Missing Covariate Research Articles

Joint modeling of longitudinal and survival data with missing and left-censored time-varying covariates.

We propose a joint model for longitudinal and survival data with time-varying covariates subject to detection limits and intermittent missingness at random. The model is motivated by data from the Multicenter AIDS Cohort Study (MACS), in which HIV+ subjects have viral load and CD4 cell count measured at repeated visits along with survival data. We model the longitudinal component using a normal linear mixed model, modeling the trajectory of CD4 cell count by regressing on viral load, and other covariates. The viral load data are subject to both left censoring because of detection limits (17%) and intermittent missingness (27%). The survival component of the joint model is a Cox model with time-dependent covariates for death because of AIDS. The longitudinal and survival models are linked using the trajectory function of the linear mixed model. A Bayesian analysis is conducted on the MACS data using the proposed joint model. The proposed method is shown to improve the precision of estimates when compared with alternative methods.

Measuring the relative effect of factors affecting species distribution model predictions

Summary Species distribution models are increasingly used to address conservation questions, so their predictive capacity requires careful evaluation. Previous studies have shown how individual factors used in model construction can affect prediction. Although some factors probably have negligible effects compared to others, their relative effects are largely unknown. We introduce a general ’virtual ecologist’ framework to study the relative importance of factors involved in the construction of species distribution models. We illustrate the framework by examining the relative importance of five key factors – a missing covariate, spatial autocorrelation due to a dispersal process in presences/absences, sample size, sampling design and modelling technique – in a real study framework based on virtual plants in a mountain landscape at regional scale, and show that, for the parameter values considered here, most of the variation in prediction accuracy is due to sample size and modelling technique. Contrary to repeatedly reported concerns, spatial autocorrelation has only comparatively small effects. This study shows the importance of using a nested statistical framework to evaluate the relative effects of factors that may affect species distribution models.

Relation of Major Depression to Survival After Coronary Artery Bypass Grafting

The primary aim was to study the association between preoperative depression and long-term survival after coronary artery bypass grafting (CABG). Our secondary objective was to analyze the association between depression and cardiovascular events or all-cause mortality. In a nationwide, population-based, cohort study, all patients who underwent CABG in Sweden from 1997 to 2008 were included from the Swedish Web-system for Enhancement and Development of Evidence-based care in Heart disease Evaluated According to Recommended Therapies registry. Individual-level data were cross-linked from other national Swedish registers. Depression status and outcomes were obtained from the National Patient Register. The study population was 56,064 patients who underwent primary, isolated, nonemergent CABG. We identified 324 patients (0.6%) with depression before CABG. During a mean follow-up of 7.5years, 114 patients (35%) with depression died, compared with 13,767 patients (25%) in the control group. Depression was significantly associated with increased mortality and the combined end point of death or rehospitalization for myocardial infarction, heart failure, or stroke (multivariate-adjusted hazard ratios [95% confidence intervals] 1.65 [1.37 to 1.99] and 1.61 [1.38 to 1.89], respectively). In conclusion, we found a strong and significant association between depression and long-term survival in patients with established ischemic heart disease who underwent CABG. Depression was also associated with an increased risk for a combination of death or rehospitalization for heart failure, myocardial infarction, or stroke.

Pesticide exposure and depression among male private pesticide applicators in the agricultural health study.

Background: Pesticide exposure may be positively associated with depression. Few previous studies have considered the episodic nature of depression or examined individual pesticides.Objective: We evaluated associations between pesticide exposure and depression among male private pesticide applicators in the Agricultural Health Study.Methods: We analyzed data for 10 pesticide classes and 50 specific pesticides used by 21,208 applicators enrolled in 1993–1997 who completed a follow-up telephone interview in 2005–2010. We divided applicators who reported a physician diagnosis of depression (n = 1,702; 8%) into those who reported a previous diagnosis of depression at enrollment but not follow-up (n = 474; 28%), at both enrollment and follow-up (n = 540; 32%), and at follow-up but not enrollment (n = 688; 40%) and used polytomous logistic regression to estimate odds ratios (ORs) and 95% CIs. We used inverse probability weighting to adjust for potential confounders and to account for the exclusion of 3,315 applicators with missing covariate data and 24,619 who did not complete the follow-up interview.Results: After weighting for potential confounders, missing covariate data, and dropout, ever-use of two pesticide classes, fumigants and organochlorine insecticides, and seven individual pesticides—the fumigants aluminum phosphide and ethylene dibromide; the phenoxy herbicide (2,4,5-trichlorophenoxy)acetic acid (2,4,5-T); the organochlorine insecticide dieldrin; and the organophosphate insecticides diazinon, malathion, and parathion—were all positively associated with depression in each case group, with ORs between 1.1 and 1.9.Conclusions: Our study supports a positive association between pesticide exposure and depression, including associations with several specific pesticides.Citation: Beard JD, Umbach DM, Hoppin JA, Richards M, Alavanja MCR, Blair A, Sandler DP, Kamel F. 2014. Pesticide exposure and depression among male private pesticide applicators in the Agricultural Health Study. Environ Health Perspect 122:984–991; http://dx.doi.org/10.1289/ehp.1307450

