Estimation Of Covariate Effects Research Articles

A note on investigating co-occurrence patterns and dynamics for many species, with imperfect detection and a log-linear modeling parameterization.

Patterns in, and the underlying dynamics of, species co‐occurrence is of interest in many ecological applications. Unaccounted for, imperfect detection of the species can lead to misleading inferences about the nature and magnitude of any interaction. A range of different parameterizations have been published that could be used with the same fundamental modeling framework that accounts for imperfect detection, although each parameterization has different advantages and disadvantages.We propose a parameterization based on log‐linear modeling that does not require a species hierarchy to be defined (in terms of dominance) and enables a numerically robust approach for estimating covariate effects.Conceptually, the parameterization is equivalent to using the presence of species in the current, or a previous, time period as predictor variables for the current occurrence of other species. This leads to natural, “symmetric,” interpretations of parameter estimates.The parameterization can be applied to many species, in either a maximum likelihood or Bayesian estimation framework. We illustrate the method using camera‐trapping data collected on three mesocarnivore species in South Texas.

Estimation of covariate effects on net survivals in the relative survival progressive illness-death model.

Recently, there has been a lot of development in relative survival field. In the absence of data on the cause of death, the research has tended to focus on the estimation of survival probability of a cancer (as a disease of interest). In many cancers, one nonfatal event that decreases the survival probability can occur. There are a few methods that assess the role of prognostic factors for multiple types of clinical events while dealing with uncertainty about the cause of death. However, these methods require proportional hazard or Markov assumptions. In practice, one or both of these assumptions might be violated. Violation of the proportional hazard assumption can lead to estimates that are biased, and difficult to interpret and violation of Markov assumption results in inconsistent estimators. In this work, we propose a semi-parametric approach to estimate the possibly time-varying regression coefficients in the likely non-Markov relative survival progressive illness-death model. The performance of the proposed estimator is investigated through simulations. We illustrate our approach using data from a study on rectal cancer resected for cure conducted in two French population-based digestive cancer registries.

Joint Modeling of Distances and Times in Point-Count Surveys

Removal and distance modeling are two common methods to adjust counts for imperfect detection in point-count surveys. Several recent articles have formulated models to combine them into a distance-removal framework. We observe that these models fall into two groups building from different assumptions about the joint distribution of observed distances and first times to detection. One approach assumes the joint distribution results from a Poisson process (PP). The other assumes an independent joint (IJ) distribution with its joint density being the product of its marginal densities. We compose an IJ+PP model that more flexibly models the joint distribution and accommodates both existing approaches as special cases. The IJ+PP model matches the bias and coverage of the true model for data simulated from either PP or IJ models. In contrast, PP models underestimate abundance from IJ simulations, while IJ models overestimate abundance from PP simulations. We apply all three models to surveys of golden-crowned sparrows in Alaska. Only the IJ+PP model reasonably fits the joint distribution of observed distances and first times to detection. Model choice affects estimates of abundance and detection but has little impact on the magnitude of estimated covariate effects on availability and perceptibility.Supplementary materials accompanying this paper appear online.

Understanding Recurrent Admissions for People with Heart Failure in New Zealand

Conventional time-to-first event analyses do not fully represent burden of a chronic disease such as heart failure (HF). Extending analyses to subsequent recurrent events is required for improved understanding of risk factors associated with repeated hospital admissions over the course of the disease. We examined occurrence and risk factors of all-cause hospital readmissions through 4 years of follow-up period for adults admitted to a NZ hospital for the first-time with HF in 2013 or 2014. Several extended Cox models were assessed that differed in how they dealt with intra-subject correlation, and in how they modelled the time between hospitalisations. Of 23,736 patients discharged alive from index hospitalisation, 88% had ≥1 readmission and/or died from CVD during 4 years of follow-up. A standard time-to-first-event Cox model would have ignored 74% of total events experienced. The hazard ratios of predictors in the time-to-first-event model differed from those in the recurrent events models, including shifts in the statistical significance of key variables (ethnicity, HF aetiology). For most variables, smaller hazard ratios and narrower confidence intervals were observed from the Cox models which account for an increase in risk of event with number of previous admissions. Recurrent events analysis should be considered to understand longer-term impact of progression of HF and the true burden of long-term conditions. We demonstrated that the type of recurrent events model may affect the estimated covariate effects and its interpretation.

