Continuous Response Data Research Articles

Mapping socio-economic status using mixed data: a hierarchical Bayesian approach

Abstract We propose a Bayesian hierarchical model to estimate a socio-economic status (SES) index based on mixed dichotomous and continuous variables. In particular, we extend Quinn’s ([2004]. Bayesian factor analysis for mixed ordinal and continuous responses. Political Analysis, 12(4), 338–353. https://doi.org/10.1093/pan/mph022) and Schliep and Hoeting’s ([2013]. Multilevel latent Gaussian process model for mixed discrete and continuous multivariate response data. Journal of Agricultural, Biological, and Environmental Statistics, 18(4), 492–513. https://doi.org/10.1007/s13253-013-0136-z) factor analysis models for mixed dichotomous and continuous variables by allowing a spatial hierarchical structure of key parameters of the model. Unlike most SES assessment models proposed in the literature, the hierarchical nature of this model enables the use of census observations at the household level without needing to aggregate any information a priori. Therefore, it better accommodates the variability of the SES between census tracts and the number of households per area. The proposed model is used in the estimation of a socio-economic index using 10% of the 2010 Ghana census in the Greater Accra Metropolitan area. Out of the 20 observed variables, the number of people per room, access to water piping and flushable toilets differentiated high and low SES areas the best.

Use of Ordered Beta Regression Unveils Cognitive Flexibility Index and Longitudinal Cognitive Training Signatures in Normal and Alzheimer's Disease Pathological Aging.

Generalized linear mixed models (GLMMs) are a cornerstone data analysis strategy in behavioral research because of their robustness in handling non-normally distributed variables. Recently, their integration with ordered beta regression (OBR), a novel statistical tool for managing percentage data, has opened new avenues for analyzing continuous response data. Here, we applied this combined approach to investigate nuanced differences between the 3xTg-AD model of Alzheimer's disease (AD) and their C57BL/6 non-transgenic (NTg) counterparts with normal aging in a 5-day Morris Water Maze (MWM) test protocol. Our longitudinal study included 22 3xTg-AD mice and 15 NTg mice (both male and female) assessed at 12 and 16 months of age. By identifying and analyzing multiple swimming strategies during three different paradigms (cue, place task, and removal), we uncovered genotypic differences in all paradigms. Thus, the NTg group exhibited a higher percentage of direct search behaviors, while an association between circling episodes and 3xTg-AD animals was found. Furthermore, we also propose a novel metric-the "Cognitive Flexibility Index"-which proved sensitive in detecting sex-related differences. Overall, our integrated GLMMs-OBR approach provides a comprehensive insight into mouse behavior in the MWM test, shedding light on the effects of aging and AD pathology.

Quantifying accuracy and precision from continuous response data in studies of spatial perception and crossmodal recalibration

The ability to detect the absolute location of sensory stimuli can be quantified with either error-based metrics derived from single-trial localization errors or regression-based metrics derived from a linear regression of localization responses on the true stimulus locations. Here we tested the agreement between these two approaches in estimating accuracy and precision in a large sample of 188 subjects who localized auditory stimuli from different azimuthal locations. A subsample of 57 subjects was subsequently exposed to audiovisual stimuli with a consistent spatial disparity before performing the sound localization test again, allowing us to additionally test which of the different metrics best assessed correlations between the amount of crossmodal spatial recalibration and baseline localization performance. First, our findings support a distinction between accuracy and precision. Localization accuracy was mainly reflected in the overall spatial bias and was moderately correlated with precision metrics. However, in our data, the variability of single-trial localization errors (variable error in error-based metrics) and the amount by which the eccentricity of target locations was overestimated (slope in regression-based metrics) were highly correlated, suggesting that intercorrelations between individual metrics need to be carefully considered in spatial perception studies. Secondly, exposure to spatially discrepant audiovisual stimuli resulted in a shift in bias toward the side of the visual stimuli (ventriloquism aftereffect) but did not affect localization precision. The size of the aftereffect shift in bias was at least partly explainable by unspecific test repetition effects, highlighting the need to account for inter-individual baseline differences in studies of spatial learning.

