Phylogenetic ANOVA: Group‐clade aggregation,biological challenges,and a refined permutation procedure

Phylogenetic regression is frequently used in macroevolutionary studies, and its statistical properties have been thoroughly investigated. By contrast, phylogenetic ANOVA has received relatively less attention, and the conditions leading to incorrect statistical and biological inferences when comparing multivariate phenotypes among groups remain underexplored. Here, we propose a refined method of randomizing residuals in a permutation procedure (RRPP) for evaluating phenotypic differences among groups while conditioning the data on the phylogeny. We show that RRPP displays appropriate statistical properties for both phylogenetic ANOVA and regression models, and for univariate and multivariate datasets. For ANOVA, we find that RRPP exhibits higher statistical power than methods utilizing phylogenetic simulation. Additionally, we investigate how group dispersion across the phylogeny affects inferences, and reveal that highly aggregated groups generate strong and significant correlations with the phylogeny, which reduce statistical power and subsequently affect biological interpretations. We discuss the broader implications of this phylogenetic group aggregation, and its relation to challenges encountered with other comparative methods where one or a few transitions in discrete traits are observed on the phylogeny. Finally, we recommend that phylogenetic comparative studies of continuous trait data use RRPP for assessing the significance of indicator variables as sources of trait variation.     

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.     

Flexible modeling via a hybrid estimation scheme in generalized mixed models for longitudinal data

To circumvent the computational complexity of likelihood inference in generalized mixed models that assume linear or more general additive regression models of covariate effects, Laplace's approximations to multiple integrals in the likelihood have been commonly used without addressing the issue of adequacy of the approximations for individuals with sparse observations. In this article, we propose a hybrid estimation scheme to address this issue. The likelihoods for subjects with sparse observations use Monte Carlo approximations involving importance sampling, while Laplace's approximation is used for the likelihoods of other subjects that satisfy a certain diagnostic check on the adequacy of Laplace's approximation. Because of its computational tractability, the proposed approach allows flexible modeling of covariate effects by using regression splines and model selection procedures for knot and variable selection. Its computational and statistical advantages are illustrated by simulation and by application to longitudinal data from a fecundity study of fruit flies, for which overdispersion is modeled via a double exponential family.     

Semiparametric analysis of recurrent events data in the presence of dependent censoring

Dependent censoring occurs in longitudinal studies of recurrent events when the censoring time depends on the potentially unobserved recurrent event times. To perform regression analysis in this setting, we propose a semiparametric joint model that formulates the marginal distributions of the recurrent event process and dependent censoring time through scale-change models, while leaving the distributional form and dependence structure unspecified. We derive consistent and asymptotically normal estimators for the regression parameters. We also develop graphical and numerical methods for assessing the adequacy of the proposed model. The finite-sample behavior of the new inference procedures is evaluated through simulation studies. An application to recurrent hospitalization data taken from a study of intravenous drug users is provided.     

Testing approaches for overdispersion in poisson regression versus the generalized poisson model

Overdispersion is a common phenomenon in Poisson modeling, and the negative binomial (NB) model is frequently used to account for overdispersion. Testing approaches (Wald test, likelihood ratio test (LRT), and score test) for overdispersion in the Poisson regression versus the NB model are available. Because the generalized Poisson (GP) model is similar to the NB model, we consider the former as an alternate model for overdispersed count data. The score test has an advantage over the LRT and the Wald test in that the score test only requires that the parameter of interest be estimated under the null hypothesis. This paper proposes a score test for overdispersion based on the GP model and compares the power of the test with the LRT and Wald tests. A simulation study indicates the score test based on asymptotic standard Normal distribution is more appropriate in practical application for higher empirical power, however, it underestimates the nominal significance level, especially in small sample situations, and examples illustrate the results of comparing the candidate tests between the Poisson and GP models. A bootstrap test is also proposed to adjust the underestimation of nominal level in the score statistic when the sample size is small. The simulation study indicates the bootstrap test has significance level closer to nominal size and has uniformly greater power than the score test based on asymptotic standard Normal distribution. From a practical perspective, we suggest that, if the score test gives even a weak indication that the Poisson model is inappropriate, say at the 0.10 significance level, we advise the more accurate bootstrap procedure as a better test for comparing whether the GP model is more appropriate than Poisson model. Finally, the Vuong test is illustrated to choose between GP and NB2 models for the same dataset.     

