Outlier effects on robust joint modelling of longitudinal and survival data

Robust joint modelling is an emerging field of research. Through the advancements in electronic patient healthcare records, the popularly of joint modelling approaches has grown rapidly in recent years providing simultaneous analysis of longitudinal and survival data. This research advances previous work through the development of a novel robust joint modelling methodology for one of the most common types of standard joint models, that which links a linear mixed model with a Cox proportional hazards model. Through t-distributional assumptions, longitudinal outliers are accommodated with their detrimental impact being down weighed and thus providing more efficient and reliable estimates. The robust joint modelling technique and its major benefits are showcased through the analysis of Northern Irish end stage renal disease patients. With an ageing population and growing prevalence of chronic kidney disease within the United Kingdom, there is a pressing demand to investigate the detrimental relationship between the changing haemoglobin levels of haemodialysis patients and their survival. As outliers within the NI renal data were found to have significantly worse survival, identification of outlying individuals through robust joint modelling may aid nephrologists to improve patient's survival. A simulation study was also undertaken to explore the difference between robust and standard joint models in the presence of increasing proportions and extremity of longitudinal outliers. More efficient and reliable estimates were obtained by robust joint models with increasing contrast between the robust and standard joint models when a greater proportion of more extreme outliers are present. Through illustration of the gains in efficiency and reliability of parameters when outliers exist, the potential of robust joint modelling is evident. The research presented in this thesis highlights the benefits and stresses the need to utilise a more robust approach to joint modelling in the presence of longitudinal outliers.

Application of Mixture Models to Survival Data

Survival models are being widely applied to the engineering field to model time-to-event data once censored data is here a common issue. Using parametric models or not, for the case of heterogeneous data, they may not always represent a good fit. The present study relays on critical pumps survival data where traditional parametric regression might be improved in order to obtain better approaches. Considering censored data and using an empiric method to split the data into two subgroups to give the possibility to fit separated models to our censored data, we’ve mixture two distinct distributions according a mixture-models approach. We have concluded that it is a good method to fit data that does not fit to a usual parametric distribution and achieve reliable parameters. A constant cumulative hazard rate policy was used as well to check optimum inspection times using the obtained model from the mixture-model, which could be a plus when comparing with the actual maintenance policies to check whether changes should be introduced or not.

Residuals for log-Burr XII regression models in survival analysis

In this paper, we compare three residuals to assess departures from the error assumptions as well as to detect outlying observations in log-Burr XII regression models with censored observations. These residuals can also be used for the log-logistic regression model, which is a special case of the log-Burr XII regression model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to the modified martingale-type residual in log-Burr XII regression models with censored data.

An EM-based Semi-Parametric Mixture Model Approach to the Regression Analysis of Competing-Risks Data

We consider a mixture model approach to the regression analysis of competing-risks data. Attention is focused on inference concerning the effects of factors on both the probability of occurrence and the hazard rate conditional on each of the failure types. These two quantities are specified in the mixture model using the logistic model and the proportional hazards model, respectively. We propose a semi-parametric mixture method to estimate the logistic and regression coefficients jointly, whereby the component-baseline hazard functions are completely unspecified. Estimation is based on maximum likelihood on the basis of the full likelihood, implemented via an expectation-conditional maximization (ECM) algorithm. Simulation studies are performed to compare the performance of the proposed semi-parametric method with a fully parametric mixture approach. The results show that when the component-baseline hazard is monotonic increasing, the semi-parametric and fully parametric mixture approaches are comparable for mildly and moderately censored samples. When the component-baseline hazard is not monotonic increasing, the semi-parametric method consistently provides less biased estimates than a fully parametric approach and is comparable in efficiency in the estimation of the parameters for all levels of censoring. The methods are illustrated using a real data set of prostate cancer patients treated with different dosages of the drug diethylstilbestrol. Copyright (C) 2003 John Wiley Sons, Ltd.

