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 Title
 Statistical Shape Analysis on Manifolds with Applications to Planar Contours and Structural Proteomics.
 Creator

Ellingson, Leif A., Patrangenaru, Vic, Mio, Washington, Zhang, Jinfeng, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

The technological advances in recent years have produced a wealth of intricate digital imaging data that is analyzed effectively using the principles of shape analysis. Such data often lies on either highdimensional or infinitedimensional manifolds. With computing power also now strong enough to handle this data, it is necessary to develop theoreticallysound methodology to perform the analysis in a computationally efficient manner. In this dissertation, we propose approaches of doing so...
Show moreThe technological advances in recent years have produced a wealth of intricate digital imaging data that is analyzed effectively using the principles of shape analysis. Such data often lies on either highdimensional or infinitedimensional manifolds. With computing power also now strong enough to handle this data, it is necessary to develop theoreticallysound methodology to perform the analysis in a computationally efficient manner. In this dissertation, we propose approaches of doing so for planar contours and the threedimensional atomic structures of protein binding sites. First, we adapt Kendall's definition of direct similarity shapes of finite planar configurations to shapes of planar contours under certain regularity conditions and utilize Ziezold's nonparametric view of Frechet mean shapes. The space of direct similarity shapes of regular planar contours is embedded in a space of HilbertSchmidt operators in order to obtain the VeroneseWhitney extrinsic mean shape. For computations, it is necessary to use discrete approximations of both the contours and the embedding. For cases when landmarks are not provided, we propose an automated, randomized landmark selection procedure that is useful for contour matching within a population and is consistent with the underlying asymptotic theory. For inference on the extrinsic mean direct similarity shape, we consider a onesample neighborhood hypothesis test and the use of nonparametric bootstrap to approximate confidence regions. Bandulasiri et al (2008) suggested using extrinsic reflection sizeandshape analysis to study the relationship between the structure and function of protein binding sites. In order to obtain meaningful results for this approach, it is necessary to identify the atoms common to a group of binding sites with similar functions and obtain proper correspondences for these atoms. We explore this problem in depth and propose an algorithm for simultaneously finding the common atoms and their respective correspondences based upon the Iterative Closest Point algorithm. For a benchmark data set, our classification results compare favorably with those of leading established methods. Finally, we discuss current directions in the field of statistics on manifolds, including a computational comparison of intrinsic and extrinsic analysis for various applications and a brief introduction of sample spaces with manifold stratification.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd0053
 Format
 Thesis
 Title
 Estimation from Data Representing a Sample of Curves.
 Creator

Auguste, Anna L., Bunea, Florentina, Mason, Patrick, Hollander, Myles, Huﬀer, Fred, Department of Statistics, Florida State University
 Abstract/Description

This dissertation introduces and assesses an algorithm to generate confidence bands for a regression function or a main effect when multiple data sets are available. In particular it proposes to construct confidence bands for different trajectories and then aggregate these to produce an overall confidence band for a mean function. An estimator of the regression function or main effect is also examined. First, nonparametric estimators and confidence bands are formed on each data set separately...
Show moreThis dissertation introduces and assesses an algorithm to generate confidence bands for a regression function or a main effect when multiple data sets are available. In particular it proposes to construct confidence bands for different trajectories and then aggregate these to produce an overall confidence band for a mean function. An estimator of the regression function or main effect is also examined. First, nonparametric estimators and confidence bands are formed on each data set separately. Then each data set is in turn treated as a testing set for aggregating the preliminary results from the remaining data sets. The criterion used for this aggregation is either the least squares (LS) criterion or a BIC type penalized LS criterion. The proposed estimator is the average over data sets of these aggregates. It is thus a weighted sum of the preliminary estimators. The proposed confidence band is the minimum L1 band of all the M aggregate bands when we only have a main effect. In the case where there is some random effect we suggest an adjustment to the confidence band. In this case, the proposed confidence band is the minimum L1 band of all the M adjusted aggregate bands. Desirable asymptotic properties are shown to hold. A simulation study examines the performance of each technique relative to several alternate methods and theoretical benchmarks. An application to seismic data is conducted.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd0286
 Format
 Thesis
 Title
 TimeVarying Coefficient Models with ARMAGARCH Structures for Longitudinal Data Analysis.
 Creator

