| Summary: | In many research areas, measurement error frequently occurs when investigators are
trying to analyze the relationship between exposure variables and response variable in
observational studies. Severe problems can be caused by the mismeasured exposure vari
ables, such as loss of power, biased estimators, and misleading conclusions. As the idea of measurement error is adopted by more and more researchers, how to adjust for such error becomes an interesting point to study. Two big barriers in solving the problems are as follows. First, the mechanism of measurement error (the existence and magnitude of the error) is always unknown to researchers. Sometimes only a small piece of information is available from previous studies. Moreover, the situation can be worsen when the
study conditions are changed in the present study, which makes previous information not
applicable. Second, some researchers may still argue about the consequences of ignoring measurement error due to its uncertainness. Thus, the adjustment for the mismeasurement turn to be a difficult, or impossible task. In this thesis, we are studying situations where the binary response variable is precisely measured, but with a misclassified binary exposure or a mismeasured continuous exposure. We propose formal approaches to estimate unknown parameters under the non-differential assumption in both exposure conditions. The uncertain variance of measurement error in the continuous exposure case, or the probabilities of misclassification
in the binary exposure case, are incorporated by our approaches. Then the posterior models are estimated via simulations generated by the Gibbs sampler and the Metropolis - Hasting algorithm. Meanwhile, we compare our formal approach with the informal or naive approach in
both continuous and exposure cases based on simulated datasets. Odds ratios on log
scales are used in comparisons of formal and informal approaches when the exposure
variable is binary or continuous. General speaking, our formal approaches result in bet
ter point estimators and less variability in estimation. Moreover, the 95% credible, or
confidence intervals are able to capture the true values more than 90% of the time.
At the very end, we apply our ideas on the QRS dataset to seek consistent conclu
sions draws from simulated datasets and real world datasets, and we are able to claim
that overall our formal approaches do a better job regardless of the type of the exposure variable.
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