如何藉由DNA微陣列資料跟存活資料的資訊來找出基因表現定型一直是個重要的議題。這些研究的主要目標是從大量的基因中找出那些真正跟存活時間或其它重要的臨床結果有顯著關係的小部分。Threshold Gradient Directed Regularization (TGDR)是ㄧ種已經被應用在高維度迴歸問題中能同時處理變數選取以及模型配適的演算法。然而，TGDR採用一種梯度投影型態的演算法使得收斂速率緩慢。在本篇論文中，我們建議新的包含Newton-Raphson求解演算法類型的改良版TGDR方法。我們建議的方法有類似TGDR的特性但卻有比較快的收斂速率。文中並利用一筆附有設限存活時間的真實微陣列癌症資料來做示範。 本篇論文的第二部份是關於適用於區間設限存活資料的重複抽樣Peto-Peto檢定。這個重複抽樣Peto-Peto檢定能夠評估存活函數估計方法的檢定力，例如Turnbull的估計方法以及Kaplan-Meier的估計方法。這個檢定方法顯示出在區間設限資料時Kaplan-Meier的估計方法的檢定力要比Turnbull的估計方法的檢定力來得低。這個檢定方法將以模擬的區間設限資料以及一筆真實關於乳癌研究的區間設限資料來說明。 / Analyzing censored survival data with high-dimensional covariates arising from the microarray data has been an important issue. The main goal is to find genes that have pivotal influence with patient's survival time or other important clinical outcomes. Threshold Gradient Directed Regularization (TGDR) method has been used for simultaneous variable selection and model building in high-dimensional regression problems. However, the TGDR method adopts a gradient-projection type of method and would have slow convergence rate. In this thesis, we proposed Modified TGDR algorithms which incorporate Newton-Raphson type of search algorithm. Our proposed approaches have the similar characteristics with TGDR but faster convergence rates. A real cancer microarray data with censored survival times is used for demonstration. The second part of this thesis is about a proposed resampling based Peto-Peto test for survival functions on interval censored data. The proposed resampling based Peto-Peto test can evaluate the power of survival function estimation methods, such as Turnbull’s Procedure and Kaplan-Meier estimate. The test shows that the power based on Kaplan-Meier estimate is lower than that based on Turnbull’s estimation on interval censored data. This proposed test is demonstrated on simulated data and a real interval censored data from a breast cancer study.

Com o objetivo de avaliar o atendimento dos pacientes submetidos à intervenção cirúrgica cardiovascular no protocolo de atendimento na via rápida (fast track recovery) em relação ao protocolo convencional, foi comparada a movimentação dos pacientes atendidos em ambos os protocolos nas diferentes unidades hospitalares. O estudo foi realizado em hospital público universitário especializado em cardiologia de 400 leitos, de referência terciária para o Sistema Único de Saúde. Foram estudados 175 pacientes, 107 (61%) homens e 68 (39%) mulheres, de idades entre 2 meses a 81 anos, dos quais 107 operados no protocolo da via rápida e 68 no protocolo convencional. Foram avaliadas variáveis demográficas, clínicas e, para avaliar a movimentação dos pacientes nas diferentes unidades hospitalares, as taxas de alta por unidade de tempo em cada unidade. A análise estatística foi feita por meio de análise exploratória, método de Kaplan Meier e modelo de riscos proporcionais de Cox. A análise de variância foi empregada para comparar o faturamento das despesas. A taxa de alta das diferentes unidades hospitalares por unidade de tempo dos portadores de cardiopatia congênita atendidos no protocolo da via rápida em relação ao protocolo da via convencional foi: a) 11,3 vezes a taxa de alta quando assistidos no protocolo na via convencional quanto ao tempo de permanência no centro cirúrgico; b) 6,3 vezes quanto à duração da intervenção cirúrgica; c) 6,8 vezes quanto à duração da anestesia; d) 1,5 vezes quanto à duração da perfusão; e) 2,8 vezes quanto à permanência na unidade de recuperação pós-operatória I; f) 6,7 vezes quanto à duração da hospitalização; g) 2,8 vezes quanto à permanência na unidade de internação pré-operatória; h) 2,1 vezes quanto à permanência na unidade de internação após a alta da unidade de terapia intensiva de recuperação pós-operatória. Para os portadores de cardiopatia isquêmica, as taxas de alta das unidades hospitalares para os protocolos de atendimento no protocolo da via rápida e no protocolo convencional não demonstraram diferença estatisticamente significante. Os valores de faturamento das despesas de internação dos portadores de cardiopatia congênita decorrentes