Dissertations / Theses on the topic 'Survival Data'

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The main objective of this research is to explore economics issues that may induce impact on lifetime of small businesses during 2002 to 2006. The group of enterprises studied was selected from database of taxpayers recorded at fiscal authority of State of CearÃ. To do that, the methodology was focused on a branch of statistics which deals with survival analysis, called duration analysis or duration modeling in economics. It was applied non-linear model whose non-parametric estimator chosen was KAPLAN-MEIER. Through that methodology, it was developed sceneries based on the following attributes: county where the enterprises were established; economics activities based on national classification, fiscal version 1.0/1.1; and, finally, the relationship between State of Cearà â as fiscal authority â and enterprises. The counties were grouped applying two parameters of stratifications: gross domestic product(GDP) per capita and investment in education per capita. Before any stratification, only counties with thirty or more enterprises starting their activities in year 2002 were considered in sceneries to analysis.
A dissertaÃÃo tem o objetivo de investigar fatores econÃmicos que possam influenciar na sobrevida de micros e pequenas empresas (MEPs) contribuintes do Imposto sobre OperaÃÃes relativas à CirculaÃÃo de Mercadorias e sobre PrestaÃÃes de ServiÃos de Transporte Interestadual e Intermunicipal e de ComunicaÃÃo (ICMS) do Estado do Cearà no perÃodo de 2002 à 2006. Para isso, aplicou-se uma tÃcnica estatÃstica denominada anÃlise de sobrevivÃncia a partir de modelos nÃo lineares cujo estimador nÃo-paramÃtrico escolhido foi o de KAPLAN-MEIER. Com os dados de sobrevivÃncia devidamente modelados, buscou-se estratificÃ-los focando os municÃpios dos logradouros das MEPs; dentro do que tange as operaÃÃes do ICMS, focando as atividades econÃmicas segundo a classificaÃÃo nacional de atividades econÃmicas (CNAE) versÃo fiscal 1.0/1.1; e, finalmente, observar a relaÃÃo do Estado â enquanto autoridade fiscal â com esses pequenos estabelecimentos, restringindo temporariamente seu faturamento ou mesmo baixando sua inscriÃÃo estadual, impossibilitando a continuidade de suas atividades. Dos municÃpios, utilizou-se como Ãndice de estratificaÃÃo entre as curvas de sobrevivÃncia o produto interno bruto (PIB) per capita e os investimentos mÃdio per capita em educaÃÃo daquelas empresas localizadas em municÃpios com 30 ou mais estabelecimentos ativados no ano de 2002. Dentre outras, duas importantes observaÃÃes foram identificar o municÃpio de Fortaleza como um âoutlinerâ frente aos outros municÃpios e a forte dominÃncia da curva de sobrevivÃncia das empresas que nÃo sofreram intervenÃÃo do fisco em suas atividades sobre aquelas que tiveram.

The terminology and ideas involved in the statistical analysis of survival data are explained including the survival function, the probability density function, the hazard function, censored observations, parametric and nonparametric estimations of these functions, the product limit estimation of the survival function, and the proportional hazards estimation of the hazard function with explanatory variables. In Appendix A these ideas are applied to the actual analysis of the survival data for 54 cervical cancer patients.

Often, in cross-sectional-follow-up studies, survival data are obtained from prevalent cases only. This sampling mechanism introduces length-bias. An added difficulty is that in some cases the times of onset cannot be ascertained or are recorded with great uncertainty. Such was the situation in the Canadian Study of Health and Aging, a nation wide study of dementia conducted by Health Canada during 1991 and 1996. This thesis proposes methods to estimate the survival function nonparametrically, when the data are length-biased and only partially observed. By using the "forward recurrence times" only, we show how one can overcome the difficulty caused by missing onset times, while by using the "backward recurrence times" only, one can avoid the cost and effort of follow-up. We illustrate our methods through an application to data derived from the CSHA.