Abstract 7352: ScanCT: A tree-based machine learning model to detect single-cell genomic features associated with clinical outcomes

Abstract Single-cell technologies represent a revolutionary approach to resolving cell-type heterogeneity, identifying cells in specialized states, and detecting rare disease-associated cells. With the cost of single-cell technology decreasing substantially, its integration into clinical studies is gaining momentum. A new computational tool is needed to accommodate different single-cell genomics and clinical data formats while accounting for unwanted confounders. The study aims to develop a tree-based machine learning model to leverage the unprecedented resolution of single-cell multi-omics data for delineating the genomic and phenotypic drivers behind diverse immunotherapy responses. The proposed model is called single-cell analysis of Clinical Tree (scanCT), inspired by the Generalized Unbiased Interaction Detection and Estimation method for unbiased gene and protein feature selection and easy interpretation. The scanCT model learns from the data to select the genomic feature that best splits the cells from distinct clinical responses for each tree node. The confounding factors will be regressors in the nodes but not be used for branch splitting, while gene and protein features of interest will split the tree but not enter the regression model in each node. scanCT is built to be free from the biased selection towards variables of a larger number of categories or values. With tree-pruning and cross-validation, scanCT overcomes the over-fitting issue and enhances model generalization, especially for clinical studies with limited patients. Particularly, scanCT naturally fits the hierarchical cell type relationship and handles marker gene and protein interaction effects efficiently. Our approach was tested on single-cell datasets from B-cell malignancy patients undergoing Chimeric Antigen Receptor (CAR)-T cell therapy. The results from the scanCT are highly interpretable. For instance, each branch is a gene-protein combination profile, and cells are naturally partitioned by clinical association. The linear regressions at each leaf node are the clinical predictions for cells following the splitting criteria. The regression intercept is an average estimation of toxicity (e.g., neurotoxicity) or efficacy after controlling for confounder (e.g., tumor burden). scanCT accommodates categorical or continuous clinical response and survival data and is robust to missing values, a frequent challenge in oncological studies. scanCT represents a significant step forward in single-cell data analysis, which merges complex genotypic and phenotypic information with clinical outcomes. The efficacy and toxicity-associated genomic signatures will inform new manufacturing strategies to optimize CAR-T cell therapy products. The model and clinical association detections are expected to go beyond the B-cell malignancy field to benefit the broader cancer research community. Citation Format: Ye Zheng, Long Nguyen, Peigen Zhou, Alexandre V. Hirayama. ScanCT: A tree-based machine learning model to detect single-cell genomic features associated with clinical outcomes [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 7352.

Diverse mutant selection windows shape spatial heterogeneity in evolving populations.

Mutant selection windows (MSWs), the range of drug concentrations that select for drug-resistant mutants, have long been used as a model for predicting drug resistance and designing optimal dosing strategies in infectious disease. The canonical MSW model offers comparisons between two subtypes at a time: drug-sensitive and drug-resistant. In contrast, the fitness landscape model with N alleles, which maps genotype to fitness, allows comparisons between N genotypes simultaneously, but does not encode continuous drug response data. In clinical settings, there may be a wide range of drug concentrations selecting for a variety of genotypes in both cancer and infectious diseases. Therefore, there is a need for a more robust model of the pathogen response to therapy to predict resistance and design new therapeutic approaches. Fitness seascapes, which model genotype-by-environment interactions, permit multiple MSW comparisons simultaneously by encoding genotype-specific dose-response data. By comparing dose-response curves, one can visualize the range of drug concentrations where one genotype is selected over another. In this work, we show how N-allele fitness seascapes allow for N * 2N-1 unique MSW comparisons. In spatial drug diffusion models, we demonstrate how fitness seascapes reveal spatially heterogeneous MSWs, extending the MSW model to more fully reflect the selection of drug resistant genotypes. Furthermore, using synthetic data and empirical dose-response data in cancer, we find that the spatial structure of MSWs shapes the evolution of drug resistance in an agent-based model. By simulating a tumor treated with cyclic drug therapy, we find that mutant selection windows introduced by drug diffusion promote the proliferation of drug resistant cells. Our work highlights the importance and utility of considering dose-dependent fitness seascapes in evolutionary medicine.