de exames e procedimentos realizados nas fases pré- e pós-operatória e dos exames da fase trans-operatória foram menores quando os pacientes foram assistidos no protocolo da via rápida. Portanto, os portadores de cardiopatias congênita apresentaram menor permanência hospitalar nos recursos médicos hospitalares instalados, quando assistidos no protocolo de atendimento na via rápida, bem como menores despesas nas fases pré- e pós- operatória da internação. / Objective - To evaluate patient assistance in pre, per and postoperative phases of cardiac surgical intervention under fast track recovering protocol compared to the conventional way. Patients - 175 patients were studied, 107 (61%) men and 68 (39%) women. Ages 2 months to 81 years old. Patients included: first surgical intervention, congenital and ischemic cardiopathy without complexity, normal ventricular function and with at least 2 preoperative ambulatory consultations. Patients submitted to emergency surgeries were excluded. Interventions - assistance submitted by fast track and conventional protocol. Statistical analysis (measures) - exploratory, uni-varied (Kaplan Meier) and multi-varied (Cox) of the time in each admission unit. Hospital installations were classified in ambulatory, preoperative admission unit, surgical center, postoperative recovery unit and postoperative admission unit; the expression of this use was the discharge rate by unit of time from the significant interaction observed between assistance protocol and the kind of cardiopathy for the stay in the surgical center, surgical intervention time, stay in postoperative recovery unit, anesthesia time and time between admission and surgery dates. Results - the patients of congenital cardiopathy who underwent the protocol of conventional way recovery in relation to the fast track protocol, in the reliability range of 95% allows one to state that discharge rate by unit of time of the congenital cardiopathy patients assisted by the fast track protocol was: 11.3 times the discharge rate when assisted by the conventional way protocol as to the time of staying in the surgical center; 6.3 times as to the duration of the surgical intervention; 6.8 times as to duration of the anesthesia; 1.5 times as to the duration of the perfusion; 2.8 times as to the stay in the postoperative recovery unit; 6.7 times as to the stay in the hospital (period of time between the admission and the discharge date); 2.8 times as to the stay in the preoperative admission unit ( period of time between the admission date and the surgery date); 2.1 times as to the stay in the postoperative unit (period of time between the date of leaving the postoperative recovery unit and the date of discharge from the hospital). For the ischemia cardiopathy patients the risks concerning the protocols of recovery by the traditional way and the fast track were the same. CONCLUSIONS - The data concerning this study allows one to suggest that the assistance can be more efficient if one takes into consideration some variables studied in the protocol of fast track recovery. The congenital and ischemic cardiopathy patients presented shorter interval of time (concerning hospital stay in doctor-hospital installed facilities) when assisted in the fast track recovery protocol as well as fewer expenses with medical and hospital assistance.

In survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment difficult, and the existing tests for goodness-of-fit do not have direct extension to these complicated types of censored data. In this work, we use empirical likelihood (Owen, 1988) approach to construct goodness-of-fit test and provide estimates for the Cox model with various types of censored data. Specifically, the problems under consideration are the two-sample Cox model and stratified Cox model with right censored data, doubly censored data and partly interval-censored data. Related computational issues are discussed, and some simulation results are presented. The procedures developed in the work are applied to several real data sets with some discussion.