Estimation of covariate effects in proportional cross-ratio model of bivariate time-to-event outcomes

Medical studies often collect bivariate survival data including time to the same type of disease in twins or time to two different diseases from the same individuals. Cross-ratio, defined as the ratio of conditional hazard functions for one event given the other, is often used as a measure of dependency between the two survival outcomes. Statistical methods have also been proposed to estimate the effect of covariates on cross-ratio in order to identify common factors influencing both survival outcomes. There are currently three estimation approaches for cross-ratio, namely, a parametric approach using the Clayton copula, a semi-parametric two-stage approach proposed by Shih and Louis, and a nonparametric pseudo-partial likelihood approach proposed by Hu et al. In this paper, we compare the three estimation approaches on estimating covariates’ effect on the cross-ratio in simulation studies. We found that the nonparametric pseudo-partial likelihood estimation approach performed well and that the method was also robust under various model assumptions. Data from a longitudinal cohort of elderly African Americans were used to illustrate the three estimation approaches.

Spline-based accelerated failure time model.

The accelerated failure time (AFT) model has been suggested as an alternative to the Cox proportional hazards model. However, a parametric AFT model requires the specification of an appropriate distribution for the event time, which is often difficult to identify in real-life studies and may limit applications. A semiparametric AFT model was developed by Komárek et al based on smoothed error distribution that does not require such specification. In this article, we develop a spline-based AFT model that also does not require specification of the parametric family of event time distribution. The baseline hazard function is modeled by regression B-splines, allowing for the estimation of a variety of smooth and flexible shapes. In comprehensive simulations, we validate the performance of our approach and compare with the results from parametric AFT models and the approach of Komárek. Both the proposed spline-based AFT model and the approach of Komárek provided unbiased estimates of covariate effects and survival curves for a variety of scenarios in which the event time followed different distributions, including both simple and complex cases. Spline-based estimates of the baseline hazard showed also a satisfactory numerical stability. As expected, the baseline hazard and survival probabilities estimated by the misspecified parametric AFT models deviated from the truth. We illustrated the application of the proposed model in a study of colon cancer.

Model pursuit and variable selection in the additive accelerated failure time model

In this paper, we propose a new semiparametric method to simultaneously select important variables, identify the model structure and estimate covariate effects in the additive AFT model, for which the dimension of covariates is allowed to increase with sample size. Instead of directly approximating the non-parametric effects as in most existing studies, we take a linear effect out to weak the condition required for model identifiability. To compute the proposed estimates numerically, we use an alternating direction method of multipliers algorithm so that it can be implemented easily and achieve fast convergence rate. Our method is proved to be selection consistent and possess an asymptotic oracle property. The performance of the proposed methods is illustrated through simulations and the real data analysis.

Regression analysis of dependent current status data with the accelerated failure time model

In this article, we discuss the regression analysis of dependent current status data under the accelerated failure time model. There exist many literatures discussing the regression analysis of current status data under different models, but few literature discussing the regression problem of dependent current status data under the AFT model. Corresponding to this, we propose a sieve maximum likelihood approach for estimation of covariate effects. In the approach, we model the correlation between the interested survival time and the observation time by the copula function. Simulation study is conducted in order to assess the finite sample behavior of the method. A real data example is provided to illustrate the application of the proposed method.

Heterogeneous regression models for clusters of spatial dependent data

ABSTRACT In economic development there are often regions that share similar socioeconomic characteristics, and econometrics models on such regions tend to produce similar covariate effect estimates. This paper proposes a Bayesian clustered regression for spatially dependent data in order to detect clusters in covariate effects. The proposed method is based on the Dirichlet process, which provides a probabilistic framework for simultaneous inference of the number of clusters and clustering configurations. The use of the method is illustrated both in simulation studies and by an application to a housing cost data set of Georgia.

A novel statistical method for modeling covariate effects in bisulfite sequencing derived measures of DNA methylation.