Analyzing clustered continuous response variables with ordinal regression models.

Continuous response data are regularly transformed to meet regression modeling assumptions. However, approaches taken to identify the appropriate transformation can be ad hoc and can increase model uncertainty. Further, the resulting transformations often vary across studies leading to difficulties with synthesizing and interpreting results. When a continuous response variable is measured repeatedly within individuals or when continuous responses arise from clusters, analyses have the additional challenge caused by within-individual or within-cluster correlations. We extend a widely used ordinal regression model, the cumulative probability model (CPM), to fit clustered, continuous response data using generalized estimating equationsfor ordinal responses. With the proposed approach, estimates of marginal model parameters, cumulative distribution functions , expectations, and quantiles conditional on covariates can be obtained without pretransformation of the response data. While computational challenges arise with large numbers of distinct values of the continuous response variable, we propose feasible and computationally efficient approaches to fit CPMs under commonly used working correlation structures. We study finite sample operating characteristics of the estimators via simulation and illustrate their implementation with two data examples. One studies predictors of CD4:CD8 ratios in a cohort living with HIV, and the other investigates the association of a single nucleotide polymorphism and lung function decline in a cohort with early chronic obstructive pulmonarydisease.

Embracing asymmetry in nature: How to account for skewness in ecological data

Asymmetric regression is an alternative to conventional linear regression that allows us to model the relationship between predictor variables and the response variable while accommodating skewness. Advantages of asymmetric regression include incorporating realistic ecological patterns observed in data, robustness to model misspecification and less sensitivity to outliers. Bayesian asymmetric regression relies on asymmetric distributions such as the asymmetric Laplace (ALD) or asymmetric normal (AND) in place of the normal distribution used in classic linear regression models. Asymmetric regression concepts can be used for process and parameter components of hierarchical Bayesian models and have a wide range of applications in data analyses. In particular, asymmetric regression allows us to fit more realistic statistical models to skewed data and pairs well with Bayesian inference. We first describe asymmetric regression using the ALD and AND. Second, we show how the ALD and AND can be used for Bayesian quantile and expectile regression for continuous response data. Third, we consider an extension to generalize Bayesian asymmetric regression to survey data consisting of counts of objects. Fourth, we describe a regression model using the ALD, and show that it can be applied to add needed flexibility, resulting in better predictive models compared to Poisson or negative binomial regression. We demonstrate concepts by analyzing a data set consisting of counts of Henslow’s sparrows following prescribed fire and provide annotated computer code to facilitate implementation. Our results suggest Bayesian asymmetric regression is an essential component of a scientist’s statistical toolbox.

Prediction of size-selective permitted daily exposures for mineral oil mist based on an in vitro study in different scenarios

ABSTRACT The incidence of DNA damage from exposure to specific types of metalworking fluids has been reported. In this research, size-selective permissible limits to prevent genotoxic damage in A549 cell lines exposed to two types of mineral oil were estimated for the first time using a benchmark dose approach and extrapolated to workers. The comet assay was performed based on Olive and Banath protocol to determine DNA damage. Then, the Benchmark Dose, the 95% lower bound confidence limit BMD, and the 95% upper-bound confidence limit BMD were determined using continuous response data. Finally, the four Benchmark Dose levels reported in the A549 cell line were extrapolated to the human population in occupational settings in two phases. This study showed when determining the permissible limits, the type used or unused, the type of injury, the organ affected in the body and the size of the particles should also be considered.