When survival data are collected as part of a prevalent cohort study, the recruited cases have already experienced their initiating event. When these initiating times are generated from a Stationary Poisson Process, these survival data are termed "length-biased". Our interest is to estimate the Survival function, from the initiating event time, which is often known only with uncertainty, to the failure or censoring time. We derive the likelihood function and propose two methods to estimate the survival function incorporating the possible uncertainty. We verify the methods by the means of simulation. We also illustrate the methods using a real set of data on survival with dementia collected as part of the Canadian Study of Health and Aging (CSHA).

The goal of this work is to expand the knowledge on the field of Venn Prediction employed with Survival Data. Standard Venn Predictors have been used with Random Forests and binary classification tasks. However, they have not been utilised to predict events with Survival Data nor in combination with Random Survival Forests. With the help of a Data Transformation, the survival task is transformed into several binary classification tasks. One key aspect of Venn Prediction are the categories. The standard number of categories is two, one for each class to predict. In this work, the usage of ten categories is explored and the performance differences between two and ten categories are investigated. Seven data sets are evaluated, and their results presented with two and ten categories. For the Brier Score and Reliability Score metrics, two categories offered the best results, while Quality performed better employing ten categories. Occasionally, the models are too optimistic. Venn Predictors rectify this performance and produce well-calibrated probabilities.
Målet med detta arbete är att utöka kunskapen om området för Venn Prediction som används med överlevnadsdata. Standard Venn Predictors har använts med slumpmässiga skogar och binära klassificeringsuppgifter. De har emellertid inte använts för att förutsäga händelser med överlevnadsdata eller i kombination med Random Survival Forests. Med hjälp av en datatransformation omvandlas överlevnadsprediktion till flera binära klassificeringsproblem. En viktig aspekt av Venn Prediction är kategorierna. Standardantalet kategorier är två, en för varje klass. I detta arbete undersöks användningen av tio kategorier och resultatskillnaderna mellan två och tio kategorier undersöks. Sju datamängder används i en utvärdering där resultaten presenteras för två och tio kategorier. För prestandamåtten Brier Score och Reliability Score gav två kategorier de bästa resultaten, medan för Quality presterade tio kategorier bättre. Ibland är modellerna för optimistiska. Venn Predictors korrigerar denna prestanda och producerar välkalibrerade sannolikheter.

L'anàlisi de la supervivència s'utilitza en diversos àmbits per tal d'analitzar dades que mesuren el temps transcorregut entre dos successos. També s'anomena anàlisi de la història dels esdeveniments, anàlisi de temps de vida, anàlisi de fiabilitat o anàlisi del temps fins a l'esdeveniment. Una de les dificultats que té aquesta àrea de l'estadística és la presència de dades censurades. El temps de vida d'un individu és censurat quan només és possible mesurar-lo de manera parcial o inexacta. Hi ha diverses circumstàncies que donen lloc a diversos tipus de censura. La censura en un interval fa referència a una situació on el succés d'interès no es pot observar directament i només tenim coneixement que ha tingut lloc en un interval de temps aleatori. Aquest tipus de censura ha generat molta recerca en els darrers anys i usualment té lloc en estudis on els individus són inspeccionats o observats de manera intermitent. En aquesta situació només tenim coneixement que el temps de vida de l'individu es troba entre dos temps d'inspecció consecutius.

Aquesta tesi doctoral es divideix en dues parts que tracten dues qüestions importants que fan referència a dades amb censura en un interval. La primera part la formen els capítols 2 i 3 els quals tracten sobre condicions formals que asseguren que la versemblança simplificada pot ser utilitzada en l'estimació de la distribució del temps de vida. La segona part la formen els capítols 4 i 5 que es dediquen a l'estudi de procediments estadístics pel problema de k mostres. El treball que reproduïm conté diversos materials que ja s'han publicat o ja s'han presentat per ser considerats com objecte de publicació.

En el capítol 1 introduïm la notació bàsica que s'utilitza en la tesi doctoral. També fem una descripció de l'enfocament no paramètric en l'estimació de la funció de distribució del temps de vida. Peto (1973) i Turnbull (1976) van ser els primers autors que van proposar un mètode d'estimació basat en la versió simplificada de la funció de versemblança. Altres autors han estudiat la unicitat de la solució obtinguda en aquest mètode (Gentleman i Geyer, 1994) o han millorat el mètode amb noves propostes (Wellner i Zhan, 1997).