A Nonparametric Multiple Imputation Approach for Data with Missing Covariate Values with Application to Colorectal Adenoma Data

A nearest neighbor-based multiple imputation approach is proposed to recover missing covariate information using the predictive covariates while estimating the association between the outcome and the covariates. To conduct the imputation, two working models are fitted to define an imputing set. This approach is expected to be robust to the underlying distribution of the data. We show in simulation and demonstrate on a colorectal data set that the proposed approach can improve efficiency and reduce bias in a situation with missing at random compared to the complete case analysis and the modified inverse probability weighted method.

Reweighting estimators for the additive hazards model with missing covariates

AbstractMissing covariate data are common in biomedical studies. In this paper, we propose a reweighting method to estimate the regression parameters in the additive hazards regression model when some of the covariates are missing at random. The resulting estimators are shown to be consistent and asymptotically normal. In addition, a lack‐of‐fit test is presented to assess the adequacy of the model with missing covariates. Simulation studies show that the proposed reweighting estimators perform well, and are more efficient than the weighted estimators for the missing covariate effects when the selection probability is small. An application to the mouse leukaemia data is provided. The Canadian Journal of Statistics 42: 285–307; 2014 © 2014 Statistical Society of Canada

Abstract P323: Arterial Stiffness and Retinal Vessel Diameters: The Atherosclerosis Risk in Communities Study - Neurocognitive Study (ARIC-NCS)

Background: The retinal microvasculature measured non-invasively by fundus photography enables examination of the role of small blood vessels in cerebrovascular disease since changes in retinal vessels may mimic that of cerebral arterioles. The association of arterial stiffness measured by pulse wave velocity (PWV) and retinal vessel diameters in a population sample is unknown, and evaluation of segment-specific PWV and retinal vessel diameters has not been conducted. Objectives: To quantify the cross-sectional association of PWV with retinal vessel diameters in a population of older adults. Methods: We examined data on PWV and retinal photography in 1,538 adults (853 females; mean age 77 years) from the population-based ARIC-NCS after excluding 43 participants with retinal diseases and 46 with missing covariates. Technicians used the Omron VP-1000 plus system following a standardized protocol to measure carotid femoral (cfPWV), brachial-ankle (baPWV), heart-femoral (hfPWV) and femoral-ankle (faPWV) twice and averaged the results. Non-mydriatic retinal fundus photography of both eyes were obtained and digital images were centrally processed with computer software to calculate central retinal arteriolar equivalent (CRAE) and central retinal vein equivalent (CRVE), which reflect diameters of retinal arterioles and venules, respectively. We used data from a randomly selected eye, and if missing, the non-missing eye was used (n=490). The relationship of PWV and CRAE and CRVE was assessed by multivariable linear regression adjusted for age, gender, race, hypertension, diabetes and smoking (current or former vs. never). Results: PWV was not associated with CRAE. The association of faPWV and CRVE was modified by gender. Among males, faPWV (cm/sec) was negatively associated with CRVE (beta= -0.01 μm, 95% confidence interval (CI): -0.02 to -0.006). This pattern was not observed among females. The association of baPWV and CRVE was modified by gender and smoking in which baPWV was only associated with CRVE in male smokers (current and former). Among male smokers, baPWV (cm/sec) was negatively associated with CRVE (beta= -0.002 μm, CI: -0.02 to -0.008). Interactions were robust to additional adjustment for systolic blood pressure, heart rate and body mass index. No association was observed between cfPWV and hfPWV with CRVE. Conclusion: Arterial stiffness was not associated with retinal arteriole diameters in older adults, but peripheral measures of arterial stiffness were associated with retinal venular diameters in males and male smokers. Whether peripheral stiffness plays a role in microvascular changes or has a shared mechanistic pathway with smoking among males requires additional investigation. The different associations of PWV and retinal measures suggest diverse pathogenic processes are involved in macrovascular and microvascular changes preceding end-organ damage.

