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Abstract Background Deep generative models naturally become nonlinear dimension reduction tools to visualize large-scale datasets such as single-cell RNA sequencing datasets for revealing latent grouping patterns or identifying outliers. The variational autoencoder (VAE) is a popular deep generative method equipped with encoder/decoder structures. The encoder and decoder are useful when a new sample is mapped to the latent space and a data point is generated from a point in a latent space. However, the VAE tends not to show grouping pattern clearly without additional annotation information. On the other hand, similarity-based dimension reduction methods such as t-SNE or UMAP present clear grouping patterns even though these methods do not have encoder/decoder structures. Results To bridge this gap, we propose a new approach that adopts similarity information in the VAE framework. In addition, for biological applications, we extend our approach to a conditional VAE to account for covariate effects in the dimension reduction step. In the simulation study and real single-cell RNA sequencing data analyses, our method shows great performance compared to existing state-of-the-art methods by producing clear grouping structures using an inferred encoder and decoder. Our method also successfully adjusts for covariate effects, resulting in more useful dimension reduction. Conclusions Our method is able to produce clearer grouping patterns than those of other regularized VAE methods by utilizing similarity information encoded in the data via the highly celebrated UMAP loss function.

Background: Deep generative models naturally become nonlinear dimension reduction tools to visualize large-scale datasets such as single-cell RNA sequencing datasets for revealing latent grouping patterns or identifying outliers. The variational autoencoder (VAE) is a popular deep generative method equipped with encoder/decoder structures. The encoder and decoder are useful when a new sample is mapped to the latent space and a data point is generated from a point in a latent space. However, the VAE tends not to show grouping pattern clearly without additional annotation information. On the other hand, similarity-based dimension reduction methods such as t-SNE or UMAP present clear grouping patterns even though these methods do not have encoder/decoder structures. Results: To bridge this gap, we propose a new approach that adopts similarity information in the VAE framework. In addition, for biological applications, we extend our approach to a conditional VAE to account for covariate effects in the dimension reduction step. In the simulation study and real single-cell RNA sequencing data analyses, our method shows great performance compared to existing state-of-the-art methods by producing clear grouping structures using an inferred encoder and decoder. Our method also successfully adjusts for covariate effects, resulting in more useful dimension reduction. Conclusions: Our method is able to produce clearer grouping patterns than those of other regularized VAE methods by utilizing similarity information encoded in the data via the highly celebrated UMAP loss function. [ABSTRACT FROM AUTHOR]

Paired outcomes are common in correlated clustered data where the main aim is to compare the distributions of the outcomes in a pair. In such clustered paired data, informative cluster sizes can occur when the number of pairs in a cluster (i.e., a cluster size) is correlated to the paired outcomes or the paired differences. There have been some attempts to develop robust rank-based tests for comparing paired outcomes in such complex clustered data. Most of these existing rank tests developed for paired outcomes in clustered data compare the marginal distributions in a pair and ignore any covariate effect on the outcomes. However, when potentially important covariate data is available in observational studies, ignoring these covariate effects on the outcomes can result in a flawed inference. In this article, using rank based weighted estimating equations, we propose a robust procedure for covariate effect adjusted comparison of paired outcomes in a clustered data that can also address the issue of informative cluster size. Through simulated scenarios and real-life neuroimaging data, we demonstrate the importance of considering covariate effects during paired testing and robust performances of our proposed method in covariate adjusted paired comparisons in complex clustered data settings.

Paired outcomes are common in correlated clustered data where the main aim is to compare the distributions of the outcomes in a pair. In such clustered paired data, informative cluster sizes can occur when the number of pairs in a cluster (i.e., a cluster size) is correlated to the paired outcomes or the paired differences. There have been some attempts to develop robust rank-based tests for comparing paired outcomes in such complex clustered data. Most of these existing rank tests developed for paired outcomes in clustered data compare the marginal distributions in a pair and ignore any covariate effect on the outcomes. However, when potentially important covariate data is available in observational studies, ignoring these covariate effects on the outcomes can result in a flawed inference. In this article, using rank based weighted estimating equations, we propose a robust procedure for covariate effect adjusted comparison of paired outcomes in a clustered data that can also address the issue of informative cluster size. Through simulated scenarios and real-life neuroimaging data, we demonstrate the importance of considering covariate effects during paired testing and robust performances of our proposed method in covariate adjusted paired comparisons in complex clustered data settings. [ABSTRACT FROM AUTHOR]

