Inference for low‐ and high‐dimensional multigroup repeated measures designs with unequal covariance matrices

We propose tests for main and simple treatment effects, time effects, as well as treatment by time interactions in possibly high‐dimensional multigroup repeated measures designs. The proposed inference procedures extend the work by Brunner et al. (2012) from two to several treatment groups and remain valid for unbalanced data and under unequal covariance matrices. In addition to showing consistency when sample size and dimension tend to infinity at the same rate, we provide finite sample approximations and evaluate their performance in a simulation study, demonstrating better maintenance of the nominal α‐level than the popular Box‐Greenhouse–Geisser and Huynh–Feldt methods, and a gain in power for informatively increasing dimension. Application is illustrated using electroencephalography (EEG) data from a neurological study involving patients with Alzheimer's disease and other cognitive impairments.     

Simulation‐selection‐extrapolation: Estimation in high‐dimensional errors‐in‐variables models

Errors‐in‐variables models in high‐dimensional settings pose two challenges in application. First, the number of observed covariates is larger than the sample size, while only a small number of covariates are true predictors under an assumption of model sparsity. Second, the presence of measurement error can result in severely biased parameter estimates, and also affects the ability of penalized methods such as the lasso to recover the true sparsity pattern. A new estimation procedure called SIMulation‐SELection‐EXtrapolation (SIMSELEX) is proposed. This procedure makes double use of lasso methodology. First, the lasso is used to estimate sparse solutions in the simulation step, after which a group lasso is implemented to do variable selection. The SIMSELEX estimator is shown to perform well in variable selection, and has significantly lower estimation error than naive estimators that ignore measurement error. SIMSELEX can be applied in a variety of errors‐in‐variables settings, including linear models, generalized linear models, and Cox survival models. It is furthermore shown in the Supporting Information how SIMSELEX can be applied to spline‐based regression models. A simulation study is conducted to compare the SIMSELEX estimators to existing methods in the linear and logistic model settings, and to evaluate performance compared to naive methods in the Cox and spline models. Finally, the method is used to analyze a microarray dataset that contains gene expression measurements of favorable histology Wilms tumors.     

Sample Size Considerations for GEE Analyses of Three‐Level Cluster Randomized Trials

Summary Cluster randomized trials in health care may involve three instead of two levels, for instance, in trials where different interventions to improve quality of care are compared. In such trials, the intervention is implemented in health care units (“clusters”) and aims at changing the behavior of health care professionals working in this unit (“subjects”), while the effects are measured at the patient level (“evaluations”). Within the generalized estimating equations approach, we derive a sample size formula that accounts for two levels of clustering: that of subjects within clusters and that of evaluations within subjects. The formula reveals that sample size is inflated, relative to a design with completely independent evaluations, by a multiplicative term that can be expressed as a product of two variance inflation factors, one that quantifies the impact of within‐subject correlation of evaluations on the variance of subject‐level means and the other that quantifies the impact of the correlation between subject‐level means on the variance of the cluster means. Power levels as predicted by the sample size formula agreed well with the simulated power for more than 10 clusters in total, when data were analyzed using bias‐corrected estimating equations for the correlation parameters in combination with the model‐based covariance estimator or the sandwich estimator with a finite sample correction.     

Multiple Comparisons Among Dependent Groups Based on a Modified One‐Step M‐Estimator

Currently, among multiple comparison procedures for dependent groups, a bootstrap‐t with a 20% trimmed mean performs relatively well in terms of both Type I error probabilities and power. However, trimmed means suffer from two general concerns described in the paper. Robust M‐estimators address these concerns, but now no method has been found that gives good control over the probability of a Type I error when sample sizes are small. The paper suggests using instead a modified one‐step M‐estimator that retains the advantages of both trimmed means and robust M‐estimators. Yet another concern is that the more successful methods for trimmed means can be too conservative in terms of Type I errors. Two methods for performing all pairwise multiple comparisons are considered. In simulations, both methods avoid a familywise error (FWE) rate larger than the nominal level. The method based on comparing measures of location associated with the marginal distributions can have an actual FWE that is well below the nominal level when variables are highly correlated. However, the method based on difference scores performs reasonably well with very small sample sizes, and it generally performs better than any of the methods studied in Wilcox (1997b).     

