A number of methods have been developed to analyze longitudinal data with dropout. However, there is no uniformly accepted approach. Model performance, in terms of the bias and accuracy of the estimator, depends on the underlying missing data mechanism and it is unclear how existing methods will perform when little is known about the missing data mechanism. Here we evaluate methods for estimating change over time in longitudinal studies with informative dropout in three settings: using a linear mixed effect (LME) estimator in the presence of multiple types of dropout; proposing an update to the pattern mixture modeling (PMM) approach in the presence of imprecision in identifying informative dropouts; and utilizing this new approach in the presence of prognostic factor by dropout interaction. We demonstrate that amount of dropout, the proportion of dropout that is informative, and the variability in outcome all affect the performance of an LME estimator in data with a mixture of informative and non-informative dropout. When the amount of dropout is moderate to large (>20% overall) the potential for relative bias greater than 10% increases, especially with large variability in outcome measure, even under scenarios where only a portion of the dropouts are informative. Under conditions where LME models do not perform well, it is necessary to take the missing data mechanism into account. We develop a method that extends the PMM approach to account for uncertainty in identifying informative dropouts. In scenarios with this uncertainty, the proposed method outperformed the traditional method in terms of bias and coverage. In the presence of interaction between dropout and a prognostic factor, the LME model performed poorly, in terms of bias and coverage, in estimating prognostic factor-specific slopes and the interaction between the prognostic factor and time. The update to the PMM approach, proposed here, outperformed both the LME and traditional PMM. Our work suggests that investigators must be cautious with any analysis of data with informative dropout. We found that particular attention must be paid to the model assumptions when the missing data mechanism is not well understood.

A principal motivação desta dissertação é um estudo realizado pelo Instituto do Câncer do Estado de São Paulo (ICESP), envolvendo oitocentos e oito pacientes com câncer em estado avançado. Cada paciente foi acompanhado a partir da primeira admissão em uma unidade de terapia intensiva (UTI) pelo motivo de câncer, por um período de no máximo dois anos. O principal objetivo do estudo é avaliar o tempo de sobrevivência e a qualidade de vida desses pacientes através do uso de um tempo ajustado pela qualidade de vida (TAQV). Segundo Gelber et al. (1989), a combinação dessas duas informações, denominada TAQV, induz a um esquema de censura informativa; consequentemente, os métodos tradicionais de análise para dados censurados, tais como o estimador de Kaplan-Meier (Kaplan e Meier, 1958) e o teste de log-rank (Peto e Peto, 1972), tornam-se inapropriados. Visando sanar essa deficiência, Zhao e Tsiatis (1997) e Zhao e Tsiatis (1999) propuseram novos estimadores para a função de sobrevivência e, em Zhao e Tsiatis (2001), foi desenvolvido um teste análogo ao teste log-rank para comparar duas funções de sobrevivência. Todos os métodos considerados levam em conta a ocorrência de censura informativa. Neste trabalho avaliamos criticamente esses métodos, aplicando-os para estimar e testar curvas de sobrevivência associadas ao TAQV no estudo do ICESP. Por fim, utilizamos um método empírico, baseado na técnica de reamostragem bootstrap, a m de propor uma generalização do teste de Zhao e Tsiatis para mais do que dois grupos. / The motivation for this research is related to a study undertaken at the Cancer Institute at São Paulo (ICESP), which comprises the follow up of eight hundred and eight patients with advanced cancer. The patients are followed up from the first admission to the intensive care unit (ICU) for a period up to two years. The main objective is to evaluate the quality-adjusted lifetime (QAL). According to Gelber et al. (1989), the combination of both this information leads to informative censoring; therefore, traditional methods of survival analisys, such as the Kaplan-Meier estimator (Kaplan and Meier, 1958) and log-rank test (Peto and Peto, 1972) become inappropriate. For these reasons, Zhao and Tsiatis (1997) and Zhao and Tsiatis (1999) proposed new estimators for the survival function, and Zhao and Tsiatis (2001) developed a test similar to the log-rank test to compare two survival functions. In this dissertation we critically evaluate and summarize these methods, and employ then in the estimation and hypotheses testing to compare survival curves derived for QAL, the proposed methods to estimate and test survival functions under informative censoring. We also propose a empirical method, based on the bootstrap resampling method, to compare more than two groups, extending the proposed test by Zhao and Tsiatis.