Abstract P245: Dry Air Triggers Paroxysmal Atrial Fibrillation in Patients with Implantable Cardioverter Defibrillators

Introduction: Atrial fibrillation (AF) is responsible for substantial morbidity and mortality, yet little is known about the environmental factors that may trigger AF episodes. Weather has been proposed as a potential precipitant of paroxysmal AF. Hypothesis: We assessed the hypothesis that changes in outdoor ambient temperature and outdoor absolute humidity may trigger paroxysmal AF in the following 24 hours. Methods: Patients with dual chamber implantable cardioverter defibrillators (ICDs) living in eastern Massachusetts were enrolled between September 2006 and March 2010 from the Tufts Medical Center Cardiac Arrhythmia Clinic (Boston, Massachusetts) and followed prospectively for episodes of paroxysmal AF lasting at least 30 seconds. Arrhythmias documented by the ICD were reviewed and interpreted by an electrophysiologist masked to exposure. The date and time of AF episodes were linked to hourly weather data measured at Boston Logan International Airport. We examined the hypothesis using a time-stratified case-crossover analysis matched on calendar month, day of week and time of day and adjusted for air pollution and barometric pressure. To reduce the possibility of over-representation of clustered events and to reflect the averaging time of the exposure, incident AF episodes were included in the analysis if at least 24 hours had passed since the previous AF episode. Results: Of 200 patients enrolled, 49 experienced at least one AF episode (n = 328 episodes). After excluding events with missing exposure or covariate information, analyses were confined to 230 AF episodes among 47 patients. The 47 patients with paroxysmal AF were followed for an average of 1.9 years, and 32 (68%) were male, 45 (96%) were Caucasian, the mean age was 67 years, 24 (51%) had a history of prior AF episodes, 27 (57%) had a pre-implantation ejection fraction < 35%, and 29 (62%) received the ICD for primary prophylaxis. Outdoor temperature in the previous 24 hours was not associated with AF (odds ratio (OR) = 1.13; 95% confidence interval (CI): 0.89, 1.43, p = 0.32, per interquartile range (IQR) decrease of 6.3°C). Lower absolute humidity in the previous 24 hours was associated with a higher risk of AF onset (OR = 1.33; 95% CI: 1.02, 1.74, p = 0.04, per IQR decrease of 3.5 g/m 3 ); this risk increased slightly for the previous 3 hours (OR = 1.39; 95% CI: 1.06, 1.82, p = 0.02, per IQR decrease of 3.7 g/m 3 ). Conclusions: In conclusion, drier air was associated with a transiently higher risk of paroxysmal AF in the following 24 hours among patients with dual chamber ICDs.

Estimation of causal effects using instrumental variables with nonignorable missing covariates: Application to effect of type of delivery NICU on premature infants

Understanding how effective high-level NICUs (neonatal intensive care units that have the capacity for sustained mechanical assisted ventilation and high volume) are compared to low-level NICUs is important and valuable for both individual mothers and for public policy decisions. The goal of this paper is to estimate the effect on mortality of premature babies being delivered in a high-level NICU vs. a low-level NICU through an observational study where there are unmeasured confounders as well as nonignorable missing covariates. We consider the use of excess travel time as an instrumental variable (IV) to control for unmeasured confounders. In order for an IV to be valid, we must condition on confounders of the IV---outcome relationship, for example, month prenatal care started must be conditioned on for excess travel time to be a valid IV. However, sometimes month prenatal care started is missing, and the missingness may be nonignorable because it is related to the not fully measured mother's/infant's risk of complications. We develop a method to estimate the causal effect of a treatment using an IV when there are nonignorable missing covariates as in our data, where we allow the missingness to depend on the fully observed outcome as well as the partially observed compliance class, which is a proxy for the unmeasured risk of complications. A simulation study shows that under our nonignorable missingness assumption, the commonly used estimation methods, complete-case analysis and multiple imputation by chained equations assuming missingness at random, provide biased estimates, while our method provides approximately unbiased estimates. We apply our method to the NICU study and find evidence that high-level NICUs significantly reduce deaths for babies of small gestational age, whereas for almost mature babies like 37 weeks, the level of NICUs makes little difference. A sensitivity analysis is conducted to assess the sensitivity of our conclusions to key assumptions about the missing covariates. The method we develop in this paper may be useful for many observational studies facing similar issues of unmeasured confounders and nonignorable missing data as ours.