The Short‐Term Effect of Occupational Levels of 50 Hz Electromagnetic Field on Human Heart Rate Variability

Previous studies have indicated that there is no consensus on the effects of extremely low‐frequency electromagnetic (ELF‐EMF) exposure on the cardiovascular system. This study aimed to explore the short‐term effect of ELF‐EMF exposure on heart rate (HR) and HR variability (HRV). The sample consisted of 34 healthy males aged 18–27 years. The participants were randomly assigned to the EMF (n = 17) or the Sham group (n = 17). We employed a double‐blind repeated‐measures design consisting of three 5 min experimental periods. The chest region of each individual in the EMF group was exposed to 50 Hz, 28 μT, linear polarized, continuous EMF during the EMF exposure period. HR and HRV data were recorded continuously by using a photoplethysmography sensor. Within‐subject statistical analysis indicated a significant HR deceleration in both the EMF and Sham groups. However, the standard deviation of the NN intervals (SDNN), root mean square of successive differences (RMSSD), low‐frequency (LF), and high‐frequency (HF) powers increased only in the EMF group and remained stable in the Sham group. We also compared the same HRV indices measured during the EMF and Sham periods between the two experimental groups. The between‐subject analysis results demonstrated significantly higher SDNN, RMSSD, LF, and HF values in the EMF group than in the Sham group. The LF/HF ratio did not change significantly within and between groups. On the basis of these results, we concluded that short‐term exposure of the chest region to ELF‐EMF could potentially enhance parasympathetic predominance during the resting condition. Bioelectromagnetics. 2021;42:60–75. © 2020 Bioelectromagnetics Society.     

Interval Estimation of Simple Difference in Dichotomous Data with Repeated Measurements

When comparing two treatments, we often use the simple difference between the probabilities of response to measure the efficacy of one treatment over the other. When the measurement of outcome is unreliable or the cost of obtaining additional subjects is high relative to that of additional measurements from the obtained subjects, we may often consider taking more than one measurement per subject to increase the precision of an interval estimator. This paper focuses discussion on interval estimation of simple difference when we take repeated measurements per subject. This paper develops four asymptotic interval estimators of simple difference for any finite number of measurements per subject. This paper further applies Monte Carlo simulation to evaluate the finite‐sample performance of these estimators in a variety of situations. Finally, this paper includes a discussion on sample size determination on the basis of both the average length and the probability of controlling the length of the resulting interval estimate proposed elsewhere.     

Nonparametric tests for two-group comparisons of dependent observations obtained at varying time points

We propose new tests for two-group comparisons of repeated measures of a response where the repeated measures might be obtained at arbitrary time points that differ over individuals. The tests are almost U-statistics in that the kernel contains some unknown parameters that need to be estimated from the data. Our methods are designed for settings in which response means of one group are strictly greater than the response means of the other group. The tests do not make any assumptions regarding the distribution of the repeated measures except that one of the tests assumes that the repeated measures can be grouped into distinct periods of observations (e.g., around fixed follow-up time points) such that the covariance between scores only depends on the periods the observations belong to and that the covariance matrices are the same in the two groups. The tests are valid even if the probability that a response is observed depends on the level of response provided that the missing data mechanism is the same in both groups. Inference can conveniently be based on resampling. We provide asymptotic results for the test statistics. We investigate size and power of the tests and use them to assess differences in viral load decline for drug-resistant and drug-sensitive human immunodeficiency virus (HIV)-1 infected patients.     

Structure and stability of genetic variance–covariance matrices: A Bayesian sparse factor analysis of transcriptional variation in the three‐spined stickleback

The genetic variance–covariance matrix ( G ) is a quantity of central importance in evolutionary biology due to its influence on the rate and direction of multivariate evolution. However, the predictive power of empirically estimated G ‐matrices is limited for two reasons. First, phenotypes are high‐dimensional, whereas traditional statistical methods are tuned to estimate and analyse low‐dimensional matrices. Second, the stability of G to environmental effects and over time remains poorly understood. Using Bayesian sparse factor analysis (BSFG) designed to estimate high‐dimensional G ‐matrices, we analysed levels variation and covariation in 10,527 expressed genes in a large (n = 563) half‐sib breeding design of three‐spined sticklebacks subject to two temperature treatments. We found significant differences in the structure of G between the treatments: heritabilities and evolvabilities were higher in the warm than in the low‐temperature treatment, suggesting more and faster opportunity to evolve in warm (stressful) conditions. Furthermore, comparison of G and its phenotypic equivalent P revealed the latter is a poor substitute of the former. Most strikingly, the results suggest that the expected impact of G on evolvability—as well as the similarity among G ‐matrices—may depend strongly on the number of traits included into analyses. In our results, the inclusion of only few traits in the analyses leads to underestimation in the differences between the G ‐matrices and their predicted impacts on evolution. While the results highlight the challenges involved in estimating G , they also illustrate that by enabling the estimation of large G ‐matrices, the BSFG method can improve predicted evolutionary responses to selection.     