Zhao, Haiyan, Niu, Xufeng, Huﬀer, Fred, Nolder, Craig, McGee, Dan, Department of Statistics, Florida State University
 Abstract/Description

The motivation of my research comes from the analysis of the Framingham Heart Study (FHS) data. The FHS is a long term prospective study of cardiovascular disease in the community of Framingham, Massachusetts. The study began in 1948 and 5,209 subjects were initially enrolled. Examinations were given biennially to the study participants and their status associated with the occurrence of disease was recorded. In this dissertation, the event we are interested in is the incidence of the coronary...
Show moreThe motivation of my research comes from the analysis of the Framingham Heart Study (FHS) data. The FHS is a long term prospective study of cardiovascular disease in the community of Framingham, Massachusetts. The study began in 1948 and 5,209 subjects were initially enrolled. Examinations were given biennially to the study participants and their status associated with the occurrence of disease was recorded. In this dissertation, the event we are interested in is the incidence of the coronary heart disease (CHD). Covariates considered include sex, age, cigarettes per day (CSM), serum cholesterol (SCL), systolic blood pressure (SBP) and body mass index (BMI, weight in kilograms/height in meters squared). Statistical literature review indicates that effects of the covariates on Cardiovascular disease or death caused by all possible diseases in the Framingham study change over time. For example, the effect of SCL on Cardiovascular disease decreases linearly over time. In this study, I would like to examine the timevarying effects of the risk factors on CHD incidence. Timevarying coefficient models with ARMAGARCH structure are developed in this research. The maximum likelihood and the marginal likelihood methods are used to estimate the parameters in the proposed models. Since highdimensional integrals are involved in the calculations of the marginal likelihood, the Laplace approximation is employed in this study. Simulation studies are conducted to evaluate the performance of these two estimation methods based on our proposed models. The KullbackLeibler (KL) divergence and the root mean square error are employed in the simulation studies to compare the results obtained from different methods. Simulation results show that the marginal likelihood approach gives more accurate parameter estimates, but is more computationally intensive. Following the simulation study, our proposed models are applied to the Framingham Heart Study to investigate the timevarying effects of covariates with respect to CHD incidence. To specify the timeseries structures of the effects of risk factors, the Bayesian Information Criterion (BIC) is used for model selection. Our study shows that the relationship between CHD and risk factors changes over time. For males, there is an obviously decreasing linear trend for age effect, which implies that the age effect on CHD is less significant for elder patients than younger patients. The effect of CSM stays almost the same in the first 30 years and decreases thereafter. There are slightly decreasing linear trends for both effects of SBP and BMI. Furthermore, the coefficients of SBP are mostly positive over time, i.e., patients with higher SBP are more likely developing CHD as expected. For females, there is also an obviously decreasing linear trend for age effect, while the effects of SBP and BMI on CHD are mostly positive and do not change too much over time.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd0527
 Format
 Thesis
 Title
 Individual PatientLevel Data MetaAnalysis: A Comparison of Methods for the Diverse Populations Collaboration Data Set.
 Creator

Dutton, Matthew Thomas, McGee, Daniel, Becker, Betsy, Niu, Xufeng, Zhang, Jinfeng, Department of Statistics, Florida State University
 Abstract/Description

