Diversos modelos têm sido propostos na literatura com o objetivo de analisar dados de sobrevivência em que a população sob estudo é assumida ser uma mistura de indivíduos suscetíveis (em risco) e não suscetíveis a um específico evento de interesse. Tais modelos são usualmente denominados modelos com sobreviventes de longa duração ou modelos com fração de cura. Neste trabalho, diversos desses modelos (nos contextos paramétrico e semi-paramétrico) foram considerados para analisar os dados de um ensaio clínico aleatorizado conduzido com o objetivo de comparar três estratégias terapêuticas (cirurgia, angioplastia e medicamentoso) utilizadas no tratamento de pacientes com doença coronariana multiarterial. Em todos os modelos, as funções de ligação logito e complemento log-log foram utilizadas para modelar a proporção de sobreviventes de longa duração (indivíduos não suscetíveis). Quanto à função de sobrevivência dos indivíduos suscetíveis, foram utilizados os modelos de Weibull e de Cox. Covariáveis foram consideradas tanto na proporção de sobreviventes de longa duração quanto na função de sobrevivência dos indivíduos suscetíveis. De modo geral, os modelos considerados se mostraram adequados para analisar os dados do ensaio clínico aleatorizado, indicando a cirurgia como a estratégia terapêutica mais eficiente. Indicaram também, que as covariáveis idade, hipertensão e diabetes mellitus exercem influência na ocorrência do óbito cardíaco, mas não no tempo até a ocorrência deste óbito nos pacientes suscetíveis. / Several models have been proposed in the literature with the aim of analyzing survival data when the population under study is assumed to be a mixture of susceptible (at risk) and not susceptible individuals to a specific event of interest. Such models are usually called long-term survivors models or cure rate models. In this work, several of these models (under both parametric and semi-parametric approaches) were considered to analyze the data from a randomized clinical trial conducted in order to compare three therapeutic strategies (surgery, angioplasty and medicine) used in the treatment of patients with multivessel coronary artery disease. For all models the logit and complementary log-log link functions were used to model the proportion of long-term survivors (not susceptible individuals). In regards to the survival function of the susceptible individuals, the Weibull and Cox models were used. Covariates were considered both in the proportion of longterm survivors and in the survival function of the susceptible individuals. Overall, the models considered were suitable for analyzing the data from the randomized clinical trial indicating surgery as the most effective therapeutic strategy. They also indicated that the covariates age, hypertension and diabetes mellitus exhibit influence on the occurrence of cardiac death, but not on the time to the occurrence of this death in susceptible patients.

Introdução: Os múltiplos e interativos efeitos protetores do aleitamento materno exclusivo (AME) na saúde e sobrevivência infantil justificam as recomendações universais para promover sua prática. Poucos são os estudos que avaliam a tendência do padrão do AME entre países. Objetivo: Analisar a mudança temporal do AME em cinco países da América Latina e Caribe (ALC) comparando dados das décadas de 1990 e 2000. Métodos: A dissertação é composta por um manuscrito, que avaliou dados de crianças de 0 a 6 meses incluídas nas amostras das pesquisas Demographic Health Survey conduzidas em Brasil, Colômbia, Haiti, Peru e República Dominicana. Foram estimadas as prevalências do AME e suas taxas anuais de variação ponderada, segundo país e ano de inquérito. A duração do AME foi estimada usando a análise de sobrevida de Kaplan-Meier, considerando a idade atual da criança como o tempo de sobrevida e o AME como variável binária, referente à situação da prática no momento da entrevista. As curvas de sobrevivência foram construídas por país, em cada década, e a comparação entre elas usou o teste log-rank. A mediana do tempo de amamentação foi calculada para cada variável independente e a relação entre essas variáveis e o desmame até os seis meses foi analisada pela técnica de regressão de Cox com modelo múltiplo. Resultados: A prevalência de AME aumentou em quatro dos cinco países estudados, com incremento ao ano mais marcante na Colômbia (11 por cento ) e no Haiti (17 por cento ). A duração mediana apresentou duas tendências de evolução: aumento com equidade na Colômbia e no Haiti, e estagnação com distribuição desigual entre os subgrupos populacionais da última década no Brasil, Peru e República Dominicana. No modelo múltiplo de regressão, variáveis de demografia e do perfil de uso dos serviços de saúde associaram-se à duração do AME. A residência em área rural foi a variável reiteradamente associada, de forma negativa no Brasil (HR=1,68; IC 95 por cento :1,06-2,67) e na Colômbia (HR=1,39; IC 95 por cento :1,03-1,87), enquanto que positivamente no Peru (HR=0,40; IC 95 por cento :0,19-0,83). Conclusão: O balanço da tendência do AME na ALC é positivo, embora não uniforme ao longo das duas décadas analisadas. Os achados sinalizam a necessidade de intervenções para a promoção do AME que levem em consideração a localização geográfica das famílias e a qualidade prestada nos serviços de saúde / Introduction: Multiple and interactive protective effects of exclusive breastfeeding (EBF) in health and child survival justify recommendations for promoting universal practice. There are few studies that assess the tendency of the pattern of EBF between countries. Objective: To analyze the temporal change of the AME in five countries in Latin America and Caribbean (LAC) comparing data from 1990 and 2000 decades. Methods: The dissertation consists of a manuscript, which evaluated data from children aged 0 to 6 months in the samples of the Demographic Health Survey conducted research in Brazil, Colombia, Haiti, Peru and the Dominican Republic. Were estimated the prevalence of exclusive breastfeeding and its weighted annual rates of change, according to country and survey year. The duration of EBF was estimated using survival analysis Kaplan-Meier method, considering the current age of the child as the survival time and EBF as binary variable, concerning the state of practice at the time of the interview. The survival curves were constructed for each country, in every decade, and the comparison between them used the log-rank test. The median duration of breastfeeding was calculated for each independent variable and the relationship between these variables and weaning at six months was analyzed using Cox regression model. Results: The prevalence of EBF increased in four of the five countries studied, increasing the most remarkable years in Colombia (II per cent ) and Haiti (17 per cent ). The median duration of evolution showed two trends: growth with equity in Colombia and Haiti, and stagnation with unequal distribution among the population subgroups of the last decade in Brazil, Peru and the Dominican Republic. In the multiple model of regression variables and the demographic profile of use of health services were associated with duration of EBF. The residence in a rural area was the variable consistently associated negatively in Brazil (HR = 1.68, CI 95 per cent : 1,06-2,67) and Colombia (HR = 1.39, CI 95 per cent : 1,03-1,87), while positively in Peru (HR = 0.40, CI 95 per cent : 0,19-0,83). Conclusion: The balance of the trend of EBF in LAC is positive, though not uniform throughout the two decades analyzed. The findings suggest the need for interventions for the promotion of exclusive breastfeeding taking into account the geographical location of families and provided quality health services

O modelo semiparamétrico de Cox é frequentemente utilizado na modelagem de dados de sobrevivência, pois é um modelo muito flexível e permite avaliar o efeito das covariáveis sobre a taxa de falha. Uma das principais vantagens é a fácil interpretação, de modo que a razão de riscos de dois indivíduos não varia ao longo do tempo. No entanto, em algumas situações a proporcionalidade dos riscos para uma dada covariável pode não ser válida e, este caso, uma abordagem que não dependa de tal suposição é necessária. Nesta tese, propomos um modelo tipo Cox em que o efeito da covariável e a função de risco basal são representadas via bases de Fourier e ondaletas de Haar clássicas e deformadas. Propomos também um procedimento de predição da função de sobrevivência para um paciente específico. Estudos de simulações e aplicações a dados reais sugerem que nosso método pode ser uma ferramenta valiosa em situações práticas em que o efeito da covariável é dependente do tempo. Por meio destes estudos, fazemos comparações entre as duas abordagens propostas, e comparações com outra já conhecida na literatura, onde verificamos resultados satisfatórios. / The semiparametric Cox model is often considered when modeling survival data. It is very flexible, allowing for the evaluation of covariates effects. One of its main advantages is the easy of interpretation, as long as the rate of the hazards for two individuals does not vary over time. However, this proportionality of the hazards may not be true in some practical situations and, in this case, an approach not relying on such assumption is needed. In this thesis we propose a Cox-type model that allows for time-varying covariate effects, for which the baseline hazard is based on Fourier series and wavelets on a time-frequency representation. We derive a prediction method for the survival of future patients with any specific set of covariates. Simulations and an application to a real data set suggest that our method may be a valuable tool to model data in practical situations where covariate effects vary over time. Through these studies, we make comparisons between the two approaches proposed here and comparisons with other already known in the literature, where we verify satisfactory results.