El capítol 2 reprodueix l'article d'Oller et al. (2004). Demostrem l'equivalència entre les diferents caracteritzacions de censura no informativa que podem trobar a la bibliografia i definim una condició de suma constant anàloga a l'obtinguda en el context de censura per la dreta. També demostrem que si la condició de no informació o la condició de suma constant són certes, la versemblança simplificada es pot utilitzar per obtenir l'estimador de màxima versemblança no paramètric (NPMLE) de la funció de distribució del temps de vida. Finalment, caracteritzem la propietat de suma constant d'acord amb diversos tipus de censura. En el capítol 3 estudiem quina relació té la propietat de suma constant en la identificació de la distribució del temps de vida. Demostrem que la distribució del temps de vida no és identificable fora de la classe dels models de suma constant. També demostrem que la probabilitat del temps de vida en cadascun dels intervals observables és identificable dins la classe dels models de suma constant. Tots aquests conceptes els
il·lustrem amb diversos exemples.

El capítol 4 s'ha publicat parcialment en l'article de revisió metodològica de Gómez et al. (2004). Proporciona una visió general d'aquelles tècniques que s'han aplicat en el problema no paramètric de comparació de dues o més mostres amb dades censurades en un interval. També hem desenvolupat algunes rutines amb S-Plus que implementen la versió permutacional del tests de Wilcoxon, Logrank i de la t de Student per a dades censurades en un interval (Fay and Shih, 1998). Aquesta part de la tesi doctoral es complementa en el capítol 5 amb diverses propostes d'extensió del test de Jonckeere. Amb l'objectiu de provar una tendència en el problema de k mostres, Abel (1986) va realitzar una de les poques generalitzacions del test de Jonckheere per a dades censurades en un interval. Nosaltres proposem altres generalitzacions d'acord amb els resultats presentats en el capítol 4. Utilitzem enfocaments permutacionals i de Monte Carlo. Proporcionem programes informàtics per a cada proposta i realitzem un estudi de simulació per tal de comparar la potència de cada proposta sota diferents models paramètrics i supòsits de tendència. Com a motivació de la metodologia, en els dos capítols s'analitza un conjunt de dades d'un estudi sobre els beneficis de la zidovudina en pacients en els primers estadis de la infecció del virus VIH (Volberding et al., 1995).

Finalment, el capítol 6 resumeix els resultats i destaca aquells aspectes que s'han de completar en el futur.
Survival analysis is used in various fields for analyzing data involving the duration between two events. It is also known as event history analysis, lifetime data analysis, reliability analysis or time to event analysis. One of the difficulties which arise in this area is the presence of censored data. The lifetime of an individual is censored when it cannot be exactly measured but partial information is available. Different circumstances can produce different types of censoring. Interval censoring refers to the situation when the event of interest cannot be directly observed and it is only known to have occurred during a random interval of time. This kind of censoring has produced a lot of work in the last years and typically occurs for individuals in a study being inspected or observed intermittently, so that an individual's lifetime is known only to lie between two successive observation times.

This PhD thesis is divided into two parts which handle two important issues of interval censored data. The first part is composed by Chapter 2 and Chapter 3 and it is about formal conditions which allow estimation of the lifetime distribution to be based on a well known simplified likelihood. The second part is composed by Chapter 4 and Chapter 5 and it is devoted to the study of test procedures for the k-sample problem. The present work reproduces several material which has already been published or has been already submitted.

In Chapter 1 we give the basic notation used in this PhD thesis. We also describe the nonparametric approach to estimate the distribution function of the lifetime variable. Peto (1973) and Turnbull (1976) were the first authors to propose an estimation method which is based on a simplified version of the likelihood function. Other authors have studied the uniqueness of the solution given by this method (Gentleman and Geyer, 1994) or have improved it with new proposals (Wellner and Zhan, 1997).