DerSimonian and Laird define metaanalysis as "the statistical analysis of a collection of analytic results for the purpose of integrating their findings. One alternative to classical metaanalytic approaches in known as Individual PatientLevel Data, or IPD, metaanalysis. Rather than depending on summary statistics calculated for individual studies, IPD metaanalysis analyzes the complete data from all included studies. Two potential approaches to incorporating IPD data into the meta...
Show moreDerSimonian and Laird define metaanalysis as "the statistical analysis of a collection of analytic results for the purpose of integrating their findings. One alternative to classical metaanalytic approaches in known as Individual PatientLevel Data, or IPD, metaanalysis. Rather than depending on summary statistics calculated for individual studies, IPD metaanalysis analyzes the complete data from all included studies. Two potential approaches to incorporating IPD data into the metaanalytic framework are investigated. A twostage analysis is first conducted, in which individual models are fit for each study and summarized using classical metaanalysis procedures. Secondly, a onestage approach that singularly models the data and summarizes the information across studies is investigated. Data from the Diverse Populations Collaboration data set are used to investigate the differences between these two methods in a specific example. The bootstrap procedure is used to determine if the two methods produce statistically different results in the DPC example. Finally, a simulation study is conducted to investigate the accuracy of each method in given scenarios.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd0620
 Format
 Thesis
 Title
 A Comparison of Estimators in Hierarchical Linear Modeling: Restricted Maximum Likelihood versus Bootstrap via Minimum Norm Quadratic Unbiased Estimators.
 Creator

Delpish, Ayesha Nneka, Niu, XuFeng, Tate, Richard L., Huﬀer, Fred W., Zahn, Douglas, Department of Statistics, Florida State University
 Abstract/Description

The purpose of the study was to investigate the relative performance of two estimation procedures, the restricted maximum likelihood (REML) and the bootstrap via MINQUE, for a twolevel hierarchical linear model under a variety of conditions. Specific focus lay on observing whether the bootstrap via MINQUE procedure offered improved accuracy in the estimation of the model parameters and their standard errors in situations where normality may not be guaranteed. Through Monte Carlo simulations,...
Show moreThe purpose of the study was to investigate the relative performance of two estimation procedures, the restricted maximum likelihood (REML) and the bootstrap via MINQUE, for a twolevel hierarchical linear model under a variety of conditions. Specific focus lay on observing whether the bootstrap via MINQUE procedure offered improved accuracy in the estimation of the model parameters and their standard errors in situations where normality may not be guaranteed. Through Monte Carlo simulations, the importance of this assumption for the accuracy of multilevel parameter estimates and their standard errors was assessed using the accuracy index of relative bias and by observing the coverage percentages of 95% confidence intervals constructed for both estimation procedures. The study systematically varied the number of groups at level2 (30 versus 100), the size of the intraclass correlation (0.01 versus 0.20) and the distribution of the observations (normal versus chisquared with 1 degree of freedom). The number of groups and intraclass correlation factors produced effects consistent with those previously reported—as the number of groups increased, the bias in the parameter estimates decreased, with a more significant effect observed for those estimates obtained via REML. High levels of the intraclass correlation also led to a decrease in the efficiency of parameter estimation under both methods. Study results show that while both the restricted maximum likelihood and the bootstrap via MINQUE estimates of the fixed effects were accurate, the efficiency of the estimates was affected by the distribution of errors with the bootstrap via MINQUE procedure outperforming the REML. Both procedures produced less efficient estimators under the chisquared distribution, particularly for the variancecovariance component estimates.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd0771
 Format
 Thesis
 Title
 Minimax Tests for Nonparametric Alternatives with Applications to High Frequency Data.
 Creator

Yu, Han, Song, KaiSheng, Professor, Jack Quine, Professor, Fred Huﬀer, Professor, Dan McGee, Department of Statistics, Florida State University
 Abstract/Description

We present a general methodology for developing an asymptotically distributionfree, asymptotic minimax tests. The tests are constructed via a nonparametric densityquantile function and the limiting distribution is derived by a martingale approach. The procedure can be viewed as a novel parametric extension of the classical parametric likelihood ratio test. The proposed tests are shown to be omnibus within an extremely large class of nonparametric global alternatives characterized by simple...
Show moreWe present a general methodology for developing an asymptotically distributionfree, asymptotic minimax tests. The tests are constructed via a nonparametric densityquantile function and the limiting distribution is derived by a martingale approach. The procedure can be viewed as a novel parametric extension of the classical parametric likelihood ratio test. The proposed tests are shown to be omnibus within an extremely large class of nonparametric global alternatives characterized by simple conditions. Furthermore, we establish that the proposed tests provide better minimax distinguishability. The tests have much greater power for detecting highfrequency nonparametric alternatives than the existing classical tests such as KolmogorovSmirnov and Cramervon Mises tests. The good performance of the proposed tests is demonstrated by Monte Carlo simulations and applications in High Energy Physics.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd0796
 Format
 Thesis
 Title
 Inference for Semiparametric TimeVarying Covariate Effect Relative Risk Regression Models.
 Creator

