Genetic association studies with bivariate mixed responses subject to measurement error and misclassification

In genetic association studies, mixed effects models have been widely used in detecting the pleiotropy effects which occur when one gene affects multiple phenotype traits. In particular, bivariate mixed effects models are useful for describing the association of a gene with a continuous trait and a binary trait. However, such models are inadequate to feature the data with response mismeasurement, a characteristic that is often overlooked. It has been well studied that in univariate settings, ignorance of mismeasurement in variables usually results in biased estimation. In this paper, we consider the setting with a bivariate outcome vector which contains a continuous component and a binary component both subject to mismeasurement. We propose an induced likelihood approach and an EM algorithm method to handle measurement error in continuous response and misclassification in binary response simultaneously. Simulation studies confirm that the proposed methods successfully remove the bias induced from the response mismeasurement.     

Meta‐analysis for diagnostic accuracy studies: a new statistical model using beta‐binomial distributions and bivariate copulas

There are still challenges when meta‐analyzing data from studies on diagnostic accuracy. This is mainly due to the bivariate nature of the response where information on sensitivity and specificity must be summarized while accounting for their correlation within a single trial. In this paper, we propose a new statistical model for the meta‐analysis for diagnostic accuracy studies. This model uses beta‐binomial distributions for the marginal numbers of true positives and true negatives and links these margins by a bivariate copula distribution. The new model comes with all the features of the current standard model, a bivariate logistic regression model with random effects, but has the additional advantages of a closed likelihood function and a larger flexibility for the correlation structure of sensitivity and specificity. In a simulation study, which compares three copula models and two implementations of the standard model, the Plackett and the Gauss copula do rarely perform worse but frequently better than the standard model. We use an example from a meta‐analysis to judge the diagnostic accuracy of telomerase (a urinary tumor marker) for the diagnosis of primary bladder cancer for illustration. Copyright © 2013 John Wiley & Sons, Ltd.     

Meta‐analysis of diagnostic tests accounting for disease prevalence: a new model using trivariate copulas

In real life and somewhat contrary to biostatistical textbook knowledge, sensitivity and specificity (and not only predictive values) of diagnostic tests can vary with the underlying prevalence of disease. In meta‐analysis of diagnostic studies, accounting for this fact naturally leads to a trivariate expansion of the traditional bivariate logistic regression model with random study effects. In this paper, a new model is proposed using trivariate copulas and beta‐binomial marginal distributions for sensitivity, specificity, and prevalence as an expansion of the bivariate model. Two different copulas are used, the trivariate Gaussian copula and a trivariate vine copula based on the bivariate Plackett copula. This model has a closed‐form likelihood, so standard software (e.g., SAS PROC NLMIXED ) can be used. The results of a simulation study have shown that the copula models perform at least as good but frequently better than the standard model. The methods are illustrated by two examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Bivariate logistic regression: modelling the association of small for gestational age births in twin gestations.

Clustered binary responses, such as disease status in twins, frequently arise in perinatal health and other epidemiologic applications. The scientific objective involves modelling both the marginal mean responses, such as the probability of disease, and the within-cluster association of the multivariate responses. In this regard, bivariate logistic regression is a useful procedure with advantages that include (i) a single maximization of the joint probability distribution of the bivariate binary responses, and (ii) modelling the odds ratio describing the pairwise association between the two binary responses in relation to several covariates. In addition, since the form of the joint distribution of the bivariate binary responses is assumed known, parameters for the regression model can be estimated by the method of maximum likelihood. Hence, statistical inferences may be based on likelihood ratio tests and profile likelihood confidence intervals. We apply bivariate logistic regression to a perinatal database comprising 924 twin foetuses resulting from 462 pregnancies to model obstetric and clinical risk factors for the association of small for gestational age births in twin gestations.     

