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.

Bootstrap confidence intervals for industrial recurrent event data

Industrial recurrent event data where an event of interest can be observed more than once in a single sample unit are presented in several areas, such as engineering, manufacturing and industrial reliability. Such type of data provide information about the number of events, time to their occurrence and also their costs. Nelson (1995) presents a methodology to obtain asymptotic confidence intervals for the cost and the number of cumulative recurrent events. Although this is a standard procedure, it can not perform well in some situations, in particular when the sample size available is small. In this context, computer-intensive methods such as bootstrap can be used to construct confidence intervals. In this paper, we propose a technique based on the bootstrap method to have interval estimates for the cost and the number of cumulative events. One of the advantages of the proposed methodology is the possibility for its application in several areas and its easy computational implementation. In addition, it can be a better alternative than asymptotic-based methods to calculate confidence intervals, according to some Monte Carlo simulations. An example from the engineering area illustrates the methodology.

Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

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.

Comparison of Roadside Crash Injury Metrics using Event Data Recorders

The occupant impact velocity (OIV) and acceleration severity index (ASI) are competing measures of crash severity used to assess occupant injury risk in full-scale crash tests involving roadside safety hardware, e.g. guardrail. Delta-V, or the maximum change in vehicle velocity, is the traditional metric of crash severity for real world crashes. This study compares the ability of the OIV, ASI, and delta-V to discriminate between serious and non-serious occupant injury in real world frontal collisions. Vehicle kinematics data from event data recorders (EDRs) were matched with detailed occupant injury information for 180 real world crashes. Cumulative probability of injury risk curves were generated using binary logistic regression for belted and unbelted data subsets. By comparing the available fit statistics and performing a separate ROC curve analysis, the more computationally intensive OIV and ASI were found to offer no significant predictive advantage over the simpler delta-V.

A multiple time scale survival model with a cure fraction

Many recent survival studies propose modeling data with a cure fraction, i.e., data in which part of the population is not susceptible to the event of interest. This event may occur more than once for the same individual (recurrent event). We then have a scenario of recurrent event data in the presence of a cure fraction, which may appear in various areas such as oncology, finance, industries, among others. This paper proposes a multiple time scale survival model to analyze recurrent events using a cure fraction. The objective is analyzing the efficiency of certain interventions so that the studied event will not happen again in terms of covariates and censoring. All estimates were obtained using a sampling-based approach, which allows information to be input beforehand with lower computational effort. Simulations were done based on a clinical scenario in order to observe some frequentist properties of the estimation procedure in the presence of small and moderate sample sizes. An application of a well-known set of real mammary tumor data is provided.

Analyzing Panel Count Data with Informative Observation Times

In this paper, we study panel count data with informative observation times. We assume nonparametric and semiparametric proportional rate models for the underlying recurrent event process, where the form of the baseline rate function is left unspecified and a subject-specific frailty variable inflates or deflates the rate function multiplicatively. The proposed models allow the recurrent event processes and observation times to be correlated through their connections with the unobserved frailty; moreover, the distributions of both the frailty variable and observation times are considered as nuisance parameters. The baseline rate function and the regression parameters are estimated by maximizing a conditional likelihood function of observed event counts and solving estimation equations. Large sample properties of the proposed estimators are studied. Numerical studies demonstrate that the proposed estimation procedures perform well for moderate sample sizes. An application to a bladder tumor study is presented to illustrate the use of the proposed methods.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.

Is postmenopausal hormone replacement therapy suitable after a cardio- or cerebrovascular event?

PURPOSE Vascular disease is the leading cause of death in women. One-third of acute events affect women below age 60, when the prevalence of menopausal symptoms is high. This raises the question if hormone replacement therapy (HRT) may be an appropriate treatment for individual women although vascular disease is generally considered a contraindication. METHODS Selective literature search was used for this study. RESULTS In healthy women, HRT increases risks for venous thromboembolism and ischemic stroke, but for cardiovascular disease apparently only beyond 10 years after menopause or 60 years of age. Limited data in women with cardio or cerebrovascular disease have not demonstrated an increased risk for a vascular recurrent event, but for the first year after initiation. In HRT users affected by a cardiovascular event continuation of HRT has not been found to be associated with adverse outcome. Low dose estradiol--preferentially as transdermal patches, if necessary combined with metabolically neutral progestins--appears to convey lower risk. CONCLUSIONS Safety data on HRT in survivors of cardiovascular events or ischemic stroke are limited, but exceptionally increased risk appears to be excluded. If off-label use of HRT is considered to be initiated or continued in women with cardio- or cerebrovascular disease, extensive counseling on the pros and cons of HRT is mandatory.

