Bayesian Measurement Error Modeling

A mixture measurement error model built upon skew normal distributions and normal distributions is developed to evaluate various impacts of measurement errors to parameter inferences in logistic regressions. Data generated from survey questionnaires are usually error contaminated. We consider two types of error, person-specific bias and random errors. Person-specific bias is modeled using skew normal distribution, and the distribution of random errors is described by a normal distribution. Intensive simulations are conducted to evaluate the contribution of each component in the mixture to outcomes of interest. The proposed method is then applied to a questionnaire data set generated from a neural tube defect study. Simulation results and real data application indicate that ignoring measurement errors or mis-specifying measurement error components can both produce misleading results, especially when measurement errors are actually skew distributed. The inferred parameters can be attenuated or inflated depending on how the measurement error components are specified. We expect the findings will self-explain the importance of adjusting measurement errors and thus benefit future data collection effort. In the second part, we discuss a semi-parametric measurement error model based on P-spline with the help of a biomarker. The measurement error model is further incorporated into polytomous logistic regression models to infer interesting factor effects. The advantage of this method is its flexibility and no requirement to gold standard or replicates when adjusting for measurement errors. Simulations are used to demonstrate the methods and compare the proposed methods with other semi-parametric approaches. Finally, we apply this method to the NTD data to study the effect of folate intakes from food and prenatal multivitamins, in which red blood cell folates is used as a biomarker to adjust for measurement errors