Confirmatory Factor Analyses in Psychological Test Adaptation and Development

Confirmatory Factor Analyses in Psychological Test Adaptation and Development

Weighted generalized estimating equations and unified estimation for longitudinal data with nonmonotone missing data patterns

Missing data are a major complication in longitudinal data analysis. Weighted generalized estimating equations (WGEEs, Robins et al, J Am Stat Assoc 1995;90:106-121) were developed to deal with missing response data. They have been extended for data with both missing responses and missing covariates (Chen et al, J Am Stat Assoc 2010;105:336-353). However, it may introduce more variability in dealing with the correlation structure of the responses. We propose new WGEEs for missing at random data where both response and (time-dependent) covariates may have values missing in nonmonotone missing data patterns. We also explain how to improve the estimation efficiency of WGEEs using a unified approach (Zhao and Liu, AStA Adv Stat Anal 2021;105(1):87-101). The proposed unified estimator is consistent and more efficient than the regular WGEE estimator. It is computationally simple and can be directly implemented in standard software. Simulation studies for both continuous response and binary response data are provided to examine the performance of the proposed estimators. A clinical trial example investigating the quality of life of women with early-stage breast cancer and the associated factors is analyzed.

Bayesian beta regression for bounded responses with unknown supports

A new Bayesian regression framework is presented for the analysis of continuous response data with support restricted to an unknown finite interval. A four-parameter beta distribution is assumed for the response conditioning on covariates, with the mean or mode depending linearly on covariates through a known link function. An informative g-prior is proposed to incorporate the prior distribution for the marginal mean or mode of the response. Byproducts of the Markov chain Monte Carlo sampling for implementing the proposed method lead to model criteria useful for model selection. Goodness-of-fit of the model is assessed using Cox-Snell residual plots. The methodology is illustrated in simulations and demonstrated in two real-life data applications. An R package, betaBayes, is developed for easy implementation of the proposed regression methodology.

Central tendency biases must be accounted for to consistently capture Bayesian cue combination in continuous response data

Observers in perceptual tasks are often reported to combine multiple sensory cues in a weighted average that improves precision—in some studies, approaching statistically optimal (Bayesian) weighting, but in others departing from optimality, or not benefitting from combined cues at all. To correctly conclude which combination rules observers use, it is crucial to have accurate measures of their sensory precision and cue weighting. Here, we present a new approach for accurately recovering these parameters in perceptual tasks with continuous responses. Continuous responses have many advantages, but are susceptible to a central tendency bias, where responses are biased towards the central stimulus value. We show that such biases lead to inaccuracies in estimating both precision gains and cue weightings, two key measures used to assess sensory cue combination. We introduce a method that estimates sensory precision by regressing continuous responses on targets and dividing the variance of the residuals by the squared slope of the regression line, “correcting-out” the error introduced by the central bias and increasing statistical power. We also suggest a complementary analysis that recovers the sensory cue weights. Using both simulations and empirical data, we show that the proposed methods can accurately estimate sensory precision and cue weightings in the presence of central tendency biases. We conclude that central tendency biases should be (and can easily be) accounted for to consistently capture Bayesian cue combination in continuous response data.

Simplifying Bias Correction for Selective Sampling: A Unified Distribution-Free Approach to Handling Endogenously Selected Samples

Unlike random sampling, selective sampling draws units based on the outcome values, such as over-sampling rare events in choice outcomes and extreme activities on continuous and count outcomes. Despite high cost effectiveness for marketing research, such endogenously selected samples must be carefully analyzed to avoid selection bias. We introduce a unified and efficient approach based on semiparametric odds ratio (SOR) models applicable for categorical, continuous and count response data collected using selective sampling. Unlike extant sampling-adjusting methods and Heckman-type selection models, the proposed approach requires neither modeling selection mechanisms nor imposing parametric distributional assumptions on the response variables, eliminating both sources of mis-specification bias. Using this approach, one can quantify and test for the relationships among variables as if samples had been collected via random sampling, simplifying bias correction of endogenously selected samples. We evaluate and illustrate the method using extensive simulation studies and two real data examples: endogenously stratified sampling for linear/nonlinear regressions to identify drivers of the share-of-wallet outcome for cigarettes smokers, and using truncated and on-site samples for count data models of store shopping demand. The evaluation shows that selective sampling followed by applying the SOR approach reduces required sample size by more than 70% compared with random sampling, and that in a wide range of selective sampling scenarios SOR offers novel solutions outperforming extant methods for selective samples with opportunities to make better managerial decisions.