Introdução: O câncer de orofaringe representa 10 a 12 % entre todos os tumores malignos do trato aero digestivo superior com incidência crescente nos Estados Unidos e Europa. O Papillomavírus humano (HPV) está associado aos tumores de orofaringe em até 63%, promovendo uma evolução e prognóstico melhor. Objetivo: Descrever a prevalência do HPV em carcinomas de células escamosas de orofaringe tratados por cirurgia. Analisar a associação entre a presença do HPV e as características demográficas, clínicas, patológicas e terapêuticas. Avaliar a importância da presença do HPV na sobrevida livre de doença e sobrevida global. Método: Pesquisamos a presença do Papillomavirus humano, por PCR, no anátomo patológico. A descrição da amostra foi realizada através de média, frequência absoluta e relativa. Foi estimada a prevalência do HPV e seu respectivo intervalo de 95% de confiança. A análise da associação entre a presença de HPV e as características demográficas, clínicas e patológicas, foi feita pelo teste de associação pelo quiquadrado. A análise da sobrevida livre de doença e sobrevida global foi feita pelo estimador produto limite de Kaplan-Meier e modelos de risco proporcionais de Cox. Resultados: Os pacientes apresentavam idade variando de 34 a 78 anos, com uma média de 56,9 anos. Apenas 10 mulheres no estudo, totalizando com 76 homens. A maioria dos pacientes eram brancos (83,7%). Até 6 meses foi o tempo que a maioria dos pacientes apresentaram como início dos sintomas (69,0%). O sintoma mais comum foi a odinofagia (38,4%). A amígadala foi a localização mais frequente (69,8%). Quanto ao estádio clínico, o III e o IV apresentavam a maior frequência (71,4%). Forma realizadas cirurgias amplas como as bucofaringectomias em 76 pacientes (88,4%). O esvaziamento cervical ipsilateral foi realizado em 81 pacientes (94,2%) e no contralateral em apenas 21 (24,4%). A prevalência do HPV foi de 57%, e o tipo mais comum foi o 16, em 83,6%. A única associação estatisticamente significativa entre as variáveis do estudo com o HPV, foi o tabagismo, onde todos os não fumantes apresentavam HPV. As taxas de sobrevida livre de doença foram 73,9%, 65,9 e 57,9% respectivamente para 12, 24 e 60 meses. Houve diferença estatisticamente significativa com piores taxas, para idade menor que 55 anos e margens comprometidas. A presença do HPV não influenciou a sobrevida livre de doença, nem a sobrevida global. As taxas de sobrevida global foram 75,6%, 54,7% e 43,0%, respectivamente aos 12, 24 e 60 meses. Houveram piores taxas para o paciente etilista e com recidiva.Conclusão:A presença do HPV não se mostrou importante, como fator prognóstico, nessa série cirúrgica se o paciente for etilista e ou tabagista / Introduction:Oropharynx cancer is considered to enact approximately 10 to 12% of the cases among all malignant tumors from the upper aero digestive tract showing significant growth in its frequency rate in The United States and Europe. Human papillomavirus (HPV) is associated to oropharynx cancer in up to 63% of the cases, promoting better evolution and prognostic.Objective:Describe the prevalence of the HPV in oropharynx squamous cells carcinoma submitted to surgery. Investigate the association between HPV presence and the demographic, clinical, pathologic and therapeutic features. Estimate the importance of the HPV existence on the diseasefree survival and overall survival. Material andMethods: The existence of Human papillomavirus was studied through the use of PCR. The sample account was conducted through average, absolute and relative frequency. It has been estimated the prevalence of HPV and its corresponding 95% confidence interval. The association analysis between the presence of HPV and the demographic, clinical and pathological features was completed by the Qui-square association test. The disease-free survival timeline and the overall survival were estimated using the product limit estimator Kaplan-Meier and Cox proportional hazards model. Results: The studied patients were aged between 34 and 78, showing an average of 56.9 years of age. There were only 10 women in the study, thus presenting 76 men. Most of the patients were white (83.7%). It has been ascertained that 69.0% of the patients presented the symptoms onset up to the sixth month of the disease. The most common symptom among 38.4% of the cases was odinophagy. In regards to the tumor