Chapter 2 reproduces the paper of Oller et al. (2004). We prove the equivalence between different characterizations of noninformative censoring appeared in the literature and we define an analogous constant-sum condition to the one derived in the context of right censoring. We prove as well that when the noninformative condition or the constant-sum condition holds, the simplified likelihood can be used to obtain the nonparametric maximum likelihood estimator (NPMLE) of the failure time distribution function. Finally, we characterize the constant-sum property according to different types of censoring. In Chapter 3 we study the relevance of the constant-sum property in the identifiability of the lifetime distribution. We show that the lifetime distribution is not identifiable outside the class of constant-sum models. We also show that the lifetime probabilities assigned to the observable intervals are identifiable inside the class of constant-sum models. We illustrate all these notions with several examples.

Chapter 4 has partially been published in the survey paper of Gómez et al. (2004). It gives a general view of those procedures which have been applied in the nonparametric problem of the comparison of two or more interval-censored samples. We also develop some S-Plus routines which implement the permutational version of the Wilcoxon test, the Logrank test and the t-test for interval censored data (Fay and Shih, 1998). This part of the PhD thesis is completed in Chapter 5 by different proposals of extension of the Jonckeere's test. In order to test for an increasing trend in the k-sample problem, Abel (1986) gives one of the few generalizations of the Jonckheree's test for interval-censored data. We also suggest different Jonckheere-type tests according to the tests presented in Chapter 4. We use permutational and Monte Carlo approaches. We give computer programs for each proposal and perform a simulation study in order compare the power of each proposal under different parametric assumptions and different alternatives. We motivate both chapters with the analysis of a set of data from a study of the benefits of zidovudine in patients in the early stages of the HIV infection (Volberding et al., 1995).

Finally, Chapter 6 summarizes results and address those aspects which remain to be completed.

The work carried out in this thesis is focused on the proposal, comparison and assessment of survival analysis models for epilepsy data. Although the Cox proportional hazards model provides a popular approach to medical recurrent events modelling, other accelerated life alternatives seem more appropriate when compared under goodness of t tests. In our research we apply the Cox proportional hazards model and two models consisting of a Poisson-Gamma mixture model that could assume the existence of a cure fraction , and which have been developed and proposed by B. Cowling[11] and J. Rogers[39] respectively. We applied these methods to the Multicentre study of early Epilepsy and Single Seizures (MESS) data set. In this epilepsy study, patients with different types of seizures were randomized to either immediate or delayed treatment, which consisted in being administered one of seven types of drugs. The aim of the study consisted in producing a prognosis with which the clinicians and patients could take an informed decision on whether or not it was preferable to take an anti-epileptic drug. We investigated the behaviour of the survival function for the Cox proportional hazards model, the joint model and the joint with cure fraction model under the epilepsy data set, under the framework of residual analysis studies, as well as empirical vs theoretical survival functions. As a final contribution of our work, we proposed modification of the accelerated life models. Since a patient cannot be diagnosed with epilepsy unless he or she presents at least two un-provoked seizures, we proposed a zero-truncated joint model, which considers the pre-randomization counts to be strictly positive. This model has been extended to consider a cure fraction of the population, but is still under development, since the corresponding parameter estimations become considerably more complicated.

Using data from Hedge Fund Research, Inc. (HFR), this study adapts and expands on existing methods in survival analysis in an attempt to investigate whether hedge funds mortality can be predicted on the basis of certain hedge funds characteristics. The main idea is to determine the characteristics which contribute the most to the survival and failure probabilities of hedge funds and interpret them. We establish hazard models with time-independent covariates, as well as time-varying covariates to interpret the selected hedge funds characteristics. Our results show that size, age, performance, strategy, annual audit, fund offshore and fund denomination are the characteristics that best explain hedge fund failure. We find that 1% increase in performance decreases the hazard by 3.3%, the small size and the less than 5 years old hedge funds are the most likely to die and the event-driven strategy is the best to use as compare to others. The risk of death is 0.668 times lower for funds who indicated that an annual audit is performed as compared to the funds who did not indicated that an annual audit is performed. The risk of death for the offshore hedge funds is 1.059 times higher than the non-offshore hedge funds.

