Browsing by Author "Anastasios A. Tsiatis, Committee Co-Chair"

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Comparing Predictive Values of Two diagnostic tests
(2009-07-29) Cho, Yoonjin; Anastasios A. Tsiatis, Committee Co-Chair; Jason Osborne, Committee Member; Daowen Zang, Committee Member; Andrzej Kosinski , Committee Chair
Positive and negative predictive values are important measures of accuracy when one compares the accuracy of diagnostic tests. When more than one diagnostic tests are available, one may has to choose one of the possible diagnostic tests due to cost, time, or ethical reason. We consider a pair study design on cohort study where two diagnostic tests are measured on every patients. Our parameter of interest is the log odds of predictive values. In first chapter, we review current methods on comparing diagnostic tests when gold standards are available on every individual. We propose our method by series of logistic regressions and derive estimator and test statistics based on likelihood method. However, it is often the case that gold standard is not observed on every patient because it may be invasive. If we only consider those who have observed gold standard, the estimator may not be biased. In Chapter 2 and 3, we extend the cases when gold standard is missing. We assume that missing gold standard is missing at random, which is to depend on observed data. In Chapter 2, we use semiparametric theory to derive a class of regular and asymptotically normal of our parameter of interest. Out of the class, we derive an estimator which is the most effcient in the class in using the information from available auxiliary covariates which may be associated with the outcome of gold standard. We also use auxiliary covariates in modeling the probability of observing gold standard. In Chapter 3, through M-estimator, we derive another consistent estimator through imputation method.
Improving Efficiency and Robustness of Doubly Robust Estimators in the Presence of Coarsened Data
(2009-11-03) Cao, Weihua; Marie Davidian, Committee Chair; Anastasios A. Tsiatis, Committee Co-Chair; Daowen Zhang, Committee Member; Dennis Boos, Committee Member
Considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data, which involve models for both the propensity score and the regression of outcome on covariates. The ``usual" doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations. In part one of this dissertation, we propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods, even with some estimated propensity scores close to zero. The second part of this dissertation focuses on drawing inference on parameters in general models in the presence of monotonely coarsened data, which can be viewed as a generalization of longitudinal data with a monotone missingness pattern, as is the case when subjects drop out of a study. Estimators for parameters of interest include both inverse probability weighted estimators and doubly robust estimators. As a generalization of methods in part one, we propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods. We apply the proposed method to data from an AIDS clinical trial.
Semiparametric approaches to inference in joint models for longitudinal and time-to-event data
(2002-05-24) Song, Xiao; Marie Davidian, Committee Co-Chair; Anastasios A. Tsiatis, Committee Co-Chair; Daowen Zhang, Committee Member; Sujit Ghosh, Committee Member; Charles E. Smith, Committee Member
In many longitudinal studies, it is of interest to characterize the relationship between a time-to-event (e.g. survival) and time-dependent and time-independent covariates. Time-dependent covariates are generally observed intermittently and with error. For a single time-dependent covariate, a popular approach is to assume a joint longitudinal data-survival model, where the time-dependent covariate follows a linear mixed effects model and the hazard of failure depends on random effects and time-independent covariates via a proportional hazards relationship. Interest may focus on inference on the longitudinal data process, which is informatively censored by death or withdrawal, or on the hazard relationship. Several methods for fitting such models have been proposed, including regression calibration and likelihood or Bayesian methods. However, most approaches require a parametric distributional assumption (normality) on the random effects. In addition, generalization to more than one time-dependent covariate may become prohibitive. For a single time-dependent covariate, Tsiatis and Davidian (2001) have proposed an approach that is easily implemented and does not require an assumption on the distribution of the random effects. We extend this technique to multiple, possibly correlated,time-dependent covariates. This approach is easy to compute. However, the conditional score approach might be less efficient relative to the likelihood approaches. In addition, inference on the longitudinal data process is not available. To improve the efficiency and meanwhile obtain an estimator for the random effects distribution, we propose to approximate the random effects distribution by the seminonparametric (SNP) densities of Gallant and Nychka (1987), which requires only the assumption that the random effects have a "smooth" density, and take a semiparametric likelihood approach. The EM algorithm is used for implementation. We demonstrate the approaches via simulations and apply them to data from an HIV clinical trial.
Semiparametric Methods for Analysis of Randomized Clinical Trials and Arbitrarily Censored Time-to-event Data.
(2009-04-03) Zhang, Min; Wenbin Lu, Committee Member; Marie Davidian, Committee Chair; Anastasios A. Tsiatis, Committee Co-Chair; Daowen Zhang, Committee Member
This dissertation includes two parts. In part one, using the theory of semiparametrics, we develop a general approach to improving efficiency of nferences in randomized clinical trials using auxiliary covariates. In part two, we study "smooth" semiparametric regression analysis for arbitrarily censored time-to-event data. The primary goal of a randomized clinical trial is to make comparisons among two or more treatments. For example, in a two-arm trial with continuous response, the focus may be on the difference in treatment means; with more than two treatments, the comparison may be based on pairwise differences. With binary outcomes, pairwise odds-ratios or log-odds ratios may be used. In general, comparisons may be based on meaningful parameters in a relevant statistical model. Standard analyses for estimation and testing in this context typically are based on the data collected on response and treatment assignment only. In many trials, auxiliary baseline covariate information may also be available, and it is of interest to exploit these data to improve the efficiency of inferences. Taking a semiparametric theory perspective, we propose a broadly-applicable approach to adjustment for auxiliary covariates to achieve more efficient estimators and tests for treatment parameters in the analysis of randomized clinical trials. Simulations and applications demonstrate the performance of the methods. A general framework for regression analysis of time-to-event data subject to arbitrary patterns of censoring is proposed. The approach is relevant when the analyst is willing to assume that distributions governing model components that are ordinarily left unspecified in popular semiparametric regression models, such as the baseline hazard function in the proportional hazards model, have densities satisfying mild "smoothness" conditions. Densities are approximated by a truncated series expansion that, for fixed degree of truncation, results in a "parametric" representation, which makes likelihood-based inference coupled with adaptive choice of the degree of truncation, and hence flexibility of the model, computationally and conceptually straightforward with data subject to any pattern of censoring. The formulation allows popular models, such as the proportional hazards, proportional odds, and accelerated failure time models, to be placed in a common framework; provides a principled basis for choosing among them; and renders useful extensions of the models straightforward. The utility and performance of the methods are demonstrated via simulations and by application to data from time-to-event studies.