In pharmacometrics, understanding a covariate effect on an interested outcome is essential for assessing the importance of the covariate. Variance-based global sensitivity analysis (GSA) can simultaneously quantify contribution of each covariate effect to the variability for the interested outcome considering with random effects. The aim of this study was to apply GSA to pharmacometric models to assess covariate effects. Simulations were conducted with pharmacokinetic models to characterize the GSA for assessment of covariate effects and with an example of quantitative systems pharmacology (QSP) models to apply the GSA to a complex model. In the simulations, covariate and random variables were generated to simulate the outcomes using the models. Ratios of variance explained by each factor (each covariate and random effect) over the overall variance of the outcome were used as sensitivity indices. The sensitivity indices were consistent with the effect size of covariate. The sensitivity indices identified the importance of creatinine clearance on the pharmacokinetic exposure for a renally-excreted drug. These sensitivity indices could be applied to plasma concentrations over time (repeated measurable outcomes over time) as interested outcomes. Using the GSA, each contribution of all of the covariate effects could be efficiently identified even in the complex QSP model. Variance-based GSA can provide insight when considering the importance of covariate effects by simultaneously and quantitatively assessing all covariate and random effects on interested outcomes in pharmacometrics. [ABSTRACT FROM AUTHOR]

Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This study examined the issue of covariate effects with FMM in the context of measurement invariance testing. Specifically, the impact of excluding and misspecifying covariate effects on measurement invariance testing and class enumeration was investigated via Monte Carlo simulations. Data were generated based on FMM models with (1) a zero covariate effect, (2) a covariate effect on the latent class variable, and (3) covariate effects on both the latent class variable and the factor. For each population model, different analysis models that excluded or misspecified covariate effects were fitted. Results highlighted the importance of including proper covariates in measurement invariance testing and evidenced the utility of a model comparison approach in searching for the correct specification of covariate effects and the level of measurement invariance. This approach was demonstrated using an empirical data set. Implications for methodological and applied research are discussed. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of modeling medical costs with covariates when the cost data are subject to right-censoring. The prevailing methods are divided into three categories, (a) the inverse probability weighted (IPW) regressions; (b) the generalized survival-adjusted estimators; and (c) the joint-modeling methods. Comparisons are made both in and between categories to demonstrate their different mechanisms to handle the informative censoring, to take into account the covariates and the way they interpret the covariates effects. Based on the above discussion, we believe that the linear or generalized linear regressions using the IPW scheme are very popular due to its convenience to fit and interpret, which could be a good choice in practice with additional conditional means to address the role of survival to some extent. The recently proposed generalized survival-adjusted estimator is very intuitive as the derivative of the estimation function naturally decomposes the effects of covariates into the intensity part and the survival part, therefore especially useful when the covariates have substantial effect on survival. The joint-modelling methods have the advantage in providing the access to the correlation between medical cost and survival, although they suffer from theoretical and computational complexity. The effect of covariates on cost through survival in this kind of joint-modelling methods could be a desirable topic for further research. [ABSTRACT FROM AUTHOR]

Researchers continue to be interested in efficient, accurate methods of estimating coefficients of covariates in mixture modeling. Including covariates related to the latent class analysis not only may improve the ability of the mixture model to clearly differentiate between subjects but also makes interpretation of latent group membership more meaningful. Very few studies have been conducted that compare the performance of various approaches to estimating covariate effects in mixture modeling, and fewer yet have considered more complicated models such as growth mixture models where the latent class variable is more difficult to identify. A Monte Carlo simulation was conducted to investigate the performance of four estimation approaches: (1) the conventional three-step approach, (2) the one-step maximum likelihood (ML) approach, (3) the pseudo class (PC) approach, and (4) the three-step ML approach in terms of their ability to recover covariate effects in the logistic regression class membership model within a growth mixture modeling framework. Results showed that when class separation was large, the one-step ML approach and the three-step ML approach displayed much less biased covariate effect estimates than either the conventional threestep approach or the PC approach. When class separation was poor, estimation of the relation between the dichotomous covariate and latent class variable was severely affected when the new three-step ML approach was used. [ABSTRACT FROM AUTHOR]

We consider copula modeling of the dependence between two or more random variables in the presence of a multivariate covariate. The dependence parameter of the conditional copula possibly depends on the value of the covariate vector. In this paper we develop a new testing methodology for some important parametric specifications of this dependence parameter: constant, linear, quadratic, etc. in the covariate values, possibly after transformation with a link function. The margins are left unspecified. Our novel methodology opens plenty of new possibilities for testing how the conditional copula depends on the multivariate covariate and also for variable selection in copula model building. The suggested test is based on a Rao-type score statistic and regularity conditions are given under which the test has a limiting chi-square distribution under the null hypothesis. For small and moderate sample sizes, a permutation procedure is suggested to assess significance. In simulations it is shown that the test performs well (even under misspecification of the copula family and/or the dependence parameter structure) in comparison to available tests designed for testing for constancy of the dependence parameter. The test is illustrated on a real data set on concentrations of chemicals in water samples. [ABSTRACT FROM AUTHOR]

