Estimation Of Covariate Effects Research Articles

A Statistical Framework for Analysis of Trial-Level Temporal Dynamics in Fiber Photometry Experiments.

Fiber photometry has become a popular technique to measure neural activity in vivo, but common analysis strategies can reduce detection of effects because they condense within-trial signals into summary measures, and discard trial-level information by averaging across-trials. We propose a novel photometry statistical framework based on functional linear mixed modeling, which enables hypothesis testing of variable effects at every trial time-point, and uses trial-level signals without averaging. This makes it possible to compare the timing and magnitude of signals across conditions while accounting for between-animal differences. Our framework produces a series of plots that illustrate covariate effect estimates and statistical significance at each trial time-point. By exploiting signal autocorrelation, our methodology yields joint 95% confidence intervals that account for inspecting effects across the entire trial and improve the detection of event-related signal changes over common multiple comparisons correction strategies. We reanalyze data from a recent study proposing a theory for the role of mesolimbic dopamine in reward learning, and show the capability of our framework to reveal significant effects obscured by standard analysis approaches. For example, our method identifies two dopamine components with distinct temporal dynamics in response to reward delivery. In simulation experiments, our methodology yields improved statistical power over common analysis approaches. Finally, we provide an open-source package and analysis guide for applying our framework.

Exploring time-to-event analysis models: A study of accelerated failure time and weighted least square estimation

Background: This study explores time-to-event analysis models, focusing on the comparison between accelerated failure time (AFT) and weighted least square estimation (WLSE) methods in analyzing survival data, emphasizing the challenge of heteroscedasticity in real-world datasets. Methods: Using the North Central Cancer Treatment Group (NCCTG) Lung Cancer dataset, five parametric AFT distributions (exponential, Weibull, log-logistic, log-normal, and generalized gamma) were evaluated. The log-likelihood method was utilized to calculate the AIC and BIC values for each distribution to determine the best fit model. Results: Among the different distributions tested, the Weibull distribution was identified as the best fit model based with the lowest AIC and BIC values of 2311.70 and 2318.56, respectively. This distribution played a crucial role in determining factors associated with the cancer data. Specifically, the variablecalories consumed at a meal (meal.cal) was associated with cancer patient recovery, with an estimate of 0.00004 and a standard error of 0.0002. Results indicated homoscedastic data through the Breusch-Pagan test. Moreover, the results demonstrated that when dealing with homoscedastic data, the Weibull AFT model outperformed WLSE in producing statistically significant effects and precise estimates. Conclusion: For data exhibiting homoscedasticity, the AFT method yielded superior results compared to WLSE in terms of statistical significance and precision. Therefore, it is advisable to employ AFT for homoscedastic data and WLSE for heteroscedastic data to enhance the accuracy of covariate effect estimates in survival analysis.

A conditional approach for regression analysis of case K interval-censored failure time data with informative censoring

This paper discusses regression analysis of case K interval-censored failure time data, a general type of failure time data, in the presence of informative censoring with the focus on simultaneous variable selection and estimation. Although many authors have considered the challenging variable selection problem for interval-censored data, most of the existing methods assume independent or non-informative censoring. More importantly, the existing methods that allow for informative censoring are frailty model-based approaches and cannot directly assess the degree of informative censoring among other shortcomings. To address these, we propose a conditional approach and develop a penalized sieve maximum likelihood procedure for the simultaneous variable selection and estimation of covariate effects. Furthermore, we establish the oracle property of the proposed method and illustrate the appropriateness and usefulness of the approach using a simulation study. Finally we apply the proposed method to a set of real data on Alzheimer's disease and provide some new insights.

Spatial Confounding and Spatial+ for Nonlinear Covariate Effects

Regression models for spatially varying data use spatial random effects to reflect spatial correlation structure. Such random effects, however, may interfere with the covariate effect estimates and make them unreliable. This problem, known as spatial confounding, is complex and has only been studied for models with linear covariate effects. However, as illustrated by a forestry example in which we assess the effect of soil, climate, and topography variables on tree health, the covariate effects of interest are in practice often unknown and nonlinear. We consider, for the first time, spatial confounding in spatial models with nonlinear effects implemented in the generalised additive models (GAMs) framework. We show that spatial+, a recently developed method for alleviating confounding in the linear case, can be adapted to this setting. In practice, spatial+ can then be used both as a diagnostic tool for investigating whether covariate effect estimates are affected by spatial confounding and for correcting the estimates for the resulting bias when it is present. Supplementary materials accompanying this paper appear online.

