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.

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.

Análise de resíduos em modelos de tempo de falha acelerado com efeito aleatório

We present residual analysis techniques to assess the fit of correlated survival data by Accelerated Failure Time Models (AFTM) with random effects. We propose an imputation procedure for censored observations and consider three types of residuals to evaluate different model characteristics. We illustrate the proposal with the analysis of AFTM with random effects to a real data set involving times between failures of oil well equipment

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.

The FGM bivariate lifetime copula model: a bayesian approach

In this paper, we propose a bivariate distribution for the bivariate survival times based on Farlie-Gumbel-Morgenstern copula to model the dependence on a bivariate survival data. The proposed model allows for the presence of censored data and covariates. For inferential purpose a Bayesian approach via Markov Chain Monte Carlo (MCMC) is considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated via a simulation study and a real dataset.

Overall Survival Improvement in Patients with Lung Cancer and Bone Metastases Treated with Denosumab Versus Zoledronic Acid Subgroup Analysis from a Randomized Phase 3 Study

Introduction: Denosumab, a fully human anti-RANKL monoclonal antibody, reduces the incidence of skeletal-related events in patients with bone metastases from solid tumors. We present survival data for the subset of patients with lung cancer, participating in the phase 3 trial of denosumab versus zoledronic acid (ZA) in the treatment of bone metastases from solid tumors (except breast or prostate) or multiple myeloma. Methods: Patients were randomized 1:1 to receive monthly subcutaneous denosumab 120 mg or intravenous ZA 4 mg. An exploratory analysis, using Kaplan-Meier estimates and proportional hazards models, was performed for overall survival among patients with non-small-cell lung cancer (NSCLC) and SCLC. Results: Denosumab was associated with improved median overall survival versus ZA in 811 patients with any lung cancer (8.9 versus 7.7 months; hazard ratio [HR] 0.80) and in 702 patients with NSCLC (9.5 versus 8.0 months; HR 0.78) (p = 0.01, each comparison). Further analysis of NSCLC by histological type showed a median survival of 8.6 months for denosumab versus 6.4 months for ZA in patients with squamous cell carcinoma (HR 0.68; p = 0.035). Incidence of overall adverse events was balanced between treatment groups; serious adverse events occurred in 66.0% of denosumab-treated patients and 72.9% of ZA-treated patients. Cumulative incidence of osteonecrosis of the jaw was similar between groups (0.7% denosumab versus 0.8% ZA). Hypocalcemia rates were 8.6% with denosumab and 3.8% with ZA. Conclusion: In this exploratory analysis, denosumab was associated with improved overall survival compared with ZA, in patients with metastatic lung cancer.

Survival Analysis of Patients with Heart Failure: Implications of Time-Varying Regression Effects in Modeling Mortality

Background: Several models have been designed to predict survival of patients with heart failure. These, while available and widely used for both stratifying and deciding upon different treatment options on the individual level, have several limitations. Specifically, some clinical variables that may influence prognosis may have an influence that change over time. Statistical models that include such characteristic may help in evaluating prognosis. The aim of the present study was to analyze and quantify the impact of modeling heart failure survival allowing for covariates with time-varying effects known to be independent predictors of overall mortality in this clinical setting. Methodology: Survival data from an inception cohort of five hundred patients diagnosed with heart failure functional class III and IV between 2002 and 2004 and followed-up to 2006 were analyzed by using the proportional hazards Cox model and variations of the Cox's model and also of the Aalen's additive model. Principal Findings: One-hundred and eighty eight (188) patients died during follow-up. For patients under study, age, serum sodium, hemoglobin, serum creatinine, and left ventricular ejection fraction were significantly associated with mortality. Evidence of time-varying effect was suggested for the last three. Both high hemoglobin and high LV ejection fraction were associated with a reduced risk of dying with a stronger initial effect. High creatinine, associated with an increased risk of dying, also presented an initial stronger effect. The impact of age and sodium were constant over time. Conclusions: The current study points to the importance of evaluating covariates with time-varying effects in heart failure models. The analysis performed suggests that variations of Cox and Aalen models constitute a valuable tool for identifying these variables. The implementation of covariates with time-varying effects into heart failure prognostication models may reduce bias and increase the specificity of such models.

