A joint Bayesian framework for missing data and measurement error using integrated nested Laplace approximations

Measurement error (ME) and missing values in covariates are often unavoidable in disciplines that deal with data, and both problems have separately received considerable attention during the past decades. However, while most researchers are familiar with methods for treating missing data, accounting for ME in covariates of regression models is less common. In addition, ME and missing data are typically treated as two separate problems, despite practical and theoretical similarities. Here, we exploit the fact that missing data in a continuous covariate is an extreme case of classical ME, allowing us to use existing methodology that accounts for ME via a Bayesian framework that employs integrated nested Laplace approximations (INLA) and thus to simultaneously account for both ME and missing data in the same covariate. As a useful by-product, we present an approach to handle missing data in INLA since this corresponds to the special case when no ME is present. In addition, we show how to account for Berkson ME in the same framework. In its broadest generality, the proposed joint Bayesian framework can thus account for Berkson ME, classical ME, and missing data, or any combination of these in the same or different continuous covariates of the family of regression models that are feasible with INLA. The approach is exemplified using both simulated and real data. We provide extensive and fully reproducible Supporting Information with thoroughly documented examples using R-INLA and inlabru.

Estimation of radiation risk in presence of classical additive and Berkson multiplicative errors in exposure doses

In this paper, the influence of measurement errors in exposure doses in a regression model with binary response is studied. Recently, it has been recognized that uncertainty in exposure dose is characterized by errors of two types: classical additive errors and Berkson multiplicative errors. The combination of classical additive and Berkson multiplicative errors has not been considered in the literature previously. In a simulation study based on data from radio-epidemiological research of thyroid cancer in Ukraine caused by the Chornobyl accident, it is shown that ignoring measurement errors in doses leads to overestimation of background prevalence and underestimation of excess relative risk. In the work, several methods to reduce these biases are proposed. They are new regression calibration, an additive version of efficient SIMEX, and novel corrected score methods.

Methods for estimation of radiation risk in epidemiological studies accounting for classical and Berkson errors in doses

With a binary response Y, the dose-response model under consideration is logistic in flavor with pr(Y=1 | D) = R (1+R)(-1), R = λ(0) + EAR D, where λ(0) is the baseline incidence rate and EAR is the excess absolute risk per gray. The calculated thyroid dose of a person i is expressed as Dimes=fiQi(mes)/Mi(mes). Here, Qi(mes) is the measured content of radioiodine in the thyroid gland of person i at time t(mes), Mi(mes) is the estimate of the thyroid mass, and f(i) is the normalizing multiplier. The Q(i) and M(i) are measured with multiplicative errors Vi(Q) and ViM, so that Qi(mes)=Qi(tr)Vi(Q) (this is classical measurement error model) and Mi(tr)=Mi(mes)Vi(M) (this is Berkson measurement error model). Here, Qi(tr) is the true content of radioactivity in the thyroid gland, and Mi(tr) is the true value of the thyroid mass. The error in f(i) is much smaller than the errors in ( Qi(mes), Mi(mes)) and ignored in the analysis. By means of Parametric Full Maximum Likelihood and Regression Calibration (under the assumption that the data set of true doses has lognormal distribution), Nonparametric Full Maximum Likelihood, Nonparametric Regression Calibration, and by properly tuned SIMEX method we study the influence of measurement errors in thyroid dose on the estimates of λ(0) and EAR. The simulation study is presented based on a real sample from the epidemiological studies. The doses were reconstructed in the framework of the Ukrainian-American project on the investigation of Post-Chernobyl thyroid cancers in Ukraine, and the underlying subpolulation was artificially enlarged in order to increase the statistical power. The true risk parameters were given by the values to earlier epidemiological studies, and then the binary response was simulated according to the dose-response model.