Browsing by Author "Sujit Ghosh, Committee Co-Chair"

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Analyzing Longitudinal Data with Non-ignorable Missing
(2006-12-28) Zhu, Liansheng; Sujit Ghosh, Committee Co-Chair; Subhashis Ghosal, Committee Co-Chair
In longitudinal studies, data are often missing despite every attempt made to collect complete data. When the missingness is informative and hence not ignorable, it is generally difficult to analyze non-ignorable missing (NIM) data since the distributional assumptions about missing data are not easily verifiable using traditional goodness of fit tests or otherwise. Selection models and pattern-mixture models are two common approaches to analyze NIM data. Each approach has its advantages and disadvantages. Methods proposed in this thesis fall into the category of pattern-mixture models. Traditionally, patterns are determined by time to occurrence of missing. This definition often results into the problem of not all parameters being identifiable. Moreover, marginalization is commonly required and can be very tricky when outcomes are discrete. It is recognized that patterns can and need to be defined by covariates, surrogate variables and⁄or time to missing. We propose two approaches to model NIM data: (i) pseudo-imputation (PI) approach, in which we first obtain predictive means within each pattern, get transformed predictive means by using a suitable link function and then fit with covariates to obtain marginal estimates; (ii) joint-modeling (JM) approach, in which patterns considered as random effects are marginalized within a generalized linear mixed model framework. The JM approach is shown to be able to capture the dependence of missing indicators on missing outcomes in some degree as is the case with NIM data. Some of the main advantages of these proposed approaches include (i) the capability to handle both continuous and discrete responses, (ii) avoidance of the problem of under-identifiability, (iii) availability of marginal estimates, and (iv) computational efficiency. When the missingness does depend on the patterns, results based on simulated data suggest that both approaches yield accurate estimates if the underlying number of patterns is specified correctly. Otherwise the PI method leads to biased results whereas the JM approach still provides reasonably accurate estimates. Finally, we extend our approaches to a generalized additive model (GAM) replacing the GLM framework. When the underlying relationship is highly non-linear, our extended approaches with a GAM framework provide flexibility and more accurate estimates. The JM approach along with generalized additive models can provide more flexibility than the PI approach since it uses a more robust model for the missing indicator
Associations Between Gaussian Markov Random Fields and Gaussian Geostatistical Models with an Application to Model the Impact of Air Pollution on Human Health
(2006-02-19) Song, Hae-Ryoung; Sujit Ghosh, Committee Co-Chair; David Dickey, Committee Member; Jerry Davis, Committee Member; Montserrat Fuentes, Committee Co-Chair; Peter Bloomfield, Committee Member
Gaussian geostatistical models (GGMs) and Gaussian Markov random fields (GMRFs) are two distinct approaches commonly used in modeling point referenced and areal data, respectively. In this dissertation, the relations between GMRFs and GGMs are explored based on approximations of GMRFs by GGMs, and vice versa. The proposed framework for the comparison of GGMS and GMRFs is based on minimizing the distance between the corresponding spectral density functions. In particular, the Kullback-Leibler discrepancy of spectral densities and the chi-squared distance between spectral densities are used as the metrics for the approximation. The proposed methodology is illustrated using empirical studies. As a part of application, we model associations between speciated fine particulate matter (PM) and mortality. Mortality counts and PM are obtained at county and point levels, respectively. To combine the variables with different spatial resolutions, we aggregate PM to the county level. The aggregated PM are modeled using GMRFs, and associations between PM and mortality are investigated based on Bayesian hierarchical spatio-temporal framework. This model is applied to speciated PM[subscript 2.5] and monthly mortality counts over the entire U.S. region for 1999-2000. We obtain high relative risks of mortality associated to PM[subscript 2.5] in the Eastern and Southern California area. Particularly, NO₃ and crustal materials have greater health effects in the Western U.S., while SO₄ and NH₄ have more of an impact in the Eastern U.S. We show that the average risk associated with PM[subscript 2.5] is approximately twice what we obtained for PM₁₀.
Variations on the Accelerated Failure Time Model: Mixture Distributions, Cure Rates, and Di fferent Censoring Scenarios
(2009-10-06) Krachey, Elizabeth Catherine; Sujit Ghosh, Committee Co-Chair; Marie Davidian, Committee Member; Brian Reich, Committee Member; Wenbin Lu, Committee Chair
The accelerated failure time (AFT) model is a popular model for time-to-event data. It provides a useful alternative when the proportional hazards assumption is in question and it provides an intuitive linear regression interpretation where the logarithm of the survival time is regressed on the covariates. We have explored several deviations from the standard AFT model. Standard survival analysis assumes that in the case of perfect follow-up, every patient will eventually experience the event of interest. However, in some clinical trials, a number of patients may never experience such an event, and in essence, are considered cured from the disease. In such a scenario, the Kaplan-Meier survival curve will level off at a nonzero proportion. Hence there is a window of time in which most or all of the events occur, while heavy censoring occurs in the tail. The two-component mixture cure model provides a means of adjusting the AFT model to account for this cured fraction. Chapters 1 and 2 propose parametric and semiparametric estimation procedures for this cure rate AFT model. Survival analysis methods for interval-censoring have been much slower to develop than for the right-censoring case. This is in part because interval-censored data have a more complex censoring mechanism and because the counting process theory developed for right-censored data does not generalize or extend to interval-censored data. Because of the analytical difficulty associated with interval-censored data, recent estimation strategies have focused on the implementation rather than the large sample theoretical justifications of the semiparametric AFT model. Chapter 3 proposes a semiparametric Bayesian estimation procedure for the AFT model under interval-censored data.