A principal motivação desta dissertação é um estudo realizado pelo Instituto do Câncer do Estado de São Paulo (ICESP), envolvendo oitocentos e oito pacientes com câncer em estado avançado. Cada paciente foi acompanhado a partir da primeira admissão em uma unidade de terapia intensiva (UTI) pelo motivo de câncer, por um período de no máximo dois anos. O principal objetivo do estudo é avaliar o tempo de sobrevivência e a qualidade de vida desses pacientes através do uso de um tempo ajustado pela qualidade de vida (TAQV). Segundo Gelber et al. (1989), a combinação dessas duas informações, denominada TAQV, induz a um esquema de censura informativa; consequentemente, os métodos tradicionais de análise para dados censurados, tais como o estimador de Kaplan-Meier (Kaplan e Meier, 1958) e o teste de log-rank (Peto e Peto, 1972), tornam-se inapropriados. Visando sanar essa deficiência, Zhao e Tsiatis (1997) e Zhao e Tsiatis (1999) propuseram novos estimadores para a função de sobrevivência e, em Zhao e Tsiatis (2001), foi desenvolvido um teste análogo ao teste log-rank para comparar duas funções de sobrevivência. Todos os métodos considerados levam em conta a ocorrência de censura informativa. Neste trabalho avaliamos criticamente esses métodos, aplicando-os para estimar e testar curvas de sobrevivência associadas ao TAQV no estudo do ICESP. Por fim, utilizamos um método empírico, baseado na técnica de reamostragem bootstrap, a m de propor uma generalização do teste de Zhao e Tsiatis para mais do que dois grupos. / The motivation for this research is related to a study undertaken at the Cancer Institute at São Paulo (ICESP), which comprises the follow up of eight hundred and eight patients with advanced cancer. The patients are followed up from the first admission to the intensive care unit (ICU) for a period up to two years. The main objective is to evaluate the quality-adjusted lifetime (QAL). According to Gelber et al. (1989), the combination of both this information leads to informative censoring; therefore, traditional methods of survival analisys, such as the Kaplan-Meier estimator (Kaplan and Meier, 1958) and log-rank test (Peto and Peto, 1972) become inappropriate. For these reasons, Zhao and Tsiatis (1997) and Zhao and Tsiatis (1999) proposed new estimators for the survival function, and Zhao and Tsiatis (2001) developed a test similar to the log-rank test to compare two survival functions. In this dissertation we critically evaluate and summarize these methods, and employ then in the estimation and hypotheses testing to compare survival curves derived for QAL, the proposed methods to estimate and test survival functions under informative censoring. We also propose a empirical method, based on the bootstrap resampling method, to compare more than two groups, extending the proposed test by Zhao and Tsiatis.