In epidemiological studies, subjects with disease (prevalent cases) differ from newly diseased (incident cases). They tend to survive longer due to sampling bias, and related covariates will also be biased. Methods for regression analyses have recently been proposed to measure the potential effects of covariates on survival. The goal is to extend the dependence measure of Kent (1983), based on the information gain, in the context of length-biased sampling. In this regard, to estimate information gain and dependence measure for length-biased data, we propose two different methods namely kernel density estimation with a regression procedure and parametric copulas. We will assess the consistency for all proposed estimators. Algorithms detailing how to generate length-biased data, using kernel density estimation with regression procedure and parametric copulas approaches, are given. Finally, the performances of the estimated information gain and dependence measure, under length-biased sampling, are demonstrated through simulation studies.

This thesis is concerned with the development of flexible continuous-time survival models based on the accelerated failure time (AFT) model for the survival time and the Cox relative risk (CRR) model for the hazard rate. The flexibility concerns on the one hand the extension of the predictor to take into account simultaneously for a variety of different forms of covariate effects. On the other hand, the often too restrictive parametric assumptions about the survival distribution are replaced by semiparametric approaches that allow very flexible shapes of survival distribution. We use the Bayesian methodology for inference. The arising problems, like e. g. the penalization of high-dimensional linear covariate effects, the smoothing of nonlinear effects as well as the smoothing of the baseline survival distribution, are solved with the application of regularization priors tailored for the respective demand. The considered expansion of the two survival model classes enables to deal with various challenges arising in practical analysis of survival data. For example the models can deal with high-dimensional feature spaces (e. g. gene expression data), they facilitate feature selection from the whole set or a subset of the available covariates and enable the simultaneous modeling of any type of nonlinear covariate effects for covariates that should always be included in the model. The option of the nonlinear modeling of covariate effects as well as the semiparametric modeling of the survival time distribution enables furthermore also a visual inspection of the linearity assumptions about the covariate effects or accordingly parametric assumptions about the survival time distribution. In this thesis it is shown, how the p>n paradigm, feature relevance, semiparametric inference for functional effect forms and the semiparametric inference for the survival distribution can be treated within a unified Bayesian framework. Due the option to control the amount of regularization of the considered priors for the linear regression coefficients, there is no need to distinguish conceptionally between the cases p<=n and p>n. To accomplish the desired regularization, the regression coefficients are associated with shrinkage, selection or smoothing priors. Since the utilized regularization priors all facilitate a hierarchical representation, the resulting modular prior structure, in combination with adequate independence assumptions for the prior parameters, enables to establish a unified framework and the possibility to construct efficient MCMC sampling schemes for joint shrinkage, selection and smoothing in flexible classes of survival models. The Bayesian formulation enables therefore the simultaneous estimation of all parameters involved in the models as well as prediction and uncertainty statements about model specification. The presented methods are inspired from the flexible and general approach for structured additive regression (STAR) for responses from an exponential family and CRR-type survival models. Such systematic and flexible extensions are in general not available for AFT models. An aim of this work is to extend the class of AFT models in order to provide such a rich class of models as resulting from the STAR approach, where the main focus relies on the shrinkage of linear effects, the selection of covariates with linear effects together with the smoothing of nonlinear effects of continuous covariates as representative of a nonlinear modeling. Combined are in particular the Bayesian lasso, the Bayesian ridge and the Bayesian NMIG (a kind of spike-and-slab prior) approach to regularize the linear effects and the P-spline approach to regularize the smoothness of the nonlinear effects and the baseline survival time distribution. To model a flexible error distribution for the AFT model, the parametric assumption for the baseline error distribution is replaced by the assumption of a finite Gaussian mixture distribution. For the special case of specifying one basis mixture component the estimation problem essentially boils down to estimation of log-normal AFT model with STAR predictor. In addition, the existing class of CRR survival models with STAR predictor, where also baseline hazard rate is approximated by a P-spline, is expanded to enable the regularization of the linear effects with the mentioned priors, which broadens further the area of application of this rich class of CRR models. Finally, the combined shrinkage, selection and smoothing approach is also introduced to the semiparametric version of the CRR model, where the baseline hazard is unspecified and inference is based on the partial likelihood. Besides the extension of the two survival model classes the different regularization properties of the considered shrinkage and selection priors are examined. The developed methods and algorithms are implemented in the public available software BayesX and in R-functions and the performance of the methods and algorithms is extensively tested by simulation studies and illustrated through three real world data sets.

