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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]

One of the important purposes in population pharmacokinetic studies is to investigate the relationships between parameters and covariates to describe parameter variability. The purpose of this study is to evaluate the model's ability to correctly detect the parameter-covariate relationship that can be observed in phase I clinical trials. Data were simulated from a two-compartment model with zero-order absorption and first-order elimination, which was built from valsartan's concentration data collected from a previously conducted study. With creatinine clearance (CLCR) being used as a covariate to be tested, 3 different significance levels of 0.001

The application of model-based meta-analysis in drug development has gained prominence recently, particularly for characterizing dose-response relationships and quantifying treatment effect sizes of competitor drugs. The models are typically nonlinear in nature and involve covariates to explain the heterogeneity in summary-level literature (or aggregate data (AD)). Inferring individual patient-level relationships from these nonlinear meta-analysis models leads to aggregation bias. Individual patient-level data (IPD) are indeed required to characterize patient-level relationships but too often this information is limited. Since combined analyses of AD and IPD allow advantage of the information they share to be taken, the models developed for AD must be derived from IPD models; in the case of linear models, the solution is a closed form, while for nonlinear models, closed form solutions do not exist. Here, we propose a linearization method based on a second order Taylor series approximation for fitting models to AD alone or combined AD and IPD. The application of this method is illustrated by an analysis of a continuous landmark endpoint, i.e., change from baseline in HbA1c at week 12, from 18 clinical trials evaluating the effects of DPP-4 inhibitors on hyperglycemia in diabetic patients. The performance of this method is demonstrated by a simulation study where the effects of varying the degree of nonlinearity and of heterogeneity in covariates (as assessed by the ratio of between-trial to within-trial variability) were studied. A dose-response relationship using an Emax model with linear and nonlinear effects of covariates on the emax parameter was used to simulate data. The simulation results showed that when an IPD model is simply used for modeling AD, the bias in the emax parameter estimate increased noticeably with an increasing degree of nonlinearity in the model, with respect to covariates. When using an appropriately derived AD model, the linearization method adequately corrected for bias. It was also noted that the bias in the model parameter estimates decreased as the ratio of between-trial to within-trial variability in covariate distribution increased. Taken together, the proposed linearization approach allows addressing the issue of aggregation bias in the particular case of nonlinear models of aggregate data. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Objective: Aflibercept (Zaltrap) is a novel antiangiogenic agent that binds to vascular endothelial growth factor (VEGF) and inhibits VEGF-dependent tumor growth. We aimed to characterize the population pharmacokinetics (PK) of free and bound aflibercept in patients with solid tumors to examine the influence of covariates on their PK and to evaluate the proposed dosing regimens by simulation. Methods: Data from 9 clinical trials with 1,506 cancer patients receiving aflibercept (2-9 mg/kg every 2 or 3 weeks; 1 h IV infusion) as a monotherapy or in combination with various chemotherapies were included. Free and bound aflibercept concentrations were analyzed using a non-linear mixed-effects modeling approach with MONOLIX 4.1.2. Results: An approximation of a target-mediated drug disposition model with irreversible binding of free aflibercept to VEGF adequately described the PK of free and bound aflibercept. The typical estimated clearances for free (CL) and bound aflibercept (CL) were 0.88 and 0.19 L/day, respectively. The volumes of distribution for free ( V) and bound ( V) aflibercept were similar (~4 L). CL and V increased with body weight and were lower in women. Patients with low albumin (ALB) or high alkaline phosphatase (ALK) had faster CL compared to a typical patient. Pancreatic cancer may be associated with changes in binding of aflibercept to VEGF. Simulations of different dosing regimens showed that adequate saturation of circulating VEGF was achieved with a dose of 4 mg/kg every 2 weeks. Conclusions: Aflibercept kinetics was most affected by gender, body weight, ALB, ALK and pancreatic cancer. Simulations supported the rationale for the recommended dose of 4 mg/kg every 2 weeks for aflibercept. [ABSTRACT FROM AUTHOR]

Abstract: High resolution digital airborne imagery offers unprecedented opportunities for observation and monitoring of vegetation, providing the potential to identify, locate and track individual vegetation objects over time. Analytical tools are required to quantify relevant information. In this paper, locations of trees over a large area of native woodland vegetation were identified using morphological image analysis techniques. Methods of spatial point process statistics were then applied to estimate the spatially-varying tree death risk, and to show that it is significantly non-uniform. [Tree deaths over the area were detected in our previous work (Wallace et al., 2008).] The study area is a major source of ground water for the city of Perth, and the work was motivated by the need to understand and quantify vegetation changes in the context of water extraction and drying climate. The influence of hydrological variables on tree death risk was investigated using spatial statistics (graphical exploratory methods, spatial point pattern modelling and diagnostics). [Copyright &y& Elsevier]

Setting of process variables to meet the required specification of quality characteristics is an important problem in the process quality control. There are often several conflicts in quality characteristics, which should be simultaneously satisfied. These types of problems are called 'Multiple Response Optimization' (MRO). When quality characteristics are correlated, MRO problems may become increasingly difficult. In design of experiments, identifying covariates effects could reduce error and uncovered variances as well as give more insight about the process. This study aims to identify process variables to consider correlated covariates and correlated quality characteristics. It also accommodates dispersion effects and specification limits as well as location effects in a unified framework based on desirability functions. The features of the proposed method are investigated and the results are compared with some existing techniques by applying two numerical examples. [ABSTRACT FROM AUTHOR]

