative information, and thus the ratios between the data values are of interest for the analysis. Due to specific features of compositional data, standard statistical methods should be applied to compositions expressed in a proper coordinate system with respect to an orthonormal basis. It is discussed how three-way compositional data can be analyzed with the Parafac model. When data are contaminated by outliers, robust estimates for the Parafac model parameters should be employed. It is demonstrated how robust estimation can be done in the context of compositional data and how the results can be interpreted. A real data example from macroeconomics underlines the usefulness of this approach.     

Significance levels for use in the analysis of combination drug trials

Proof of efficacy of fixed combination drugs under current guidelines requires that the combination be statistically significantly superior to each component and that, to insure model validity, each component be statistically significantly superior to a placebo. Simulations indicate that if each of these four tests is performed at a significance level of 0,05 then the actual test of effectiveness of the fixed combination drug is done at a significance level that can be as small as 0.0001. This would seem to be excessively conservative. Further simulations indicate that significance levels of approximately 0,10 to 0.20 should be employed for all tests except in unusual circumstances.     

Analogies for Helping Clinicians and Investigators Better Understand the Principles and Practice of Biostatistics

For the interaction between the biostatistician and the clinician or research investigator to be successful, it is important not only for the investigator to be able to explain biological and medical principles in a way that can be understood by the biostatistician, so, too, the biostatistician needs tools to help the investigator understand both the practice of statistics and specific statistical methods. In our practice, we have found it useful to draw analogies between statistical concepts and familiar medical or everyday ideas. These analogies help to stress a point or provide an understanding on the part of the investigator. For example, explaining the reason for using a nonparametric procedure (a general procedure used when the underlying distribution of the data is not known or cannot be assumed) by comparing it to using broad spectrum antibiotics (a general antibiotic used when the specific bacteria causing infection is unknown or cannot be assumed) can be an effective teaching tool. We present a variety of useful (and hopefully amusing) analogies that can be adopted by statisticians to help investigators at all levels of experience better understand principles and practice of statistics.     

Use of simulation to compare the performance of minimization with stratified blocked randomization

Minimization is an alternative method to stratified permuted block randomization, which may be more effective at balancing treatments when there are many strata. However, its use in the regulatory setting for industry trials remains controversial, primarily due to the difficulty in interpreting conventional asymptotic statistical tests under restricted methods of treatment allocation. We argue that the use of minimization should be critically evaluated when designing the study for which it is proposed. We demonstrate by example how simulation can be used to investigate whether minimization improves treatment balance compared with stratified randomization, and how much randomness can be incorporated into the minimization before any balance advantage is no longer retained. We also illustrate by example how the performance of the traditional model-based analysis can be assessed, by comparing the nominal test size with the observed test size over a large number of simulations. We recommend that the assignment probability for the minimization be selected using such simulations.     

Editorial collaborators

Traditionally, the bioequivalence of a generic drug with the innovator's product is assessed by comparing their pharmacokinetic profiles determined from the blood or plasma concentration-time curves. This method may only be applicable to formulations where blood drug or metabolites levels adequately characterize absorption and metabolism. For non-systematic drugs categorized by the lack of systemic presence, such as metered dose inhalers (MDI), anti-ulcer agents and topical antifungals and vaginal antifungals, new definition of therapeutic equivalency and criteria for acceptance should be used. When pharmacologic effects of the drugs can be easily measured, pharmacodynamic effect studies can be used to assess the therapeutic equivalence of non-systemic drugs. When analytical methods or other tests cannot be developed to permit use of the pharmacodynamic method, clinical trials to compare one or several clinical endpoints may be the only suitable method to establishing therapeutic equivalence. In this paper we evaluate by Monte-Carlo simulations the fixed sample performances of some two one-sided tests procedures which may be used to assess the therapeutic equivalence of non-systemic drugs with binary clinical endpoints. Formulae of sample size determination for therapeutic equivalence clinical trials are also given.     

Inferential estimation,likelihood, and linear pivotals

A linear pivotal is introduced as a generalization of an estimate. The defining feature of a linear pivotal is that it generates a likelihood function in the same way as does a statistic. This allows the efficiency and sufficiency of the pivotal to be examined. The efficient reduction of data to a linear pivotal can often be achieved when it cannot be achieved using an estimate. Maximum-likelihood estimation can be interpreted as a method of generating approximate sufficient linear pivotals.     

Bivariate log Birnbaum–Saunders distribution

Univariate Birnbaum–Saunders distribution has received a considerable amount of attention in recent years. Rieck and Nedelman (A log-linear model for the Birnbaum–Saunders distribution. Technometrics, 1991;33:51–60) introduced a log Birnbaum–Saunders distribution. The main aim of this paper is to introduce bivariate log Birnbaum–Saunders distribution. The proposed model is symmetric and it has five parameters. It can be obtained using Gaussian copula. Different properties can be obtained using copula structure. It is observed that the maximum likelihood estimators (MLEs) cannot be obtained explicitly. Two-dimensional profile likelihood approach may be adopted to compute the MLEs. We propose some alternative estimators also, which can be obtained quite conveniently. The analysis of one data set is performed for illustrative purposes. Finally, it is observed that this model can be used as a bivariate log-linear model, and its multivariate generalization is also quite straight forward.     