Identifying disease‐associated changes in DNA methylation can help us gain a better understanding of disease etiology. Bisulfite sequencing allows the generation of high‐throughput methylation profiles at single‐base resolution of DNA. However, optimally modeling and analyzing these sparse and discrete sequencing data is still very challenging due to variable read depth, missing data patterns, long‐range correlations, data errors, and confounding from cell type mixtures. We propose a regression‐based hierarchical model that allows covariate effects to vary smoothly along genomic positions and we have built a specialized EM algorithm, which explicitly allows for experimental errors and cell type mixtures, to make inference about smooth covariate effects in the model. Simulations show that the proposed method provides accurate estimates of covariate effects and captures the major underlying methylation patterns with excellent power. We also apply our method to analyze data from rheumatoid arthritis patients and controls. The method has been implemented in R package SOMNiBUS.

A spatial partial differential equation approach to addressing unit misalignments in Bayesian poisson space-time models

Spatial analyses using data from geographic areas that change shape and location over time, like US ZIP codes, produce biased results to the extent that unit misalignments are related to covariate effects. To address this issue, one method has incorporated a fixed effect measure of population shifts and a spatial structure as a block-diagonal neighborhood adjacency matrix within a Besag-York-Mollié (BYM) model. However, this approach assumes that spatial relationships among units change with time and precludes the assessment of temporal dynamic effects. Here, we assume that a continuous Gaussian random field underlies misaligned data and apply a stochastic partial differential equation (SPDE) approach to modeling area outcomes. We compare SPDE and BYM methods and show that both provide similar estimates of covariate effects. Importantly, we demonstrate that the SPDE approach can additionally identify autoregressive processes underlying the development of problematic health outcomes using data observed across Pennsylvania over 11 years.

Inverse probability weighting methods for Cox regression with right-truncated data.

Right-truncated data arise when observations are ascertained retrospectively, and only subjects who experience the event of interest by the time of sampling are selected. Such a selection scheme, without adjustment, leads to biased estimation of covariate effects in the Cox proportional hazards model. The existing methods for fitting the Cox model to right-truncated data, which are based on the maximization of the likelihood or solving estimating equations with respect to both the baseline hazard function and the covariate effects, are numerically challenging. We consider two alternative simple methods based on inverse probability weighting (IPW) estimating equations, which allow consistent estimation of covariate effects under a positivity assumption and avoid estimation of baseline hazards. We discuss problems of identifiability and consistency that arise when positivity does not hold and show that although the partial tests for null effects based on these IPW methods can be used in some settings even in the absence of positivity, they are not valid in general. We propose adjusted estimating equations that incorporate the probability of observation when it is known from external sources, which results in consistent estimation. We compare the methods in simulations and apply them to the analyses of human immunodeficiency virus latency.

Using lorelograms to measure and model correlation in binary data: Applications to ecological studies

Abstract Tools for describing correlation structures in binary data are underrepresented in the ecological literature, and methods commonly applied to continuous data are inappropriate because of intrinsic features of binary data (e.g. variance dependent on the mean). Describing how correlation changes in time and space, or in response to different stimuli, can provide insights into the ecological processes generating observed patterns. Moreover, proper modelling of correlation structures is necessary for reliably estimating covariate effects. We introduce ecologists to the lorelogram (Heagerty & Zeger, 1998), a tool used to identify and describe dependency structures in binary data. Lorelograms can help guide data aggregation efforts to facilitate independence, or alternatively, to inform appropriate structures for modelling correlated data. We developed the r‐package, lorelogram, for estimating and plotting lorelograms and show how it can be used to identify various dependency structures using simulated data. We analyse data from the North American Breeding Bird Survey and camera trap data from a carnivore study in Minnesota to demonstrate how the lorelogram can describe spatial and temporal dependencies, respectively. In the latter case, we show how the lorelogram can identify short‐term dependencies (e.g. individuals that linger at the camera site for several minutes), longer‐term dependencies (i.e. diel activity patterns) and effects of site‐specific covariates such as attractants. We then illustrate how this information can be incorporated in a modelling framework that accounts for these correlation structures (e.g. when modelling daily activity patterns). The lorelogram is a promising tool for quantifying correlation in binary data over space or time. In addition to the applications presented in our paper, it could be used to identify independent sampling units for occupancy modelling or to quantify behavioural responses to covariates such as anthropogenic stressors or recent presence of prey, predators or competitors.

