Simple Incorporation of Interactions into Additive Models

Often, the functional form of covariate effects in an additive model varies across groups defined by levels of a categorical variable. This structure represents a factor-by-curve interaction. This article presents penalized spline models that incorporate factor-by-curve interactions into additive models. A mixed model formulation for penalized splines allows for straightforward model fitting and smoothing parameter selection. We illustrate the proposed model by applying it to pollen ragweed data in which seasonal trends vary by year.     

Predicting protein concentrations with ELISA microarray assays, monotonic splines and Monte Carlo simulation

Making sound proteomic inferences using ELISA microarray assay requires both an accurate prediction of protein concentration and a credible estimate of its error. We present a method using monotonic spline statistical models (MS), penalized constrained least squares fitting (PCLS) and Monte Carlo simulation (MC) to predict ELISA microarray protein concentrations and estimate their prediction errors. We contrast the MSMC (monotone spline Monte Carlo) method with a LNLS (logistic nonlinear least squares) method using simulated and real ELISA microarray data sets.MSMC rendered good fits in almost all tests, including those with left and/or right clipped standard curves. MS predictions were nominally more accurate; especially at the extremes of the prediction curve. MC provided credible asymmetric prediction intervals for both MS and LN fits that were superior to LNLS propagation-of-error intervals in achieving the target statistical confidence. MSMC was more reliable when automated prediction across simultaneous assays was applied routinely with minimal user guidance.     

Using semiparametric‐mixed model and functional linear model to detect vulnerable prenatal window to carcinogenic polycyclic aromatic hydrocarbons on fetal growth

Prenatal exposure to carcinogenic polycyclic aromatic hydrocarbons (c‐PAHs) through maternal inhalation induces higher risk for a wide range of fetotoxic effects. However, the most health‐relevant dose function from chronic gestational exposure remains unclear. Whether there is a gestational window during which the human embryo/fetus is particularly vulnerable to PAHs has not been examined thoroughly. We consider a longitudinal semiparametric‐mixed effect model to characterize the individual prenatal PAH exposure trajectory, where a nonparametric cyclic smooth function plus a linear function are used to model the time effect and random effects are used to account for the within‐subject correlation. We propose a penalized least squares approach to estimate the parametric regression coefficients and the nonparametric function of time. The smoothing parameter and variance components are selected using the generalized cross‐validation (GCV) criteria. The estimated subject‐specific trajectory of prenatal exposure is linked to the birth outcomes through a set of functional linear models, where the coefficient of log PAH exposure is a fully nonparametric function of gestational age. This allows the effect of PAH exposure on each birth outcome to vary at different gestational ages, and the window associated with significant adverse effect is identified as a vulnerable prenatal window to PAHs on fetal growth. We minimize the penalized sum of squared errors using a spline‐based expansion of the nonparametric coefficient function to draw statistical inferences, and the smoothing parameter is chosen through GCV.     

Implications of absence of measurement invariance for detecting sex limitation and genotype by environment interaction.

Using univariate sum scores in genetic studies of twin data is common practice. This practice precludes an investigation of the measurement model relating the individual items to an underlying factor. Absence of measurement invariance across a grouping variable such as gender or environmental exposure refers to group differences with respect to the measurement model. It is shown that a decomposition of a sum score into genetic and environmental variance components leads to path coefficients of the additive genetic factor that are biased differentially across groups if individual items are non-invariant. The arising group differences in path coefficients are identical to what is known as "scalar sex limitation" when gender is the grouping variable, or as "gene by environment interaction" when environmental exposure is the grouping variable. In both cases the interpretation would be in terms of a group-specific effect size of the genetic factor. This interpretation may be incorrect if individual items are non-invariant.     

Smoothing spline-based score tests for proportional hazards models

We propose "score-type" tests for the proportional hazards assumption and for covariate effects in the Cox model using the natural smoothing spline representation of the corresponding nonparametric functions of time or covariate. The tests are based on the penalized partial likelihood and are derived by viewing the inverse of the smoothing parameter as a variance component and testing an equivalent null hypothesis that the variance component is zero. We show that the tests have a size close to the nominal level and good power against general alternatives, and we apply them to data from a cancer clinical trial.     

Structural inference in transition measurement error models for longitudinal data

We propose a new class of models, transition measurement error models, to study the effects of covariates and the past responses on the current response in longitudinal studies when one of the covariates is measured with error. We show that the response variable conditional on the error-prone covariate follows a complex transition mixed effects model. The naive model obtained by ignoring the measurement error correctly specifies the transition part of the model, but misspecifies the covariate effect structure and ignores the random effects. We next study the asymptotic bias in naive estimator obtained by ignoring the measurement error for both continuous and discrete outcomes. We show that the naive estimator of the regression coefficient of the error-prone covariate is attenuated, while the naive estimators of the regression coefficients of the past responses are generally inflated. We then develop a structural modeling approach for parameter estimation using the maximum likelihood estimation method. In view of the multidimensional integration required by full maximum likelihood estimation, an EM algorithm is developed to calculate maximum likelihood estimators, in which Monte Carlo simulations are used to evaluate the conditional expectations in the E-step. We evaluate the performance of the proposed method through a simulation study and apply it to a longitudinal social support study for elderly women with heart disease. An additional simulation study shows that the Bayesian information criterion (BIC) performs well in choosing the correct transition orders of the models.     