Liver morphology with emphasis on bile ducts changes and survival analysis in mice submitted to multiple Schistosoma mansoni infections and chemotherapy

In an attempt to be as close as possible to the infected and treated patients of the endemic areas of schistosomiasis (S. mansoni) and in order to achieve a long period of follow-up, mice were repeatedly infected with a low number of cercariae. Survival data and histological variables such as schistosomal granuloma, portal changes, hepatocellular necrosis, hepatocellular regeneration, schistosomotic pigment, periductal fibrosis and chiefly bile ducts changes were analysed in the infected treated and non treated mice. Oxamniquine chemotherapy in repeatedly infected mice prolonged survival significantly when compared to non-treated animals (chi-square 9.24, p = 0.0024), thus confirming previous results with a similar experimental model but with a shorter term follow-up. Furthermore, mortality decreased rapidly after treatment suggesting an abrupt reduction in the severity of hepatic lesions. A morphological and immunohistochemical study of the liver was carried out. Portal fibrosis, with a pattern resembling human Symmers fibrosis was present at a late phase in the infected animals. Bile duct lesions were quite close to those described in human Mansonian schistosomiasis. Schistosomal antigen was observed in one isolated altered bile duct cell. The pathogenesis of the bile duct changes and its relation to the parasite infection and/or their antigens are discussed.

Estimation of statistical cure from cancer using population-based data

Dissertação de mestrado em Estatística

Prolonged survival with valproic acid use in the EORTC/NCIC temozolomide trial for glioblastoma.

Objective: This analysis was performed to assess whether antiepileptic drugs (AEDs) modulate the effectiveness of temozolomide radiochemotherapy in patients with newly diagnosed glioblastoma.Methods: The European Organization for Research and Treatment of Cancer (EORTC) 26981-22981/National Cancer Institute of Canada (NCIC) CE.3 clinical trial database of radiotherapy (RT) with or without temozolomide (TMZ) for newly diagnosed glioblastoma was examined to assess the impact of the interaction between AED use and chemoradiotherapy on survival. Data were adjusted for known prognostic factors.Results: When treatment began, 175 patients (30.5%) were AED-free, 277 (48.3%) were taking any enzyme-inducing AED (EIAED) and 135 (23.4%) were taking any non-EIAED. Patients receiving valproic acid (VPA) only had more grade 3/4 thrombopenia and leukopenia than patients without an AED or patients taking an EIAED only. The overall survival (OS) of patients who were receiving an AED at baseline vs not receiving any AED was similar. Patients receiving VPA alone (97 [16.9%]) appeared to derive more survival benefit from TMZ/RT (hazard ratio [HR] 0.39, 95% confidence interval [CI] 0.24-0.63) than patients receiving an EIAED only (252 [44%]) (HR 0.69, 95% CI 0.53-0.90) or patients not receiving any AED (HR 0.67, 95% CI 0.49-0.93). Conclusions: VPA may be preferred over an EIAED in patients with glioblastoma who require an AED during TMZ-based chemoradiotherapy. Future studies are needed to determine whether VPA increases TMZ bioavailability or acts as an inhibitor of histone deacetylases and thereby sensitizes for radiochemotherapy in vivo.

Univariate Parametric Survival Analysis using GS-distributions

The GS-distribution is a family of distributions that provide an accurate representation of any unimodal univariate continuous distribution. In this contribution we explore the utility of this family as a general model in survival analysis. We show that the survival function based on the GS-distribution is able to provide a model for univariate survival data and that appropriate estimates can be obtained. We develop some hypotheses tests that can be used for checking the underlying survival model and for comparing the survival of different groups.

The role of molecular, clinical and socioeconomic factors in the long-term survival of axillary node negative breast cancer patients