Copula selection models for non-Gaussian outcomes that are missing not at random

Missing not at random (MNAR) data pose key challenges for statistical inference because the substantive model of interest is typically not identifiable without imposing further (eg, distributional) assumptions. Selection models have been routinely used for handling MNAR by jointly modeling the outcome and selection variables and typically assuming that these follow a bivariate normal distribution. Recent studies have advocated parametric selection approaches, for example, estimated by multiple imputation and maximum likelihood, that are more robust to departures from the normality assumption compared with those assuming that nonresponse and outcome are jointly normally distributed. However, the proposed methods have been mostly restricted to a specific joint distribution (eg, bivariate t-distribution). This paper discusses a flexible copula-based selection approach (which accommodates a wide range of non-Gaussian outcome distributions and offers great flexibility in the choice of functional form specifications for both the outcome and selection equations) and proposes a flexible imputation procedure that generates plausible imputed values from the copula selection model. A simulation study characterizes the relative performance of the copula model compared with the most commonly used selection models for estimating average treatment effects with MNAR data. We illustrate the methods in the REFLUX study, which evaluates the effect of laparoscopic surgery on long-term quality of life in patients with reflux disease. We provide software code for implementing the proposed copula framework using the R package GJRM .     

A general frailty model to accommodate individual heterogeneity in the acquisition of multiple infections: An application to bivariate current status data

The analysis of multivariate time-to-event (TTE) data can become complicated due to the presence of clustering, leading to dependence between multiple event times. For a long time, (conditional) frailty models and (marginal) copula models have been used to analyze clustered TTE data. In this article, we propose a general frailty model employing a copula function between the frailty terms to construct flexible (bivariate) frailty distributions with the application to current status data. The model has the advantage to impose a less restrictive correlation structure among latent frailty variables as compared to traditional frailty models. Specifically, our model uses a copula function to join the marginal distributions of the frailty vector. In this article, we considered different copula functions, and we relied on marginal gamma distributions due to their mathematical convenience. Based on a simulation study, our novel model outperformed the commonly used additive correlated gamma frailty model, especially in the case of a negative association between the frailties. At the end of the article, the new methodology is illustrated on real-life data applications entailing bivariate serological survey data.     

Copula-based regression models for a bivariate mixed discrete and continuous outcome

This paper is concerned with regression models for correlated mixed discrete and continuous outcomes constructed using copulas. Our approach entails specifying marginal regression models for the outcomes, and combining them via a copula to form a joint model. Specifically, we propose marginal regression models (e.g. generalized linear models) to link the outcomes' marginal means to covariates. To account for associations between outcomes, we adopt the Gaussian copula to indirectly specify their joint distributions. Our approach has two advantages over current methods: one, regression parameters in models for both outcomes are marginally meaningful, and two, the association is 'margin-free', in the sense that it is characterized by the copula alone. By assuming a latent variable framework to describe discrete outcomes, the copula used still uniquely determines the joint distribution. In addition, association measures between outcomes can be interpreted in the usual way. We report results of simulations concerning the bias and efficiency of two likelihood-based estimation methods for the model. Finally, we illustrate the model using data on burn injuries.     

Copula bivariate probit models: with an application to medical expenditures

The bivariate probit model is frequently used for estimating the effect of an endogenous binary regressor (the ‘treatment’) on a binary health outcome variable. This paper discusses simple modifications that maintain the probit assumption for the marginal distributions while introducing non‐normal dependence using copulas. In an application of the copula bivariate probit model to the effect of insurance status on the absence of ambulatory health care expenditure, a model based on the Frank copula outperforms the standard bivariate probit model. Copyright © 2011 John Wiley & Sons, Ltd.     