location 69.8% were found in the amygdala.Clinical stagings III and IV were found to be the ones with greater representation among patients (71.4%). Extensive surgeries such as bucopharyngectomy were performed in 76 patients (88.4%). In order to treat ipsilateral neck 81 patients underwent neck dissection (94.2%). Contralateral neck dissection was applied in 21 patients (24.4%). The prevalence of HPV was of 57%, and the most common type was 16, present in 83.6% of the cases. It was possible to notice smoking as the only statistically significant association, which showed all nonsmoking having HPV. The disease-free survival rates were of 73.9%, 65.9% and 57.9% to 12, 24 and 60 months respectively. The study has shown significant statistical difference with worse rates, to the ones under 55 years of age and presenting compromised margins. HPV presence did not influence the disease-free survival timeline, or the overall survival. The overall survival rates were of 75.6%, 54.7% and 43.0% to 12, 24 and 60 months respectively. Worse rates were found in alcoholic patients as well as in relapse cases. Conclusion: In these surgical series, HPV existence was not identified as an important prognosis factor when considering smokers and/or alcoholic patients

Many breast cancer diagnoses and second cancers are associated with BRCA gene mutations. Early detection of cancer is necessary to improve health outcomes, particularly with second cancers. Little is known about the influence of risk factors on time to diagnosis of second primary cancers after diagnosis with BRCA-related breast cancer. The purpose of this cohort study was to examine the risk of diagnosis of second primary cancers among women diagnosed with breast cancer after adjusting for BRCA status, age, and ethnicity. The study was guided by the empirical evidence supporting the mechanism of action in the mutation of BRCA leading to the development of cancer. Composite endpoint was used to define second primary cancer occurrences, and Kaplan-Meier survival curves were used to compare the median time-to-event among comparison groups and BRCA gene mutation status. Cox proportional hazards was used to examine the relationships between age at diagnosis, ethnicity, BRCA gene mutation status, and diagnosis of a second primary cancer. The overall median time to event for diagnosis of second primary cancers was 14 years. The hazard ratios for BRCA2 = 1.47, 95% CI [1.03 - 2.11], White = 1.511, 95% CI [1.18 - 1.94], and American Indian/Hawaiian = 1.424, 95% CI [1.12 -1.81] showing positive significant associations between BRCA2 mutation status and risk of diagnosis of second primary colorectal, endometrial, cervical, kidney, thyroid, and bladder cancers. Data on risk factors for development of second cancers would allow for identification of appropriate and timely screening procedures, determining the best course of action for prevention and treatment, and improving quality of life among breast cancer survivors.

成比例危險迴歸模式常被用於分析存活資料，Weibull模式更是其中惟一兼具加速失敗特性者。本論文將利用兩種分析方法，以研究任意設限及截斷資料的Weibull迴歸模式。第一種方法是利用最大概似估計法求算設限及截斷資料下的參數估計值（MLE），第二種方法則是對左設限及區間設限分別以所在區間之中點代入，稱其為中點估計法，再求算模式中的參數估計值（MDE）。並對此兩種估計方法進行比較。模擬結果顯示，相當地大樣本之下，最大概似估計法在許多情況均優於中點估計法；而在樣本少、危險率為平穩或接近平穩且區間設限比率約為0.5時，中點估計法是可被推薦的。而且，本論文亦提出對設限及截斷資料的Weibull模式之適合度檢驗程序。 / The proportional hazards regression model is most commonly used model for lifetime data. The Weibull model is the only parametric model which has both a proportional hazards representation and an accelerated failure-time representation. This paper studies the use of a Weibull-based proportional hazards regression model when any censored and truncated data are observed. Two alternative methods of analysis are considered. First, the maximum likelihood estimates（MLEs） of parameters are computed for the observed censoring and truncation pattern. Second, the estimates where midpoints are substituted for left- and interval-censored data（midpoint estimation, MDE）are computed. Then, MLEs are compared with MDEs. Simulation studies indicate that for relative large samples there are many instances when the MLE is superior to the MDE. For small samples where the hazard rate is flat or nearly so, and the percentage of interval-censored data is nearly half of samples, the MDE is adequate. Also, an evaluation of the adequacy of the Weibull model for any censored and truncated data is proposed.