Hierarchical Bayesian modeling of spatially correlated health service outcome and utilization rates

We present Bayesian hierarchical spatial models for spatially correlated small-area health service outcome and utilization rates, with a particular emphasis on the estimation of both measured and unmeasured or unknown covariate effects. This Bayesian hierarchical model framework enables simultaneous modeling of fixed covariate effects and random residual effects. The random effects are modeled via Bayesian prior specifications reflecting spatial heterogeneity globally and relative homogeneity among neighboring areas. The model inference is implemented using Markov chain Monte Carlo methods. Specifically, a hybrid Markov chain Monte Carlo algorithm (Neal, 1995, Bayesian Learning for Neural Networks; Gustafson, MacNab, and Wen, 2003, Statistics and Computing, to appear) is used for posterior sampling of the random effects. To illustrate relevant problems, methods, and techniques, we present an analysis of regional variation in intraventricular hemorrhage incidence rates among neonatal intensive care unit patients across Canada.     

Exploratory Bayesian model selection for serial genetics data

Characterizing the process by which molecular and cellular level changes occur over time will have broad implications for clinical decision making and help further our knowledge of disease etiology across many complex diseases. However, this presents an analytic challenge due to the large number of potentially relevant biomarkers and the complex, uncharacterized relationships among them. We propose an exploratory Bayesian model selection procedure that searches for model simplicity through independence testing of multiple discrete biomarkers measured over time. Bayes factor calculations are used to identify and compare models that are best supported by the data. For large model spaces, i.e., a large number of multi-leveled biomarkers, we propose a Markov chain Monte Carlo (MCMC) stochastic search algorithm for finding promising models. We apply our procedure to explore the extent to which HIV-1 genetic changes occur independently over time.     

Spirituality as a Scientific Construct: Testing Its Universality across Cultures and Languages

Using data obtained from 4004 participants across eight countries (Canada, India, Japan, Korea, Poland, Slovakia, Uganda, and the U.S.), the factorial reliability, validity and structural/measurement invariance of a 30-item version of Expressions of Spirituality Inventory (ESI-R) was evaluated. The ESI-R measures a five factor model of spirituality developed through the conjoint factor analysis of several extant measures of spiritual constructs. Exploratory factor analyses of pooled data provided evidence that the five ESI-R factors are reliable. Confirmatory analyses comparing four and five factor models revealed that the five dimensional model demonstrates superior goodness-of-fit with all cultural samples and suggest that the ESI-R may be viewed as structurally invariant. Measurement invariance, however, was not supported as manifested in significant differences in item and dimension scores and in significantly poorer fit when factor loadings were constrained to equality across all samples. Exploratory analyses with a second adjective measure of spirituality using American, Indian, and Ugandan samples identified three replicable factors which correlated with ESI-R dimensions in a manner supportive of convergent validity. The paper concludes with a discussion of the meaning of the findings and directions needed for future research.     

Merging the Idiographic Filter With Dynamic Factor Analysis to Model Process

To model processes we propose merging idiographic filter measurement with dynamic factor analysis. This involves testing whether or not the same latent dynamics (concurrent and lagged factor interrelations) can describe different individuals' observed multivariate time series. The methodology allows fitting, across different individuals, dynamic factor models that are invariant with respect to the latent dynamics, but not necessarily the factor loadings (measurement model). This methodology allows the same latent process to manifest differently from one individual to another, thus recognizing that the process is general but its realization in a given person is to some degree idiosyncratic. The approach is illustrated with empirical data.     

Bayesian Inference for the Spatio-Temporal Invasion of Alien Species

In this paper we develop a Bayesian approach to parameter estimation in a stochastic spatio-temporal model of the spread of invasive species across a landscape. To date, statistical techniques, such as logistic and autologistic regression, have outstripped stochastic spatio-temporal models in their ability to handle large numbers of covariates. Here we seek to address this problem by making use of a range of covariates describing the bio-geographical features of the landscape. Relative to regression techniques, stochastic spatio-temporal models are more transparent in their representation of biological processes. They also explicitly model temporal change, and therefore do not require the assumption that the species' distribution (or other spatial pattern) has already reached equilibrium as is often the case with standard statistical approaches. In order to illustrate the use of such techniques we apply them to the analysis of data detailing the spread of an invasive plant, Heracleum mantegazzianum, across Britain in the 20th Century using geo-referenced covariate information describing local temperature, elevation and habitat type. The use of Markov chain Monte Carlo sampling within a Bayesian framework facilitates statistical assessments of differences in the suitability of different habitat classes for H. mantegazzianum, and enables predictions of future spread to account for parametric uncertainty and system variability. Our results show that ignoring such covariate information may lead to biased estimates of key processes and implausible predictions of future distributions.     