Business Process Management and Process Mining within a Real Business Environment: An Empirical Analysis of Event Logs Data in a Consulting Project

Il presente elaborato esplora l’attitudine delle organizzazioni nei confronti dei processi di business che le sostengono: dalla semi-assenza di struttura, all’organizzazione funzionale, fino all’avvento del Business Process Reengineering e del Business Process Management, nato come superamento dei limiti e delle problematiche del modello precedente. All’interno del ciclo di vita del BPM, trova spazio la metodologia del process mining, che permette un livello di analisi dei processi a partire dagli event data log, ossia dai dati di registrazione degli eventi, che fanno riferimento a tutte quelle attività supportate da un sistema informativo aziendale. Il process mining può essere visto come naturale ponte che collega le discipline del management basate sui processi (ma non data-driven) e i nuovi sviluppi della business intelligence, capaci di gestire e manipolare l’enorme mole di dati a disposizione delle aziende (ma che non sono process-driven). Nella tesi, i requisiti e le tecnologie che abilitano l’utilizzo della disciplina sono descritti, cosi come le tre tecniche che questa abilita: process discovery, conformance checking e process enhancement. Il process mining è stato utilizzato come strumento principale in un progetto di consulenza da HSPI S.p.A. per conto di un importante cliente italiano, fornitore di piattaforme e di soluzioni IT. Il progetto a cui ho preso parte, descritto all’interno dell’elaborato, ha come scopo quello di sostenere l’organizzazione nel suo piano di improvement delle prestazioni interne e ha permesso di verificare l’applicabilità e i limiti delle tecniche di process mining. Infine, nell’appendice finale, è presente un paper da me realizzato, che raccoglie tutte le applicazioni della disciplina in un contesto di business reale, traendo dati e informazioni da working papers, casi aziendali e da canali diretti. Per la sua validità e completezza, questo documento è stata pubblicato nel sito dell'IEEE Task Force on Process Mining.

Population versus clinical view of case fatality from acute coronary heart disease - Results from the WHO MONICA Project 1985-1990

Background The clinical view of case fatality (CF) from acute myocardial infarction (AMI) in those reaching the hospital alive is different from the population view. Registration of both hospitalized AMI cases and out-of-hospital coronary heart disease (CHD) deaths in the WHO MONICA Project allows both views to be reconciled. The WHO MONICA Project provides the largest data set worldwide to explore the relationship between CHD CF and age, sex, coronary event rate, and first versus recurrent event. Methods and Results All 79 669 events of definite AMI or possible coronary death, occurring from 1985 to 90 among 5 725 762 people, 35 to 64 years of age, in 29 MONICA populations are the basis for CF calculations. Age-adjusted CF (percentage of CHD events that were fatal) was calculated across populations, stratified for different time periods, and related to age, sex, and CHD event rate. Median 28-day population CF was 49% (range, 35% to 60%) in men and 51% (range, 34% to 70%) in women and was particularly higher in women than men in populations in which CHD event rates were low. Median 28-day CF for hospitalized events was much lower: in men 22% (range, 15% to 36%) and in women 27% (range, 19% to 46%). Among hospitalized events CF was twice as high for recurrent as for first events. Conclusions Overall 28-day CF is halved for hospitalized events compared with all events and again nearly halved for hospitalized 24-hour survivors. Because approximately two thirds of 28-day CHD deaths in men and women occurred before reaching the hospital, opportunities for reducing CF through improved care in the acute event are limited. Major emphasis should be on primary and secondary prevention.

A general hazard model for lifetime data in the presence of cure rate

Historically, the cure rate model has been used for modeling time-to-event data within which a significant proportion of patients are assumed to be cured of illnesses, including breast cancer, non-Hodgkin lymphoma, leukemia, prostate cancer, melanoma, and head and neck cancer. Perhaps the most popular type of cure rate model is the mixture model introduced by Berkson and Gage [1]. In this model, it is assumed that a certain proportion of the patients are cured, in the sense that they do not present the event of interest during a long period of time and can found to be immune to the cause of failure under study. In this paper, we propose a general hazard model which accommodates comprehensive families of cure rate models as particular cases, including the model proposed by Berkson and Gage. The maximum-likelihood-estimation procedure is discussed. A simulation study analyzes the coverage probabilities of the asymptotic confidence intervals for the parameters. A real data set on children exposed to HIV by vertical transmission illustrates the methodology.

Forecasting human entrances at a commercial store using facial recognition data

Dissertação de mestrado integrado em Engenharia e Gestão de Sistemas de Informação

Estimação da função de sobrevivência em dados de eventos recorrentes com censura pela direita

Dissertação de mestrado em Estatística