This dissertation addresses problems found in observational cohort studies where the repeated outcomes of interest are truncated by both death and by dropout. In particular, we consider methods that make inference for the population of survivors at each time point, otherwise known as 'partly conditional inference'. Partly conditional inference distinguishes between the reasons for missingness; failure to make this distinction will cause inference to be based not only on pre-death outcomes which exist but also on post-death outcomes which fundamentally do not exist. Such inference is called 'immortal cohort inference'. Investigations of health and cognitive outcomes in two studies - the 'Origins of Variance in the Old Old' and the 'Health and Retirement Study' - are conducted. Analysis of these studies is complicated by outcomes of interest being missing because of death and dropout. We show, first, that linear mixed models and joint models (that model both the outcome and survival processes) produce immortal cohort inference. This makes the parameters in the longitudinal (sub-)model difficult to interpret. Second, a thorough comparison of well-known methods used to handle missing outcomes - inverse probability weighting, multiple imputation and linear increments - is made, focusing particularly on the setting where outcomes are missing due to both dropout and death. We show that when the dropout models are correctly specified for inverse probability weighting, and the imputation models are correctly specified for multiple imputation or linear increments, then the assumptions of multiple imputation and linear increments are the same as those of inverse probability weighting only if the time of death is included in the dropout and imputation models. Otherwise they may not be. Simulation studies show that each of these methods gives negligibly biased estimates of the partly conditional mean when its assumptions are met, but potentially biased estimates if its assumptions are not met. In addition, we develop new augmented inverse probability weighted estimating equations for making partly conditional inference, which offer double protection against model misspecification. That is, as long as one of the dropout and imputation models is correctly specified, the partly conditional inference is valid. Third, we describe methods that can be used to make partly conditional inference for non-ignorable missing data. Both monotone and non-monotone missing data are considered. We propose three methods that use a tilt function to relate the distribution of an outcome at visit j among those who were last observed at some time before j to those who were observed at visit j. Sensitivity analyses to departures from ignorable missingness assumptions are conducted on simulations and on real datasets. The three methods are: i) an inverse probability weighted method that up-weights observed subjects to represent subjects who are still alive but are not observed; ii) an imputation method that replaces missing outcomes of subjects who are alive with their conditional mean outcomes given past observed data; and iii) a new augmented inverse probability method that combines the previous two methods and is doubly-robust against model misspecification.

Este trabalho de tese tem como objetivo principal propor uma abordagem alternativa para analisar dados Birnbaum-Saunders (BS) correlacionados com base em equações de estimação. Da classe ótima de funções de estimação proposta por Crowder (1987), derivamos uma classe ótima para a análise de dados correlacionados em que as distribuições marginais são assumidas log-BS e log-BS-t, respectivamente. Derivamos um processo iterativo para estimação dos parâmetros, métodos de diagnóstico, tais como análise de resíduos, distância de Cook e influência local sob três diferentes esquemas de perturbação: ponderação de casos, perturbação da variável resposta e perturbação individual de covariáveis. Estudos de simulação são desenvolvidos para cada modelo para avaliar as propriedades empíricas dos estimadores dos parâmetros de localização, forma e correlação. A abordagem apresentada é discutida em duas aplicações: o primeiro exemplo referente a um banco de dados sobre a produtividade de capital público nos 48 estados norte-americanos contíguos de 1970 a 1986 e o segundo exemplo referente a um estudo realizado na Escola de Educação Física e Esporte da Universidade de São Paulo (USP) durante 2016 em que 70 corredores foram avaliados em corridas em esteiras em três períodos distintos. / The aim of this thesis is to propose an alternative approach to analyze correlated Birnbaum-Saunders (BS) data based on estimating equations. From the optimal estimating functions class proposed by Crowder (1987), we derive an optimal class for the analysis of correlated data in which the marginal distributions are assumed either log-BS or log-BS-t. It is derived an iterative process, diagnostic procedures such as residual analysis, Cooks distance and local influence under three different perturbation schemes: case-weights, response variable perturbation and single-covariate perturbation. Simulation studies to assess the empirical properties of the parameters estimates are performed for each proposed model. The proposed methodology is discussed in two applications: the first one on a data set of public capital productivity of the contiguous 48 USA states, from 1970 to 1986, and the second data set refers to a study conducted in the School of Physical Education and Sport of the University of São Paulo (USP), during 2016, in which 70 runners were evaluated in running machines races in three periods.

