Topics in interval estimation for two problems using double sampling.
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This dissertation addresses two distinct topics. The first considers interval estimation methods of the odds ratio parameter in two by two cohort studies with misclassified data. That is, we derive two first-order likelihood-based confidence intervals and two pseudo-likelihood-based confidence intervals for the odds ratio in a two by two cohort study subject to differential misclassification and non-differential misclassification using a double-sampling paradigm for binary data. Specifically, we derive the Wald, score, profile likelihood, and approximate integrated likelihood-based confidence intervals for the odds ratio of a two by two cohort study. We then compare coverage properties and median interval widths of the newly derived confidence intervals via a Monte Carlo simulation. Our simulation results reveal the consistent superiority of the approximate integrated likelihood confidence interval, especially when the degree of misclassification is high. The second topic is concerned with interval estimation methods of a Poisson rate parameter in the presence of count misclassification. More specifically, we derive multiple first-order asymptotic confidence intervals for estimating a Poisson rate parameter using a double sample for data containing false-negative and false-positive observations in one case and for data with only false-negative observations in another case. We compare the new confidence intervals in terms of coverage probability and median interval width via a simulation experiment. We then apply our derived confidence intervals to real-data examples. Over the parameter configurations and observation-opportunity sizes considered here, our investigation demonstrates that the Wald interval is the best omnibus interval estimator for a Poisson rate parameter using data subject to over-and under-counts. Also, the profile log-likelihood-based confidence interval is the best omnibus confidence interval for a Poisson rate parameter using data subject to visibility bias.
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