Distribution-free regression model selection with a nested spatial correlation structure

In spatial regression analysis, a suitable specification of the mean regression model is crucial for unbiased analysis. Also, to enhance statistical efficiency of the mean regression analysis, we need to suitably account for the underlying spatial correlation structure. In this paper, we focus on selection of an appropriate mean model in spatial regression analysis under a general anisotropic nested correlation structure considered in Adegboye et al. (2018). We propose a distribution-free model selection criterion, called the Spatial Information Criterion (SIC), which is an estimate of the weighted mean squared error for predicting the response variable, and relies on assumptions only for the first two moments of the spatial response data. The simulations under the settings of covariate selection reveal that the SIC performs well for covariate selection in the mean model regardless of the correlation structure is nested/non-nested (multi-source or not), isotropic/anisotropic (direction-dependent or not). Also, the SIC accommodates both continuous and count response data. We illustrate the utility of the proposed method by a real data application concerning the predictive regression model for the fine particulate matter (PM2.5) concentration.

R$^{2}$s for Correlated Data: Phylogenetic Models, LMMs, and GLMMs

Many researchers want to report an $R^{2}$ to measure the variance explained by a model. When the model includes correlation among data, such as phylogenetic models and mixed models, defining an $R^{2}$ faces two conceptual problems. (i) It is unclear how to measure the variance explained by predictor (independent) variables when the model contains covariances. (ii) Researchers may want the $R^{2}$ to include the variance explained by the covariances by asking questions such as "How much of the data is explained by phylogeny?" Here, I investigated three $R^{2}$s for phylogenetic and mixed models. $R^{2}_{resid}$ is an extension of the ordinary least-squares $R^{2}$ that weights residuals by variances and covariances estimated by the model; it is closely related to $R^{2}_{glmm}$ presented by Nakagawa and Schielzeth (2013. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods Ecol. Evol. 4:133-142). $R^{2}_{pred}$ is based on predicting each residual from the fitted model and computing the variance between observed and predicted values. $R^{2}_{lik}$ is based on the likelihood of fitted models, and therefore, reflects the amount of information that the models contain. These three $R^{2}$s are formulated as partial $R^{2}$s, making it possible to compare the contributions of predictor variables and variance components (phylogenetic signal and random effects) to the fit of models. Because partial $R^{2}$s compare a full model with a reduced model without components of the full model, they are distinct from marginal $R^{2}$s that partition additive components of the variance. I assessed the properties of the $R^{2}$s for phylogenetic models using simulations for continuous and binary response data (phylogenetic generalized least squares and phylogenetic logistic regression). Because the $R^{2}$s are designed broadly for any model for correlated data, I also compared $R^{2}$s for linear mixed models and generalized linear mixed models. $R^{2}_{resid}$, $R^{2}_{pred}$, and $R^{2}_{lik}$ all have similar performance in describing the variance explained by different components of models. However, $R^{2}_{pred}$ gives the most direct answer to the question of how much variance in the data is explained by a model. $R^{2}_{resid}$ is most appropriate for comparing models fit to different data sets, because it does not depend on sample sizes. And $R^{2}_{lik}$ is most appropriate to assess the importance of different components within the same model applied to the same data, because it is most closely associated with statistical significance tests.

Analyzing continuous randomized response data with an indifference-zone selection procedure

ABSTRACTA review of the randomized response model introduced by Warner (1965) is given, then a randomized response model applicable to continuous data that considers a mixture of two normal distributions is considered. The target here is not to estimate any parameter, but rather to select the population with the best parameter value. This article provides a study on how to choose the best population between k distinct populations using an indifference-zone procedure. Also, this article includes tables for the required sample size needed in order to have a probability of correct selection higher than some specified value in the preference zone for the randomized response model considered.