Power analysis and sample size estimation for RNA-Seq differential expression

It is crucial for researchers to optimize RNA-seq experimental designs for differential expression detection. Currently, the field lacks general methods to estimate power and sample size for RNA-Seq in complex experimental designs, under the assumption of the negative binomial distribution. We simulate RNA-Seq count data based on parameters estimated from six widely different public data sets (including cell line comparison, tissue comparison, and cancer data sets) and calculate the statistical power in paired and unpaired sample experiments. We comprehensively compare five differential expression analysis packages (DESeq, edgeR, DESeq2, sSeq, and EBSeq) and evaluate their performance by power, receiver operator characteristic (ROC) curves, and other metrics including areas under the curve (AUC), Matthews correlation coefficient (MCC), and F-measures. DESeq2 and edgeR tend to give the best performance in general. Increasing sample size or sequencing depth increases power; however, increasing sample size is more potent than sequencing depth to increase power, especially when the sequencing depth reaches 20 million reads. Long intergenic noncoding RNAs (lincRNA) yields lower power relative to the protein coding mRNAs, given their lower expression level in the same RNA-Seq experiment. On the other hand, paired-sample RNA-Seq significantly enhances the statistical power, confirming the importance of considering the multifactor experimental design. Finally, a local optimal power is achievable for a given budget constraint, and the dominant contributing factor is sample size rather than the sequencing depth. In conclusion, we provide a power analysis tool (http://www2.hawaii.edu/~lgarmire/RNASeqPowerCalculator.htm) that captures the dispersion in the data and can serve as a practical reference under the budget constraint of RNA-Seq experiments.     

Differential expression analysis for sequence count data

High-throughput sequencing assays such as RNA-Seq, ChIP-Seq or barcode counting provide quantitative readouts in the form of count data. To infer differential signal in such data correctly and with good statistical power, estimation of data variability throughout the dynamic range and a suitable error model are required. We propose a method based on the negative binomial distribution, with variance and mean linked by local regression and present an implementation, DESeq, as an R/Bioconductor package.     

RNA-Seq is not required to determine stable reference genes for qPCR normalization

Assessment of differential gene expression by qPCR is heavily influenced by the choice of reference genes. Although numerous statistical approaches have been proposed to determine the best reference genes, they can give rise to conflicting results depending on experimental conditions. Hence, recent studies propose the use of RNA-Seq to identify stable genes followed by the application of different statistical approaches to determine the best set of reference genes for qPCR data normalization. In this study, however, we demonstrate that the statistical approach to determine the best reference genes from commonly used conventional candidates is more important than the preselection of ‘stable’ candidates from RNA-Seq data. Using a qPCR data normalization workflow that we have previously established; we show that qPCR data normalization using conventional reference genes render the same results as stable reference genes selected from RNA-Seq data. We validated these observations in two distinct cross-sectional experimental conditions involving human iPSC derived microglial cells and mouse sciatic nerves. These results taken together show that given a robust statistical approach for reference gene selection, stable genes selected from RNA-Seq data do not offer any significant advantage over commonly used reference genes for normalizing qPCR assays.     

A comparison of statistical methods for detecting differentially expressed genes from RNA-seq data

RNA-Seq technologies are quickly revolutionizing genomic studies, and statistical methods for RNA-seq data are under continuous development. Timely review and comparison of the most recently proposed statistical methods will provide a useful guide for choosing among them for data analysis. Particular interest surrounds the ability to detect differential expression (DE) in genes. Here we compare four recently proposed statistical methods, edgeR, DESeq, baySeq, and a method with a two-stage Poisson model (TSPM), through a variety of simulations that were based on different distribution models or real data. We compared the ability of these methods to detect DE genes in terms of the significance ranking of genes and false discovery rate control. All methods compared are implemented in freely available software. We also discuss the availability and functions of the currently available versions of these software.     

The clustering of regression models method with applications in gene expression data

Identification of differentially expressed genes and clustering of genes are two important and complementary objectives addressed with gene expression data. For the differential expression question, many "per-gene" analytic methods have been proposed. These methods can generally be characterized as using a regression function to independently model the observations for each gene; various adjustments for multiplicity are then used to interpret the statistical significance of these per-gene regression models over the collection of genes analyzed. Motivated by this common structure of per-gene models, we proposed a new model-based clustering method--the clustering of regression models method, which groups genes that share a similar relationship to the covariate(s). This method provides a unified approach for a family of clustering procedures and can be applied for data collected with various experimental designs. In addition, when combined with per-gene methods for assessing differential expression that employ the same regression modeling structure, an integrated framework for the analysis of microarray data is obtained. The proposed methodology was applied to two microarray data sets, one from a breast cancer study and the other from a yeast cell cycle study.     

