Modelling and Analysis of Recurrent Event Data with Multiple Causes

This thesis Entitled “modelling and analysis of recurrent event data with multiple causes.Survival data is a term used for describing data that measures the time to occurrence of an event.In survival studies, the time to occurrence of an event is generally referred to as lifetime.Recurrent event data are commonly encountered in longitudinal studies when individuals are followed to observe the repeated occurrences of certain events. In many practical situations, individuals under study are exposed to the failure due to more than one causes and the eventual failure can be attributed to exactly one of these causes.The proposed model was useful in real life situations to study the effect of covariates on recurrences of certain events due to different causes.In Chapter 3, an additive hazards model for gap time distributions of recurrent event data with multiple causes was introduced. The parameter estimation and asymptotic properties were discussed .In Chapter 4, a shared frailty model for the analysis of bivariate competing risks data was presented and the estimation procedures for shared gamma frailty model, without covariates and with covariates, using EM algorithm were discussed. In Chapter 6, two nonparametric estimators for bivariate survivor function of paired recurrent event data were developed. The asymptotic properties of the estimators were studied. The proposed estimators were applied to a real life data set. Simulation studies were carried out to find the efficiency of the proposed estimators.

Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

Destructive weighted Poisson cure rate models

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow a compound weighted Poisson distribution. This model is more flexible in terms of dispersion than the promotion time cure model. Moreover, it gives an interesting and realistic interpretation of the biological mechanism of the occurrence of event of interest as it includes a destructive process of the initial risk factors in a competitive scenario. In other words, what is recorded is only from the undamaged portion of the original number of risk factors.

COM-Poisson cure rate survival models and an application to a cutaneous melanoma data

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow the Conway-Maxwell Poisson distribution. This model includes as special cases some of the well-known cure rate models discussed in the literature. Next, we discuss the maximum likelihood estimation of the parameters of this cure rate survival model. Finally, we illustrate the usefulness of this model by applying it to a real cutaneous melanoma data. (C) 2009 Elsevier B.V. All rights reserved.

Mixture Cure Survival Models with Dependent Censoring

A number of authors have studies the mixture survival model to analyze survival data with nonnegligible cure fractions. A key assumption made by these authors is the independence between the survival time and the censoring time. To our knowledge, no one has studies the mixture cure model in the presence of dependent censoring. To account for such dependence, we propose a more general cure model which allows for dependent censoring. In particular, we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time using a class of Archimedean copula models. Within this framework, we consider the parameter estimation, the cure detection, and the two-sample comparison of latency distribution in the presence of dependent censoring when a proportion of patients is deemed cured. Large sample results using the martingale theory are obtained. We applied the proposed methodologies to the SEER prostate cancer data.

Influence of patient age and implantation technique on the probability of re-replacement of the homograft aortic valve

Background and aim of the study: Results of valve re-replacement (reoperation) in 898 patients undergoing aortic valve replacement with cryopreserved homograft valves between 1975 and 1998 are reported. The study aim was to provide estimates of unconditional probability of valve reoperation and cumulative incidence function (actual risk) of reoperation. Methods: Valves were implanted by subcoronary insertion (n = 500), inclusion cylinder (n = 46), and aortic root replacement (n = 352). Probability of reoperation was estimated by adopting a mixture model framework within which estimates were adjusted for two risk factors: patient age at initial replacement, and implantation technique. Results: For a patient aged 50 years, the probability of reoperation in his/her lifetime was estimated as 44% and 56% for non-root and root replacement techniques, respectively. For a patient aged 70 years, estimated probability of reoperation was 16% and 25%, respectively. Given that a reoperation is required, patients with non-root replacement have a higher hazard rate than those with root replacement (hazards ratio = 1.4), indicating that non-root replacement patients tend to undergo reoperation earlier before death than root replacement patients. Conclusion: Younger patient age and root versus non-root replacement are risk factors for reoperation. Valve durability is much less in younger patients, while root replacement patients appear more likely to live longer and hence are more likely to require reoperation.

Influence of noninjecting and injecting drug use on mortality, retention in the cohort, and antiretroviral therapy, in participants in the Swiss HIV Cohort Study.