Simultaneous Quantification of the Acetylome and Succinylome by ‘One‐Pot’ Affinity Enrichment

Protein posttranslational modifications (PTMs) are of increasing interest in biomedical research, yet studies rarely examine more than one PTM. One barrier to multi‐PTM studies is the time cost for both sample preparation and data acquisition, which scale linearly with the number of modifications. The most prohibitive requirement is often the need for large amounts of sample, which must be increased proportionally with the number of PTM enrichment steps. Here, a streamlined, quantitative label‐free proteomic workflow—“one‐pot” PTM enrichment—that enables comprehensive identification and quantification of peptides containing acetylated and succinylated lysine residues from a single sample containing as little as 1 mg mitochondria protein is described. Coupled with a label‐free, data‐independent acquisition (DIA), 2235 acetylated and 2173 succinylated peptides with the one‐pot method are identified and quantified and peak areas are shown to be highly correlated between the one‐pot and traditional single‐PTM enrichments. The ‘one‐pot’ method makes possible detection of multiple PTMs occurring on the same peptide, and it is shown that it can be used to make unique biological insights into PTM crosstalk. Compared to single‐PTM enrichments, the one‐pot workflow has equivalent reproducibility and enables direct assessment of PTM crosstalk from biological samples in less time from less tissue.     

No evidence of kin bias in dispersion of young‐of‐the‐year Atlantic salmon Salmo salar L. in a natural stream

Ninety‐one young‐of‐the‐year Atlantic salmon Salmo salar were captured using a non‐invasive snorkelling technique in a 38 m section of Catamaran Brook, New Brunswick, Canada, to test whether related fish settle closer to one another than unrelated fish. A maximum likelihood estimate of parentage relationships assessed by genotyping eight microsatellite loci revealed five half‐sibling families in the sample of fish. Related juvenile S. salar were not found closer to one another than unrelated fish in three analyses at two spatial scales: a comparison of the relatedness of focal fish to their nearest neighbour and to their four nearest neighbours, and a correlation of the pair‐wise relatedness and distance matrices for all fish in the sample. The lack of a kin‐biased dispersion pattern may be related to the lower density of fish or the scarcity of full‐siblings at the study site compared to laboratory conditions.     

A METHOD FOR ASSESSING PHYLOGENETIC LEAST SQUARES MODELS FOR SHAPE AND OTHER HIGH‐DIMENSIONAL MULTIVARIATE DATA

Studies of evolutionary correlations commonly use phylogenetic regression (i.e., independent contrasts and phylogenetic generalized least squares) to assess trait covariation in a phylogenetic context. However, while this approach is appropriate for evaluating trends in one or a few traits, it is incapable of assessing patterns in highly multivariate data, as the large number of variables relative to sample size prohibits parametric test statistics from being computed. This poses serious limitations for comparative biologists, who must either simplify how they quantify phenotypic traits, or alter the biological hypotheses they wish to examine. In this article, I propose a new statistical procedure for performing ANOVA and regression models in a phylogenetic context that can accommodate high‐dimensional datasets. The approach is derived from the statistical equivalency between parametric methods using covariance matrices and methods based on distance matrices. Using simulations under Brownian motion, I show that the method displays appropriate Type I error rates and statistical power, whereas standard parametric procedures have decreasing power as data dimensionality increases. As such, the new procedure provides a useful means of assessing trait covariation across a set of taxa related by a phylogeny, enabling macroevolutionary biologists to test hypotheses of adaptation, and phenotypic change in high‐dimensional datasets.     

Interim analysis incorporating short‐ and long‐term binary endpoints

Designs incorporating more than one endpoint have become popular in drug development. One of such designs allows for incorporation of short‐term information in an interim analysis if the long‐term primary endpoint has not been yet observed for some of the patients. At first we consider a two‐stage design with binary endpoints allowing for futility stopping only based on conditional power under both fixed and observed effects. Design characteristics of three estimators: using primary long‐term endpoint only, short‐term endpoint only, and combining data from both are compared. For each approach, equivalent cut‐off point values for fixed and observed effect conditional power calculations can be derived resulting in the same overall power. While in trials stopping for futility the type I error rate cannot get inflated (it usually decreases), there is loss of power. In this study, we consider different scenarios, including different thresholds for conditional power, different amount of information available at the interim, different correlations and probabilities of success. We further extend the methods to adaptive designs with unblinded sample size reassessments based on conditional power with inverse normal method as the combination function. Two different futility stopping rules are considered: one based on the conditional power, and one from P‐values based on Z‐statistics of the estimators. Average sample size, probability to stop for futility and overall power of the trial are compared and the influence of the choice of weights is investigated.     