Joint modeling of longitudinal and survival data with missing and left-censored time-varying covariates

Joint modeling of longitudinal and survival data with missing and left-censored time-varying covariates

Bayesian Analysis of Nonlinear Reproductive Dispersion Mixed Models for Longitudinal Data with Nonignorable Missing Covariates

This article proposes a Bayesian approach, which can simultaneously obtain the Bayesian estimates of unknown parameters and random effects, to analyze nonlinear reproductive dispersion mixed models (NRDMMs) for longitudinal data with nonignorable missing covariates and responses. The logistic regression model is employed to model the missing data mechanisms for missing covariates and responses. A hybrid sampling procedure combining the Gibber sampler and the Metropolis-Hastings algorithm is presented to draw observations from the conditional distributions. Because missing data mechanism is not testable, we develop the logarithm of the pseudo-marginal likelihood, deviance information criterion, the Bayes factor, and the pseudo-Bayes factor to compare several competing missing data mechanism models in the current considered NRDMMs with nonignorable missing covaraites and responses. Three simulation studies and a real example taken from the paediatric AIDS clinical trial group ACTG are used to illustrate the proposed methodologies. Empirical results show that our proposed methods are effective in selecting missing data mechanism models.

GLCCI1 rs37973 does not influence treatment response to inhaled corticosteroids in white subjects with asthma

GLCCI1 rs37973 does not influence treatment response to inhaled corticosteroids in white subjects with asthma

Identifiability of subgroup causal effects in randomized experiments with nonignorable missing covariates

Although randomized experiments are widely regarded as the gold standard for estimating causal effects, missing data of the pretreatment covariates makes it challenging to estimate the subgroup causal effects. When the missing data mechanism of the covariates is nonignorable, the parameters of interest are generally not pointly identifiable, and we can only get bounds for the parameters of interest, which may be too wide for practical use. In some real cases, we have prior knowledge that some restrictions may be plausible. We show the identifiability of the causal effects and joint distributions for four interpretable missing data mechanisms and evaluate the performance of the statistical inference via simulation studies. One application of our methods to a real data set from a randomized clinical trial shows that one of the nonignorable missing data mechanisms fits better than the ignorable missing data mechanism, and the results conform to the study's original expert opinions. We also illustrate the potential applications of our methods to observational studies using a data set from a job-training program.

Constrained inference for generalized linear models with incomplete covariate data

Missing data are common in many experiments, including surveys, clinical trials, epidemiological studies, and environmental studies. Unconstrained likelihood inferences for generalized linear models (GLMs) with nonignorable missing covariates have been studied extensively in the literature. However, parameter orderings or constraints may occur naturally in practice, and thus the efficiency of a statistical method may be improved by incorporating parameter constraints into the likelihood function. In this paper, we consider constrained inference for analysing GLMs with nonignorable missing covariates under linear inequality constraints on the model parameters. Specifically, constrained maximum likelihood (ML) estimation is based on the gradient projection expectation maximization approach. Further, we investigate the asymptotic null distribution of the constrained likelihood ratio test (LRT). Simulations study the empirical properties of the constrained ML estimators and LRTs, which demonstrate improved precision of these constrained techniques. An application to contaminant levels in an environmental study is also presented.