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.

Effect of initial treatment strategy on survival of patients with advanced-stage Hodgkin's lymphoma: a systematic review and network meta-analysis

BACKGROUND Several treatment strategies are available for adults with advanced-stage Hodgkin's lymphoma, but studies assessing two alternative standards of care-increased dose bleomycin, etoposide, doxorubicin, cyclophosphamide, vincristine, procarbazine, and prednisone (BEACOPPescalated), and doxorubicin, bleomycin, vinblastine, and dacarbazine (ABVD)-were not powered to test differences in overall survival. To guide treatment decisions in this population of patients, we did a systematic review and network meta-analysis to identify the best initial treatment strategy. METHODS We searched the Cochrane Library, Medline, and conference proceedings for randomised controlled trials published between January, 1980, and June, 2013, that assessed overall survival in patients with advanced-stage Hodgkin's lymphoma given BEACOPPbaseline, BEACOPPescalated, BEACOPP variants, ABVD, cyclophosphamide (mechlorethamine), vincristine, procarbazine, and prednisone (C[M]OPP), hybrid or alternating chemotherapy regimens with ABVD as the backbone (eg, COPP/ABVD, MOPP/ABVD), or doxorubicin, vinblastine, mechlorethamine, vincristine, bleomycin, etoposide, and prednisone combined with radiation therapy (the Stanford V regimen). We assessed studies for eligibility, extracted data, and assessed their quality. We then pooled the data and used a Bayesian random-effects model to combine direct comparisons with indirect evidence. We also reconstructed individual patient survival data from published Kaplan-Meier curves and did standard random-effects Poisson regression. Results are reported relative to ABVD. The primary outcome was overall survival. FINDINGS We screened 2055 records and identified 75 papers covering 14 eligible trials that assessed 11 different regimens in 9993 patients, providing 59 651 patient-years of follow-up. 1189 patients died, and the median follow-up was 5·9 years (IQR 4·9-6·7). Included studies were of high methodological quality, and between-trial heterogeneity was negligible (τ(2)=0·01). Overall survival was highest in patients who received six cycles of BEACOPPescalated (HR 0·38, 95% credibility interval [CrI] 0·20-0·75). Compared with a 5 year survival of 88% for ABVD, the survival benefit for six cycles of BEACOPPescalated is 7% (95% CrI 3-10)-ie, a 5 year survival of 95%. Reconstructed individual survival data showed that, at 5 years, BEACOPPescalated has a 10% (95% CI 3-15) advantage over ABVD in overall survival. INTERPRETATION Six cycles of BEACOPPescalated significantly improves overall survival compared with ABVD and other regimens, and thus we recommend this treatment strategy as standard of care for patients with access to the appropriate supportive care.

Loss of DAXX and ATRX are associated with chromosome instability and reduced survival of patients with pancreatic neuroendocrine tumors

