Outcome-dependent-sampling ODS) schemes have long been used to reduce the cost for epidemiology studies. In ODS designs, one observes the exposure/covariates with a probability that depends on the outcome variable. Po...
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Outcome-dependent-sampling ODS) schemes have long been used to reduce the cost for epidemiology studies. In ODS designs, one observes the exposure/covariates with a probability that depends on the outcome variable. Popular ODS designs include case-control for binary outcome, and case-cohort for time-to-event outcome. Most studies have multiple endpoints of interest in addition to the primary outcome. This means that investigators often need to reuse the already collected data to evaluate the association between a secondary outcome and the covariates. This is referred to as secondary analysis. However performing secondary analysis in ODS designs can be tricky as the ODS data is not representative of the general population. In this dissertation, we study how to correctly and efficiently conduct secondary analysis in ODS *** consider analyzing a secondary outcome in case-cohort studies. We proposed a maximum estimated likelihood approach, where the likelihood is based on jointly modeling the time-to-failure outcome and the secondary outcome. It is shown that our proposed estimated likelihood estimator has greater statistical efficiency over two inverse probability weighted type estimators. We apply our method to a data from Sister *** the second part of the dissertation, we investigate how to properly analyze a secondary outcome under an ODS scheme discussed in Zhou et al. 2002). In this ODS design, supplemental samples are taken from different strata of the continuous outcome variable in addition to a simple random sample. We do not make any parametric assumptions on the outcome variables, and only specify the form of the regression mean. Inverse probability weighted IPW) and augmented inverse probability weighted AIPW) estimating equations are proposed to conduct secondary analysis. Data from Collaborative Perinatal Project CPP) is utilized to illustrate our ***, we proposed efficient secondary analysis techniques for data from two-phase studie
A one-shot device, such as an automobile airbag, electro-explosive unit or munition, is a product that can be used only once. Its actual lifetime is unobservable, rendering the corresponding reliability analysis quite...
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A one-shot device, such as an automobile airbag, electro-explosive unit or munition, is a product that can be used only once. Its actual lifetime is unobservable, rendering the corresponding reliability analysis quite challenging. In this paper, two non-parametric methodologies-maximum likelihood estimation via EM-algorithm and Nelson-Aalen based estimation are developed for identical testing environment on one-shot devices. The EM-algorithm is usually used for unobserved failure times under some specific parametric models. But, here the EM-algorithm is adopted for the number of failures in each time interval in a nonparametric manner. Next, a semi-parametric approach, based on proportional hazards assumption, is developed for nonidentical testing environments, such as under an accelerated life-test. A Monte Carlo simulation study is then carried out for evaluating the performance of the inferential methods developed here. Finally, two data sets are analyzed for illustrative purpose.
The receiver operating characteristic (ROC) curve is often used to assess the usefulness of a diagnostic test. We present a new method to estimate the parameters of a popular semi-parametric ROC model, called the bino...
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The receiver operating characteristic (ROC) curve is often used to assess the usefulness of a diagnostic test. We present a new method to estimate the parameters of a popular semi-parametric ROC model, called the binormal model. Our method is based on minimization of the functional distance between two estimators of an unknown transformation postulated by the model, and has a simple, closed-form solution. We study the asymptotics of our estimators, show via Simulation that they compare favorably with existing estimators, and illustrate how covariates may be incorporated into the norm minimization framework.
Many authors have exploited the fact that the distribution of the multivariate probability integral transformation (PIT) of a continuous random vector X is an element of R-d with cumulative distribution function F-X i...
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Many authors have exploited the fact that the distribution of the multivariate probability integral transformation (PIT) of a continuous random vector X is an element of R-d with cumulative distribution function F-X is free of the marginal distributions. While most of these methods are based on the cdf of W = F-X(X), this paper introduces the weighted characteristic function (WCf) of W. A sample version of the WCf of W based on pseudo-observations is proposed and its weak limit in a space of complex functions is formally established. This result can be used to define test statistics for multivariate independence and goodness-of-fit in copula models, whose asymptotic behaviour comes from the weak convergence of the empirical WCf process. Simulations show the good sampling properties of these new tests, and an illustration is given on the multivariate Cook and Johnson dataset.
We develop methods for analysing the 'interaction' or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely non-parametric study of interactions is possi...
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We develop methods for analysing the 'interaction' or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely non-parametric study of interactions is possible using an analogue of the K-function. Alternatively one may assume a semi-parametric model in which a (parametrically specified) homogeneous Markov point process is subjected to (non-parametric) inhomogeneous independent thinning. The effectiveness of these approaches is tested on datasets representing the positions of trees in forests.
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likeli...
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Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE) for sigma(2) is biased and inconsistent. This raises the question whether the posterior is able to correct the MLE in this case. By developing a new proving strategy that uses refined properties of the posterior distribution, we find that the marginal posterior is inconsistent for any i.i.d. prior on the mean parameters. In particular, no assumption on the decay of the prior needs to be imposed. Surprisingly, we also find that consistency can be retained for a hierarchical prior based on Gaussian mixtures. In this case we also establish a limiting shape result and determine the limit distribution. In contrast to the classical Bernstein-von Mises theorem, the limit is non-Gaussian. We show that the Bayesian analysis leads to new statistical estimators outperforming the correctly calibrated MLE in a numerical simulation study.
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