Modelos de customer scoring são utilizados para mensurar o risco de crédito de clientes de instituições financeiras. Neste trabalho, são apresentadas três estratégias que podem ser utilizadas para o desenvolvimento desses modelos. São discutidas as vantagens de cada uma dessas estratégias, bem como os modelos e a teoria estatística associada a elas. Algumas medidas de performance usualmente utilizadas na comparação de modelos de risco de crédito são descritas. Modelos para cada uma das estratégias são ajustados utilizando-se dados reais obtidos de uma instituição financeira. A performance das estratégias para esse conjunto de dados é comparada a partir de medidas usualmente utilizadas na avaliação de modelos de risco de crédito. Uma simulação também é desenvolvida com o propósito de comparar o desempenho das estratégias em condições controladas. / Customer scoring models are used to measure the credit risk of financial institution´s customers. In this work, we present three strategies that can be used to develop these models. We discuss the advantages of each of the strategies, as well as the models and statistical theory related with them. We fit models for each of these strategies using real data of a financial institution. We compare the strategies´s performance through some measures that are usually used to validate credit risk models. We still develop a simulation to study the strategies under controlled conditions.

Longitudinal data analysis is common in biomedical research area. Generalized estimating equations (GEE) approach is widely used for longitudinal marginal models. The GEE method is known to provide consistent regression parameter estimates regardless of the choice of working correlation structure, provided the square root of n consistent nuisance parameters are used. However, it is important to use the appropriate working correlation structure in small samples, since it improves the statistical efficiency of β estimate. Several working correlation selection criteria have been proposed (Rotnitzky and Jewell, 1990; Pan, 2001; Hin and Wang, 2009; Shults et. al, 2009). However, these selection criteria have the same limitation in that they perform poorly when over-parameterized structures are considered as candidates. In this dissertation, new working correlation selection criteria are developed based on generalized eigenvalues. A set of generalized eigenvalues is used to measure the disparity between the bias-corrected sandwich variance estimator under the hypothesized working correlation matrix and the model-based variance estimator under a working independence assumption. A summary measure based on the set of the generalized eigenvalues provides an indication of the disparity between the true correlation structure and the misspecified working correlation structure. Motivated by the test statistics in MANOVA, three working correlation selection criteria are proposed: PT (Pillai's trace type criterion),WR (Wilks' ratio type criterion) and RMR (Roy's Maximum Root type criterion). The relationship between these generalized eigenvalues and the CIC measure is revealed. In addition, this dissertation proposes a method to penalize for the over-parameterized working correlation structures. The over-parameterized structure converges to the true correlation structure, using extra parameters. Thus, the true correlation structure and the over-parameterized structure tend to provide similar variance estimate of the estimated β and similar working correlation selection criterion values. However, the over-parameterized structure is more likely to be chosen as the best working correlation structure by "the smaller the better" rule for criterion values. This is because the over-parameterization leads to the negatively biased sandwich variance estimator, hence smaller selection criterion value. In this dissertation, the over-parameterized structure is penalized through cluster detection and an optimization function. In order to find the group ("cluster") of the working correlation structures that are similar to each other, a cluster detection method is developed, based on spacings of the order statistics of the selection criterion measures. Once a cluster is found, the optimization function considering the trade-off between bias and variability provides the choice of the "best" approximating working correlation structure. The performance of our proposed criterion measures relative to other relevant criteria (QIC, RJ and CIC) is examined in a series of simulation studies.

There are three broad areas of public administration that require valuation for public goods. One of these areas is concerned with value for cost benefit analysis. The concept here is quantitative, in money terms, and the purpose is to aid decision making. Planners and economists either calculate, or estimate total costs and total benefits of programs or projects as an aid to decision making. The second broad area involves justifying, or allocating public resources. Benefits bestowed by intangibles such as the arts, or questions that affect the environment are difficult to quantify as value may involve concepts the beneficiaries find difficult to identify or describe. The concept of value involves total costs, but also may involve perceptions of the community about value. Valuation costs may be calculated from the aggregate demand, but estimating demand can be difficult. The third broad area involves estimating demand for government services such as those provided by the Bureau of Statistics, and the Department of Administrative Services, as well as many others, who are being required to charge fees for services previously provided without direct charge. This development is part of the trend called corporatisation now occurring in many countries, including Australia. Economists and planners have a range of approaches available to assist them in the estimation of value, whether it be for the purpose of comparing costs with benefits, or for estimating the demand for tangible or intangible items like the arts or statistics. Surveys have been used for many years to assist a wide range of decisions by private enterprise. The use of surveys by government in Australia has been limited, but is increasing. US and European governments have used surveys to value both more and less tangible public goods since 1970. Surveys have also proved useful to assist many other decisions, including policy making, developing the means for implementing policies, monitoring and adjusting programs, and evaluation. This paper is primarily concerned with surveys. A particular type of survey, known as contingent valuation (CV), has been developed to assist the estimation of value for intangible public goods. Also discussed are other applications of surveys for government decision making, and other ways of imputing or estimating values, largely developed by economists and planners to assist cost benefit analysis. Three examples of surveys used to estimate values are discussed. These include a survey of Sydney households to help estimate the value of clean water; an Australia wide survey to help estimate the value of the arts; and a survey of Australians to help estimate the value of Coronation Hill without mining development. While the paper suggests that surveys have potential to assist a range of government decisions, examples also demonstrate the care required to obtain results that are reasonably precise and reliable.