A hierarchical eigenmodel for pooled covariance estimation

Summary.  Although the covariance matrices corresponding to different populations are unlikely to be exactly equal they can still exhibit a high degree of similarity. For example, some pairs of variables may be positively correlated across most groups, whereas the correlation between other pairs may be consistently negative. In such cases much of the similarity across covariance matrices can be described by similarities in their principal axes, which are the axes that are defined by the eigenvectors of the covariance matrices. Estimating the degree of across-population eigenvector heterogeneity can be helpful for a variety of estimation tasks. For example, eigenvector matrices can be pooled to form a central set of principal axes and, to the extent that the axes are similar, covariance estimates for populations having small sample sizes can be stabilized by shrinking their principal axes towards the across-population centre. To this end, the paper develops a hierarchical model and estimation procedure for pooling principal axes across several populations. The model for the across-group heterogeneity is based on a matrix-valued antipodally symmetric Bingham distribution that can flexibly describe notions of 'centre' and 'spread' for a population of orthogonal matrices.     

Approximations for Gibbs Distribution Normalising Constants

A key difficulty in the use of Gibbs prior distributions in Bayesian image analysis is the intractability of the normalisation constant. One approach is to perform off-line simulations which allow a calibration of normalisation constant against prior parameter. In this paper the reverse-logistic regression approach to calibration will be examined for various Gibbs distributions and explicit parametric equations will be proposed. A simple method for combining separate calibrations will be illustrated and the relationship between normalisation constant and image size will be explored with an empirical approximation proposed.     

The Folded Logistic Distribution

ABSTRACT

Physical measurements like dimensions, including time, and angles in scientific experiments are frequently recorded without their algebraic sign. The directions of those physical quantities measured with respect to a frame of reference in most practical applications are considered to be unimportant and are ignored. As a consequence, the underlying distribution of measurements is replaced by a distribution of absolute measurements. When the underlying distribution is logistic, the resulting distribution is called the “folded logistic distribution”. Here, the properties of the folded logistic distribution will be presented and the techniques for estimating parameters will be given. The advantages of using this folded logistic distribution over the folded normal distribution will be discussed and some examples will be cited.     

Choosing Priors for Constrained Analysis of Variance: Methods Based on Training Data

Abstract. This article combines the best of both objective and subjective Bayesian inference in specifying priors for inequality and equality constrained analysis of variance models. Objectivity can be found in the use of training data to specify a prior distribution, subjectivity can be found in restrictions on the prior to formulate models. The aim of this article is to find the best model in a set of models specified using inequality and equality constraints on the model parameters. For the evaluation of the models an encompassing prior approach is used. The advantage of this approach is that only a prior for the unconstrained encompassing model needs to be specified. The priors for all constrained models can be derived from this encompassing prior. Different choices for this encompassing prior will be considered and evaluated.     

Comparing Predictive Accuracy

We propose and evaluate explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts. In contrast to previously developed tests, a wide variety of accuracy measures can be used (in particular, the loss of function need not be quadratic and need not even be symmetric), and forecast errors can be non-Gaussian, nonzero mean, serially correlated, and contemporaneously correlated. Asymptotic and exact finite-sample tests are proposed, evaluated, and illustrated.     

A Study of Interval Censoring in Parametric Regression Models

Parametric models for interval censored data can now easily be fitted with minimal programming in certain standard statistical software packages. Regression equations can be introduced, both for the location and for the dispersion parameters. Finite mixture models can also be fitted, with a point mass on right (or left) censored observations, to allow for individuals who cannot have the event (or already have it). This mixing probability can also be allowed to follow a regression equation.Here, models based on nine different distributions are compared for three examples of heavily censored data as well as a set of simulated data. We find that, for parametric models, interval censoring can often be ignored and that the density, at centres of intervals, can be used instead in the likelihood function, although the approximation is not always reliable. In the context of heavily interval censored data, the conclusions from parametric models are remarkably robust with changing distributional assumptions and generally more informative than the corresponding non-parametric models.     

Synergy evaluation of non-normalizable dose–response data: Generalization of combination index for the linear effect of drugs

The study of drug synergy plays a prominent role in the search for drug combinations with beneficial interactions. Firstly, in this process, the drug-effect response of individual parts and the mixture needs to be derived. This function is usually well described by Hill (or other logistic or sigmoid) curve. Due to its boundedness, it allows the measured data to be normalized. The normalized data can then be processed by interaction analysis using the Loewe, Bliss, or other models to evaluate possible synergy or antagonism of two or more drugs. However, sometimes, the drug-effect responses observed in pharmaceutical research do not appear to be bounded. Theoretically, the drug-effect curve cannot grow to infinity, but it may be impossible to determine its upper bound within the observed region. In this case, standard models cannot be used, since they assume that data are normalized. The approach of this article bypasses the need to normalize the data, allowing its broader application and usefulness in finding potential synergies in pharmaceutical research.