Semiparametric analysis of correlated recurrent and terminal events

In clinical and observational studies, recurrent event data (e.g., hospitalization) with a terminal event (e.g., death) are often encountered. In many instances, the terminal event is strongly correlated with the recurrent event process. In this article, we propose a semiparametric method to jointly model the recurrent and terminal event processes. The dependence is modeled by a shared gamma frailty that is included in both the recurrent event rate and terminal event hazard function. Marginal models are used to estimate the regression effects on the terminal and recurrent event processes, and a Poisson model is used to estimate the dispersion of the frailty variable. A sandwich estimator is used to achieve additional robustness. An analysis of hospitalization data for patients in the peritoneal dialysis study is presented to illustrate the proposed method.     

Power and Sample Size Determination in the Rasch Model: Evaluation of the Robustness of a Numerical Method to Non-Normality of the Latent Trait

Patient-reported outcomes (PRO) have gained importance in clinical and epidemiological research and aim at assessing quality of life, anxiety or fatigue for instance. Item Response Theory (IRT) models are increasingly used to validate and analyse PRO. Such models relate observed variables to a latent variable (unobservable variable) which is commonly assumed to be normally distributed. A priori sample size determination is important to obtain adequately powered studies to determine clinically important changes in PRO. In previous developments, the Raschpower method has been proposed for the determination of the power of the test of group effect for the comparison of PRO in cross-sectional studies with an IRT model, the Rasch model. The objective of this work was to evaluate the robustness of this method (which assumes a normal distribution for the latent variable) to violations of distributional assumption. The statistical power of the test of group effect was estimated by the empirical rejection rate in data sets simulated using a non-normally distributed latent variable. It was compared to the power obtained with the Raschpower method. In both cases, the data were analyzed using a latent regression Rasch model including a binary covariate for group effect. For all situations, both methods gave comparable results whatever the deviations from the model assumptions. Given the results, the Raschpower method seems to be robust to the non-normality of the latent trait for determining the power of the test of group effect.     

Assessing the robustness of randomization tests: examples from behavioural studies

Behavioural studies are commonly plagued with data that violate the assumptions of parametric statistics. Consequently, classic nonparametric methods (e.g. rank tests) and novel distribution-free methods (e.g. randomization tests) have been used to a great extent by behaviourists. However, the robustness of such methods in terms of statistical power and type I error have seldom been evaluated. This probably reflects the fact that empirical methods, such as Monte Carlo approaches, are required to assess these concerns. In this study we show that analytical methods cannot always be used to evaluate the robustness of statistical tests, but rather Monte Carlo approaches must be employed. We detail empirical protocols for estimating power and type I error rates for parametric, nonparametric and randomization methods, and demonstrate their application for an analysis of variance and a regression/correlation analysis design. Together, this study provides a framework from which behaviourists can compare the reliability of different methods for data analysis, serving as a basis for selecting the most appropriate statistical test given the characteristics of data at hand. Copyright 2001 The Association for the Study of Animal Behaviour.     

A comparison of different ways of including baseline counts in negative binomial models for data from falls prevention trials

A common design for a falls prevention trial is to assess falling at baseline, randomize participants into an intervention or control group, and ask them to record the number of falls they experience during a follow‐up period of time. This paper addresses how best to include the baseline count in the analysis of the follow‐up count of falls in negative binomial (NB) regression. We examine the performance of various approaches in simulated datasets where both counts are generated from a mixed Poisson distribution with shared random subject effect. Including the baseline count after log‐transformation as a regressor in NB regression (NB‐logged) or as an offset (NB‐offset) resulted in greater power than including the untransformed baseline count (NB‐unlogged). Cook and Wei's conditional negative binomial (CNB) model replicates the underlying process generating the data. In our motivating dataset, a statistically significant intervention effect resulted from the NB‐logged, NB‐offset, and CNB models, but not from NB‐unlogged, and large, outlying baseline counts were overly influential in NB‐unlogged but not in NB‐logged. We conclude that there is little to lose by including the log‐transformed baseline count in standard NB regression compared to CNB for moderate to larger sized datasets.