Ye, Gang, McKeague, Ian W., Wang, Xiaoming, Huffer, Fred W., Song, KaiSheng, Department of Statistics, Florida State University
 Abstract/Description

A major interest of survival analysis is to assess covariate effects on survival via appropriate conditional hazard function regression models. The Cox proportional hazards model, which assumes an exponential form for the relative risk, has been a popular choice. However, other regression forms such as Aalen's additive risk model may be more appropriate in some applications. In addition, covariate effects may depend on time, which can not be reflected by a Cox proportional hazards model. In...
Show moreA major interest of survival analysis is to assess covariate effects on survival via appropriate conditional hazard function regression models. The Cox proportional hazards model, which assumes an exponential form for the relative risk, has been a popular choice. However, other regression forms such as Aalen's additive risk model may be more appropriate in some applications. In addition, covariate effects may depend on time, which can not be reflected by a Cox proportional hazards model. In this dissertation, we study a class of timevarying covariate effect regression models in which the link function (relative risk function) is a twice continuously differentiable and prespecified, but otherwise general given function. This is a natural extension of the PrenticeSelf model, in which the link function is general but covariate effects are modelled to be time invariant. In the first part of the dissertation, we focus on estimating the cumulative or integrated covariate effects. The standard martingale approach based on counting processes is utilized to derive a likelihoodbased iterating equation. An estimator for the cumulative covariate effect that is generated from the iterating equation is shown to be ¡Ìnconsistent. Asymptotic normality of the estimator is also demonstrated. Another aspect of the dissertation is to investigate a new test for the above timevarying covariate effect regression model and study consistency of the test based on martingale residuals. For Aalen's additive risk model, we introduce a test statistic based on the HufferMcKeague weightedleastsquares estimator and show its consistency against some alternatives. An alternative way to construct a test statistic based on Bayesian Bootstrap simulation is introduced. An application to real lifetime data will be presented.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd0949
 Format
 Thesis
 Title
 Age Effects in the Extinction of Planktonic Foraminifera: A New Look at Van Valen's Red Queen Hypothesis.
 Creator

Wiltshire, Jelani, Huﬀer, Fred, Parker, William, Chicken, Eric, Sinha, Debajyoti, Department of Statistics, Florida State University
 Abstract/Description

Van Valen's Red Queen hypothesis states that within a homogeneous taxonomic group the age is statistically independent of the rate of extinction. The case of the Red Queen hypothesis being addressed here is when the homogeneous taxonomic group is a group of similar species. Since Van Valen's work, various statistical approaches have been used to address the relationship between taxon duration (age) and the rate of extinction. Some of the more recent approaches to this problem using Planktonic...
Show moreVan Valen's Red Queen hypothesis states that within a homogeneous taxonomic group the age is statistically independent of the rate of extinction. The case of the Red Queen hypothesis being addressed here is when the homogeneous taxonomic group is a group of similar species. Since Van Valen's work, various statistical approaches have been used to address the relationship between taxon duration (age) and the rate of extinction. Some of the more recent approaches to this problem using Planktonic Foraminifera (Foram) extinction data include Weibull and Exponential modeling (Parker and Arnold, 1997), and Cox proportional hazards modeling (Doran et al. 2004,2006). I propose a general class of test statistics that can be used to test for the effect of age on extinction. These test statistics allow for a varying background rate of extinction and attempt to remove the effects of other covariates when assessing the effect of age on extinction. No model is assumed for the covariate effects. Instead I control for covariate effects by pairing or grouping together similar species. I use simulated data sets to compare the power of the statistics. In applying the test statistics to the Foram data, I have found age to have a positive effect on extinction.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd0952
 Format
 Thesis
 Title
 Transformation Models for Survival Data Analysis and Applications.
 Creator

Liu, Yang, Niu, XuFeng, Lloyd, Donald, McGee, Dan, Sinha, Debajyoti, Department of Statistics, Florida State University
 Abstract/Description