交通事故每日無時無刻在世界各地發生，每次之交通事故均產生一連串椱雜之處理程序，該程序常涉及多方之關係人，包括消費者、保險公司、車禍處理人員、理賠人員、汽車修理廠與汽車製造商等。交通事故所致之汽車損壞，其處理程序，其實是相當值得觀察的，包括賠案登錄、損失金額之認定、賠款之處理與賠案之稽核等，均須耗費龐大之人力。 　　於台灣，汽車損失金額之認定，傳統上均由汽車修理廠師傅依其主觀判斷加以衡量，因為缺乏客觀標準與不夠精確，因此常導致消費者、汽車修理廠與保險人間之糾紛。由於估價不夠精確，因此影響汽車保險之經營甚劇。歐美先進國家產險業者，為達到汽車製造商要求之水準，保障被保險人行車安全，常以共同危險團體管理人自居，力求汽車修理成本之控制，保障被保險人之權益；而為了消弭理賠糾紛、提升保險公司服務品質與商譽，更致力於保險理賠的電腦化、標準化、數位化，以期提供公正、客觀、高效率之理賠。有鑑於此德國Audatex公司早在六○年代便極力發展此種電腦估價系統，運用電腦之資料處理簡化車輛估價之理念。 　　台灣地區汽車保險業務十年來平均占產物保險業總業務之59%，汽車保險理賠問題嚴重且持續，一套正確、客觀、有效率之估價系統，可以真實反映損失狀況，對於公平合理之費率釐定有重大之意義。 　　本文乃從實務角度探討Audatex電腦估價系統在台灣產險市場運用之可行性及其效益分析，比較英國、日本等先進國家之經驗，並發現該系統之運作不但對保險公司經營汽車保險有極大之助益，對消費者權益之維護亦有相當大之幫助。於後並建議於引進Audatex電腦估價系統之前，應先成立汽車修理研究中心，使兩者之能夠相輔相成，期能為業界提供決策與方針，加強管理技術，提供消費者更完善之服務。 / Road traffic accidents occur every day and spark a sequence of complex claim settlement procedure to consumers, motor insurers, accidents managers, loss assessors, repairers, motor manufacturers and many other related parties. In each claim of motor damages, a few linked stages need to be observed, i.e. claim registration, estimating and approving the repair cost, completing the repair work, auditing and invoicing claim settlement. 　　In Taiwan, it is conventional that car repairers estimate motor damages by their individual discretion and opinions case by case. Given lack of objectiveness and accuracy, it often causes a lot of arguments and conflicts among consumers, motor insurers and car repairers. Under such a circumstance, it calls for a need for an end-to-end and comprehensive system to manage the above procedure. 　　The Audatex system, a computerized estimating and integrated claims management system, is adopted in many developed countries to assist motor insurers in claim handling and cost estimating more efficiently. It could not only reduce duplication and errors, but also improve authorization turnaround time. All estimates are calculated and validated through the system, with the rate and terms of business agreed between individual repairers and work providers. Based on the most up-to-date parts and labor information, a fully cost assessment, is automatically sent to the work provider in the approved format. 　　This paper is to examine the feasibility of introducing the Audatex to the motor insurance market in Taiwan. The main theme of this paper is to examine the feasibility of the Audatex in Taiwan motor insurance market. It analyzes the cost of establishing such a system and compares the experiences in certain countries, such as Japan and U.K. It observes that a computerized estimating system would be invaluable both for repairers and work providers. It is suggested that Taiwan shall firstly have a motor vehicle repair research center in place and then a computerized estimating system such as the Audatex.

Abstract This thesis considers some linear and nonlinear time series models. In the linear case, the analysis of a large number of short time series generated by a first order autoregressive type model is considered. The conditional and exact maximum likelihood procedures are developed to estimate parameters. Simulation results are presented and compare the bias and the mean square errors of the parameter estimates. In Chapter 3, five important nonlinear models are considered and their time series properties are discussed. The estimating function approach for nonlinear models is developed in detail in Chapter 4 and examples are added to illustrate the theory. A simulation study is carried out to examine the finite sample behavior of these proposed estimates based on the estimating functions.