Object Discrimination Reversal As a Method to Assess Cognitive Impairment in Nonhuman Primate Enhanced Pre‐ and Postnatal Developmental (ePPND) Studies: Statistical Power Analysis

An important aspect of the enhanced pre‐ and postnatal developmental (ePPND) toxicity study in nonhuman primates (NHP) is that it combines in utero and postnatal assessments in a single study. However, it is unclear if NHP ePPND studies are suitable to perform all of the evaluations incorporated into rodent PPND studies. To understand the value of including cognitive assessment in a NHP ePPND toxicity study, we performed a power analysis of object discrimination reversal task data using a modified Wisconsin General Testing Apparatus (ODR‐WGTA) from two NHP ePPND studies. ODR‐WGTA endpoints evaluated were days to learning and to first reversal, and number of reversals. With α = 0.05 and a one‐sided t‐test, a sample of seven provided 80% power to predict a 100% increase in all three of the ODR‐WGTA endpoints; a sample of 25 provided 80% power to predict a 50% increase. Similar power analyses were performed with data from the Cincinnati Water Maze (CWM) and passive avoidance tests from three rat PPND toxicity studies. Groups of 5 and 15 in the CWM and passive avoidance test, respectively, provided 80% power to detect a 100% change. While the power of the CWM is not far superior to the NHP ODR‐WGTA, a clear advantage is the routine use of larger sample size, with a group of 20 rats the CWM provides ～90% power to detect a 50% change. Due to the limitations on the number of animals, the ODR‐WGTA may not be suitable for assessing cognitive impairment in NHP ePPND studies.     

Septum volume and food‐storing behavior are related in parids

The hippocampal formation (HF) of food‐storing birds is larger than non‐storing species, and the size of the HF in food‐storing Black‐Capped Chickadees (Poecile atricapillus) varies seasonally. We examined whether the volume of the septum, a medial forebrain structure that shares reciprocal connections with the HF, demonstrates the same species and seasonal variation as has been shown in the HF. We compared septum volume in three parid species; non‐storing Blue Tits (Parus caeruleus) and Great Tits (Parus major), and food‐storing Black‐Capped Chickadees. We found the relative septum volume to be larger in chickadees than in the non‐storing species. We also compared septum and nucleus of the diagonal band (NDB) volume of Black‐Capped Chickadees at different times of the year. We found that the relative septum volume varies seasonally in food‐storing birds. The volume of the NDB does not vary seasonally. Due to the observed species and seasonal variation, the septum, like the hippocampal formation of food‐storing birds, may be specialized for some aspects of food‐storing and spatial memory. © 2002 Wiley Periodicals, Inc. J Neurobiol 51: 215–222, 2002     

Measures of precision for dissimilarity‐based multivariate analysis of ecological communities

Ecological studies require key decisions regarding the appropriate size and number of sampling units. No methods currently exist to measure precision for multivariate assemblage data when dissimilarity‐based analyses are intended to follow. Here, we propose a pseudo multivariate dissimilarity‐based standard error (MultSE) as a useful quantity for assessing sample‐size adequacy in studies of ecological communities. Based on sums of squared dissimilarities, MultSE measures variability in the position of the centroid in the space of a chosen dissimilarity measure under repeated sampling for a given sample size. We describe a novel double resampling method to quantify uncertainty in MultSE values with increasing sample size. For more complex designs, values of MultSE can be calculated from the pseudo residual mean square of a permanova model, with the double resampling done within appropriate cells in the design. R code functions for implementing these techniques, along with ecological examples, are provided.     

Testing the Intraclass Version of Kappa Coeffcient of Agreement with Binary Scale and Sample Size Determination

The intraclass version of kappa coefficient has been commonly applied as a measure of agreement for two ratings per subject with binary outcome in reliability studies. We present an efficient statistic for testing the strength of kappa agreement using likelihood scores, and derive asymptotic power and sample size formula. Exact evaluation shows that the score test is generally conservative and more powerful than a method based on a chi‐square goodness‐of‐fit statistic (Donner and Eliasziw , 1992, Statistics in Medicine 11 , 1511–1519). In particular, when the research question is one directional, the one‐sided score test is substantially more powerful and the reduction in sample size is appreciable.     

