With increasingly massive data sets in biopharmaceutical research, particularly in genomic and related applications, there is concern about how well multiple comparisons methods "scale up" with increasing number of tests (k). Familywise error rate-controlling methods do not scale up well, and false discovery rate-controlling methods do scale up well with increasing k. But neither method scales up well with increasing sample size (n) when testing point nulls. We develop a loss function approach to investigate scale-up properties of various methods; we find that while Efron's recent proposal scales up best when both sample size n and number of tests k increase, but its performance otherwise can be erratic.
A model for analyzing multiple categorical dependent variables is presented and developed for use in organizational research. A primary example occurs in the foreign market entry literature, in which choice of ownership (majority, equal, or minority) and function (acquisition or joint venture) are simultaneously endogenous; only separate univariate ownership-based and function-based choice models are considered in the literature. Another example is in the comparison of gender and race across organizational units, controlling for confounders such as experience and qualification. Subsuming univariate categorical dependent variables as a special case, the model unifies existing organizational research methods, mitigates bias associated with univariate methods, provides more powerful testing methods, and provides a flexible modeling framework that allows hypotheses to be modeled and tested that are not possible with univariate models. Standard software may be used for estimation and testing; examples are given.
Abstract An experiment was conducted to examine the role that maximal lifting power has in predicting maximum acceptable weight of lift (MAWL) for a frequency of one lift per 8 h. The secondary aim of the study was to compare the ability of power to predict MAWL to previously used measures of capacity including two measures of isometric strength, five measures of isokinetic strength, and isoinertial capacity on an incremental lifting test. Twenty-five male subjects volunteered to participate in the experiment. The isometric tests involved maximum voluntary contractions for composite lifting strength at vertical heights of 15 and 75 cm. Peak isokinetic strength was measured at velocities of 0.1, 0.2, 0.4, 0.6 and 0.8 m s−1 using a modified CYBEX® II isokinetic dynamometer. Isoinertial lifting capactity was measured on the X-factor incremental lifting machine and peak power was measured on the incremental lifting machine by having subjects lift a 25 kg load as quickly as possible. The results indicate that peak isoinertial power is significantly correlated with MAWL, and this correlation was higher than any of the correlations between the other predictor variables and MAWL. The relationships between the isokinetic strength measures and MAWL were stronger than the relationships between the isometric measures and MAWL. Overall, the results suggest that tests used to predict MAWL should be dynamic rather than static. Keywords: Manual Materials HandlingLiftingStrength TestingHuman Power.
Closed multiple testing procedures are common in biopharmaceutical protocols. Whether their directional error rates are controlled is largely an open problem. In this article, directional error rates are investigated using analytical, numerical, and Monte Carlo methods. This article presents a Monte Carlo variance-reduction method amenable to this purpose. A factorial design is used to identify possible problem areas, and directional error rates are simulated. No cases of excess directional error are found for typical applications involving noncentral multivariate T distributions. However, directional error rates in excess of the nominal are found when using regression function tests with nearly collinear linear combinations, both for one-sided and two-sided tests.
In pharmaceutical research, making multiple statistical inferences is standard practice. Unless adjustments are made for multiple testing, the probability of making erroneous determinations of significance increases with the number of inferences. Closed testing is a flexible and easily explained approach to controlling the overall error rate that has seen wide use in pharmaceutical research, particularly in clinical trials settings. In this article, we first give a general review of the uses of multiple testing in pharmaceutical research, with particular emphasis on the benefits and pitfalls of closed testing procedures. We then provide a more technical examination of a class of closed tests that use additive-combination-based and minimum-based p-value statistics, both of which are commonly used in pharmaceutical research. We show that, while the additive combination tests are generally far superior to minimum p-value tests for composite hypotheses, the reverse is true for multiple comparisons using closure-based testing. The loss of power of additive combination tests is explained in terms worst-case "hurdles" that must be cleared before significance can be determined via closed testing. We prove mathematically that this problem can result in the power of a closure-based minimum p-value test approaching 1, while the power of an closure-based additive combination test approaches 0. Finally, implications of these results to pharmaceutical researchers are given.