It is often assumed that all uncensored subjects will eventually experience the event of interest in standard survival models. However, in some situations when the event considered is not death, it will never occur for a proportion of subjects. Survival models with a cure fraction are becoming popular in analyzing this type of study. We propose a generalized transformation model motivated by Zeng et al's (2006) transformed proportional time cure model. In our proposed model, fractional...
Show moreIt is often assumed that all uncensored subjects will eventually experience the event of interest in standard survival models. However, in some situations when the event considered is not death, it will never occur for a proportion of subjects. Survival models with a cure fraction are becoming popular in analyzing this type of study. We propose a generalized transformation model motivated by Zeng et al's (2006) transformed proportional time cure model. In our proposed model, fractional polynomials are used instead of the simple linear combination of the covariates. The proposed models give us more flexibility without loosing any good properties of the original model, such as asymptotic consistency and asymptotic normality of the regression coefficients. The proposed model will better fit the data where the relationship between a response variable and covariates is nonlinear. We also provide a power selection procedure based on the likelihood function. A simulation study is carried out to show the accuracy of the proposed power selection procedure. The proposed models are applied to coronary heart disease and cancer related medical data from both observational cohort studies and clinical trials
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd1155
 Format
 Thesis
 Title
 Ultrafast Lattice Dynamics in Metal Thin Films and NanoParticles.
 Creator

Wang, Xuan, Cao, Jim, Yang, Wei, Bonesteel, Nicholas, Riley, Mark, Xiong, Peng, Department of Physics, Florida State University
 Abstract/Description

This thesis presents the new development of the 3rd generation femtosecond diffractometer (FED) in Professor Jim Cao's group and its application to study ultrafast structural dynamics of solid state materials. The 3rd generation FED prevails its former type and other similar FED instruments by a DC electron gun that can generate much higher energy electron pulses, and a more efficient imaging system. This combination together with miscellaneous improvements significantly boosts the signalto...
Show moreThis thesis presents the new development of the 3rd generation femtosecond diffractometer (FED) in Professor Jim Cao's group and its application to study ultrafast structural dynamics of solid state materials. The 3rd generation FED prevails its former type and other similar FED instruments by a DC electron gun that can generate much higher energy electron pulses, and a more efficient imaging system. This combination together with miscellaneous improvements significantly boosts the signaltonoise ratio and thus enables us to study more complex solid state materials. Two main thrusts are discussed in details in this thesis. The first one is the dynamics of coherent phonon generation by ultrafast heating in gold thin film and nanoparticles, which emphasizes the electronic thermal stress. The other one is the ultrafast dynamics in Nickel, which shows that the mutual interactions among lattice, spin and electron subsystems can significantly alter the ultrafast lattice dynamics. In these studies, we exploit the advantage of FED instrument as an ideal tool that can directly and simultaneously monitor the coherent and random motion of lattice.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1247
 Format
 Thesis
 Title
 Association Models for Clustered Data with Binary and Continuous Responses.
 Creator

Lin, Lanjia, Sinha, Debajyoti, Hurt, Myra, Lipsitz, Stuart R., McGee, Daniel, Department of Statistics, Florida State University
 Abstract/Description

This dissertation develops novel single random effect models as well as bivariate correlated random effects model for clustered data with bivariate mixed responses. Logit and identity link functions are used for the binary and continuous responses. For the ease of interpretation of the regression effects, random effect of the binary response has bridge distribution so that the marginal model of mean of the binary response after integrating out the random effect preserves logistic form. And...
Show moreThis dissertation develops novel single random effect models as well as bivariate correlated random effects model for clustered data with bivariate mixed responses. Logit and identity link functions are used for the binary and continuous responses. For the ease of interpretation of the regression effects, random effect of the binary response has bridge distribution so that the marginal model of mean of the binary response after integrating out the random effect preserves logistic form. And the marginal regression function of the continuous response preserves linear form. Withincluster and withinsubject associations could be measured by our proposed models. For the bivariate correlated random effects model, we illustrate how different levels of the association between two random effects induce different Kendall's tau values for association between the binary and continuous responses from the same cluster. Fully parametric and semiparametric Bayesian methods as well as maximum likelihood method are illustrated for model analysis. In the semiparametric Bayesian model, normality assumption of the regression error for the continuous response is relaxed by using a nonparametric Dirichlet Process prior. Robustness of the bivariate correlated random effects model using ML method to misspecifications of regression function as well as random effect distribution is investigated by simulation studies. The Bayesian and likelihood methods are applied to a developmental toxicity study of ethylene glycol in mice.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd1330
 Format
 Thesis
 Title
 Multistate Intensity Model with ARGARCH Random Effect for Corporate Credit Rating Transition Analysis.
 Creator