Integrating machine learning and Bayesian nonparametrics for flexible modeling of point pattern data

Two common approaches to analyze point pattern (location-only) data are mixture models and log-Gaussian Cox processes. The former provides a flexible model for the intensity surface at the expense of no covariate effect estimates while the latter estimates covariate effects at the expense of computation. A bridge is built between these two methods that leverages the strengths of both approaches. Namely, Bayesian nonparametrics are first used to flexibly model the intensity surface. The posterior draws of the fitted intensity surface are then transformed into the equivalent representation under the log-Gaussian Cox process approach. Using principles of machine learning, estimates of covariate effects are obtained. The proposed two-step approach results in accurate estimates of parameters, with proper uncertainty quantification, which is illustrated with real and simulated examples.

Analysis of Multivariate Survival Data under Semiparametric Copula Models

AbstractModelling multivariate survival data is complicated by the complex association structure among the responses. To balance model flexibility and interpretability, we propose a semiparametric copula model to modulate multivariate survival data, with the marginal distributions of the response components described by semiparametric linear transformation models. To conduct inference about the model parameters, we develop a two‐stage maximum likelihood method and a three‐stage pseudo‐likelihood estimation procedure. We investigate the impact of model misspecification on the estimation of covariate effects and identify a scenario in which consistent estimation of the marginal parameters is retained even when the copula model is misspecified. The proposed methods are justified both theoretically and empirically. An application to a real dataset is provided to demonstrate the utility of the proposed method.

A spatio-temporal hierarchical model to account for temporal misalignment in American Community Survey explanatory variables

The American Community Survey (ACS) is one of the most vital public sources for demographic and socioeconomic characteristics of communities in the United States and is administered by the U.S. Census Bureau every year. The ACS publishes 5-year estimates of community characteristics for all geographical areas and 1-year estimates for areas with population of at least 65,000. Many epidemiological and public health studies use 5-year ACS estimates as explanatory variables in models. However, doing so ignores the uncertainty and averages over variability during the time-period which may lead to biased estimates of covariate effects of interest. In this paper, we propose a Bayesian hierarchical model that accounts for the uncertainty and disentangles the temporal misalignment in the ACS multi-year time-period estimates. We show via simulation that our proposed model more accurately recovers covariate effects compared to models that ignore the temporal misalignment. Lastly, we implement our proposed model to quantify the relationship between yearly, county-level characteristics and the prevalence of frequent mental distress for counties in North Carolina from 2014 to 2018.

Pseudo-value regression of clustered multistate current status data with informative cluster sizes.

Multistate current status data presents a more severe form of censoring due to the single observation of study participants transitioning through a sequence of well-defined disease states at random inspection times. Moreover, these data may be clustered within specified groups, and informativeness of the cluster sizes may arise due to the existing latent relationship between the transition outcomes and the cluster sizes. Failure to adjust for this informativeness may lead to a biased inference. Motivated by a clinical study of periodontal disease, we propose an extension of the pseudo-value approach to estimate covariate effects on the state occupation probabilities for these clustered multistate current status data with informative cluster or intra-cluster group sizes. In our approach, the proposed pseudo-value technique initially computes marginal estimators of the state occupation probabilities utilizing nonparametric regression. Next, the estimating equations based on the corresponding pseudo-values are reweighted by functions of the cluster sizes to adjust for informativeness. We perform a variety of simulation studies to study the properties of our pseudo-value regression based on the nonparametric marginal estimators under different scenarios of informativeness. For illustration, the method is applied to the motivating periodontal disease dataset, which encapsulates the complex data-generation mechanism.