Differential item functioning of the SF-12 in a population-based regional joint replacement registry

BackgroundJoint replacement, an increasingly common procedure amongst older adults, can substantially improve health-related quality of life (HRQoL). However, differential item functioning (DIF) may affect the accurate interpretation of differences in HRQoL amongst patients with different demographic and health status characteristics but the same underlying (i.e., latent) level of the investigated construct. This study tested for DIF in pre-operative SF-12 physical health (PH) and mental health (MH) sub-scale items amongst patients undergoing total hip arthroplasty (THA) and total knee arthroplasty (TKA).MethodsData were from a population-based joint replacement registry from the Canadian province of Manitoba. TKA and THA patients who had surgery between 2009 and 2015 and completed a pre-operative assessment were included. DIF was tested using the multiple indicators multiple causes (MIMIC) method with sex, age group, body weight status, and presence of multiple comorbid conditions (i.e., multimorbidity) as covariates. Analyses were stratified by joint type.ResultsThe study cohort included 8820 patients; 42.1% underwent THA, 57.3% were female, 32.7% were 70+ years, and 52.8% were obese. For each sub-scale, four of the six items exhibited DIF in both THA and TKA groups. Differences in the covariate effect estimates for DIF and No-DIF models on the MH latent variable were largest for age and body weight status for the THA group, and for sex and multimorbidity for the TKA group. All of the differences were small for PH. Multimorbidity had the strongest association with PH and age and sex had the strongest association with MH in the DIF models.ConclusionsDemographic and health status characteristics influenced SF-12 PH and MH item responses in joint replacement populations, although the size of the effects were not large for PH. We recommend testing and adjusting for DIF effects to ensure comparability of HRQoL measures in joint replacement populations.

Differential Effects of Cognitive Reserve on the Neurocognitive Functioning of Polysubstance Users: an Exploratory Analysis Using Mixture Regression

We aimed to identify latent classes based on differential effects of cognitive reserve on neurocognitive variables, and to determine which variables of polysubstance use predict class membership. One hundred sixty-six male participants in residential treatment were recruited in Mexico City and evaluated with Montreal Cognitive Assessment, Tower of Hanoi, Cognitive Reserve Index Questionnaire, and a structured interview for substance use. We performed three independent mixture regression models with cognitive reserve as predictor and neurocognitive variables as outcomes, and we estimated covariate effects of age of onset, years of substance use, and past 30 days of use on class membership. Two class solutions for the three models, all demonstrating differential effects (e.g., for overall cognitive functioning, education seems to serve as a protective factor against impairment for most of the cases, whereas only for some few individuals both education and leisure may protect). No variable of substance use affected the probabilities of membership to latent classes. Individuals at risk of substance-induced neurocognitive impairment may be identified by the association between variables of cognitive performance and cognitive reserve.

Prediction models for network-linked data

Prediction algorithms typically assume the training data are independent samples, but in many modern applications samples come from individuals connected by a network. For example, in adolescent health studies of risk-taking behaviors, information on the subjects’ social network is often available and plays an important role through network cohesion, the empirically observed phenomenon of friends behaving similarly. Taking cohesion into account in prediction models should allow us to improve their performance. Here we propose a network-based penalty on individual node effects to encourage similarity between predictions for linked nodes, and show that incorporating it into prediction leads to improvement over traditional models both theoretically and empirically when network cohesion is present. The penalty can be used with many loss-based prediction methods, such as regression, generalized linear models, and Cox’s proportional hazard model. Applications to predicting levels of recreational activity and marijuana usage among teenagers from the AddHealth study based on both demographic covariates and friendship networks are discussed in detail and show that our approach to taking friendships into account can significantly improve predictions of behavior while providing interpretable estimates of covariate effects.

A quick and accurate method for the estimation of covariate effects based on empirical Bayes estimates in mixed-effects modeling: Correction of bias due to shrinkage.