OBJECTIVES: We studied the influence of noninjecting and injecting drug use on mortality, dropout rate, and the course of antiretroviral therapy (ART), in the Swiss HIV Cohort Study (SHCS). METHODS: Cohort participants, registered prior to April 2007 and with at least one drug use questionnaire completed until May 2013, were categorized according to their self-reported drug use behaviour. The probabilities of death and dropout were separately analysed using multivariable competing risks proportional hazards regression models with mutual correction for the other endpoint. Furthermore, we describe the influence of drug use on the course of ART. RESULTS: A total of 6529 participants (including 31% women) were followed during 31 215 person-years; 5.1% participants died; 10.5% were lost to follow-up. Among persons with homosexual or heterosexual HIV transmission, noninjecting drug use was associated with higher all-cause mortality [subhazard rate (SHR) 1.73; 95% confidence interval (CI) 1.07-2.83], compared with no drug use. Also, mortality was increased among former injecting drug users (IDUs) who reported noninjecting drug use (SHR 2.34; 95% CI 1.49-3.69). Noninjecting drug use was associated with higher dropout rates. The mean proportion of time with suppressed viral replication was 82.2% in all participants, irrespective of ART status, and 91.2% in those on ART. Drug use lowered adherence, and increased rates of ART change and ART interruptions. Virological failure on ART was more frequent in participants who reported concomitant drug injections while on opiate substitution, and in current IDUs, but not among noninjecting drug users. CONCLUSIONS: Noninjecting drug use and injecting drug use are modifiable risks for death, and they lower retention in a cohort and complicate ART.

How binding are legal limits? Transitions from temporary to permanent work in Spain

This paper studies the duration pattern of xed-term contracts and the determinantsof their conversion into permanent ones in Spain, where the share of xed-termemployment is the highest in Europe. We estimate a duration model for temporaryemployment, with competing risks of terminating into permanent employment versusalternative states, and exible duration dependence. We nd that conversion rates aregenerally below 10%. Our estimated conversion rates roughly increase with tenure,with a pronounced spike at the legal limit, when there is no legal way to retain theworker on a temporary contract. We argue that estimated di¤erences in conversionrates across categories of workers can stem from di¤erences in worker outside optionsand thus the power to credibly threat to quit temporary jobs.

Risks in R&D Collaboration between Small and Large Firms

The main aim of this thesis was to find out what kinds of risks arise from collabo-ration in R&D between small and large firms. The suitability and gain of some buyer/supplier risk frameworks in examining of R&D collaboration has been in-vestigated. A risk model has been based on the buyer/supplier risks models found in the literature. Its applicability has been tested empirically by means of theme interviews with firm representatives. The risk classification framework received some confirmation. But the study also showed that the theoretical framework was not completely adequate, as a new risk class arose from communication. Collaboration causes risks, and these risks should be taken into account when R&D collaboration is planned. The advantage of risk examination is the possibility to decrease failures and losses, and to in-crease possibilities for success and economical benefits. This study should be used as a managerial analysis tool in trying to understand the form and concept of risk in risk expectancy.

The role of adjuvant chemotherapy for lymph node-positive upper tract urothelial carcinoma following radical nephroureterectomy: a retrospective study.

OBJECTIVE: To evaluate the effect of adjuvant chemotherapy (AC) on mortality after radical nephroureterectomy (RNU) for upper tract urothelial carcinoma (UTUC) with positive lymph nodes (LNs) and to identify patient subgroups that are most likely to benefit from AC. PATIENTS AND METHODS: We retrospectively analysed data of 263 patients with LN-positive UTUC, who underwent full surgical resection. In all, 107 patients (41%) received three to six cycles of AC, while 156 (59.3%) were treated with RNU alone. UTUC-related mortality was evaluated using competing-risks regression models. RESULTS: In all patients (Tall N+), administration of AC had no significant impact on UTUC-related mortality on univariable (P = 0.49) and multivariable (P = 0.11) analysis. Further stratified analyses showed that only N+ patients with pT3-4 disease benefited from AC. In this subgroup, AC reduced UTUC-related mortality by 34% (P = 0.019). The absolute difference in mortality was 10% after the first year and increased to 23% after 5 years. On multivariable analysis, administration of AC was associated with significantly reduced UTUC-related mortality (subhazard ratio 0.67, P = 0.022). Limitations of this study are the retrospective non-randomised design, selection bias, absence of a central pathological review and different AC protocols. CONCLUSIONS: AC seems to reduce mortality in patients with pT3-4 LN-positive UTUC after RNU. This subgroup of LN-positive patients could serve as target population for an AC prospective randomised trial.