In many complex experiments, nuisance factor may have large effects that must be accounted for. Covariates are one of the most important kinds of nuisance factors that can be measured but cannot be controlled within the experimental runs. In this paper a novel approach is proposed, based on goal programming, to find the best combination of factors so as to optimize multiresponse-multicovariate surfaces with consideration of location and dispersion effects. Furthermore, it is supposed that several covariates considered in the experiment have probability distributions of known form. One objective is to find the most probable values of each covariate. For this purpose, a multiobjective mathematical optimization model is proposed and its efficacy is demonstrated by two numerical examples. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

recent survey reported that many commuter-cyclists had enjoyed leisure bicycling on a regular basis prior to becoming a commuter-cyclist. While bicycling for leisure, it is assumed that they considered various factors that led them to consider becoming commuter-cyclists. This study began with the question of how long it would take for a leisure-cyclist to become a commuter-cyclist, and it focused on the time that elapsed between leisure-cyclists transitioning to commuter-cycling. In order to analyze the time frame, it was hypothesized that the probability that a leisure-cyclist would become a commuter-cyclist at a certain time would be conditional on the duration that elapsed from the onset of leisure cycling till that time, which represents the 'snowballing' or 'inertial' dynamics of duration. A robust methodology, which is known as the 'hazard model,' was adopted to accommodate such characteristics of a time period. In addition, various external covariates such as individual-specific characteristics, variables associated with the current or previous commuting mode, supply variables regarding bicycle facilities, and individual latent propensities were adopted to account for the duration of changes that would be generally applicable. As a result, many useful results were derived that could be used in fomenting policies to promote cycling to work. It was found that government should invest in establishing segregated lanes for leisure- and commuter-cyclists. It also turned out that a long distance to work hinders a leisure-cyclist from progressing to commuter-cycling. According to the results, young white-collar workers who live in high-rise apartments and enjoy intensive leisure-cycling in groups, are a good target toward whom promotions for commuter-cycling should be focused. However, an unfortunate development was that, when compared with car-commuters, it was found that transit-commuters are more likely to become commuter-cyclists. [ABSTRACT FROM AUTHOR]

This article presents methods for testing covariate effect in the Cox proportional hazards model based on Kullback-Leibler divergence and Renyi's information measure. Renyi's measure is referred to as the information divergence of order γ (γ ≠ 1) between two distributions. In the limiting case γ → 1, Renyi's measure becomes Kullback-Leibler divergence. In our case, the distributions correspond to the baseline and one possibly due to a covariate effect. Our proposed statistics are simple transformations of the parameter vector in the Cox proportional hazards model, and are compared with the Wald, likelihood ratio and score tests that are widely used in practice. Finally, the methods are illustrated using two real-life data sets. [ABSTRACT FROM AUTHOR]

To characterize the population pharmacokinetics of bevacizumab and the influence of demographic factors, disease severity, and concomitantly used chemotherapy agents on it’s pharmacokinetic behavior. Data from eight clinical trials with bevacizumab administered by intravenous infusion were included. A total of 4,629 bevacizumab concentrations from 491 patients with solid tumors, who received bevacizumab doses ranging from 1 to 20 mg/kg at a dosing frequency ranging from weekly to every 3 weeks, were analyzed using a nonlinear mixed-effects modeling approach (NONMEM). The best structural model was a two-compartment model with first-order elimination. In the final model, estimated clearance (CL) and central compartment volume of distribution ( V c) were 0.207 L/day and 2.39 L for a typical female. The terminal half-life estimate was ∼20 days for both men and women. Body weight and gender were the most significant covariates to explain interpatient variability for CL and V c. Clearance was 26% faster in men than in women. Patients with low serum albumin and high serum alkaline phosphatase had 19 and 23% faster CL, respectively, than a typical patient. Consistent with the long elimination half life, simulations showed that similar steady-state exposures can be maintained when the weekly mg/kg dose rate is maintained, therefore allowing administration of bevacizumab to coincide with the frequency of administration of the cytotoxic agents. The PK parameters were consistent with those of other IgG molecules. The results support dosing bevacizumab on a once every 2 weeks or once every 3 weeks dosing schedule on a mg/kg basis. [ABSTRACT FROM AUTHOR]

The receiver operating characteristic (ROC) curve has been a popular statistical tool for characterizing the discriminating power of a classifier, such as a biomarker or an imaging modality for disease screening or diagnosis. It has been recognized that the accuracy of a given procedure may depend on some underlying factors, such as subject's demographic characteristics or disease risk factors, among others. Non-parametric- or parametric-based methods tend to be either inefficient or cumbersome when evaluating effect of multiple covariates is the main focus. Here we propose a semi-parametric linear regression framework to model covariate effect. It allows the estimation of sensitivity at given specificity to vary according to the covariates and provides a way to model the area under the ROC curve indirectly. Estimation procedure and asymptotic theory are presented. Extensive simulation studies have been conducted to investigate the validity of the proposed method. We illustrate the new method on a diagnostic test dataset.