Nonlinear mixed-effects modeling is a popular approach to describe the temporal trajectory of repeated measurements of clinical endpoints collected over time in clinical trials, to distinguish the within-subject and the between-subject variabilities, and to investigate clinically important risk factors (covariates) that may partly explain the between-subject variability. Due to the complex computing algorithms involved in nonlinear mixed-effects modeling, estimation of covariate effects is often time-consuming and error-prone owing to local convergence. We develop a fast and accurate estimation method based on empirical Bayes estimates from the base mixed-effects model without covariates, and simple regressions outside of the nonlinear mixed-effect modeling framework. Application of the method is illustrated using a pharmacokinetic dataset from an anticoagulation drug for the prevention of major cardiovascular events in patients with acute coronary syndrome. Both the application and extensive simulations demonstrated that the performance of this high-throughput method is comparable to the commonly used maximum likelihood estimation in nonlinear mixed-effects modeling.

Three problems with the conventional delta-model for biomass sampling data, and a computationally efficient alternative

Ecologists often analyse biomass sampling data that result in many zeros, where remaining samples can take any positive real number. Samples are often analysed using a “delta-model” that combines two separate generalized linear models, GLMs (for encounter probability and positive catch rates), or less often using a compound Poisson-gamma (CPG) distribution that is computationally expensive. I discuss three theoretical problems with the conventional delta-model: difficulty interpreting covariates for encounter probability, the assumed independence of the two GLMs, and the biologically implausible form when eliminating covariates for either GLM. I then derive an alternative “Poisson-link model” that solves these problems. To illustrate, I use biomass samples for 113 fish populations to show that the Poisson-link model improves fit (and decreases residual spatial variation) for >80% of populations relative to the conventional delta-model. A simulation experiment illustrates that CPG and Poisson-link models estimate covariate effects that are similar and biologically interpretable. I therefore recommend the Poisson-link model as a useful alternative to the conventional delta-model with similar properties to the CPG distribution.

Progression of diabetes, ischemic heart disease, and chronic kidney disease in a three chronic conditions multistate model

BackgroundDiabetes mellitus, ischemic heart disease, and chronic kidney disease are three major chronic conditions that develop with increasing risks among adults as they get older. The interconnectedness of these three chronic conditions is well known, while each condition acts as a prognostic risk factor for the other two. It is important to understand the progressive relationships of these three conditions over time in terms of transitioning between clinical states and the impact on patients’ survival.MethodsWe investigate the survival characteristics of a Medicare population aged 65 years and above in a multistate system that contained clinical states specified by death and diagnosis combinations of three chronic conditions. The study was conducted using Hawaii Medicare claims data from 2009 to 2013. To evaluate the progression of a subject with one of the newly diagnosed chronic conditions, we analyzed quantities such as state occupation probabilities in eight states and hazards of sixteen transition types. We quantified effects and significances of potential covariates such as age, gender, race/ethnicity, comorbidity burden and financial status on these temporal functions. Nonparametric method of estimating state occupation probabilities and pseudo-value based method for estimating covariate effects of a survival system were utilized.ResultsWe found a range of age, gender, race/ethnicity and financial status based interesting covariate influences on transitions and state occupation probabilities of the system.ConclusionSurvival characteristics of the disease system are influenced by subject-specific effects. Subgroup-specific interventions/screenings should be considered for the optimal prevention and care.

A Comparison of Approaches for Estimating Covariate Effects in Nonparametric Multilevel Latent Class Models

The inclusion of covariates improves the prediction of class memberships in latent class analysis (LCA). Several methods for examining covariate effects have been developed over the past decade; however, researchers have limited to the comparisons of the performance among these methods in cases of the single-level LCA. The present study investigated the performance of three different methods for examining covariate effects in a multilevel setting. We conducted a simulation to compare the performance of the three methods when level-1 and level-2 covariates were simultaneously incorporated into the nonparametric multilevel latent class model to predict latent class membership at each level. The simulation results revealed that the bias-adjusted three-step maximum likelihood method performed equally well as the one-step method when the sample sizes were sufficiently large and the latent classes were distinct from each other. However, the unadjusted three-step method significantly underestimated the level-1 covariate effect in most conditions.Keywords: covariate effects, latent class models, multilevel modeling