Sector-Specific on-the-Job Training: Evidence from U.S. Data.

Using data from the National Longitudinal Survey of Youth (NLSY), we re-examine the effect of formal on-the-job training on mobility patterns of young American workers. By employing parametric duration models, we evaluate the economic impact of training on productive time with an employer. Confirming previous studies, we find a positive and statistically significant impact of formal on-the-job training on tenure with the employer providing the training. However, the expected net duration of the time spent in the training program is generally not significantly increased. We proceed to document and analyze intra-sectoral and cross-sectoral mobility patterns in order to infer whether training provides firm-specific, industry-specific, or general human capital. The econometric analysis rejects a sequential model of job separation in favor of a competing risks specification. We find significant evidence for the industry-specificity of training. The probability of sectoral mobility upon job separation decreases with training received in the current industry, whether with the last employer or previous employers, and employment attachment increases with on-the-job training. These results are robust to a number of variations on the base model.

La néphrectomie partielle chez les patients atteints du cancer du rein de stade T1b

Objectif : La néphrectomie partielle est reconnue actuellement comme le traitement de choix des tumeurs de moins de 7 cm. Le but de notre étude est de comparer le taux de mortalité lié au cancer du rein suite au traitement par néphrectomie partielle ou radicale chez les patients de stade T1b, de présenter la tendance temporelle du taux d'intervention par néphrectomie partielle pour les tumeurs de stade T1b et d’identifier les facteurs sociodémographiques et tumoraux qui influencent le choix thérapeutique entre les deux types de traitement chirurgical. Méthode : Il s’agit d’une étude épidémiologique de type rétrospective. La population de patients provient de la base de donnée SEER (Surveillance, Epidemiology, and End Results) qui regroupe une grande proportion de la population nord-américaine. Dans notre étude, nous avons utilisé l’analyse par régression logistique pour identifier les facteurs sociodémographiques associés à l'intervention par néphrectomie partielle. Dans un deuxième temps, nous avons comparé la mortalité liée au cancer entre les deux options chirurgicales, après association par score de tendance pour diminuer les différences de base entre les deux populations. Nos critères étaient l’âge, la race, le sexe, l’état civil, le niveau socioéconomique, la taille tumorale, le grade nucléaire, l’histologie et la localité du centre hospitalier. L’analyse des données a été faite par le logiciel SPSS. Résultats : Le taux d'interventions par néphrectomie partielle a augmenté de 1,2% en 1988 à 15,9% en 2008 (p <0,001). Les jeunes patients, les tumeurs de petite taille, les patients de race noire, ainsi que les hommes sont plus susceptibles d'être traités par néphrectomie partielle (tous les p < 0,002). Parmi le groupe ciblé, le taux de mortalité lié au cancer à 5 ans et à 10 ans est de 4,4 et de 6,1% pour les néphrectomies partielles et de 6,0 et 10,4% pour les néphrectomies radicales (p = 0,03). Après ajustement de toutes les autres variables, les analyses de régression montrent que le choix entre les deux types de néphrectomie n’est pas associé à la mortalité lié au cancer (hazard ratio: 0,89, p = 0,5). Conclusion : Malgré un contrôle oncologique équivalent, le taux d'intervention par néphrectomie partielle chez les patients ayant un cancer du rein T1b est faible en comparaison à la néphrectomie radicale.

Reliability Nonparametric Bayesian Estimation in Parallel Systems

Relevant results for (sub-)distribution functions related to parallel systems are discussed. The reverse hazard rate is defined using the product integral. Consequently, the restriction of absolute continuity for the involved distributions can be relaxed. The only restriction is that the sets of discontinuity points of the parallel distributions have to be disjointed. Nonparametric Bayesian estimators of all survival (sub-)distribution functions are derived. Dual to the series systems that use minimum life times as observations, the parallel systems record the maximum life times. Dirichlet multivariate processes forming a class of prior distributions are considered for the nonparametric Bayesian estimation of the component distribution functions, and the system reliability. For illustration, two striking numerical examples are presented.

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis - latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.