Li, Zhi, Niu, Xufeng, Huﬀer, Fred, Kercheval, Alec, Wu, Wei, Department of Statistics, Florida State University
 Abstract/Description

This thesis presents a stochastic process and time series study on corporate credit rating and market implied rating transitions. By extending an existing model, this paper incorporates the generalized autoregressive conditional heteroscedastic (GARCH) random effects to capture volatility changes in the instantaneous transition rates. The GARCH model is a crucial part in financial research since its ability to model volatility changes gives the market practitioners flexibility to build more...
Show moreThis thesis presents a stochastic process and time series study on corporate credit rating and market implied rating transitions. By extending an existing model, this paper incorporates the generalized autoregressive conditional heteroscedastic (GARCH) random effects to capture volatility changes in the instantaneous transition rates. The GARCH model is a crucial part in financial research since its ability to model volatility changes gives the market practitioners flexibility to build more accurate models on high frequency financial data. The corporate rating transition modeling was historically dealing with low frequency data which did not have the need to specify the volatility. However, the newly published Moody's market implied ratings are exhibiting much higher transition frequencies. Therefore, we feel that it is necessary to capture the volatility component and make extensions to existing models to reflect this fact. The theoretical model specification and estimation details are discussed thoroughly in this dissertation. The performance of our models is studied on several simulated data sets and compared to the original model. Finally, the models are applied to both Moody's issuer rating and market implied rating transition data as an application.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1426
 Format
 Thesis
 Title
 The Effect of Risk Factors on Coronary Heart Disease: An AgeRelevant Multivariate Meta Analysis.
 Creator

Li, Yan, McGee, Dan, She, Yiyuan, Eberstein, Ike, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

The importance of major risk factors, such as hypertension, total cholesterol, body mass index, diabetes, smoking, for predicting incidence and mortality of Coronary Heart Disease (CHD) is well known. In light of the fact that age is also a major risk factor for CHD death, a natural question is whether the risk effects on CHD change with age. This thesis focuses on examining the interaction between age and risk factors using data from multiple studies containing differing age ranges. The aim...
Show moreThe importance of major risk factors, such as hypertension, total cholesterol, body mass index, diabetes, smoking, for predicting incidence and mortality of Coronary Heart Disease (CHD) is well known. In light of the fact that age is also a major risk factor for CHD death, a natural question is whether the risk effects on CHD change with age. This thesis focuses on examining the interaction between age and risk factors using data from multiple studies containing differing age ranges. The aim of my research is to use statistical methods to determine whether we can combine these diverse results to obtain an overall summary, using which one can find how the risk effects on CHD death change with age. One intuitive approach is to use classical meta analysis based on generalized linear models. More specifically, one can fit a logistic model with CHD death as response and age, a risk factor and their interaction as covariates for each of the studies, and conduct meta analysis on every set of three coefficients in the multivariate setting to obtain 'synthesized' coefficients. Another aspect of the thesis is a new method, meta analysis with respect to curves that goes beyond linear models. The basic idea is that one can choose the same spline with the same knots on covariates, say age and systolic blood pressure (SBP), for all the studies to ensure common basis functions. The knotbased tensor product basis coefficients obtained from penalized logistic regression can be used for multivariate meta analysis. Using the common basis functions and the 'synthesized' knotbased basis coefficients from meta analysis, a twodimensional smooth surface on the ageSBP domain is estimated. By cutting through the smooth surface along two axes, the resulting slices show how the risk effect on CHD death change at an arbitrary age as well as how the age effect on CHD death change at an arbitrary SBP value. The application to multiple studies will be presented.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1428
 Format
 Thesis
 Title
 Flexible Additive Risk Models Using Piecewise Constant Hazard Functions.
 Creator