Spatial heterogeneity automatic detection and estimation

Spatial regression is widely used for modeling the relationship between a dependent variable and explanatory covariates. Oftentimes, the linear relationships vary across space, such that some covariates have location-specific effects on the response. One fundamental question is how to detect the systematic variation in the model and identify which locations share common regression coefficients and which do not. Only a correct model structure can assure unbiased estimation of coefficients and valid inferences. A new procedure is proposed, called Spatial Heterogeneity Automatic Detection and Estimation (SHADE), for automatically and simultaneously subgrouping and estimating covariate effects for spatial regression models. The SHADE employs a class of spatially-weighted fusion type penalty on all pairs of observations, with location-specific weight constructed using spatial information, to cluster coefficients into subgroups. Under certain regularity conditions, the SHADE is shown to be able to identify the true model structure with probability approaching one and estimate regression coefficients consistently. An alternating direction method of multiplier algorithm (ADMM) is developed to compute the SHADE. In numerical studies, the empirical performance of the SHADE is demonstrated by using different choices of weights and comparing their accuracy. The results suggest that spatial information can enhance subgroup structure analysis in challenging situations when the spatial variation among regression coefficients is small or the number of repeated measures is small. Finally, the SHADE is applied to find the relationship between a natural resource survey and a land cover data layer to identify spatially interpretable groups.

Fifty Years of the Cox Model

The Cox model is now 50 years old. The seminal paper of Sir David Cox has had an immeasurable impact on the analysis of censored survival data, with applications in many different disciplines. This work has also stimulated much additional research in diverse areas and led to important theoretical and practical advances. These include semiparametric models, nonparametric efficiency, and partial likelihood. In addition to quickly becoming the go-to method for estimating covariate effects, Cox regression has been extended to a vast number of complex data structures, to all of which the central idea of sampling from the set of individuals at risk at time t can be applied. In this article, we review the Cox paper and the evolution of the ideas surrounding it. We then highlight its extensions to competing risks, with attention to models based on cause-specific hazards, and to hazards associated with the subdistribution or cumulative incidence function. We discuss their relative merits and domains of application. The analysis of recurrent events is another major topic of discussion, including an introduction to martingales and complete intensity models as well as the more practical marginal rate models. We include several worked examples to illustrate the main ideas.

Adaptive Bayesian sum of trees model for covariate-dependent spectral analysis.

This paper introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture complex dependencies and interactions between covariates and the power spectrum, which are often observed in studies of biomedical time series. Local power spectra corresponding to terminal nodes within trees are estimated nonparametrically using Bayesian penalized linear splines. The trees are considered to be random and fit using a Bayesian backfitting Markov chain Monte Carlo (MCMC) algorithm that sequentially considers tree modifications via reversible-jump MCMC techniques. For high-dimensional covariates, a sparsity-inducing Dirichlet hyperprior on tree splitting proportions is considered, which provides sparse estimation of covariate effects and efficient variable selection. By averaging over the posterior distribution of trees, the proposed method can recover both smooth and abrupt changes in the power spectrum across multiple covariates. Empirical performance is evaluated via simulations to demonstrate the proposed method's ability to accurately recover complex relationships and interactions. The proposed methodology is used to study gait maturation in young children by evaluating age-related changes in power spectra of stride interval time series in the presence of othercovariates.

Joint integrative analysis of multiple data sources with correlated vector outcomes

We propose a distributed quadratic inference function framework to jointly estimate regression parameters from multiple potentially heterogeneous data sources with correlated vector outcomes. The primary goal of this joint integrative analysis is to estimate covariate effects on all outcomes through a marginal regression model in a statistically and computationally efficient way. We develop a data integration procedure for statistical estimation and inference of regression parameters that is implemented in a fully distributed and parallelized computational scheme. To overcome computational and modeling challenges arising from the high-dimensional likelihood of the correlated vector outcomes, we propose to analyze each data source using Qu, Lindsay and Li’s (Biometrika 87 (2000) 823–836) quadratic inference functions and then to jointly reestimate parameters from each data source by accounting for correlation between data sources using a combined meta-estimator in a similar spirit to the generalized method of moments put forward by Hansen (Econometrica 50 (1982) 1029–1054). We show both theoretically and numerically that the proposed method yields efficiency improvements and is computationally fast. We illustrate the proposed methodology with the joint integrative analysis of the association between smoking and metabolites in a large multicohort study and provide an R package for ease of implementation.