Explained variation measures are used to quantify the amount of information in a model and especially how useful the model might be when predicting future observations. Such measures are useful in guiding model choice for all types of predictive regression models, including linear and generalized linear models and survival analysis. The first part of this thesis considers explained variation for survival data and we investigate how individual observations in a data set can influence the value of various proposed statistics. Influence of a subject is a measure of the effect on estimates of deleting him/her from the data set. Influence on regression coefficients has had much attention but there has not been work in influence for explained variation for survival data analysis or other measures of predictive accuracy. Generally in reasonable size data sets the deletion of a single subject has no effect on conclusions. However, examination of distance between measures with and without the subject can be useful in distinguishing abnormal observations. In the second part of the thesis we investigate how measures of explained variation for survival data can be extended to recurrent event data. We describe an existing rank-based measure and we investigate a new statistic based on observed and expected event count processes. Both methods can be used for all models. Adjustments for missing data are proposed for the count measure and demonstrated through simulation to be effective. We compare the population values of the two statistics and illustrate their use in comparing an array of non-nested models for data on recurrent episodes of infant diarrhea. There is evidence that the rank-based method is robust to ignored random effects and also to the presence of unusual observations. The count-based method more directly compares observed and expected intensities. We assess influence of individual observation on these measures.

Joint modelling is the simultaneous modelling of longitudinal and survival data, while taking into account a possible association between them. A common approach in joint modelling studies is to assume that the repeated measurements follow a lin- ear mixed e�ects model and the survival data is modelled using a Cox proportional hazards model. The Cox model, however, requires a strong proportionality assump- tion, which seems to be violated quite often. We, thus, propose the use of parametric survival models. Additionally, joint modelling literature mainly deals with right- censoring only and does not consider left-truncation, which can cause bias. The joint model proposed here considers left-truncation and right-censoring.

Noncompliance to treatment allocation is likely to complicate estimation of causal effects in clinical trials. The ubiquitous nonrandom phenomenon of noncompliance renders per-protocol and as- treated analyses or even simple regression adjustments for noncompliance inadequate for causal inference. For survival data, several specialist methods have been developed when noncompliance is related to risk. The Causal Accelerated Life Model (CALM) allows time-dependent departures from randomized treatment in either arm and relates each observed event time to a potential event time that would have been observed if the control treatment had been given throughout the trial. Alternatively, the structural Proportional Hazards (C-Prophet) model accounts for all-or-nothing noncompliance in the treatment arm only while the CHARM estimator allows time-dependent departures from randomized treatment by considering survival outcome as a sequence of binary outcomes to provide an 'approximate' overall hazard ratio estimate which is adjusted for compliance. The problem of efficacy estimation is compounded for two-active treatment trials (additional noncompliance) where the ITT estimate provides a biased estimator for the true hazard ratio even under homogeneous treatment effects assumption. Using plausible arm-specific predictors of compliance, principal stratification methods can be applied to obtain principal effects for each stratum. The present work applies the above methods to data from the Esprit trials study which was conducted to ascertain whether or not unopposed oestrogen (hormone replacement therapy - HRT) reduced the risk of further cardiac events in postmenopausal women who survive a first myocardial infarction. We use statistically designed simulation studies to evaluate the performance of these methods in terms of bias and 95% confidence interval coverage. We also apply a principal stratification method to adjust for noncompliance in two treatment arms trial originally developed for binary data for survival analysis in terms of causal risk ratio. In a Bayesian framework, we apply the method to Esprit data to account for noncompliance in both treatment arms and estimate principal effects. We apply statistically designed simulation studies to evaluate the performance of the method in terms of bias in the causal effect estimates for each stratum. ITT analysis of the Esprit data showed the effects of taking HRT tablets was not statistically significantly different from placebo for both all cause mortality and myocardial reinfarction outcomes. Average compliance rate for HRT treatment was 43% and compliance rate decreased as the study progressed. CHARM and C-Prophet methods produced similar results but CALM performed best for Esprit: suggesting HRT would reduce risk of death by 50%. Simulation studies comparing the methods suggested that while both C-Prophet and CHARM methods performed equally well in terms of bias, the CALM method performed best in terms of both bias and 95% confidence interval coverage albeit with the largest RMSE. The principal stratification method failed for the Esprit study possibly due to the strong distribution assumption implicit in the method and lack of adequate compliance information in the data which produced large 95% credible intervals for the principal effect estimates. For moderate value of sensitivity parameter, principal stratification results suggested compliance with HRT tablets relative to placebo would reduce risk of mortality by 43% among the most compliant. Simulation studies on performance of this method showed narrower corresponding mean 95% credible intervals corresponding to the the causal risk ratio estimates for this subgroup compared to other strata. However, the results were sensitive to the unknown sensitivity parameter.

