A Bayesian Adjustment for Covariate Misclassification with Correlated Binary Outcome Data

Estimated associations between an outcome variable and misclassified covariates tend to be biased when the methods of estimation that ignore the classification error are applied. Available methods to account for misclassification often require the use of a validation sample (i.e. a gold standard). In practice, however, such a gold standard may be unavailable or impractical. We propose a Bayesian approach to adjust for misclassification in a binary covariate in the random effect logistic model when a gold standard is not available. This Markov Chain Monte Carlo (MCMC) approach uses two imperfect measures of a dichotomous exposure under the assumptions of conditional independence and non-differential misclassification. A simulated numerical example and a real clinical example are given to illustrate the proposed approach. Our results suggest that the estimated log odds of inpatient care and the corresponding standard deviation are much larger in our proposed method compared with the models ignoring misclassification. Ignoring misclassification produces downwardly biased estimates and underestimate uncertainty.     

Addressing misclassification for binary data: probit and t-link regressions

Generalized linear models are addressed to describe the dependence of data on explanatory variables when the binary outcome is subject to misclassification. Both probit and t-link regressions for misclassified binary data under Bayesian methodology are proposed. The computational difficulties have been avoided by using data augmentation. The idea of using a data augmentation framework (with two types of latent variables) is exploited to derive efficient Gibbs sampling and expectation–maximization algorithms. Besides, this formulation has allowed to obtain the probit model as a particular case of the t-link model. Simulation examples are presented to illustrate the model performance when comparing with standard methods that do not consider misclassification. In order to show the potential of the proposed approaches, a real data problem arising when studying hearing loss caused by exposure to occupational noise is analysed.     

Bayesian adjustment for unidirectional misclassification in ordinal covariates

In this paper, we study the identification of Bayesian regression models, when an ordinal covariate is subject to unidirectional misclassification. Xia and Gustafson [Bayesian regression models adjusting for unidirectional covariate misclassification. Can J Stat. 2016;44(2):198–218] obtained model identifiability for non-binary regression models, when there is a binary covariate subject to unidirectional misclassification. In the current paper, we establish the moment identifiability of regression models for misclassified ordinal covariates with more than two categories, based on forms of observable moments. Computational studies are conducted that confirm the theoretical results. We apply the method to two datasets, one from the Medical Expenditure Panel Survey (MEPS), and the other from Translational Research Investigating Underlying Disparities in Acute Myocardial infarction Patients Health Status (TRIUMPH).     

Misclassification of current status data

We describe a simple method for nonparametric estimation of a distribution function based on current status data where observations of current status information are subject to misclassification. Nonparametric maximum likelihood techniques lead to use of a straightforward set of adjustments to the familiar pool-adjacent-violators estimator used when misclassification is assumed absent. The methods consider alternative misclassification models and are extended to regression models for the underlying survival time. The ideas are motivated by and applied to an example on human papilloma virus (HPV) infection status of a sample of women examined in San Francisco.     

Bayesian misclassification and propensity score methods for clustered observational studies

Bayesian propensity score regression analysis with misclassified binary responses is proposed to analyse clustered observational data. This approach utilizes multilevel models and corrects for misclassification in the responses. Using the deviance information criterion (DIC), the performance of the approach is compared with approaches without correcting for misclassification, multilevel structure specification, or both in the study of the impact of female employment on the likelihood of physical violence. The smallest DIC confirms that our proposed model best fits the data. We conclude that female employment has an insignificant impact on the likelihood of physical spousal violence towards women. In addition, a simulation study confirms that the proposed approach performed best in terms of bias and coverage rate. Ignoring misclassification in response or multilevel structure of data would yield biased estimation of the exposure effect.     

One-way analysis of proportions for misclassified binomial data

We consider data with a nominal grouping variable and a binary response variable. The grouping variable is measured without error, but the response variable is measured using a fallible device subject to misclassification. To achieve model identifiability, we use the double-sampling scheme which requires obtaining a subsample of the original data or another independent sample. This sample is then classified by both the fallible device and another infallible device regarding the response variable. We propose two Wald tests for testing the association between the two variables and illustrate the test using traffic data. The Type-I error rate and power of the tests are examined using simulations and a modified Wald test is recommended.     

Bayes methods in the ecological fallacy cntext:estimation of individual correlation from aggregate data

The ecological fallacy is related to Simpson's paradox (1951) where relationships among group means may be counterintuitive and substantially different from relationships within groups, where the groups are usually geographic entities such as census tracts. We consider the problem of estimating the correlation between two jointly normal random variables where only ecological data (group means) are available. Two empirical Bayes estimators and one fully Bayesian estimator are derived and compared with the usual ecological estimator, which is simply the Pearson correlation coefficient of the group sample means. We simulate the bias and mean squared error performance of these estimators, and also give an example employing a dataset where the individual level data are available for model checking. The results indicate superiority of the empirical Bayes estimators in a variety of practical situations where, though we lack individual level data, other relevant prior information is available.     