Uhm, Daiho, Huﬀer, Fred W., Kercheval, Alec, McGee, Dan, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

We study a weighted least squares (WLS) estimator for Aalen's additive risk model which allows for a very flexible handling of covariates. We divide the followup period into intervals and assume a constant hazard rate in each interval. The model is motivated as a piecewise approximation of a hazard function composed of three parts: arbitrary nonparametric functions for some covariate effects, smoothly varying functions for others, and known (or constant) functions for yet others. The...
Show moreWe study a weighted least squares (WLS) estimator for Aalen's additive risk model which allows for a very flexible handling of covariates. We divide the followup period into intervals and assume a constant hazard rate in each interval. The model is motivated as a piecewise approximation of a hazard function composed of three parts: arbitrary nonparametric functions for some covariate effects, smoothly varying functions for others, and known (or constant) functions for yet others. The proposed estimator is an extension of the grouped data version of the HufferMcKeague estimator (1991). Our estimator may also be regarded as a piecewise constant analog of the semiparametric estimates of McKeague & Sasieni (1994), and Lin & Ying (1994). By using a fairly large number of intervals, we should get an essentially semiparametric model similar to the McKeagueSasieni and LinYing approaches. For our model, since the number of parameters is finite (although large), conventional approaches (such as maximum likelihood) are easy to formulate and implement. The approach is illustrated by simulations, and is applied to data from the Framingham heart study.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd1464
 Format
 Thesis
 Title
 A Class of MixedDistribution Models with Applications in Financial Data Analysis.
 Creator

Tang, Anqi, Niu, Xufeng, Cheng, Yingmei, Wu, Wei, Huﬀer, Fred, Department of Statistics, Florida State University
 Abstract/Description

Statisticians often encounter data in the form of a combination of discrete and continuous outcomes. A special case is zeroinflated longitudinal data where the response variable has a large portion of zeros. These data exhibit correlation because observations are obtained on the same subjects over time. In this dissertation, we propose a twopart mixed distribution model to model zeroinflated longitudinal data. The first part of the model is a logistic regression model that models the...
Show moreStatisticians often encounter data in the form of a combination of discrete and continuous outcomes. A special case is zeroinflated longitudinal data where the response variable has a large portion of zeros. These data exhibit correlation because observations are obtained on the same subjects over time. In this dissertation, we propose a twopart mixed distribution model to model zeroinflated longitudinal data. The first part of the model is a logistic regression model that models the probability of nonzero response; the other part is a linear model that models the mean response given that the outcomes are not zeros. Random effects with AR(1) covariance structure are introduced into both parts of the model to allow serial correlation and subject specific effect. Estimating the twopart model is challenging because of high dimensional integration necessary to obtain the maximum likelihood estimates. We propose a Monte Carlo EM algorithm for estimating the maximum likelihood estimates of parameters. Through simulation study, we demonstrate the good performance of the MCEM method in parameter and standard error estimation. To illustrate, we apply the twopart model with correlated random effects and the model with autoregressive random effects to executive compensation data to investigate potential determinants of CEO stock option grants.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd1710
 Format
 Thesis
 Title
 A Method for Finding the Nadir of NonMonotonic Relationships.
 Creator

Tan, Fei, McGee, Daniel, Lloyd, Donald, Huﬀer, Fred, Niu, Xufeng, Dutton, Gareth, Department of Statistics, Florida State University
 Abstract/Description