Thesis (Ph. D.)--Florida State University, 2009.
Advisor: Xu-Feng Niu, Florida State University, College of Arts and Sciences, Dept. of Statistics. Title and description from dissertation home page (viewed on Nov. 18, 2009). Document formatted into pages; contains x, 97 pages. Includes bibliographical references.

This work arises from a hepatitis C cohort study and focuses on estimating the effects of covariates on progression to cirrhosis. In hepatitis C cohort studies, patients may be recruited to the cohort with referral bias because clinically the patients with more rapid disease progression are preferentially referred to liver clinics. This referral bias can lead to significantly biased estimates of the effects of covariates on progression to cirrhosis.

Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2006.
Title from electronic title page (viewed Oct. 10, 2007). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biostatistics, School of Public Health." Discipline: Biostatistics; Department/School: Public Health.

Objectives. (i) to develop a computationally efficient algorithm of tree-growing for censored survival data, (ii) to assess the performance of two validation schemes, and (iii) to evaluate the performance of computationally inexpensive model selection criteria in relation to cross-validation.
Background. In the tree-growing literature, a number of computationally inexpensive model selection criteria were suggested; however, none of them were systematically investigated for their performance. RECursive Partition and AMalgamation (RECPAM) is one of the existing tree-growing algorithms that provide such built-in model selection criteria. Application of RECPAM's different model selection criteria leads to a wide range of models (40). Since RECPAM is an exploratory data analysis tool, it is desirable to reduce its computational cost and establish the general properties of its model selection criteria so that clear guidelines can be suggested.
Methods. A computationally efficient tree-growing algorithm for prognostic classification and subgroup analysis is developed by employing the Cox score statistic and the Mantel-Haenszel estimator of the relative hazard. Two validation schemes, restricting validation to pruning and parameter estimation and validating the whole process of tree growing, are implemented and evaluated in simulation. Three model selection criteria--the elbow approach, minimum Akaike Information Criterion (AIC), and the one standard error (ISE) rule--were compared to cross-validation under a broad range of scenarios using simulation. Examples of medical data analyses are presented.
Conclusions. A gain in computational efficiency is achieved while obtaining the same result as the original RECPAM approach. The restricted validation scheme is computationally less expensive, however, it is biased. In the case of subgroup analysis, to adjust properly for influential prognostic factors, we suggest constructing a prognostic classification on such factors and using the resulting classification as strata in conducting the subgroup analysis. None of the model selection criteria studied exhibit a consistently superior performance over the range of scenarios considered here. Therefore, we propose a two-stage model selection strategy in which cross-validation is employed at the first step, and if according to this step there is evidence of structure in the data set, then the elbow rule is recommended in the second step.