La survie nette est un indicateur très utilisé en épidémiologie des cancers. Il s'agit de la survie que l'on observerait si la seule cause de mortalité était le cancer ; il est le seul indicateur épidémiologique utilisable à des fins de comparaisons de survie (entre périodes/pays) car il s'affranchit des éventuelles différences de mortalité dues aux autres causes que le cancer. Le premier objectif de notre travail était d'analyser les performances des différentes méthodes d'estimation de la survie nette sur données simulées ainsi que sur données réelles afin que les méthodes non biaisées soient reconnues scientifiquement et soient les seules à être utilisées par la suite. Nous avons ainsi démontré que deux approches étaient capables d'estimer sans biais la survie nette : l'approche non paramétrique de Pohar-Perme et l'approche reposant sur une modélisation multivariée du taux de mortalité en excès dû au cancer. Cette dernière approche impose une stratégie de construction difficile à mettre en place. Le deuxième objectif était de développer une boîte à outils composée de différents tests permettant de vérifier les différentes hypothèses faites lors de la construction d'un modèle de régression du taux de mortalité en excès. Ces hypothèses concernent habituellement la proportionnalité ou non de l'effet des covariables, leur forme fonctionnelle, ainsi que la fonction de lien utilisée. Le troisième objectif était une application épidémiologique qui visait à étudier l'impact des facteurs pronostiques, tel que le stade au diagnostic, sur la survie nette conditionnelle, en d'autres termes sur la dynamique du taux de mortalité en excès, après la survenue d'un cancer du côlon / Net survival is one of the most important indicators in cancer epidemiology. It is defined as the survival that would be observed if cancer were the only cause of death. This is the only one indicator allowing comparisons of cancer impact between countries or time periods because it is not influenced by death because of other causes. The first objective of this work was to compare the performance of several estimators of the net survival in a simulation study and then on real data in order to promote unbiased methods. Those methods are the non-parametric Pohar-Perme method and the parametric multivariable excess rate model. The latest one needs a model building strategy. The use of diagnostic procedures for model checking is an essential part of the modeling process. The second objective was to develop a tool box composed of diagnostic tools allowing to check hypothesis usually considered when constructing an excess mortality rate model, that is, the proportionality or not of the effect of covariates, their functional form and the link function. The third objective deals with the study of the impact of prognostic variables, such as stage at diagnosis, on conditional net survival, that is, on the dynamic of the excess hazard mortality after the diagnosis of colon cancer

Cure rate models, introduced by Boag (1949), are very commonly used while modelling lifetime data involving long time survivors. Applications of cure rate models can be seen in biomedical science, industrial reliability, finance, manufacturing, demography and criminology. In this thesis, cure rate models are discussed under a competing cause scenario, with the assumption of proportional odds (PO) lifetime distributions for the susceptibles, and statistical inferential methods are then developed based on right-censored data. In Chapter 2, a flexible cure rate model is discussed by assuming the number of competing causes for the event of interest following the Conway-Maxwell (COM) Poisson distribution, and their corresponding lifetimes of non-cured or susceptible individuals can be described by PO model. This provides a natural extension of the work of Gu et al. (2011) who had considered a geometric number of competing causes. Under right censoring, maximum likelihood estimators (MLEs) are obtained by the use of expectation-maximization (EM) algorithm. An extensive Monte Carlo simulation study is carried out for various scenarios, and model discrimination between some well-known cure models like geometric, Poisson and Bernoulli is also examined. The goodness-of-fit and model diagnostics of the model are also discussed. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. Next, in Chapter 3, the destructive cure rate models, introduced by Rodrigues et al. (2011), are discussed under the PO assumption. Here, the initial number of competing causes is modelled by a weighted Poisson distribution with special focus on exponentially weighted Poisson, length-biased Poisson and negative binomial distributions. Then, a damage distribution is introduced for the number of initial causes which do not get destroyed. An EM-type algorithm for computing the MLEs is developed. An extensive simulation study is carried out for various scenarios, and model discrimination between the three weighted Poisson distributions is also examined. All the models and methods of estimation are evaluated through a simulation study. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. In Chapter 4, frailty cure rate models are discussed under a gamma frailty wherein the initial number of competing causes is described by a Conway-Maxwell (COM) Poisson distribution in which the lifetimes of non-cured individuals can be described by PO model. The detailed steps of the EM algorithm are then developed for this model and an extensive simulation study is carried out to evaluate the performance of the proposed model and the estimation method. A cutaneous melanoma dataset as well as a simulated data are used for illustrative purposes. Finally, Chapter 5 outlines the work carried out in the thesis and also suggests some problems of further research interest. / Thesis / Doctor of Philosophy (PhD)