A Bayesian approach for misclassified ordinal response data

ABSTRACT

Motivated by a longitudinal oral health study, the Signal-Tandmobiel^® study, a Bayesian approach has been developed to model misclassified ordinal response data. Two regression models have been considered to incorporate misclassification in the categorical response. Specifically, probit and logit models have been developed. The computational difficulties have been avoided by using data augmentation. This idea is exploited to derive efficient Markov chain Monte Carlo methods. Although the method is proposed for ordered categories, it can also be implemented for unordered ones in a simple way. The model performance is shown through a simulation-based example and the analysis of the motivating study.     

Verification bias on sensitivity and specificity measurements in diagnostic medicine: a comparison of some approaches used for correction

Verification bias may occur when the test results of not all subjects are verified by using a gold standard. The correction for this bias can be made using different approaches depending on whether missing gold standard test results are random or not. Some of these approaches with binary test and gold standard results include the correction method by Begg and Greenes, lower and upper limits for diagnostic measurements by Zhou, logistic regression method, multiple imputation method, and neural networks. In this study, all these approaches are compared by employing a real and simulated data under different conditions.     

Bayesian comparison of diagnostic tests with largely non-informative missing data

This work was motivated by a real problem of comparing binary diagnostic tests based upon a gold standard, where the collected data showed that the large majority of classifications were incomplete and the feedback received from the medical doctors allowed us to consider the missingness as non-informative. Taking into account the degree of data incompleteness, we used a Bayesian approach via MCMC methods for drawing inferences of interest on accuracy measures. Its direct implementation by well-known software demonstrated serious problems of chain convergence. The difficulties were overcome by the proposal of a simple, efficient and easily adaptable data augmentation algorithm, performed through an ad hoc computer program.     

Bayesian estimation of varying-coefficient models with missing data,with application to the Singapore Longitudinal Aging Study

Motivated by the Singapore Longitudinal Aging Study (SLAS), we propose a Bayesian approach for the estimation of semiparametric varying-coefficient models for longitudinal continuous and cross-sectional binary responses. These models have proved to be more flexible than simple parametric regression models. Our development is a new contribution towards their Bayesian solution, which eases computational complexity. We also consider adapting all kinds of familiar statistical strategies to address the missing data issue in the SLAS. Our simulation results indicate that a Bayesian imputation (BI) approach performs better than complete-case (CC) and available-case (AC) approaches, especially under small sample designs, and may provide more useful results in practice. In the real data analysis for the SLAS, the results for longitudinal outcomes from BI are similar to AC analysis, differing from those with CC analysis.     

Bayesian adaptive Lasso for quantile regression models with nonignorably missing response data

Abstract

Handling data with the nonignorably missing mechanism is still a challenging problem in statistics. In this paper, we develop a fully Bayesian adaptive Lasso approach for quantile regression models with nonignorably missing response data, where the nonignorable missingness mechanism is specified by a logistic regression model. The proposed method extends the Bayesian Lasso by allowing different penalization parameters for different regression coefficients. Furthermore, a hybrid algorithm that combined the Gibbs sampler and Metropolis-Hastings algorithm is implemented to simulate the parameters from posterior distributions, mainly including regression coefficients, shrinkage coefficients, parameters in the non-ignorable missing models. Finally, some simulation studies and a real example are used to illustrate the proposed methodology.     

Fast Bayesian variable screenings for binary response regressions with small sample size

Screening procedures play an important role in data analysis, especially in high-throughput biological studies where the datasets consist of more covariates than independent subjects. In this article, a Bayesian screening procedure is introduced for the binary response models with logit and probit links. In contrast to many screening rules based on marginal information involving one or a few covariates, the proposed Bayesian procedure simultaneously models all covariates and uses closed-form screening statistics. Specifically, we use the posterior means of the regression coefficients as screening statistics; by imposing a generalized g-prior on the regression coefficients, we derive the analytical form of their posterior means and compute the screening statistics without Markov chain Monte Carlo implementation. We evaluate the utility of the proposed Bayesian screening method using simulations and real data analysis. When the sample size is small, the simulation results suggest improved performance with comparable computational cost.     

BINARY REGRESSION WITH A CLASS OF SKEWED t LINK MODELS

ABSTRACT

In this paper we propose a class of skewed t link models for analyzing binary response data with covariates. It is a class of asymmetric link models designed to improve the overall fit when commonly used symmetric links, such as the logit and probit links, do not provide the best fit available for a given binary response dataset. Introducing a skewed t distribution for the underlying latent variable, we develop the class of models. For the analysis of the models, a Bayesian and non-Bayesian methods are pursued using a Markov chain Monte Carlo (MCMC) sampling based approach. Necessary theories involved in modelling and computation are provided. Finally, a simulation study and a real data example are used to illustrate the proposed methodology.     