Comparison of Methods for Handling Missing Covariate Data

Missing covariate data is a common problem in nonlinear mixed effects modelling of clinical data. The aim of this study was to implement and compare methods for handling missing covariate data in nonlinear mixed effects modelling under different missing data mechanisms. Simulations generated data for 200 individuals with a 50% difference in clearance between males and females. Three different types of missing data mechanisms were simulated and information about sex was missing for 50% of the individuals. Six methods for handling the missing covariate were compared in a stochastic simulations and estimations study where 200 data sets were simulated. The methods were compared according to bias and precision of parameter estimates. Multiple imputation based on weight and response, full maximum likelihood modelling using information on weight and full maximum likelihood modelling where the proportion of males among the individuals lacking information about sex was estimated (EST) gave precise and unbiased estimates in the presence of missing data when data were missing completely at random or missing at random. When data were missing not at random, the only method resulting in low bias and high parameter precision was EST.

Bayesian semiparametric models for nonignorable missing mechanisms in generalized linear models

Semiparametric models provide a more flexible form for modeling the relationship between the response and the explanatory variables. On the other hand in the literature of modeling for the missing variables, canonical form of the probability of the variable being missing (p) is modeled taking a fully parametric approach. Here we consider a regression spline based semiparametric approach to model the missingness mechanism of nonignorably missing covariates. In this model the relationship between the suitable canonical form of p (e.g. probit p) and the missing covariate is modeled through several splines. A Bayesian procedure is developed to efficiently estimate the parameters. A computationally advantageous prior construction is proposed for the parameters of the semiparametric part. A WinBUGS code is constructed to apply Gibbs sampling to obtain the posterior distributions. We show through an extensive Monte Carlo simulation experiment that response model coefficent estimators maintain better (when the true missingness mechanism is nonlinear) or equivalent (when the true missingness mechanism is linear) bias and efficiency properties with the use of proposed semiparametric missingness model compared to the conventional model.

Nonlinear multiple imputation for continuous covariate within semiparametric Cox model: application to HIV data in Senegal

Multiple imputation is commonly used to impute missing covariate in Cox semiparametric regression setting. It is to fill each missing data with more plausible values, via a Gibbs sampling procedure, specifying an imputation model for each missing variable. This imputation method is implemented in several softwares that offer imputation models steered by the shape of the variable to be imputed, but all these imputation models make an assumption of linearity on covariates effect. However, this assumption is not often verified in practice as the covariates can have a nonlinear effect. Such a linear assumption can lead to a misleading conclusion because imputation model should be constructed to reflect the true distributional relationship between the missing values and the observed values. To estimate nonlinear effects of continuous time invariant covariates in imputation model, we propose a method based on B-splines function. To assess the performance of this method, we conducted a simulation study, where we compared the multiple imputation method using Bayesian splines imputation model with multiple imputation using Bayesian linear imputation model in survival analysis setting. We evaluated the proposed method on the motivated data set collected in HIV-infected patients enrolled in an observational cohort study in Senegal, which contains several incomplete variables. We found that our method performs well to estimate hazard ratio compared with the linear imputation methods, when data are missing completely at random, or missing at random.

MASTOR: Mixed-Model Association Mapping of Quantitative Traits in Samples with Related Individuals

Genetic association studies often sample individuals with known familial relationships in addition to unrelated individuals, and it is common for some individuals to have missing data (phenotypes, genotypes, or covariates). When some individuals in a sample are related, power can be gained by incorporating all individuals in the analysis, including individuals with partially missing data, while properly accounting for the dependence among them. We propose MASTOR, a mixed-model, retrospective score test for genetic association with a quantitative trait. MASTOR achieves high power in samples that contain related individuals by making full use of the relationship information to incorporate partially missing data in the analysis while correcting for dependence. Individuals with available phenotype and covariate information who are not genotyped but have genotyped relatives in the sample can still contribute to the association analysis because of the dependence among genotypes. Similarly, individuals who are genotyped but are missing covariate or phenotype information can contribute to the analysis. MASTOR is valid even when the phenotype model is misspecified and with either random or phenotype-based ascertainment. In simulations, we demonstrate the correct type 1 error of MASTOR, the increase in power that comes from making full use of the relationship information, the robustness to misspecification of the phenotype model, and the improvement in power that comes from modeling the heritability. We show that MASTOR is computationally feasible and practical in genome-wide association studies. We apply MASTOR to data on high-density lipoprotein cholesterol from the Framingham Heart study.