The overall objective of this study was to investigate factors associated with long-term survival in axillary node negative (ANN) breast cancer patients. Clinical and biological factors included stage, histopathologic grade, p53 mutation, Her-2/neu amplification, estrogen receptor status (ER), progesterone receptor status (PR) and vascular invasion. Census derived socioeconomic (SES) indicators included median individual and household income, proportions of university educated individuals, housing type, "incidence" of low income and an indicator of living in an affluent neighbourhood. The effects of these measures on breast cancer-specific survival and competing cause survival were investigated. A cohort study examining survival among axillary node negative (ANN) breast cancer patients in the greater Toronto area commenced in 1 989. Patients were followed up until death, lost-to-follow up or study termination in 2004. Data were collected from several sources measuring patient demographics, clinical factors, treatment, recurrence of disease and survival. Census level SES data were collected using census geo-coding of patient addresses' at the time of diagnosis. Additional survival data were acquired from the Ontario Cancer Registry to enhance and extend the observation period of the study. Survival patterns were examined using KaplanMeier and life table procedures. Associations were examined using log-rank and Wilcoxon tests of univariate significance. Multivariate survival analyses were perfonned using Cox proportional hazards models. Analyses were stratified into less than and greater than 5 year survival periods to observe whether known markers of short-tenn survival were also associated with reductions in long-tenn survival among breast cancer patients. The 15 year survival probabilities in this cohort were: for breast cancerspecific survival 0.88, competing causes survival 0.89 and for overall survival 0.78. Estrogen receptor (ER) and progesterone receptor (PR) status (Hazard Ratio (HR) ERIPR- versus ER+/PR+, 8.15,95% CI, 4.74, 14.00), p53 mutation (HR, 3.88, 95% CI, 2.00, 7.53) and Her-2 amplification (HR, 2.66, 95% CI, 1.36, 5.19) were associated with significant reductions in short-tenn breast cancer-specific survival «5 years following diagnosis), however, not with long-term survival in univariate analyses. Stage, histopathologic grade and ERiPR status were the clinicallbiologieal factors that were associated with short-term breast cancer specific survival in multivariate results. Living in an affluent neighbourhood (top quintile of median household income compared to the rest of the population) was associated with the largest significant increase in long-tenn breast cancer-specific survival after adjustment for stage, histopathologic grade and treatment (HR, 0.36, 95% CI, 0.12, 0.89).

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.

The log-exponentiated Weibull regression model for interval-censored data

In interval-censored survival data, the event of interest is not observed exactly but is only known to occur within some time interval. Such data appear very frequently. In this paper, we are concerned only with parametric forms, and so a location-scale regression model based on the exponentiated Weibull distribution is proposed for modeling interval-censored data. We show that the proposed log-exponentiated Weibull regression model for interval-censored data represents a parametric family of models that include other regression models that are broadly used in lifetime data analysis. Assuming the use of interval-censored data, we employ a frequentist analysis, a jackknife estimator, a parametric bootstrap and a Bayesian analysis for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Furthermore, for different parameter settings, sample sizes and censoring percentages, various simulations are performed; in addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to a modified deviance residual in log-exponentiated Weibull regression models for interval-censored data. (C) 2009 Elsevier B.V. All rights reserved.

On the unification of long-term survival models

In this paper we extend the long-term survival model proposed by Chen et al. [Chen, M.-H., Ibrahim, J.G., Sinha, D., 1999. A new Bayesian model for survival data with a surviving fraction. journal of the American Statistical Association 94, 909-919] via the generating function of a real sequence introduced by Feller [Feller, W., 1968. An Introduction to Probability Theory and its Applications, third ed., vol. 1, Wiley, New York]. A direct consequence of this new formulation is the unification of the long-term survival models proposed by Berkson and Gage [Berkson, J., Gage, R.P., 1952. Survival cure for cancer patients following treatment. journal of the American Statistical Association 47, 501-515] and Chen et al. (see citation above). Also, we show that the long-term survival function formulated in this paper satisfies the proportional hazards property if, and only if, the number of competing causes related to the occurrence of an event of interest follows a Poisson distribution. Furthermore, a more flexible model than the one proposed by Yin and Ibrahim [Yin, G., Ibrahim, J.G., 2005. Cure rate models: A unified approach. The Canadian journal of Statistics 33, 559-570] is introduced and, motivated by Feller`s results, a very useful competing index is defined. (c) 2008 Elsevier B.V. All rights reserved.

Oviposition and survival in females of Procornitermes araujoi under laboratory conditions (Isoptera, Termitidae, Nasutitermitinae)

After an enormous swarming of Procornitermes araujoi when a great number of females were collected, we investigated the occurrence of parthenogenesis beyond oviposition and survival of these females under laboratory conditions. The groups of virgin females were faster in their first oviposition than females of male-female pairs, nevertheless their eggs never hatch. The survival data showed higher longevity in the group of three females when compared with groups of two and four females.