Factor analytic models of clustered multivariate data with informative censoring

This article describes a general class of factor analytic models for the analysis of clustered multivariate data in the presence of informative missingness. We assume that there are distinct sets of cluster-level latent variables related to the primary outcomes and to the censoring process, and we account for dependency between these latent variables through a hierarchical model. A linear model is used to relate covariates and latent variables to the primary outcomes for each subunit. A generalized linear model accounts for covariate and latent variable effects on the probability of censoring for subunits within each cluster. The model accounts for correlation within clusters and within subunits through a flexible factor analytic framework that allows multiple latent variables and covariate effects on the latent variables. The structure of the model facilitates implementation of Markov chain Monte Carlo methods for posterior estimation. Data from a spermatotoxicity study are analyzed to illustrate the proposed approach.     

Bayesian distributed lag models: estimating effects of particulate matter air pollution on daily mortality

Summary .  A distributed lag model (DLagM) is a regression model that includes lagged exposure variables as covariates; its corresponding distributed lag (DL) function describes the relationship between the lag and the coefficient of the lagged exposure variable. DLagMs have recently been used in environmental epidemiology for quantifying the cumulative effects of weather and air pollution on mortality and morbidity. Standard methods for formulating DLagMs include unconstrained, polynomial, and penalized spline DLagMs. These methods may fail to take full advantage of prior information about the shape of the DL function for environmental exposures, or for any other exposure with effects that are believed to smoothly approach zero as lag increases, and are therefore at risk of producing suboptimal estimates. In this article, we propose a Bayesian DLagM (BDLagM) that incorporates prior knowledge about the shape of the DL function and also allows the degree of smoothness of the DL function to be estimated from the data. We apply our BDLagM to its motivating data from the National Morbidity, Mortality, and Air Pollution Study to estimate the short-term health effects of particulate matter air pollution on mortality from 1987 to 2000 for Chicago, Illinois. In a simulation study, we compare our Bayesian approach with alternative methods that use unconstrained, polynomial, and penalized spline DLagMs. We also illustrate the connection between BDLagMs and penalized spline DLagMs. Software for fitting BDLagM models and the data used in this article are available online.     

Estimating covariate‐adjusted measures of diagnostic accuracy based on pooled biomarker assessments

There is a need for epidemiological and medical researchers to identify new biomarkers (biological markers) that are useful in determining exposure levels and/or for the purposes of disease detection. Often this process is stunted by high testing costs associated with evaluating new biomarkers. Traditionally, biomarker assessments are individually tested within a target population. Pooling has been proposed to help alleviate the testing costs, where pools are formed by combining several individual specimens. Methods for using pooled biomarker assessments to estimate discriminatory ability have been developed. However, all these procedures have failed to acknowledge confounding factors. In this paper, we propose a regression methodology based on pooled biomarker measurements that allow the assessment of the discriminatory ability of a biomarker of interest. In particular, we develop covariate‐adjusted estimators of the receiver‐operating characteristic curve, the area under the curve, and Youden's index. We establish the asymptotic properties of these estimators and develop inferential techniques that allow one to assess whether a biomarker is a good discriminator between cases and controls, while controlling for confounders. The finite sample performance of the proposed methodology is illustrated through simulation. We apply our methods to analyze myocardial infarction (MI) data, with the goal of determining whether the pro‐inflammatory cytokine interleukin‐6 is a good predictor of MI after controlling for the subjects' cholesterol levels.     

Semiparametric Transformation Models with Time‐Varying Coefficients for Recurrent and Terminal Events

Summary In this article, we propose a family of semiparametric transformation models with time‐varying coefficients for recurrent event data in the presence of a terminal event such as death. The new model offers great flexibility in formulating the effects of covariates on the mean functions of the recurrent events among survivors at a given time. For the inference on the proposed models, a class of estimating equations is developed and asymptotic properties of the resulting estimators are established. In addition, a lack‐of‐fit test is provided for assessing the adequacy of the model, and some tests are presented for investigating whether or not covariate effects vary with time. The finite‐sample behavior of the proposed methods is examined through Monte Carlo simulation studies, and an application to a bladder cancer study is also illustrated.     