In dependence modelling using conditional copulas, one often imposes the working assumption that the covariate influences the conditional copula solely through the marginal distributions. This so-called (pairwise) simplifying assumption is almost standardly made in vine copula constructions. However, in recent literature evidence was provided that such an assumption might not be justified. Among the first issues is thus to test for its appropriateness. In this paper nonparametric tests for the null hypothesis of the simplifying assumption are proposed, and their asymptotic behaviours, under the null hypothesis and under some local alternatives, are established. The tests are fully nonparametric in nature: not requiring choices of copula families nor knowledge of the marginals. In a simulation study, the finite-sample size and power performances of the tests are investigated, and compared with these of the few available tests. A real data application illustrates the use of the tests. [ABSTRACT FROM AUTHOR]

Background: Next generation sequencing provides a count of RNA molecules in the form of short reads, yielding discrete, often highly non-normally distributed gene expression measurements. Although Negative Binomial (NB) regression has been generally accepted in the analysis of RNA sequencing (RNA-Seq) data, its appropriateness has not been exhaustively evaluated. We explore logistic regression as an alternative method for RNA-Seq studies designed to compare cases and controls, where disease status is modeled as a function of RNA-Seq reads using simulated and Huntington disease data. We evaluate the effect of adjusting for covariates that have an unknown relationship with gene expression. Finally, we incorporate the data adaptive method in order to compare false positive rates. Results: When the sample size is small or the expression levels of a gene are highly dispersed, the NB regression shows inflated Type-I error rates but the Classical logistic and Bayes logistic (BL) regressions are conservative. Firth's logistic (FL) regression performs well or is slightly conservative. Large sample size and low dispersion generally make Type-I error rates of all methods close to nominal alpha levels of 0.05 and 0.01. However, Type-I error rates are controlled after applying the data adaptive method. The NB, BL, and FL regressions gain increased power with large sample size, large log2 fold-change, and low dispersion. The FL regression has comparable power to NB regression. Conclusions: We conclude that implementing the data adaptive method appropriately controls Type-I error rates in RNA-Seq analysis. Firth's logistic regression provides a concise statistical inference process and reduces spurious associations from inaccurately estimated dispersion parameters in the negative binomial framework. [ABSTRACT FROM AUTHOR]

Purpose: Clinical Trial Simulations (CTS) are a valuable tool for decision-making during drug development. However, to obtain realistic simulation scenarios, the patients included in the CTS must be representative of the target population. This is particularly important when covariate effects exist that may affect the outcome of a trial. The objective of our investigation was to evaluate and compare CTS results using re-sampling from a population pool and multivariate distributions to simulate patient covariates. Methods: COPD was selected as paradigm disease for the purposes of our analysis, FEV1 was used as response measure and the effects of a hypothetical intervention were evaluated in different populations in order to assess the predictive performance of the two methods. Results: Our results show that the multivariate distribution method produces realistic covariate correlations, comparable to the real population. Moreover, it allows simulation of patient characteristics beyond the limits of inclusion and exclusion criteria in historical protocols. Conclusion: Both methods, discrete resampling and multivariate distribution generate realistic pools of virtual patients. However the use of a multivariate distribution enable more flexible simulation scenarios since it is not necessarily bound to the existing covariate combinations in the available clinical data sets. [ABSTRACT FROM AUTHOR]

In today's manufacturing and service systems, entities are progressed across the several stages of operations wherein one or more quality characteristic may be formed. The quality of final system outputs depends on the quality of intermediate characteristics as well as design parameters in each stage. This paper presents a new mathematical program to simultaneously optimize multiple quality characteristics in multiple stage systems. Multivariate form response surface methodology is applied with iterative seemingly unrelated regression as the estimation method to extract the relationships between the outputs and inputs in each stage. Because the intermediate response variables may act as covariates in the next stages, the probabilistic patterns of the response surfaces are considered by association with the quality of the previous stages. The objective function in the proposed model is the acceptance probability of the outputs based on predefined specification limits. A combination of Monte Carlo simulation and the genetic algorithm is also proposed to solve the final stochastic optimization model. At the end, the applicability of the proposed approach is illustrated by a numerical example. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A recent approach to structural equation modelling based on so-called extended redundancy analysis (ERA) has been proposed in the literature, enhanced with the added characteristic of generalizing redundancy analysis (GRA) models for more than two blocks. In this approach, the relationships between the observed exogenous variables and the observed endogenous variables are moderated by the presence of unobservable composites, estimated as linear combinations of exogenous variables. However, in presence of direct effects linking exogenous and endogenous variables, the composite scores are estimated by ignoring the presence of the specified direct effects. In this paper, we generalize the ERA, extending this new class of models to allow for external covariate effects. In particular, covariates are allowed to affect endogenous indicators indirectly through the composites and/or directly. The method proposed herein is called GRA, which allows us to specify and fit a variety of relationships among composites and endogenous variables. In the paper we propose two simulation studies aimed to illustrate the advantages of GRA over ERA in terms of recovery of the original underlying structure of the data in small samples. Moreover, other than the proposal of this new methodology, a second aspect of originality of this paper is that, to our knowledge, no existing empirical research addresses the behaviour of ERA with external covariate effect in simulation studies. [ABSTRACT FROM AUTHOR]