In survival analysis interest often lies in the relationship between the survival function and a certain number of covariates. It usually happens that for some individuals we cannot observe the event of interest, due to the presence of right censoring and/or left truncation. A typical example is given by a retrospective medical study, in which one is interested in the time interval between birth and death due to a certain disease. Patients who die of the disease at early age will rarely have entered the study before death and are therefore left truncated. On the other hand, for patients who are alive at the end of the study, only a lower bound of the true survival time is known and these patients are hence right censored. In the case of censored and/or truncated responses, lots of models exist in the literature that describe the relationship between the survival function and the covariates (proportional hazards model or Cox model, log-logistic model, accelerated failure time model, additive risks model, etc.). In these models, the regression coefficients are usually supposed to be constant over time. In practice, the structure of the data might however be more complex, and it might therefore be better to consider coefficients that can vary over time. In the previous examples, certain covariates (e.g. age at diagnosis, type of surgery, extension of tumor, etc.) can have a relatively high impact on early age survival, but a lower influence at higher age. This motivated a number of authors to extend the Cox model to allow for time-dependent coefficients or consider other type of time-dependent coefficients models like the additive hazards model. In practice it is of great use to have at hand a method to check the validity of the above mentioned models. First we consider a very general model, which includes as special cases the above mentioned models (Cox model, additive model, log-logistic model, linear transformation models, etc.) with time-dependent coefficients and study the parameter estimation by means of a least squares approach. The response is allowed to be subject to right censoring and/or left truncation. Secondly we propose an omnibus goodness-of-fit test that will test if the general time-dependent model considered above fits the data. A bootstrap version, to approximate the critical values of the test is also proposed. In this dissertation, for each proposed method, the finite sample performance is evaluated in a simulation study and then applied to a real data set.

The focus of this thesis was the development of failure prognosis methods (prognostics) in rotating machinery with use of multiple sensors digital signal processing and machine learning techniques. The motivation stems from the void in literature concerning prognostics in meshing gearboxes. Moreover, there are several but inconclusive works regarding bearing prognosis. Few research groups have studied multi-hour fatigue gear experiments and this was one of the contributions of this thesis. Moreover, the study expanded beyond the sheer application of vibration monitoring with the addition of an Oil Debris Monitoring probe (ODM) as well as Acoustic emission (AE). The method of AE monitoring is, once again, proposed as a robust technique for failure prognosis being better correlated with gear pitting level compared to the classic vibration monitoring technique. Moreover, judging from ODM recordings the gear pitting comprises of two phases i) a linear phase, with an almost constant pitting rate and ii) a very short non linear phase where the pitting rate increases exponentially, an explicit indication of a critical failure. Multi-hour gear experiments that are close to real scale applications are very demanding in time as well as in invested capital. To bypass this shortfall a gear failure like simulation is proposed. The simulation framework is based on real life