BACKGROUND & AIMS Sporadic pancreatic neuroendocrine tumors (pNETs) are rare and genetically heterogeneous. Chromosome instability (CIN) has been detected in pNETs from patients with poor outcomes, but no specific genetic factors have been associated with CIN. Mutations in death domain-associated protein gene (DAXX) or ATR-X gene (ATRX) (which both encode proteins involved in chromatin remodeling) have been detected in 40% of pNETs, in association with activation of alternative lengthening of telomeres. We investigated whether loss of DAXX or ATRX, and consequent alternative lengthening of telomeres, are related to CIN in pNETs. We also assessed whether loss of DAXX or ATRX is associated with specific phenotypes of pNETs. METHODS We collected well-differentiated primary pNET samples from 142 patients at the University Hospital Zurich and from 101 patients at the University Hospital Bern (both located in Switzerland). Clinical follow-up data were obtained for 149 patients from general practitioners and tumor registries. The tumors were reclassified into 3 groups according to the 2010 World Health Organization classification. Samples were analyzed by immunohistochemistry and telomeric fluorescence in situ hybridization. We correlated loss of DAXX, or ATRX, expression, and activation of alternative lengthening of telomeres with data from comparative genomic hybridization array studies, as well as with clinical and pathological features of the tumors and relapse and survival data. RESULTS Loss of DAXX or ATRX protein and alternative lengthening of telomeres were associated with CIN in pNETs. Furthermore, loss of DAXX or ATRX correlated with tumor stage and metastasis, reduced time of relapse-free survival, and decreased time of tumor-associated survival. CONCLUSIONS Loss of DAXX or ATRX is associated with CIN in pNETs and shorter survival times of patients. These results support the hypothesis that DAXX- and ATRX-negative tumors are a more aggressive subtype of pNET, and could lead to identification of strategies to target CIN in pancreatic tumors.

Estimating the mean and standard deviation of concentration distributions using censored samples

Environmental data sets of pollutant concentrations in air, water, and soil frequently include unquantified sample values reported only as being below the analytical method detection limit. These values, referred to as censored values, should be considered in the estimation of distribution parameters as each represents some value of pollutant concentration between zero and the detection limit. Most of the currently accepted methods for estimating the population parameters of environmental data sets containing censored values rely upon the assumption of an underlying normal (or transformed normal) distribution. This assumption can result in unacceptable levels of error in parameter estimation due to the unbounded left tail of the normal distribution. With the beta distribution, which is bounded by the same range of a distribution of concentrations, $\rm\lbrack0\le x\le1\rbrack,$ parameter estimation errors resulting from improper distribution bounds are avoided. This work developed a method that uses the beta distribution to estimate population parameters from censored environmental data sets and evaluated its performance in comparison to currently accepted methods that rely upon an underlying normal (or transformed normal) distribution. Data sets were generated assuming typical values encountered in environmental pollutant evaluation for mean, standard deviation, and number of variates. For each set of model values, data sets were generated assuming that the data was distributed either normally, lognormally, or according to a beta distribution. For varying levels of censoring, two established methods of parameter estimation, regression on normal ordered statistics, and regression on lognormal ordered statistics, were used to estimate the known mean and standard deviation of each data set. The method developed for this study, employing a beta distribution assumption, was also used to estimate parameters and the relative accuracy of all three methods were compared. For data sets of all three distribution types, and for censoring levels up to 50%, the performance of the new method equaled, if not exceeded, the performance of the two established methods. Because of its robustness in parameter estimation regardless of distribution type or censoring level, the method employing the beta distribution should be considered for full development in estimating parameters for censored environmental data sets. ^

Influence of EMS-physician presence on survival after out-of-hospital cardiopulmonary resuscitation: systematic review and meta-analysis