Cette thèse a été conçu pour explorer les modèles dynamiques de régression, d’évaluer les inférences statistiques pour l’analyse des données de survie et de fiabilité. Ces modèles de régression dynamiques que nous avons considérés, y compris le modèle des hasards proportionnels paramétriques et celui de la vie accélérée avec les variables qui peut-être dépendent du temps. Nous avons discuté des problèmes suivants dans cette thèse.Nous avons présenté tout d’abord une statistique de test du chi-deux généraliséeY2nquiest adaptative pour les données de survie et fiabilité en présence de trois cas, complètes,censurées à droite et censurées à droite avec les covariables. Nous avons présenté en détailla forme pratique deY2nstatistique en analyse des données de survie. Ensuite, nous avons considéré deux modèles paramétriques très flexibles, d’évaluer les significations statistiques pour ces modèles proposées en utilisantY2nstatistique. Ces modèles incluent du modèle de vie accélérés (AFT) et celui de hasards proportionnels (PH) basés sur la distribution de Hypertabastic. Ces deux modèles sont proposés pour étudier la distribution de l’analyse de la duré de survie en comparaison avec d’autre modèles paramétriques. Nous avons validé ces modèles paramétriques en utilisantY2n. Les études de simulation ont été conçus.Dans le dernier chapitre, nous avons proposé les applications de ces modèles paramétriques à trois données de bio-médicale. Le premier a été fait les données étendues des temps de rémission des patients de leucémie aiguë qui ont été proposées par Freireich et al. sur la comparaison de deux groupes de traitement avec des informations supplémentaires sur les log du blanc du nombre de globules. Elle a montré que le modèle Hypertabastic AFT est un modèle précis pour ces données. Le second a été fait sur l’étude de tumeur cérébrale avec les patients de gliome malin, ont été proposées par Sauerbrei & Schumacher. Elle a montré que le meilleur modèle est Hypertabastic PH à l’ajout de cinq variables de signification. La troisième demande a été faite sur les données de Semenova & Bitukov, à concernant les patients de myélome multiple. Nous n’avons pas proposé un modèle exactement pour ces données. En raison de cela était les intersections de temps de survie.Par conséquent, nous vous conseillons d’utiliser un autre modèle dynamique que le modèle de la Simple Cross-Effect à installer ces données. / This thesis was designed to explore the dynamic regression models, assessing the sta-tistical inference for the survival and reliability data analysis. These dynamic regressionmodels that we have been considered including the parametric proportional hazards andaccelerated failure time models contain the possibly time-dependent covariates. We dis-cussed the following problems in this thesis.At first, we presented a generalized chi-squared test statisticsY2nthat is a convenient tofit the survival and reliability data analysis in presence of three cases: complete, censoredand censored with covariates. We described in detail the theory and the mechanism to usedofY2ntest statistic in the survival and reliability data analysis. Next, we considered theflexible parametric models, evaluating the statistical significance of them by usingY2nandlog-likelihood test statistics. These parametric models include the accelerated failure time(AFT) and a proportional hazards (PH) models based on the Hypertabastic distribution.These two models are proposed to investigate the distribution of the survival and reliabilitydata in comparison with some other parametric models. The simulation studies were de-signed, to demonstrate the asymptotically normally distributed of the maximum likelihood estimators of Hypertabastic’s parameter, to validate of the asymptotically property of Y2n test statistic for Hypertabastic distribution when the right censoring probability equal 0% and 20%.n the last chapter, we applied those two parametric models above to three scenes ofthe real-life data. The first one was done the data set given by Freireich et al. on thecomparison of two treatment groups with additional information about log white blood cellcount, to test the ability of a therapy to prolong the remission times of the acute leukemiapatients. It showed that Hypertabastic AFT model is an accurate model for this dataset.The second one was done on the brain tumour study with malignant glioma patients, givenby Sauerbrei & Schumacher. It showed that the best model is Hypertabastic PH onadding five significance covariates. The third application was done on the data set given by Semenova & Bitukov on the survival times of the multiple myeloma patients. We did not propose an exactly model for this dataset. Because of that was an existing oneintersection of survival times. We, therefore, suggest fitting other dynamic model as SimpleCross-Effect model for this dataset.

The objective of the study was to identify the factors that affect the survival lifetime of HIV+ terminal patients in rural district hospitals of Albert Luthuli municipality in the Mpumalanga province of South Africa. A cohort of HIV+ terminal patients was retrospectively followed from 2010 to 2017 until a patient died, was lost to follow-up or was still alive at the end of the observation period. Nonparametric survival analysis and semiparametric survival analysis methods were used to analyse the data. Through Cox proportional hazards regression modelling, it was found that ART adherence (poor, fair, good), Age, Follow-up mass, Baseline sodium, Baseline viral load, Follow CD4 count by Treatment (Regimen 1) interaction and Follow-up lymphocyte by TB history (yes, no) interaction had significant effects on survival lifetime of HIV+ terminal patients (p-values<0.1). Furthermore, through quantile regression modelling, it was found that short, medium and long survival times of HIV+ patients, respectively represented by the 0.1, 0.5 and 0.9 quantiles, were not necessarily significantly affected by the same factors. / Statistics / M. Sc. (Statistics)