experiments and is applied to assess a number of data-driven Remaining Useful Life (RUL) estimation techniques namely i) Proportional Hazards Μodel (PHM), ii) ε- Support Vector Regression ε-SVR and iii) Exponential extrapolation based on bootstrap sampling. In the current thesis a feature extraction scheme for prognosis is proposed and assessed based on time domain, frequency domain statistical features and Wavelet Packet (WP) energy derived from AE and vibration recordings. ICA is proposed as a preferable fusion technique for gear failure prognostics. Application of ICA for feature fusion provided a clear improvement regarding the earlier presented bootstrap extrapolation technique. Bearings are also taken into account since they are closely connected to gearboxes. In the current thesis a wavelet denoising method is proposed for bearing vibration recordings aiming to the improvement of the diagnostic and prognostic potential of vibration. Finally the importance of data fusion is highlighted in the case of bearings. It is observed that a feature extraction scheme can generalize the application of prognostics, even in cases where RMS may yield no important degradation trend. / Η παρούσα εργασία εστιάζεται στην ανάπτυξη μεθοδολογιών πρόβλεψης τελικής αστοχίας σε περιστρεφόμενα συστήματα με χρήση πολλαπλών αισθητήρων και μεθόδων μηχανικής μάθησης και επεξεργασίας σήματος. Το κίνητρο προήλθε από το κενό που υπάρχει στη βιβλιογραφία όσον αφορά την προγνωστική σε κιβώτια ταχυτήτων. Η προγνωστική σε έδρανα έχει μεν μελετηθεί αλλά σε μικρό βαθμό και η παρούσα εργασία έρχεται να συμβάλλει και σε αυτό τον τομέα. Στα πλαίσια αυτής της εργασίας εκπονήθηκε ένας αριθμός πειραμάτων κόπωσης κιβωτίων ταχυτήτων. Η μελέτη επεκτάθηκε πέραν της παρακολούθησης κατάστασης με τη μέθοδο των κραδασμών και συγκεκριμένα μελετήθηκαν καταγραφές σωματιδίων σιδήρου στο λιπαντικό (ODM) καθώς και Ακουστική Εκπομπής (AE). Η μέθοδος ΑΕ ευρέθη πιο στενά συσχετισμένη με τη σταδιακή υποβάθμιση της ακεραιότητας του κιβωτίου ταχυτήτων σε σχέση με τις καταγραφές κραδασμών. Επίσης με βάση τις καταγραφές του αισθητήρα σωματιδίων σιδήρου διακρίθηκαν δύο στάδια  υποβάθμισης i) μια γραμμική περιοχή με σχεδόν σταθερό ρυθμό απελευθέρωσης υλικού από την επιφάνεια των δοντιών και ii) μια σύντομη αλλά έντονα μη γραμμική αύξηση στο ρυθμό αυτό πολύ κοντά στο τέλος της λειτουργίας του κιβωτίου. Tα πολύωρα πειράματα κόπωσης σε γρανάζια είναι πολύ απαιτητικά. Για να παρακαμφθεί αυτή η δυσκολία αναπτύχθηκε ένα φαινομενολογικό μοντέλο για αναπαραγωγή χρονοσειρών που ομοιάζουν σε καταγραφές γραναζιών σε κόπωση. Το μοντέλο αυτό στηρίχθηκε σε πραγματικά πειράματα κόπωσης. Έτσι έγινε δυνατό να εξεταστούν και να συγκριθούν ένας αριθμός μεθοδολογιών εκτίμησης εναπομένουσας ζωής και συγκεκριμένα i) Proportional Hazards Model (PHM), ii) ε- Support Vector Regression ε-SVR και iii) Exponential extrapolation βασισμένο σε μια διαδικασία bootstrap sampling. Στην παρούσα μελέτη προτείνεται ένα σύνολο παραμέτρων προερχόμενο από το πεδίο της συχνότητας, του χρόνου και κυματοπακέτων. Αυτό, συνδυαζόμενο με μια διαδικασία σύμπτυξης δεδομένων (ανάλυση σε πρωταρχικές και ανεξάρτητες συνιστώσες) αξιοποιείται για πρόγνωση σε γρανάζια σε κόπωση. Η τεχνική ανεξάρτητων συνιστωσών προτείνεται σαν προτιμότερη από τη σκοπιά της προγνωστικής καθώς βελτιώνει την εκτίμηση της εναπομένουσας ζωής. Η εργασία επεκτάθηκε και σε έδρανα κύλισης. Προτάθηκε μια διαδικασία wavelet denoising η οποία ενισχύει τόσο τη διαγνωστική όσο και την προγνωστική δυνατότητα του αισθητήρα κραδασμών. Τέλος, η σημασία της εξαγωγής παραμέτρων υπογραμμίζεται και στην περίπτωση της προγνωστικής σε έδρανα. Συνδυάζοντας πολλαπλές παραμέτρους και αισθητήρες κραδασμών μαζί με ένα μοντέλο ε-SVR παρέχεται ένα ολοκληρωμένο μοντέλο πιθανοτικής εκτίμησης εναπομένουσας ζωής σε έδρανα κύλισης ακόμα και σε περιπτώσεις που η τιμή RMS των κραδασμών δεν παρέχει πληροφορία.