O5-4 Technology-based physical activity interventions acceptability in obese females: a latent profile transition analysis

BackgroundTechnology-based physical activity interventions (TbPAI) have recently been shown to be effective for care of obese women (Cotie et al., 2018). Therefore, it is necessary to assess the acceptability of TbPAI to ensure dissemination and usage in the treatment of obesity (Venkatesh et al., 2012).As such, the purpose of this study was to: (1) identify acceptability profiles of three TbPAI in obesity care (e.g., active video games, mobile applications, videoconferencing); (2) examine the issues of consistency or change of acceptability profiles for the same individual across the three technology; and (3) explore whether technology acceptability profiles were associated with motivation for physical activity (PA), general causality orientations for PA and sociodemographic data.MethodsThree hundred and twelve women with a mean age of 30.7 (SD=7.1) years, and a mean BMI of 34.9 (SD=9.2) kg/m2 were recruited from health services that provide obesity management. Enrolled participants completed an online survey including the following measures: motivation for PA, general causality orientations for PA, TbPAI acceptability for the three selected technologies based on the UTAUT2 model (Venkatesh et al., 2012), and sociodemographic data. Ethical approval was gained by local committee, and informed consent were obtained from the participants before data collected. We used a Latent Profile Transition Analysis (LPTA) approach.ResultsA 2-class model (high and low acceptability) best described latent classes for each technology. Acceptability profiles changed over the technologies. Among our sample, only 8.0% (n = 25) of women have low acceptability of all technologies, and 57.7% (n = 180) have high acceptability of all technologies. The covariate effect estimates showed significant effects of: (a) age and control causality orientation on video games acceptability profiles, (b) intrinsic motivation and impersonal causality orientation on videoconferencing profiles, and (c) control and impersonal causality orientations on mobile applications profiles.ConclusionsA LPTA approach may prove usefulness in understanding TbPAI acceptability in the obesity treatment and have implications for implementation and dissemination of such technologies.

Active-set algorithm-based statistical inference for shape-restricted generalized additive Cox regression models

Recently the shape-restricted inference has gained popularity in statistical and econometric literature to relax the linear or quadratic covariate effect in regression analyses. The typical shape-restricted covariate effect includes monotone increasing, decreasing, convexity or concavity. In this paper, we introduce the shape-restricted inference to the celebrated Cox regression model (SR-Cox), in which the covariate response is modelled as shape-restricted additive functions. The SR-Cox regression approximates the shape-restricted functions using a spline basis expansion with data-driven choice of knots. The underlying minimization of negative log-likelihood function is formulated as a convex optimization problem, which is solved with an active-set optimization algorithm. The highlight of this algorithm is that it eliminates the superfluous knots automatically. When covariate effects include combinations of convex or concave terms with unknown forms and linear terms, the most interesting finding is that SR-Cox produces accurate linear covariate effect estimates which are comparable to the maximum partial likelihood estimates if indeed the forms are known. We conclude that concave or convex SR-Cox models could significantly improve nonlinear covariate response recovery and model goodness of fit.

Spatial+: A novel approach to spatial confounding.

In spatial regression models, collinearity between covariates and spatial effects can lead to significant bias in effect estimates. This problem, known as spatial confounding, is encountered modeling forestry data to assess the effect of temperature on tree health. Reliable inference is difficult as results depend on whether or not spatial effects are included in the model. We propose a novel approach, spatial+, for dealing with spatial confounding when the covariate of interest is spatially dependent but not fully determined by spatial location. Using a thin plate spline model formulation we see that, in this case, the bias in covariate effect estimates is a direct result of spatial smoothing. Spatial+ reduces the sensitivity of the estimates to smoothing by replacing the covariates by their residuals after spatial dependence has been regressed away. Through asymptotic analysis we show that spatial+ avoids the bias problems of the spatial model. This is also demonstrated in a simulation study. Spatial+ is straightforward to implement using existing software and, as the response variable is the same as that of the spatial model, standard model selection criteria can be used for comparisons. A major advantage of the method is also that it extends to models with non-Gaussian response distributions. Finally, while our results are derived in a thin plate spline setting, the spatial+ methodology transfers easily to other spatial modelformulations.

Association testing for binary trees-A Markov branching process approach.

We propose a new approach to test associations between binary trees and covariates. In this approach, binary‐tree structured data are treated as sample paths of binary fission Markov branching processes (bMBP). We propose a generalized linear regression model and developed inference procedures for association testing, including variable selection and estimation of covariate effects. Simulation studies show that these procedures are able to accurately identify covariates that are associated with the binary tree structure by impacting the rate parameter of the bMBP. The problem of association testing on binary trees is motivated by modeling hierarchical clustering dendrograms of pixel intensities in biomedical images. By using semi‐synthetic data generated from a real brain‐tumor image, our simulation studies show that the bMBP model is able to capture the characteristics of dendrogram trees in brain‐tumor images. Our final analysis of the glioblastoma multiforme brain‐tumor data from The Cancer Imaging Archive identified multiple clinical and genetic variables that are potentially associated with brain‐tumor heterogeneity.