CHAID模型在巩义市新生儿低出生体重影响因素筛选中的应用

[目的]使用决策树中分类方法的CHAID算法模型和非条件Logistic回归模型,探讨新生儿低出生体重危险因素,并比较决策树的和Logistic模型间结果的异同。[方法]根据新生儿是否低出生体重分类。分别建立决策树CHAID模型和非条件Logistic模型。[结果]母亲孕周是新生儿低出生体重最主要的影响因素,在孕周小于37周的亚群中,多胎的新生儿发生低出生体重的风险更高。[结论在二分类结果变量的危险因素分析中,非条件Logistic模型和决策树模型都有较高的应用价值,两种方法可以相互结合,得到更为全面的结果。     

Adverse subpopulation regression for multivariate outcomes with high‐dimensional predictors

Biomedical studies have a common interest in assessing relationships between multiple related health outcomes and high‐dimensional predictors. For example, in reproductive epidemiology, one may collect pregnancy outcomes such as length of gestation and birth weight and predictors such as single nucleotide polymorphisms in multiple candidate genes and environmental exposures. In such settings, there is a need for simple yet flexible methods for selecting true predictors of adverse health responses from a high‐dimensional set of candidate predictors. To address this problem, one may either consider linear regression models for the continuous outcomes or convert these outcomes into binary indicators of adverse responses using predefined cutoffs. The former strategy has the disadvantage of often leading to a poorly fitting model that does not predict risk well, whereas the latter approach can be very sensitive to the cutoff choice. As a simple yet flexible alternative, we propose a method for adverse subpopulation regression, which relies on a two‐component latent class model, with the dominant component corresponding to (presumed) healthy individuals and the risk of falling in the minority component characterized via a logistic regression. The logistic regression model is designed to accommodate high‐dimensional predictors, as occur in studies with a large number of gene by environment interactions, through the use of a flexible nonparametric multiple shrinkage approach. The Gibbs sampler is developed for posterior computation. We evaluate the methods with the use of simulation studies and apply these to a genetic epidemiology study of pregnancy outcomes. Copyright © 2012 John Wiley & Sons, Ltd.     

Identifying perinatal risk factors for infant maltreatment: an ecological approach

Background  

Child maltreatment and its consequences are a persistent problem throughout the world. Public health workers, human services officials, and others are interested in new and efficient ways to determine which geographic areas to target for intervention programs and resources. To improve assessment efforts, selected perinatal factors were examined, both individually and in various combinations, to determine if they are associated with increased risk of infant maltreatment. State of Georgia birth records and abuse and neglect data were analyzed using an area-based, ecological approach with the census tract as a surrogate for the community. Cartographic visualization suggested some correlation exists between risk factors and child maltreatment, so bivariate and multivariate regression were performed. The presence of spatial autocorrelation precluded the use of traditional ordinary least squares regression, therefore a spatial regression model coupled with maximum likelihood estimation was employed.     

A trivariate continual reassessment method for phase I/II trials of toxicity,efficacy, and surrogate efficacy

Recently, many Bayesian methods have been developed for dose finding when simultaneously modeling both toxicity and efficacy outcomes in a blended phase I/II fashion. A further challenge arises when all the true efficacy data cannot be obtained quickly after the treatment so that surrogate markers are instead used (e.g., in cancer trials). We propose a framework to jointly model the probabilities of toxicity, efficacy, and surrogate efficacy given a particular dose. Our trivariate binary model is specified as a composition of two bivariate binary submodels. In particular, we extend the bivariate continual reassessment method (CRM), as well as utilize a particular Gumbel copula. The resulting trivariate algorithm utilizes all the available data at any given time point and can flexibly stop the trial early for either toxicity or efficacy. Our simulation studies demonstrate that our proposed method can successfully improve dosage targeting efficiency and guard against excess toxicity over a variety of true model settings and degrees of surrogacy. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic prediction in functional concurrent regression with an application to child growth

In many studies, it is of interest to predict the future trajectory of subjects based on their historical data, referred to as dynamic prediction. Mixed effects models have traditionally been used for dynamic prediction. However, the commonly used random intercept and slope model is often not sufficiently flexible for modeling subject‐specific trajectories. In addition, there may be useful exposures/predictors of interest that are measured concurrently with the outcome, complicating dynamic prediction. To address these problems, we propose a dynamic functional concurrent regression model to handle the case where both the functional response and the functional predictors are irregularly measured. Currently, such a model cannot be fit by existing software. We apply the model to dynamically predict children's length conditional on prior length, weight, and baseline covariates. Inference on model parameters and subject‐specific trajectories is conducted using the mixed effects representation of the proposed model. An extensive simulation study shows that the dynamic functional regression model provides more accurate estimation and inference than existing methods. Methods are supported by fast, flexible, open source software that uses heavily tested smoothing techniques.     

