Browsing by Subject "Confidence intervals."
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Item Bayesian and pseudo-likelihood interval estimation for comparing two Poisson rate parameters using under-reported data.(2009-04-01T15:56:04Z) Greer, Brandi A.; Young, Dean M.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.We present interval estimation methods for comparing Poisson rate parameters from two independent populations with under-reported data for the rate difference and the rate ratio. In addition, we apply the Bayesian paradigm to derive credible intervals for both the ratio and the difference of the Poisson rates. We also construct pseudo-likelihood-based confidence intervals for the ratio of the rates. We begin by considering two cases for analyzing under-reported Poisson counts: inference when training data are available and inference when they are not. From these cases we derive two marginal posterior densities for the difference in Poisson rates and corresponding credible sets. First, we perform Monte Carlo simulation analyses to examine the effects of differing model parameters on the posterior density. Then we perform additional simulations to study the robustness of the posterior density to misspecified priors. In addition, we apply the new Bayesian credible intervals for the difference of Poisson rates to an example concerning the mortality rates due to acute lower respiratory infection in two age groups for children in the Upper River Division in Gambia and to an example comparing automobile accident injury rates for male and female drivers. We also use the Bayesian paradigm to derive two closed-form posterior densities and credible intervals for the Poisson rate ratio, again in the presence of training data and without it. We perform a series of Monte Carlo simulation studies to examine the properties of our new posterior densities for the Poisson rate ratio and apply our Bayesian credible intervals for the rate ratio to the same two examples mentioned above. Lastly, we derive three new pseudo-likelihood-based confidence intervals for the ratio of two Poisson rates using the double-sampling paradigm for under-reported data. Specifically, we derive profile likelihood-, integrated likelihood-, and approximate integrated likelihood-based intervals. We compare coverage properties and interval widths of the newly derived confidence intervals via a Monte Carlo simulation. Then we apply our newly derived confidence intervals to an example comparing cervical cancer rates.Item Maximum-likelihood-based confidence regions and hypothesis tests for selected statistical models.(2007-02-07T18:56:44Z) Riggs, Kent Edward.; Young, Dean M.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.We apply maximum likelihood methods for statistical inference on parameters of interest for three different types of statistical models. The models are a seemingly unrelated regression model, a bivariate Poisson regression model, and a model of two inversely-related Poisson rate parameters with misclassified data. The seemingly unrelated regression (SUR) model promotes more efficient estimation as opposed to an ordinary least squares approach (OLS). However, the exact distribution of the SUR estimator is complex and does not yield easily-formed confidence regions of a coefficient parameter. Therefore, one can apply maximum likelihood (ML) asymptotic-based methods to construct a confidence region. Here, we invert a Wald statistic with a size-corrected critical value to construct a confidence region for a coefficient parameter vector. We compare the coverage and ellipsoidal volume properties of three SUR ML-related confidence regions and two SUR two-stage confidence region methods in a Monte Carlo simulation study, and demonstrated how they yield smaller confidence regions as compared to the OLS approach. The bivariate Poisson regression model allows for joint estimation of two Poisson counts as a function of possibly-different covariates. We derive the Wald, score, and likelihood ratio test statistics for testing a single coefficient parameter vector. Also, we derive a Wald statistic for testing the equality of two coefficient parameter vectors. In addition, we derive a confidence interval for the covariance parameter. We then study the size and power of the test statistics and the coverage properties of the confidence interval in a Monte Carlo simulation. Lastly, we consider confidence interval estimation for parameters in a Poisson count model where the rate parameters are inversely related and the data is subject to misclassification. We derive confidence intervals for a Poisson rate parameter by inverting the appropriate Wald, score, and likelihood ratio statistics. We also derive confidence intervals for a misclassification parameter by inverting the appropriate Wald, score, and likelihood ratio statistics. Another interesting parameter is the difference of the two complementary Poisson rate parameters, for which we derive a Wald-type confidence interval. We then examine the coverage and length properties of these confidence intervals via a Monte Carlo simulation study.Item Topics in interval estimation for two problems using double sampling.(2014-01-28) Njoh, Linda.; Young, Dean M.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.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.Item Topics in odds ratio estimation in the case-control studies and the bioequivalence testing in the crossover studies.(2011-12-19) Markova, Denka G.; Young, Dean M.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.The double-sampling paradigm, which has become an important part of the epidemiological designs, includes two stages. First, individuals are classified into groups by disease and exposure levels using a fallible test, and second, some individuals are classified into a subset using a ``gold standard" test. The parameter of interest in our study is the odds ratio as an association between disease level and exposure level. Here we compare four confidence intervals for the odds ratio under the assumption of differential or non-differential misclassification. More specifically, we compare the coverage and interval widths of the Wald, score, profile likelihood, and approximate integrated likelihood intervals with different specificity and sensitivity values, as well as different sample sizes and odds ratios for the case-control clinical studies. Our investigations implies the consistent superiority of the approximate integrated confidence interval. Also, we eliminate the effect of several parameters on a bioequivalence testing procedure that plays an important role in the development of generic drugs. The current FDA criteria is not flexible with respect to highly variable drugs, and this characteristic has caused many good drugs to be rejected. Most often in the literature, we find studies examining the sample size or the within-subject variability as the main factors affecting the outcome of a bioequivalence test. Frequently, pharmaceutical companies have tried to convince the FDA that their product would meet the bioequivalence criteria just by increasing the sample size. Here we examine the effect of the between-subject variability as well as the effect of the mean ratio difference between the test and reference formulations. We use a Monte Carlo simulation to draw conclusions based on the importance of these two sources of variability and to show that simply increasing the sample size is insufficient to meet the bioequivalence criteria.