Testing for constancy in varying coefficient models

We consider varying coefficient models, which are an extension of the classical linear regression models in the sense that the regression coefficients are replaced by functions in certain variables (for example, time), the covariates are also allowed to depend on other variables. Varying coefficient models are popular in longitudinal data and panel data studies, and have been applied in fields such as finance and health sciences. We consider longitudinal data and estimate the coefficient functions by the flexible B-spline technique. An important question in a varying coefficient model is whether an estimated coefficient function is statistically different from a constant (or zero). We develop testing procedures based on the estimated B-spline coefficients by making use of nice properties of a B-spline basis. Our method allows longitudinal data where repeated measurements for an individual can be correlated. We obtain the asymptotic null distribution of the test statistic. The power of the proposed testing procedures are illustrated on simulated data where we highlight the importance of including the correlation structure of the response variable and on real data.     

Bayesian Semiparametric Modelling in Quantile Regression

Abstract. We propose a Bayesian semiparametric methodology for quantile regression modelling. In particular, working with parametric quantile regression functions, we develop Dirichlet process mixture models for the error distribution in an additive quantile regression formulation. The proposed non‐parametric prior probability models allow the shape of the error density to adapt to the data and thus provide more reliable predictive inference than models based on parametric error distributions. We consider extensions to quantile regression for data sets that include censored observations. Moreover, we employ dependent Dirichlet processes to develop quantile regression models that allow the error distribution to change non‐parametrically with the covariates. Posterior inference is implemented using Markov chain Monte Carlo methods. We assess and compare the performance of our models using both simulated and real data sets.     

Non nested model selection for spatial count regression models with application to health insurance

In this paper we consider spatial regression models for count data. We examine not only the Poisson distribution but also the generalized Poisson capable of modeling over-dispersion, the negative Binomial as well as the zero-inflated Poisson distribution which allows for excess zeros as possible response distribution. We add random spatial effects for modeling spatial dependency and develop and implement MCMC algorithms in $R$ for Bayesian estimation. The corresponding R library ‘spatcounts’ is available on CRAN. In an application the presented models are used to analyze the number of benefits received per patient in a German private health insurance company. Since the deviance information criterion is only appropriate for exponential family models, we use in addition the Vuong and Clarke test with a Schwarz correction to compare possibly non nested models. We illustrate how they can be used in a Bayesian context.     

A Bayesian mixture of experts approach to covariate misclassification

This article considers misclassification of categorical covariates in the context of regression analysis; if unaccounted for, such errors usually result in mis-estimation of model parameters. With the presence of additional covariates, we exploit the fact that explicitly modelling non-differential misclassification with respect to the response leads to a mixture regression representation. Under the framework of mixture of experts, we enable the reclassification probabilities to vary with other covariates, a situation commonly caused by misclassification that is differential on certain covariates and/or by dependence between the misclassified and additional covariates. Using Bayesian inference, the mixture approach combines learning from data with external information on the magnitude of errors when it is available. In addition to proving the theoretical identifiability of the mixture of experts approach, we study the amount of efficiency loss resulting from covariate misclassification and the usefulness of external information in mitigating such loss. The method is applied to adjust for misclassification on self-reported cocaine use in the Longitudinal Studies of HIV-Associated Lung Infections and Complications.     

Bayesian analysis of complementary Poisson rate parameters with data subject to misclassification

We formulate closed-form Bayesian estimators for two complementary Poisson rate parameters using double sampling with data subject to misclassification and error free data. We also derive closed-form Bayesian estimators for two misclassification parameters in the modified Poisson model we assume. We use our results to determine credible sets for the rate and misclassification parameters. Additionally, we use MCMC methods to determine Bayesian estimators for three or more rate parameters and the misclassification parameters. We also perform a limited Monte Carlo simulation to examine the characteristics of these estimators. We demonstrate the efficacy of the new Bayesian estimators and highest posterior density regions with examples using two real data sets.     

Local and omnibus goodness-of-fit tests in classical measurement error models

We consider functional measurement error models, i.e. models where covariates are measured with error and yet no distributional assumptions are made about the mismeasured variable. We propose and study a score-type local test and an orthogonal series-based, omnibus goodness-of-fit test in this context, where no likelihood function is available or calculated-i.e. all the tests are proposed in the semiparametric model framework. We demonstrate that our tests have optimality properties and computational advantages that are similar to those of the classical score tests in the parametric model framework. The test procedures are applicable to several semiparametric extensions of measurement error models, including when the measurement error distribution is estimated non-parametrically as well as for generalized partially linear models. The performance of the local score-type and omnibus goodness-of-fit tests is demonstrated through simulation studies and analysis of a nutrition data set.