Normal frailty probit model for clustered interval‐censored failure time data

Clustered interval‐censored data commonly arise in many studies of biomedical research where the failure time of interest is subject to interval‐censoring and subjects are correlated for being in the same cluster. A new semiparametric frailty probit regression model is proposed to study covariate effects on the failure time by accounting for the intracluster dependence. Under the proposed normal frailty probit model, the marginal distribution of the failure time is a semiparametric probit model, the regression parameters can be interpreted as both the conditional covariate effects given frailty and the marginal covariate effects up to a multiplicative constant, and the intracluster association can be summarized by two nonparametric measures in simple and explicit form. A fully Bayesian estimation approach is developed based on the use of monotone splines for the unknown nondecreasing function and a data augmentation using normal latent variables. The proposed Gibbs sampler is straightforward to implement since all unknowns have standard form in their full conditional distributions. The proposed method performs very well in estimating the regression parameters as well as the intracluster association, and the method is robust to frailty distribution misspecifications as shown in our simulation studies. Two real‐life data sets are analyzed for illustration.     

Dynamic species co‐occurrence networks require dynamic biodiversity surrogates

In conservation it is inevitable that surrogates be selected to represent the occurrence of hard‐to‐find species and find priority locations for management. However, species co‐occurrence can vary over time. Here we demonstrate how temporal dynamics in species co‐occurrence influence the ability of managers to choose the best surrogate species. We develop an efficient optimisation formulation that selects the optimal set of complementary surrogate species from any co‐occurrence network. We apply it to two Australian datasets on successional bird responses to disturbances of revegetation and fire. We discover that a surprisingly small number of species are required to represent the majority of species co‐occurrences at any one time. Because co‐occurrence patterns are temporally dynamic, the optimal set of surrogates, and the number of surrogates required to achieve a desired surrogacy power, depend on sampling effort and the successional state of a system. Overlap in optimal sets of surrogates for representing 70% of co‐occurring species ranges from zero to 57% depending on when the surrogacy decision is made. Surrogate sets representing early successional communities over‐estimate the power of surrogacy decisions at later times. Our results show that in dynamic systems, optimal surrogates might be selected in different ways: 1) use short‐term monitoring to choose a larger number of static less‐informative surrogates; 2) use long‐term monitoring to choose a smaller number of static high‐power surrogates that may poorly represent early successional co‐occurrence; 3) develop adaptive surrogate selection frameworks with high short‐term and long‐term surrogacy power that update surrogate sets and capture temporal dynamics in species co‐occurrence. Our results suggest vigilance is needed when selecting surrogates for other co‐occurring species in dynamic landscapes, as selected surrogates from one time may have reduced effectiveness at a different time. Ultimately, decisions that fail to acknowledge dynamic species co‐occurrence will lead to uninformative or redundant surrogates.     

Power analysis for trend in ordinal cover classes: implications for long‐term vegetation monitoring

Question: We provide a method to calculate the power of ordinal regression models for detecting temporal trends in plant abundance measured as ordinal cover classes. Does power depend on the shape of the unobserved (latent) distribution of percentage cover? How do cover class schemes that differ in the number of categories affect power? Methods: We simulated cover class data by “cutting‐up” a continuous logit‐beta distributed variable using 7‐point and 15‐point cover classification schemes. We used Monte Carlo simulation to estimate power for detecting trends with two ordinal models, proportional odds logistic regression (POM) and logistic regression with cover classes re‐binned into two categories, a model we term an assessment point model (APM). We include a model fit to the logit‐transformed percentage cover data for comparison, which is a latent model. Results: The POM had equal or higher power compared to the APM and latent model, but power varied in complex ways as a function of the assumed latent beta distribution. We discovered that if the latent distribution is skewed, a cover class scheme with more categories might yield higher power to detect trend. Conclusions: Our power analysis method maintains the connection between the observed ordinal cover classes and the unmeasured (latent) percentage cover variable, allowing for a biologically meaningful trend to be defined on the percentage cover scale. Both the shape of the latent beta distribution and the alternative hypothesis should be considered carefully when determining sample size requirements for long‐term vegetation monitoring using cover class measurements.