Different methods have been proposed to model the Jshaped or Ushaped relationship between a risk factor and mortality so that the optimal riskfactor value (nadir) associated with the lowest mortality can be estimated. The basic model considered is the Cox Proportional Hazards model. Current methods include a quadratic method, a method with transformation, fractional polynomials, a change point method and fixedknot spline regression. A quadratic method contains both the linear and the...
Show moreDifferent methods have been proposed to model the Jshaped or Ushaped relationship between a risk factor and mortality so that the optimal riskfactor value (nadir) associated with the lowest mortality can be estimated. The basic model considered is the Cox Proportional Hazards model. Current methods include a quadratic method, a method with transformation, fractional polynomials, a change point method and fixedknot spline regression. A quadratic method contains both the linear and the quadratic term of the risk factor, it is simple but often it generates unrealistic nadir estimates. The transformation method converts the original risk factor so that after transformation it has a Normal distribution, but this may not work when there is no good transformation to normality. Fractional polynomials are an extended class of regular polynomials that applies negative and fractional powers to the risk factor. Compared with the quadratic method or the transformation method it does not always have a good model interpretation and inferences about it do not incorporate the uncertainty coming from preselection of powers and degree. A change point method models the prognostic index using two pieces of upward quadratic functions that meet at their common nadir. This method assumes the knot and the nadir are the same, which is not always true. Fixedknot spline regression has also been used to model nonlinear prognostic indices. But its inference does not account for variation arising from knot selections. Here we consider spline regressions with free knots, a natural generalization of the quadratic, the change point and the fixedknot spline method. They can be applied to risk factors that do not have a good transformation to normality as well as keep intuitive model interpretations. Asymptotic normality and consistency of the maximum partial likelihood estimators are established under certain condition. When the condition is not satisfied simulations are used to explore asymptotic properties. The new method is motivated by and applied to the nadir estimation in nonmonotonic relationships between BMI (body mass index) and allcause mortality. Its performance is compared with that of existing methods, adopting criteria of nadir estimation ability and goodness of fit.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd1719
 Format
 Thesis
 Title
 Logistic Regression, Measures of Explained Variation, and the Base Rate Problem.
 Creator

Sharma, Dinesh R., McGee, Daniel L., Hurt, Myra, Niu, XuFeng, Chicken, Eric, Department of Statistics, Florida State University
 Abstract/Description

One of the desirable properties of the coefficient of determinant (R2 measure) is that its values for different models should be comparable whether the models differ in one or more predictors, or in the dependent variable, or whether the models are specified as being different for different subsets of a dataset. This allows researchers to compare adequacy of models across subgroups of the population or models with different but related dependent variables. However, the various analogs of the...
Show moreOne of the desirable properties of the coefficient of determinant (R2 measure) is that its values for different models should be comparable whether the models differ in one or more predictors, or in the dependent variable, or whether the models are specified as being different for different subsets of a dataset. This allows researchers to compare adequacy of models across subgroups of the population or models with different but related dependent variables. However, the various analogs of the R2 measure used for logistic regression analysis are highly sensitive to the base rate (proportion of successes in the sample) and thus do not possess this property. An R2 measure sensitive to the base rate is not suitable to comparison for the same or different model on different datasets, different subsets of a dataset or different but related dependent variables. We evaluated 14 R2 measures that have been suggested or might be useful to measure the explained variation in the logistic regression models based on three criteria 1) intuitively reasonable interpret ability; 2) numerical consistency with the Rho2 of underlying model, and 3) the base rate sensitivity. We carried out a Monte Carlo Simulation study to examine the numerical consistency and the base rate dependency of the various R2 measures for logistic regression analysis. We found all of the parametric R2 measures to be substantially sensitive to the base rate. The magnitude of the base rate sensitivity of these measures tends to be further influenced by the rho2 of the underlying model. None of the measures considered in our study are found to perform equally well in all of the three evaluation criteria used. While R2L stands out for its intuitively reasonable interpretability as a measures of explained variation as well as its independence from the base rate, it appears to severely underestimate the underlying rho2. We found R2CS to be numerically most consistent with the underlying Rho2, with R2N its nearest competitor. In addition, the base rate sensitivity of these two measures appears to be very close to that of the R2L, the most base rate invariant parametric R2 measure. Therefore, we suggest to use R2CS and R2N for logistic regression modeling, specially when it is reasonable to believe that a underlying latent variable exists. However, when the latent variable does not exit, comparability with theunderlying rho2 is not an issue and R2L might be a better choice over all the R2 measures.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd1789
 Format
 Thesis