BACKGROUND Evidence suggests that EMS-physician-guided cardiopulmonary resuscitation (CPR) in out-of-hospital cardiac arrest (OOHCA) may be associated with improved outcomes, yet randomized controlled trials are not available. The goal of this meta-analysis was to determine the association between EMS-physician- versus paramedic-guided CPR and survival after OOHCA. METHODS AND RESULTS Studies that compared EMS-physician- versus paramedic-guided CPR in OOHCA published until June 2014 were systematically searched in MEDLINE, EMBASE and Cochrane databases. All studies were required to contain survival data. Data on study characteristics, methods, and as well as survival outcomes were extracted. A random-effects model was used for the meta-analysis due to a high degree of heterogeneity among the studies (I (2)  = 44 %). Return of spontaneous circulation [ROSC], survival to hospital admission, and survival to hospital discharge were the outcome measures. Out of 3,385 potentially eligible studies, 14 met the inclusion criteria. In the pooled analysis (n = 126,829), EMS-physician-guided CPR was associated with significantly improved outcomes compared to paramedic-guided CPR: ROSC 36.2 % (95 % confidence interval [CI] 31.0 - 41.7 %) vs. 23.4 % (95 % CI 18.5 - 29.2 %) (pooled odds ratio [OR] 1.89, 95 % CI 1.36 - 2.63, p < 0.001); survival to hospital admission 30.1 % (95 % CI 24.2 - 36.7 %) vs. 19.2 % (95 % CI 12.7 - 28.1 %) (pooled OR 1.78, 95 % CI 0.97 - 3.28, p = 0.06); and survival to discharge 15.1 % (95 % CI 14.6 - 15.7 %) vs. 8.4 % (95 % CI 8.2 - 8.5 %) (pooled OR 2.03, 95 % CI 1.48 - 2.79, p < 0.001). CONCLUSIONS This systematic review suggests that EMS-physician-guided CPR in out-of-hospital cardiac arrest is associated with improved survival outcomes.

Response to chemotherapy, recurrence and survival in advanced-stage ovarian, fallopian tube and primary peritoneal cancer patients with non-Ashkenazi Jewish BRCA mutations, compared to those without

Objectives. Previous studies have shown a survival advantage in ovarian cancer patients with Ashkenazi-Jewish (AJ) BRCA founder mutations, compared to sporadic ovarian cancer patients. The purpose of this study was to determine if this association exists in ovarian cancer patients with non-Ashkenazi Jewish BRCA mutations. In addition, we sought to account for possible "survival bias" by minimizing any lead time that may exist between diagnosis and genetic testing. ^ Methods. Patients with stage III/IV ovarian, fallopian tube, or primary peritoneal cancer and a non-Ashkenazi Jewish BRCA1 or 2 mutation, seen for genetic testing January 1996-July 2007, were identified from genetics and institutional databases. Medical records were reviewed for clinical factors, including response to initial chemotherapy. Patients with sporadic (non-hereditary) ovarian, fallopian tube, or primary peritoneal cancer, without family history of breast or ovarian cancer, were compared to similar cases, matched by age, stage, year of diagnosis, and vital status at time interval to BRCA testing. When possible, 2 sporadic patients were matched to each BRCA patient. An additional group of unmatched, sporadic ovarian, fallopian tube and primary peritoneal cancer patients was included for a separate analysis. Progression-free (PFS) & overall survival (OS) were calculated by the Kaplan-Meier method. Multivariate Cox proportional hazards models were calculated for variables of interest. Matched pairs were treated as clusters. Stratified log rank test was used to calculate survival data for matched pairs using paired event times. Fisher's exact test, chi-square, and univariate logistic regression were also used for analysis. ^ Results. Forty five advanced-stage ovarian, fallopian tube and primary peritoneal cancer patients with non-Ashkenazi Jewish (non-AJ) BRCA mutations, 86 sporadic-matched and 414 sporadic-unmatched patients were analyzed. Compared to the sporadic-matched and sporadic-unmatched ovarian cancer patients, non-AJ BRCA mutation carriers had longer PFS (17.9 & 13.8 mos. vs. 32.0 mos., HR 1.76 [95% CI 1.13–2.75] & 2.61 [95% CI 1.70–4.00]). In relation to the sporadic- unmatched patients, non-AJ BRCA patients had greater odds of complete response to initial chemotherapy (OR 2.25 [95% CI 1.17–5.41]) and improved OS (37.6 mos. vs. 101.4 mos., HR 2.64 [95% CI 1.49–4.67]). ^ Conclusions. This study demonstrates a significant survival advantage in advanced-stage ovarian cancer patients with non-AJ BRCA mutations, confirming the previous studies in the Jewish population. Our efforts to account for "survival bias," by matching, will continue with collaborative studies. ^

Bayesian and survival model for tumor relapse status and disease-specific survival, with applications to breast cancer