Binary Regression Analysis with Pooled Exposure Measurements: A Regression Calibration Approach

Summary It has become increasingly common in epidemiological studies to pool specimens across subjects to achieve accurate quantitation of biomarkers and certain environmental chemicals. In this article, we consider the problem of fitting a binary regression model when an important exposure is subject to pooling. We take a regression calibration approach and derive several methods, including plug‐in methods that use a pooled measurement and other covariate information to predict the exposure level of an individual subject, and normality‐based methods that make further adjustments by assuming normality of calibration errors. Within each class we propose two ways to perform the calibration (covariate augmentation and imputation). These methods are shown in simulation experiments to effectively reduce the bias associated with the naive method that simply substitutes a pooled measurement for all individual measurements in the pool. In particular, the normality‐based imputation method performs reasonably well in a variety of settings, even under skewed distributions of calibration errors. The methods are illustrated using data from the Collaborative Perinatal Project.     

The Quest for Comparability: Studying the Invariance of the Teachers’ Sense of Self-Efficacy (TSES) Measure across Countries

Teachers’ self-efficacy is an important motivational construct that is positively related to a variety of outcomes for both the teachers and their students. This study addresses challenges associated with the commonly used ‘Teachers’ Sense of Self-Efficacy (TSES)’ measure across countries and provides a synergism between substantive research on teachers’ self-efficacy and the novel methodological approach of exploratory structural equation modeling (ESEM). These challenges include adequately representing the conceptual overlap between the facets of self-efficacy in a measurement model (cross-loadings) and comparing means and factor structures across countries (measurement invariance). On the basis of the OECD Teaching and Learning International Survey (TALIS) 2013 data set comprising 32 countries (N = 164,687), we investigate the effects of cross-loadings in the TSES measurement model on the results of measurement invariance testing and the estimation of relations to external constructs (i.e., working experience, job satisfaction). To further test the robustness of our results, we replicate the 32-countries analyses for three selected sub-groups of countries (i.e., Nordic, East and South-East Asian, and Anglo-Saxon country clusters). For each of the TALIS 2013 participating countries, we found that the factor structure of the self-efficacy measure is better represented by ESEM than by confirmatory factor analysis (CFA) models that do not allow for cross-loadings. For both ESEM and CFA, only metric invariance could be achieved. Nevertheless, invariance levels beyond metric invariance are better achieved with ESEM within selected country clusters. Moreover, the existence of cross-loadings did not affect the relations between the dimensions of teachers’ self-efficacy and external constructs. Overall, this study shows that a conceptual overlap between the facets of self-efficacy exists and can be well-represented by ESEM. We further argue for the cross-cultural generalizability of the corresponding measurement model.     

Bayesian Models for Multiple Outcomes Nested in Domains

Summary We consider the problem of estimating the effect of exposure on multiple continuous outcomes, when the outcomes are measured on different scales and are nested within multiple outcome classes, or “domains.” Our Bayesian model extends the linear mixed models approach to allow the exposure effect to differ across domains and across outcomes within domains. Our model can be parameterized to allow shrinkage of the effects within the different levels of nesting, or to allow fixed domain‐specific effects with no shrinkage. Our model also allows covariate effects to differ across outcomes and domains. Our methodology is applied to data on prenatal methylmercury exposure and multiple outcomes in four domains measured at 9 years of age on children enrolled in the Seychelles Child Development Study. We use three different priors and found that our main conclusions were not sensitive to the choice of prior. Simulation studies examine the model performance under alternative scenarios. Our results demonstrate that a sizeable increase in power is possible.     

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 other covariates.     

Measurement Invariance of the WHODAS 2.0 in a Population-Based Sample of Youth

The World Health Organization Disability Assessment Schedule 2.0 (WHODAS 2.0) is a brief measure of global disability originally developed for adults, which has since been implemented among samples of children and youth. However, evidence of its validity for use among youth, particularly measurement invariance, is lacking. Investigations of measurement invariance assess the extent to which the psychometric properties of observed items in a measure are generalizable across samples. Satisfying the assumption of measurement invariance is critical for any inferences about between-group differences. The objective of this paper was to empirically assess the measurement invariance of the 12-item interview version of the WHODAS 2.0 measure in an epidemiological sample of youth (15 to 17 years) and adults (≥ 18 years) in Canada. Multiple-group confirmatory factor analysis using a categorical variable framework allowed for the sequential testing of increasingly restrictive models to evaluate measurement invariance of the WHODAS 2.0 between adults and youth. Findings provided evidence for full measurement invariance of the WHODAS 2.0 in youth aged 15 to 17 years. The final model fit the data well: χ²(159) = 769.04, p < .001; CFI = 0.950, TLI = 0.958, RMSEA (90% CI) = 0.055 [0.051, 0.059]. Results from this study build on previous work supporting the validity of the WHODAS 2.0. Findings indicate that the WHODAS 2.0 is valid for making substantive comparisons of disability among youth as young as 15 years of age.