Openness to experience and adapting to change: Cardiovascular stress habituation to change in acute stress exposure.

Underlying psychophysiological mechanisms of effect linking openness to experience to health outcomes, and particularly cardiovascular well-being, are unknown. This study examined the role of openness in the context of cardiovascular responsivity to acute psychological stress. Continuous cardiovascular response data were collected for 74 healthy young female adults across an experimental protocol, including differing counterbalanced acute stressors. Openness was measured via self-report questionnaire. Analysis of covariance revealed openness was associated with systolic blood pressure (SBP; p = .016), and diastolic blood pressure (DBP; p = .036) responsivity across the protocol. Openness was also associated with heart rate (HR) responding to the initial stress exposure (p = .044). Examination of cardiovascular adaptation revealed that higher openness was associated with significant SBP (p = .001), DBP (p = .009), and HR (p = .002) habituation in response to the second differing acute stress exposure. Taken together, the findings suggest persons higher in openness are characterized by an adaptive cardiovascular stress response profile within the context of changing acute stress exposures. This study is also the first to demonstrate individual differences in cardiovascular adaptation across a protocol consisting of differing stress exposures. More broadly, this research also suggests that future research may benefit from conceptualizing an adaptive fitness of openness within the context of change. In summary, the present study provides evidence that higher openness stimulates short-term stress responsivity, while ensuring cardiovascular habituation to change in stress across time.

A Cognitive Diagnosis Model for Continuous Response

Nondichotomous response models have been of greater interest in recent years due to the increasing use of different scoring methods and various performance measures. As an important alternative to dichotomous scoring, the use of continuous response formats has been found in the literature. To assess finer-grained skills or attributes and to extract information with diagnostic value from continuous response data, a multidimensional skills diagnosis model for continuous response is proposed. An expectation-maximization implementation of marginal maximum likelihood estimation is developed to estimate its parameters. The viability of the proposed model is shown via a simulation study and a real data example. The proposed model is also shown to provide a substantial improvement in attribute classification when compared to a model based on dichotomized continuous responses.

Continuously evolving ‘chemical tongue’ biosensor for detecting proteins

We developed a unique continuously evolving colorimetric sensor array based on AuNPs decorated by two single-stranded oligonucleotides with different molar ratios for protein discrimination. The number of differential receptors in this sensor array could be easily extended by adjusting the molar ratios of two DNA, resulting in continuously improved discrimination ability. The continuous response data of target samples against our sensing system could be easily obtained and exclude abnormal signals. The sensing system could discriminate twelve proteins at the concentration of 200nM in the presence of 50% human urine with accuracy of 100%, showing feasible potential for diagnostic applications. Remarkably, HSA at various concentrations, the pure Lys and HSA, and the mixture of these two proteins with different molar ratios had been successfully discriminated in LDA plot as well in the presence of human urine sample. This novel strategy will be very promising for the design of cheaper and more reliable sensor arrays for target samples.

Study on probability of detection (POD) determination using lock-in thermography for nondestructive inspection (NDI) of CFRP composite materials

In this work, an extension laser beam was used as heating source to evaluate the composite material by active thermographic method. In particular, a series of carbon-fiber-reinforced polymer (CFRP) specimens with various depth and sizes of flat-bottom holes (FBH) were inspected using lock-in thermography (LIT). The quantitative LIT phase was employed to identification the subsurface defect using the phase decision threshold (PDT, a phase deference between defective area and the sound one), and then the detectable and undetectable defects were expressed as 1 and 0 (hit/miss data), respectively. The POD curves of continuous phase response data and the hit/miss data processing were used for estimation the detection capability and reliability of LIT phase image for NDI&E of CFRP composites, and the effects of PDT value and modulation frequency on POD curves were compared.