Semiparametric Bayesian joint modeling of a binary and continuous outcome with applications in toxicological risk assessment

Many dose–response studies collect data on correlated outcomes. For example, in developmental toxicity studies, uterine weight and presence of malformed pups are measured on the same dam. Joint modeling can result in more efficient inferences than independent models for each outcome. Most methods for joint modeling assume standard parametric response distributions. However, in toxicity studies, it is possible that response distributions vary in location and shape with dose, which may not be easily captured by standard models. To address this issue, we propose a semiparametric Bayesian joint model for a binary and continuous response. In our model, a kernel stick‐breaking process prior is assigned to the distribution of a random effect shared across outcomes, which allows flexible changes in distribution shape with dose shared across outcomes. The model also includes outcome‐specific fixed effects to allow different location effects. In simulation studies, we found that the proposed model provides accurate estimates of toxicological risk when the data do not satisfy assumptions of standard parametric models. We apply our method to data from a developmental toxicity study of ethylene glycol diethyl ether. Copyright © 2013 John Wiley & Sons, Ltd.     

Changes in the spatial pattern of low birth weight in a southern California county: the role of individual and neighborhood level factors

Individual-level maternal risk factors have been able to explain only a small proportion of low birth weight (LBW) births in the US to date and neighborhood-level factors have not been recognized as important predictors of reproductive outcomes. At the US/Mexico border, tremendous demographic changes have taken place between 1980 and 1990. Whether high population growth, economic pressures, and community instability have affected reproductive health in this region is not known. We used spatial epidemiologic methods to investigate the importance of changes in neighborhood and individual-level risk factors in predicting changes in two measures of adverse reproductive health: term and preterm LBW. Using approximately 16,000 births in 1980 and 24,000 births in 1990, we produced a continuous surface of LBW change (Z scores for difference in proportions) for southern San Diego County, CA, and identified statistically significant "hot spots" of elevated risk. Using a geographic information system, data from the 1980 and 1990 US Census were smoothed to link neighborhood-level variables with individual-level data from the 1980 and 1990 California birth certificates. Multivariate regression models were developed to identify individual- and neighborhood-level variables of 1980-1990 changes which were predictive of Z scores of LBW change. Results of conditional autoregressive models were used to assess effects of spatial autocorrelation. The continuous surface of LBW identified areas with statistically significant increases (17 areas for term LBW and 14 areas for preterm LBW). While individual- and neighborhood-level variables explained about an equal amount of variance in term LBW, only neighborhood-level variables were significant predictors of preterm LBW. While changes in maternal race/ethnicity composition and a measure of stability were related to term LBW, measures of affluence were related to preterm LBW. This study highlights the importance of socioeconomic and demographic changes in a woman's neighborhood on reproductive health.     

A mixed effect model for bivariate meta‐analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta‐analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re‐analysing the data of two published meta‐analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R . Copyright © 2015 John Wiley & Sons, Ltd.     

Proportional hazard model estimation under dependent censoring using copulas and penalized likelihood

This paper considers Cox proportional hazard models estimation under informative right censored data using maximum penalized likelihood, where dependence between censoring and event times are modelled by a copula function and a roughness penalty function is used to restrain the baseline hazard as a smooth function. Since the baseline hazard is nonnegative, we propose a special algorithm where each iteration involves updating regression coefficients by the Newton algorithm and baseline hazard by the multiplicative iterative algorithm. The asymptotic properties for both regression coefficients and baseline hazard estimates are developed. The simulation study investigates the performance of our method and also compares it with an existing maximum likelihood method. We apply the proposed method to a dementia patients dataset.     