Breast cancer is the most common non-skin cancer and the second leading cause of cancer-related death in women in the United States. Studies on ipsilateral breast tumor relapse (IBTR) status and disease-specific survival will help guide clinic treatment and predict patient prognosis.^ After breast conservation therapy, patients with breast cancer may experience breast tumor relapse. This relapse is classified into two distinct types: true local recurrence (TR) and new ipsilateral primary tumor (NP). However, the methods used to classify the relapse types are imperfect and are prone to misclassification. In addition, some observed survival data (e.g., time to relapse and time from relapse to death)are strongly correlated with relapse types. The first part of this dissertation presents a Bayesian approach to (1) modeling the potentially misclassified relapse status and the correlated survival information, (2) estimating the sensitivity and specificity of the diagnostic methods, and (3) quantify the covariate effects on event probabilities. A shared frailty was used to account for the within-subject correlation between survival times. The inference was conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in softwareWinBUGS. Simulation was used to validate the Bayesian method and assess its frequentist properties. The new model has two important innovations: (1) it utilizes the additional survival times correlated with the relapse status to improve the parameter estimation, and (2) it provides tools to address the correlation between the two diagnostic methods conditional to the true relapse types.^ Prediction of patients at highest risk for IBTR after local excision of ductal carcinoma in situ (DCIS) remains a clinical concern. The goals of the second part of this dissertation were to evaluate a published nomogram from Memorial Sloan-Kettering Cancer Center, to determine the risk of IBTR in patients with DCIS treated with local excision, and to determine whether there is a subset of patients at low risk of IBTR. Patients who had undergone local excision from 1990 through 2007 at MD Anderson Cancer Center with a final diagnosis of DCIS (n=794) were included in this part. Clinicopathologic factors and the performance of the Memorial Sloan-Kettering Cancer Center nomogram for prediction of IBTR were assessed for 734 patients with complete data. Nomogram for prediction of 5- and 10-year IBTR probabilities were found to demonstrate imperfect calibration and discrimination, with an area under the receiver operating characteristic curve of .63 and a concordance index of .63. In conclusion, predictive models for IBTR in DCIS patients treated with local excision are imperfect. Our current ability to accurately predict recurrence based on clinical parameters is limited.^ The American Joint Committee on Cancer (AJCC) staging of breast cancer is widely used to determine prognosis, yet survival within each AJCC stage shows wide variation and remains unpredictable. For the third part of this dissertation, biologic markers were hypothesized to be responsible for some of this variation, and the addition of biologic markers to current AJCC staging were examined for possibly provide improved prognostication. The initial cohort included patients treated with surgery as first intervention at MDACC from 1997 to 2006. Cox proportional hazards models were used to create prognostic scoring systems. AJCC pathologic staging parameters and biologic tumor markers were investigated to devise the scoring systems. Surveillance Epidemiology and End Results (SEER) data was used as the external cohort to validate the scoring systems. Binary indicators for pathologic stage (PS), estrogen receptor status (E), and tumor grade (G) were summed to create PS+EG scoring systems devised to predict 5-year patient outcomes. These scoring systems facilitated separation of the study population into more refined subgroups than the current AJCC staging system. The ability of the PS+EG score to stratify outcomes was confirmed in both internal and external validation cohorts. The current study proposes and validates a new staging system by incorporating tumor grade and ER status into current AJCC staging. We recommend that biologic markers be incorporating into revised versions of the AJCC staging system for patients receiving surgery as the first intervention.^ Chapter 1 focuses on developing a Bayesian method to solve misclassified relapse status and application to breast cancer data. Chapter 2 focuses on evaluation of a breast cancer nomogram for predicting risk of IBTR in patients with DCIS after local excision gives the statement of the problem in the clinical research. Chapter 3 focuses on validation of a novel staging system for disease-specific survival in patients with breast cancer treated with surgery as the first intervention. ^