The sharing of needles among injection drug users (IDUs) is a common route of Human Immunodeficiency Virus and Hepatitis C Virus transmission. Through the increased utilization of social network analysis, researchers have been able to examine how the interpersonal relationships of IDUs affect injection risk behaviour. This study involves a secondary analysis of data from a cross-sectional study of 156 IDUs from Winnipeg, Manitoba titled “Social Network Analysis of Injection Drug Users”. Multiple logistic regression analysis was used to assess the individual and the social network characteristics associated with needle sharing among the IDUs. Generalized Estimating Equations analysis was used to determine the injecting dyad characteristics which influence needle sharing behaviour between the IDUs and their injection drug using network members. The results revealed five key thematic findings that were significantly associated with needle sharing: (1) types of drug use, (2) socio-demographic status, (3) injecting in semi-public locations, (4) intimacy, and (5) social influence. The findings from this study suggest that comprehensive prevention approaches that target individuals and their network relationships may be necessary for sustainable reductions in needle sharing among IDUs. / February 2006

Estimating functions have been widely used for parameter estimation in various statistical problems. Regular estimating functions produce parameter estimators which have desirable properties, such as consistency and asymptotic normality. In quasi-likelihood inference, an important example of estimating functions, correct specification of the first two moments of the underlying distribution leads to the information unbiasedness, which states that two forms of the information matrix: the negative sensitivity matrix (negative expectation of the first order derivative of an estimating function) and the variability matrix (variance of an estimating function) are equal, or in other words, the analogue of the Fisher information is equivalent to the Godambe information. Consequently, the information unbiasedness indicates that the model-based covariance matrix estimator and sandwich covariance matrix estimator are equivalent. By comparing the model-based and sandwich variance estimators, we propose information ratio (IR) statistics for testing model misspecification of variance/covariance structure under correctly specified mean structure, in the context of linear regression models, generalized linear regression models and generalized estimating equations. Asymptotic properties of the IR statistics are discussed. In addition, through intensive simulation studies, we show that the IR statistics are powerful in various applications: test for heteroscedasticity in linear regression models, test for overdispersion in count data, and test for misspecified variance function and/or misspecified working correlation structure. Moreover, the IR statistics appear more powerful than the classical information matrix test proposed by White (1982). In the literature, model selection criteria have been intensively discussed, but almost all of them target choosing the optimal mean structure. In this thesis, two model selection procedures are proposed for selecting the optimal variance/covariance structure among a collection of candidate structures. One is based on a sequence of the IR tests for all the competing variance/covariance structures. The other is based on an ``information discrepancy criterion" (IDC), which provides a measurement of discrepancy between the negative sensitivity matrix and the variability matrix. In fact, this IDC characterizes the relative efficiency loss when using a certain candidate variance/covariance structure, compared with the true but unknown structure. Through simulation studies and analyses of two data sets, it is shown that the two proposed model selection methods both have a high rate of detecting the true/optimal variance/covariance structure. In particular, since the IDC magnifies the difference among the competing structures, it is highly sensitive to detect the most appropriate variance/covariance structure.

The receiver operating characteristic (ROC) curve methodology is the statistical methodology for assessment of the accuracy of diagnostics tests or bio-markers. Currently most widely used statistical methods for the inferences of ROC curves are complete-data based parametric, semi-parametric or nonparametric methods. However, these methods cannot be used in diagnostic applications with missing data. In practical situations, missing diagnostic data occur more commonly due to various reasons such as medical tests being too expensive, too time consuming or too invasive. This dissertation aims to develop new nonparametric statistical methods for evaluating the accuracy of diagnostic tests or biomarkers in the presence of missing data. Specifically, novel nonparametric statistical methods will be developed with different types of missing data for (i) the inference of the area under the ROC curve (AUC, which is a summary index for the diagnostic accuracy of the test) and (ii) the joint inference of the sensitivity and the specificity of a continuous-scale diagnostic test. In this dissertation, we will provide a general framework that combines the empirical likelihood and general estimation equations with nuisance parameters for the joint inferences of sensitivity and specificity with missing diagnostic data. The proposed methods will have sound theoretical properties. The theoretical development is challenging because the proposed profile log-empirical likelihood ratio statistics are not the standard sum of independent random variables. The new methods have the power of likelihood based approaches and jackknife method in ROC studies. Therefore, they are expected to be more robust, more accurate and less computationally intensive than existing methods in the evaluation of competing diagnostic tests.