Darbo metu buvo išnagrinėta įvairių faktorių (kovariančių) įtaka reumatoidiniu artritu sergančio 531 ligonio mirtingumui. Buvo taikomas vienas iš regresinių išgyvenamumo modelių – Cox’o modelis. Iš minėtos 531 ligonio imties mirę buvo 32 ligoniai. Iš pradžių buvo tiriama ligonių imtis laiko nuo ligos pradžios aspektu. Šiuo atveju prognozuojantys veiksniai buvo amžius, kada liga buvo diagnozuota (AMZDGN), lytis (LYTKOD), gydymas Metotreksatu (GYD_MTX) ir gydymas Azatriopinu/Imuranu (AZA_IMUR). Vėliau, tiriant ligonių mirtingumą kaip amžiaus funkciją, nustatyti svarbiausi lemiantys veiksniai buvo šie: ligonių lytis (LYTKOD) ir gydymas Azatriopinu/Imuranu (AZA_IMUR). Gauti rezultatai, t.y. ligonių išgyvenamumą lemiančios kovariantės (veiksniai), beveik visiškai sutampa su gydytojų nurodytais. Tai dar kartą patvirtina matematinių statistinių modelių, šiuo atveju nagrinėjamo Cox‘o modelio, taikymo realiame gyvenime, svarbą. Kitai duomenų imčiai, t.y. vėžiu sergančių ligonių duomenų aibei, buvo taikomas Persikertančių mirimų intensyvumų (SCE) modelis, t.y. tikrinama Cox‘o modelio adekvatumo duomenims hipotezė. Hipotezė buvo atmesta, nes minėtiems duomenims Cox‘o modelis negalioja. Pagrindinis darbo rezultatas yra šis: gautas kriterijus Cox‘o modelio adekvatumui tikrinti, naudojant nupjautus iš kairės ir cenzūruotus iš dešinės duomenis, sudarytos programos kriterijui realizuoti. Reumatoidinio artrito ligonių duomenų aibei, t.y. nupjautiems iš kairės ir cenzūruotiems iš dešinės... [toliau žr. visą tekstą] / In this work the Cox proportional hazards model was applied to investigate the influence of various factors (covariates) to mortality of rheumatoid arthritis patients of Vilnius. In the first case, the sample of 531 patients was analysed. Analysing survival of patients of the sample as function of time from the beginnig of the disease, the prognostic factors were LYTKOD (the sex of patients), AMZDGN (patients‘ age, when the rheumatoid arthritis was diagnosed), GYD_MTX (treatment with metotrexat) and AZA_IMUR (treatment with Azatriopin/Imuran). When survival was analysed as function of age then the prognostic factor were LYTKOD (the sex of patients) and AZA_IMUR (treatment with Azatriopin/Imuran). The results are almost identical to those, which doctors suggested. This fact confirms the importance of using mathematical statistical models to solve the problems of the real life. In this case, the importance of using the Cox model. On the other hand, Simple cross-effects (SCE) model was aplied for the sample of canser patients. In the case of this model the hypothesis of Cox model fiting for canser patients‘ data was rejected. The most important result of this work is that the criterion of Cox model fitting to left truncated and right censored data was constructed. Also a program of SAS for the criterion was created. The the hypothesis of Cox model fiting for the rheumatoid arthritis patients wasn‘t rejected, because Cox model fit for these data.

Many epidemiological studies assess the effects of time-dependent exposures, where both the exposure status and its intensity vary over time. The analysis of such studies poses the challenge of modelling the association between complex time-dependent drug exposure and the risk, especially given the uncertainty about the etiological relevance of doses taken in different time periods. / To address this challenge, I developed a flexible method for modelling cumulative effects of time-varying exposures, weighted by recency, represented by time-dependent covariates in the Cox proportional hazards model. The function that assigns weights to doses taken in the past is estimated using cubic regression splines. Models with different number of knots and constraints are estimated. Bootstrap techniques are used to obtain pointwise confidence bands around the weight functions, accounting for both the sampling variation of the regression coefficients, and the uncertainty at the model selection stage, i.e. the additional variance due to a posteriori selection of the number of knots. / To assess the method in simulations, I had to develop and validate a novel algorithm to generate event times conditional on time-dependent covariates and compared it with the algorithms available in the literature. The proposed algorithm extends a previously proposed permutational algorithm to include a rejection sampler. While all the algorithms generated data sets that, once analyzed, provided virtually unbiased estimates with comparable variances, the algorithm that I proposed reduced the computational time by more than 50 per cent relative to alternative methods. I used simulations to systematically investigate the properties of the weighted cumulative dose method. Six different weight functions were considered. Simulations showed that in most situations, the proposed method was able to capture the shape of the true weight functions and to produce estimates of the magnitude of the exposure effect on the risk that were close to those used to generate the data. I finally illustrated the use of the weighted cumulative dose modelling by reassessing the association between the use of selected benzodiazepines and fall-related injuries, using administrative data on a cohort of elderly who initiated their use of benzodiazepines between 1990 and 2004.