Within any epidemiological study missing data is almost inevitable. This missing data is often ignored; however, unless we can assume quite restrictive mechanisms, this will lead to biased estimates. Our motivation are data collected to study the long-term effect of severity of disability upon survival in children with cerebral palsy (henceforth CP). The analysis of such an old data set brings to light statistical difficulties. The main issue in this data is the amount of missing covariate data. We raise concerns about the mechanism causing data to be missing. We present a flexible class of joint models for the survival times and the missing data mechanism which allows us to vary the mechanism causing the missing data. Simulation studies prove this model to be both precise and reliable in estimating survival with missing data. We show that long term survival in the moderately disabled is high and, therefore, a large proportion will be surviving to times when they require care specifically for elderly CP sufferers. In particular, our models suggest that survival from diagnosis is considerably higher than has been previously estimated from this data. This thesis contributes to the discussion of possible methods for dealing with NMAR data.

In clinical studies of survival, additional endpoints on patients may be collected over the course of the study that give additional insight into a treatment's effect. We propose three methods to analyze right censored survival data in the presence of multiple outcomes. In order to make limited parametric assumptions on the data-generating mechanisms, the methods are based on Wilcoxon-type rank statistics. Each method is applied to a recent clinical trial of Ceftriaxone in patients with amyotrophic lateral sclerosis. In chapter 1, we modify the Gehan-Wilcoxon test for survival to account for auxiliary information on intermediate disease states (e.g. progression) that subjects may pass through before failure. We use multi-state modeling to compute expected ranks for each subject conditional on their last observed disease states and censoring time, and these ranks form the basis of our test statistic. Simulations demonstrate that the proposed test can improve power over the log-rank and generalized Wilcoxon tests in some settings while maintaining the nominal type 1 error rate. In chapter 2, we propose an estimator for an accelerated failure time model based on the test statistic proposed in chapter 1. We use the statistic as an estimating equation for a parameter that accelerates the time to each subsequent disease state. The estimator incorporates the intermediate states in a manner relevant to the survival outcome, yielding interpretable treatment and covariate effects that consider the entire trajectory of the patient. Simulations demonstrate that the estimator is unbiased, and that the proposed standard error estimator is near the empirical value. In chapter 3, we aim to assess the treatment effect globally across any types of multiple endpoints. The test we propose is based on a simple scoring mechanism applied to each pair of subjects for each endpoint. The scores for each pair of subjects are then reduced to a summary score, and a rank-sum test is applied to the summary scores. This can be seen as a generalization of several other global rank tests in the literature. Additionally, for certain statistics we describe optimal weighting schemes with respect to statistical power, and provide a method of selecting outcome weights adaptively.
Biostatistics

This work develops a marginal screening test to detect the presence of significant predictors for a right-censored time-to-event outcome under a high-dimensional accelerated failure time (AFT) model. Establishing a rigorous screening test in this setting is challenging, not only because of the right censoring, but also due to the post-selection inference. The oracle property in such situations fails to ensure adequate control of the family-wise error rate, and this raises questions about the applicability of standard inferential methods. McKeague and Qian (2015) constructed an adaptive resampling test to circumvent this problem under ordinary linear regression. To accommodate right censoring, we develop a test statistic based on a maximally selected Koul--Susarla--Van Ryzin estimator from a marginal AFT model. A regularized bootstrap method is used to calibrate the test. Our test is more powerful and less conservative than the Bonferroni correction and other competing methods. This proposed method is evaluated in simulation studies and applied to two real data sets.

碩士
國立中山大學
應用數學系研究所
102
Since 1982, cancer has become one of the leading causes of death in Taiwan. The focus of this thesis survival analysis for ovarian cancer. The first part of the thesis is analysis to the risk factors for recurrence in patients with borderline ovarian tumors. We used Cox proportional hazard model to analyze the risk of many factors. In the second part, we analyzed the risk factors for recurrence in patients with invasive ovarian tumors. These patients have longitudinal CA125 data. So we employed a joint model to explore the relationship between longitudinal CA125 profile and recurrence. In the final part of this section, we predicted patients’s recurrence probabilities after three years post surgery to validate our model. In the last part, we estimated the time-varying effects of the risk factors in ovarian cancer. In the Cox proportional hazards model, the hazard ratio is assumed to be indepen- dent of time. But in fact, the hazard ratio of many variables is not a constant. So applied an extended Cox model to estimate how the hazard ratio of these time-varying coefficients varies with time.