Understanding Regression Analysis unifies diverse regression applications including the classical model, ANOVA models, generalized models including Poisson, Negative binomial, logistic, and survival, neural networks, and decision trees under a common umbrella -- namely, the conditional distribution model. It explains why the conditional distribution model is the correct model, and it also explains (proves) why the assumptions of the classical regression model are wrong. Unlike other regression books, this one from the outset takes a realistic approach that all models are just approximations. Hence, the emphasis is to model Nature's processes realistically, rather than to assume (incorrectly) that Nature works in particular, constrained ways. Key features of the book include: Numerous worked examples using the R software Key points and self-study questions displayed "just-in-time" within chapters Simple mathematical explanations ("baby proofs") of key concepts Clear explanations and applications of statistical significance (p-values), incorporating the American Statistical Association guidelines Use of "data-generating process" terminology rather than "population" Random-X framework is assumed throughout (the fixed-X case is presented as a special case of the random-X case) Clear explanations of probabilistic modelling, including likelihood-based methods Use of simulations throughout to explain concepts and to perform data analyses This book has a strong orientation towards science in general, as well as chapter-review and self-study questions, so it can be used as a textbook for research-oriented students in the social, biological and medical, and physical and engineering sciences. As well, its mathematical emphasis makes it ideal for a text in mathematics and statistics courses. With its numerous worked examples, it is also ideally suited to be a reference book for all scientists.
Abstract Abstract Large-sample covariance matrices for the analysis of variance (ANOVA), minimum norm quadratic unbiased estimator (MINQUE), restricted maximum likelihood (REML), and maximum likelihood (ML) estimates of variance components are presented for the unbalanced one-way model when the underlying distributions are not necessarily normal. The limiting variances depend on the design sequence, on the actual values of the variance components, and on the kurtosis parameters of the underlying distributions. (The skewness parameters and other moments do not affect the limiting distributions.) Because all estimates are consistent and asymptotically normal, it is reasonable to compare the estimates using their asymptotic variances. Thus the efficiency of one estimate relative to another is defined as the ratio of their asymptotic variances, and these efficiencies are evaluated numerically and analytically for a variety of nonnormal situations. Various authors, including Hocking and Kutner (1975), Corbeil and Searle (1976), and Swallow and Monahan (1984), have compared the variances and/or mean squared errors of variance component estimates in a variety of finite-sample models assuming normally distributed effects. The purpose of this article is to extend this line of research to incorporate nonnormal distributions and large samples. Some special cases of MINQUE considered in this article are called MINQUE(0), MINQUE(1), MINQUE(∞), and MIVQUE (minimum variance quadratic unbiased estimator); these are defined by setting the a priori variance ratio to 0, 1, infinity (in a sense to be explained), and to the actual variance ratio, respectively. Because the actual variance ratio is usually unknown, the MIVQUE estimates cannot be computed for unbalanced designs. (In balanced designs MIVQUE and ANOVA correspond.) It turns out, however, that ML and REML are asymptotically equivalent to MIVQUE, implying that only the asymptotic variance of MIVQUE is needed for evaluating efficiencies relative to ML or REML. Finite-sample efficiencies certainly may differ from the asymptotic counterparts, and the theoretical results are supplemented with a modest simulation study. This study indicates that the asymptotic results are reasonably close in moderate sample sizes for a particular type of design. The MIVQUE estimates have minimum variance within the class of invariant quadratic unbiased estimators under normality, but it is demonstrated that other commonly used estimates may be more efficient in nonnormal situations. The potential gain in efficiency, however, is often small relative to the potential loss of efficiency relative to MIVQUE. These results imply that the REML and ML estimates, whose derivations depend on the assumption that the data follow a multivariate normal distribution, are good choices in some nonnormal situations. Analysis of the large-sample variance shows that certain comparisons are invariant to the underlying distributions. For example, the efficiency of the ANOVA to MIVQUE estimates of between-classes variance becomes independent of the kurtosis parameters at the extreme values of the variance ratio, implying that REML and ML also dominate ANOVA (at least asymptotically) at these extremes. As the variance ratio tends to infinity, it may also be demonstrated that the efficiency of the MINQUE(0) estimate of the error variance (relative to ANOVA and MIVQUE) tends to 0 for arbitrary underlying distributions. This result supplements the simulation studies of Swallow and Monahan (1984), who observed similar behavior in normally distributed models. The phrase arbitrary underlying distributions is used throughout the article, but it is tacitly assumed that certain moment constraints must be satisfied. Key Words: ANOVA estimateEfficiencyKurtosisLarge-sample theoryMINQUEMIVQUEMixed modelMaximum likelihoodRestricted maximum likelihood
