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Evaluating the performance of simulation extrapolation and Bayesian adjustments for measurement error Romann, Alexandra

Abstract

Measurement error is a frequent issue in many research areas. For instance, in health research it is often of interest to understand the relationship be tween an outcome and an exposure, which is often mismeasured if the study is observational or a gold standard is costly or absent. Measurement error in the explanatory variable can have serious effects, such as biased parame ter estimation, loss of power, and masking of the features of the data. The structure of the measurement error is usually not known to the investigators, leading to many difficulties in finding solutions for its correction. In this thesis, we consider problems involving a correctly measured con tinuous or binary response, a mismeasured continuous exposure variable, along with another correctly measured covariate. We compare our proposed Bayesian approach to the commonly used simulation extrapolation (SIMEX) method. The Bayesian model incorporates the uncertainty of the measure ment error variance and the posterior distribution is generated by using the Gibbs sampler as well as the random walk Metropolis algorithm. The com parison between the Bayesian and SIMEX approaches is conducted using different cases of a simulated data including validation data, as well as the Framingham Heart Study data which provides replicates but no validation data. The Bayesian approach is more robust to changes in the measurement error variance or validation sample size, and consistently produces wider credible intervals as it incorporates more uncertainty. The underlying theme of this thesis is the uncertainty involved in the es timation of the measurement error variance. We investigate how accurately this parameter has to be estimated and how confident one has to be about this estimate in order to produce better results by choosing the Bayesian measurement error correction over the naive analysis where measurement error is ignored.

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Attribution-NonCommercial-NoDerivatives 4.0 International

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