Bayesian subcohort selection for longitudinal covariate measurements in follow‐up studies

AbstractWe propose an approach for the planning of longitudinal covariate measurements in follow‐up studies where covariates are time‐varying. We assume that the entire cohort cannot be selected for longitudinal measurements due to financial limitations, and study how a subset of the cohort should be selected optimally, in order to obtain precise estimates of covariate effects in a survival model. In our approach, the study will be designed sequentially utilizing the data collected in previous measurements of the individuals as prior information. We propose using a Bayesian optimality criterion in the subcohort selections, which is compared with simple random sampling using simulated and real follow‐up data. Our work improves the computational approach compared to the previous research on the topic so that designs with several covariates and measurement points can be implemented. As an example we derive the optimal design for studying the effect of body mass index and smoking on all‐cause mortality in a Finnish longitudinal study. Our results support the conclusion that the precision of the estimates can be clearly improved by optimal design.

Robust nonparametric integrative analysis to decipher heterogeneity and commonality across subgroups using sparse boosting.

In many biomedical problems, data are often heterogeneous, with samples spanning multiple patient subgroups, where different subgroups may have different disease subtypes, stages, or other medical contexts. These subgroups may be related, but they are also expected to have differences with respect to the underlying biology. The heterogeneous data presents a precious opportunity to explore the heterogeneities and commonalities between related subgroups. Unfortunately, effective statistical analysis methods are still lacking. Recently, several novel methods based on integrative analysis have been proposed to tackle this challenging problem. Despite promising results, the existing studies are still limited by ignoring data contamination and making strict assumptions of linear effects of covariates on response. As such, we develop a robust nonparametric integrative analysis approach to identify heterogeneity and commonality, as well as select important covariates and estimate covariate effects. Possible data contamination is accommodated by adopting the Cauchy loss function, and a nonparametric model is built to accommodate nonlinear effects. The proposed approach is based on a sparse boosting technique. The advantages of the proposed approach are demonstrated in extensive simulations. The analysis of The Cancer Genome Atlas data on glioblastoma multiforme and lung adenocarcinoma shows that the proposed approach makes biologically meaningful findings with satisfactory prediction.

Hierarchical Bayesian estimation of covariate effects on airway and alveolar nitric oxide

Exhaled breath biomarkers are an important emerging field. The fractional concentration of exhaled nitric oxide (FeNO) is a marker of airway inflammation with clinical and epidemiological applications (e.g., air pollution health effects studies). Systems of differential equations describe FeNO—measured non-invasively at the mouth—as a function of exhalation flow rate and parameters representing airway and alveolar sources of NO in the airway. Traditionally, NO parameters have been estimated separately for each study participant (Stage I) and then related to covariates (Stage II). Statistical properties of these two-step approaches have not been investigated. In simulation studies, we evaluated finite sample properties of existing two-step methods as well as a novel Unified Hierarchical Bayesian (U-HB) model. The U-HB is a one-step estimation method developed with the goal of properly propagating uncertainty as well as increasing power and reducing type I error for estimating associations of covariates with NO parameters. We demonstrated the U-HB method in an analysis of data from the southern California Children’s Health Study relating traffic-related air pollution exposure to airway and alveolar airway inflammation.

Double penalized regularization estimation for partially linear instrumental variable models with ultrahigh dimensional instrumental variables

Under ultrahigh dimensional instrumental variables, we consider the estimation for a class of partially linear models with endogenous covariates. To overcome the difficulty of ultrahigh dimensionality of the instrumental variables, we propose a double penalized regularization estimation procedure for identifying the optimal instrumental variables, and estimating covariate effects of the parametric and nonparametric components. With some regularity conditions, some asymptotic properties of the proposed estimation are derived, such as the consistency of the resulting estimators for parametric and nonparametric components. Lastly, we examine the finite sample performance of the proposed method by some simulation studies and a real data analysis.