Abstract P382: Differential Distributions of Carotid-Femoral and Brachial-Ankle Pulse Wave Velocity with Age and Race: The ARIC Study

Background: Carotid-femoral PWV (cfPWV), a well-studied measure of central arterial stiffness is associated with cardiovascular disease and mortality. Brachial-ankle PWV (baPWV) is commonly used in Asian countries as a measure of peripheral arterial stiffness. Few studies have evaluated the population distributions of cfPWV and baPWV and the degree to which they may measure the same arterial characteristics. Objectives: Characterize cfPWV and baPWV in a population of older adults by age, gender and race. Methods: We analyzed 2,403 adults (1473 females; mean age 75 years) from the population-based Atherosclerosis Risk in Communities (ARIC) study who had data on cfPWV and baPWV, after excluding 763 individuals due to arrhythmias, 165 with BMI >40 kg/m2, and 300 with missing covariates of interest. Technicians used Omron VP-1000 plus system (Colin Co., Komaki, Japan) and followed a standardized protocol, to measure cfPWV and baPWV twice, and the results were averaged. The cumulative distributions of cfPWV and the right baPWV by age dichotomized at median, sex and race (African American (AA) and non-AA) were evaluated with the Kolmogorov-Smirnov test and the relationship between cfPWV and baPWV assessed by the Pearson correlation coefficient. Results: The mean (SD) cfPWV and baPWV was 1159 (303) and 1736 (319) cm/sec. The empirical distribution function of both these measures was higher (p<0.001) among those 75 years and older than those younger than 75 years i.e., mean (SD) of cfPWV was 1229 (321) vs.1099 (274) cm/sec, respectively, and mean (SD) of baPWV was 1814 (328) vs. 1670 (295) cm/sec, respectively. The distribution function of cfPWV was higher among AAs (p<0.001) but the distribution of baPWV was not different by race (p=0.76). The mean (SD) in cm/sec for AA participants compared to non-AA participants for cfPWV was 1232 (335) vs. 1138 (290), and baPWV was 1725 (324) vs. 1740 (317). The distributions of cfPWV and baPWV did not differ by gender, p=0.21 and p=0.23, respectively. The mean (SD) cfPWV and baPWV among males was 1174 (305) and 1728 (318), and among to females was 1150 (302) and 1742 (320) cm/sec. Correlation analysis showed that cfPWV and baPWV were positively correlated, r=0.45, (p<0.001). Conclusion: The distributions of cfPWV and baPWV were similar by gender but were different by age and by race. Despite having comparable measure of peripheral vascular stiffness, African Americans showed a higher degree of central vascular stiffness compared to non-African Americans. Our findings indicate that cfPWV and baPWV are correlated measures of arterial stiffness but likely reflect different aspects of segment-specific vascular impairment and cardiovascular risk.

Feedback and Modularization in a Bayesian Meta–analysis of Tree Traits Affecting Forest Dynamics

We describe a unique application of modularization in the context of a Bayesian meta–analysis of quantitative information obtained from the literature. Incomplete reporting, resulting in large amounts of missing data, is common in many meta–analyses, and, in this study, it led to poor mixing and identifiability problems in a fully Bayesian meta–analysis model. As an alternative to the full Bayesian approach, we modularized model components (e.g., modules of covariates, sample sizes, and standard errors) to prevent missing covariate data in these modules from allowing feedback that would otherwise affect parameters in the covariate module (direct feedback control) or affect covariate effects parameters in the mean model for the response (indirect feedback control). The combination of direct and indirect feedback control greatly improves mixing and facilitates convergence of Markov chain Monte Carlo (MCMC), yielding realistic pseudo–posteriors. Thus, our modularization approach allowed us to address important limitations of existing meta–analytic methods by accommodating incomplete reporting and by considering all model quantities as stochastic, including the response variable of interest (e.g., a sample mean) and sample sizes, standard errors, and all covariates, reported or not. We illustrate our approach using data summaries extracted from literature on specific leaf area (SLA) of trees, an important functional trait linked to tree growth and forest dynamics and a key parameter in models of forest responses to climate change. A hierarchical model based on taxonomic relationships allows borrowing of strength to infer SLA for 305 tree species in the United States based on information for 158 of those species. In the context of the SLA meta–analysis, we discuss problems that arise from feedback among model components and provide ecological arguments for modularization—for “cutting feedback.” We anticipate that our approach may be applied to meta–analyses of other important tree traits and to similar meta–analytical studies in general.