A copula‐based mixed Poisson model for bivariate recurrent events under event‐dependent censoring

In many chronic disease processes subjects are at risk of two or more types of events. We describe a bivariate mixed Poisson model in which a copula function is used to model the association between two gamma distributed random effects. The resulting model is a bivariate negative binomial process in which each type of event arises from a negative binomial process. Methods for parameter estimation are described for parametric and semiparametric models based on an EM algorithm. We also consider the issue of event‐dependent censoring based on one type of event, which arises when one event is sufficiently serious that its occurence may influence the decision of whether to withdraw a patient from a study. The asymptotic biases of estimators of rate and mean functions from naive marginal analyses are discussed, as well as associated treatment effects. Because the joint model is fit based on a likelihood, consistent estimates are obtained. Simulation studies are carried out to evaluate the empirical performance of the proposed estimators with independent and event‐dependent censoring and applications to a trial of breast cancer patients with skeletal metastases and a study of patients with chronic obstructive pulmonary disease illustrate the approach. Copyright © 2010 John Wiley & Sons, Ltd.     

A stratified generalized additive model and permutation test for temporal heterogeneity of smoothed bivariate spatial effects

Generalized additive models (GAMs) with bivariate smoothers are frequently used to map geographic disease risks in epidemiology studies. A challenge in identifying health disparities has been the lack of intuitive and computationally feasible methods to assess whether the pattern of spatial effects varies over time. In this research, we accommodate time-stratified smoothers into the GAM framework to estimate time-specific spatial risk patterns while borrowing information from confounding effects across time. A backfitting algorithm for model estimation is proposed along with a permutation testing framework for assessing temporal heterogeneity of geospatial risk patterns across two or more time points. Simulation studies show that our proposed permuted mean squared difference (PMSD) test performs well with respect to type I error and power in various settings when compared with existing methods. The proposed model and PMSD test are used geospatial risk patterns of patent ductus arteriosus (PDA) in the state of Massachusetts over 2003-2009. We show that there is variation over time in spatial patterns of PDA risk, adjusting for other known risk factors, suggesting the presence of potential time-varying and space-related risk factors other than the adjusted ones.     

A tutorial on Bayesian bivariate meta‐analysis of mixed binary‐continuous outcomes with missing treatment effects

Bivariate random‐effects meta‐analysis (BVMA) is a method of data synthesis that accounts for treatment effects measured on two outcomes. BVMA gives more precise estimates of the population mean and predicted values than two univariate random‐effects meta‐analyses (UVMAs). BVMA also addresses bias from incomplete reporting of outcomes. A few tutorials have covered technical details of BVMA of categorical or continuous outcomes. Limited guidance is available on how to analyze datasets that include trials with mixed continuous‐binary outcomes where treatment effects on one outcome or the other are not reported. Given the advantages of Bayesian BVMA for handling missing outcomes, we present a tutorial for Bayesian BVMA of incompletely reported treatment effects on mixed bivariate outcomes. This step‐by‐step approach can serve as a model for our intended audience, the methodologist familiar with Bayesian meta‐analysis, looking for practical advice on fitting bivariate models. To facilitate application of the proposed methods, we include our WinBUGS code. As an example, we use aggregate‐level data from published trials to demonstrate the estimation of the effects of vitamin K and bisphosphonates on two correlated bone outcomes, fracture, and bone mineral density. We present datasets where reporting of the pairs of treatment effects on both outcomes was ‘partially’ complete (i.e., pairs completely reported in some trials), and we outline steps for modeling the incompletely reported data. To assess what is gained from the additional work required by BVMA, we compare the resulting estimates to those from separate UVMAs. We discuss methodological findings and make four recommendations. Copyright © 2015 John Wiley & Sons, Ltd.