Network of recurrent events for the Olami-Feder-Christensen model

We numerically study the dynamics of a discrete spring-block model introduced by Olami, Feder, and Christensen (OFC) to mimic earthquakes and investigate to what extent this simple model is able to reproduce the observed spatiotemporal clustering of seismicity. Following a recently proposed method to characterize such clustering by networks of recurrent events [J. Davidsen, P. Grassberger, and M. Paczuski, Geophys. Res. Lett. 33, L11304 (2006)], we find that for synthetic catalogs generated by the OFC model these networks have many nontrivial statistical properties. This includes characteristic degree distributions, very similar to what has been observed for real seismicity. There are, however, also significant differences between the OFC model and earthquake catalogs, indicating that this simple model is insufficient to account for certain aspects of the spatiotemporal clustering of seismicity.

Preventing recurrent events long term after coronary artery bypass graft: Suboptimal use of medications in a population study

Background There are few population-based data on long-term management of patients after coronary artery bypass graft (CABG), despite the high risk for future major vascular events among this group. We assessed the prevalence and correlates of pharmacotherapy for prevention of new cardiac events in a large population-based series. Methods A postal survey was conducted of 2500 randomly selected survivors from a state population of patients 6 to 20 years after first CABG. Results Response was 82% (n = 2061). Use of antiplatelet agents (80%) and statins (64%) declined as age increased. Other independent predictors of antiplatelet use included statin use (odds ratio [OR] 1.6, 95% CI 1.26-2.05) and recurrent angina (OR 1.6, CI 1.17-2.06). Current smokers were less likely to use aspirin (OR 0.59, CI 0.4-0.89). Statin use was associated with reported high cholesterol (OR 24.4, CI 8.4-32.4), management by a cardiologist (OR 2.3, CI 1.8-3.0), and the use of calcium channel-blockers. Patients reporting hypertension or heart failure, in addition to high cholesterol, were less likely to use statins. Angiotensin-converting enzyme inhibitors were the most commonly prescribed agents for management of hypertension (59%) and were more frequently used among patients with diabetes and those with symptoms of heart failure. Overall 42% of patients were on angiotensin-converting enzyme inhibitors and 36% on beta-blockers. Conclusions Gaps exist in the use of-recommended medications after CABG. Lower anti-platelet and statin use was associated with older age, freedom from angina, comorbid heart failure or hypertension, and not regularly visiting a cardiologist. Patients who continue to smoke might be less likely to adhere to prescribed medications.

Empirical study of correlated survival times for recurrent events with proportional hazards margins and the effect of correlation and censoring.

Background: In longitudinal studies where subjects experience recurrent incidents over a period of time, such as respiratory infections, fever or diarrhea, statistical methods are required to take into account the within-subject correlation. Methods: For repeated events data with censored failure, the independent increment (AG), marginal (WLW) and conditional (PWP) models are three multiple failure models that generalize Cox"s proportional hazard model. In this paper, we revise the efficiency, accuracy and robustness of all three models under simulated scenarios with varying degrees of within-subject correlation, censoring levels, maximum number of possible recurrences and sample size. We also study the methods performance on a real dataset from a cohort study with bronchial obstruction. Results: We find substantial differences between methods and there is not an optimal method. AG and PWP seem to be preferable to WLW for low correlation levels but the situation reverts for high correlations. Conclusions: All methods are stable in front of censoring, worsen with increasing recurrence levels and share a bias problem which, among other consequences, makes asymptotic normal confidence intervals not fully reliable, although they are well developed theoretically.

Empirical study of correlated survival times for recurrent events with proportional hazards margins and the effect of correlation and censoring.

Background: In longitudinal studies where subjects experience recurrent incidents over a period of time, such as respiratory infections, fever or diarrhea, statistical methods are required to take into account the within-subject correlation. Methods: For repeated events data with censored failure, the independent increment (AG), marginal (WLW) and conditional (PWP) models are three multiple failure models that generalize Cox"s proportional hazard model. In this paper, we revise the efficiency, accuracy and robustness of all three models under simulated scenarios with varying degrees of within-subject correlation, censoring levels, maximum number of possible recurrences and sample size. We also study the methods performance on a real dataset from a cohort study with bronchial obstruction. Results: We find substantial differences between methods and there is not an optimal method. AG and PWP seem to be preferable to WLW for low correlation levels but the situation reverts for high correlations. Conclusions: All methods are stable in front of censoring, worsen with increasing recurrence levels and share a bias problem which, among other consequences, makes asymptotic normal confidence intervals not fully reliable, although they are well developed theoretically.

Mortality and recurrent cardiac events after coronary artery bypass graft: long term outcomes in a population study

Objective: To determine 30 day mortality, long term survival, and recurrent cardiac events after coronary artery bypass graft (CABG) in a population. Design: Follow up study of patients prospectively entered on to a cardiothoracic surgical database. Record linkages were used to obtain data on readmissions and deaths. Patients: 8910 patients undergoing isolated first CABG between 1980 and 1993 in Western Australia. Main outcome measures: 30 day and long term survival, readmission for cardiac event (acute myocardial infarction, unstable angina, percutaneous transluminal coronary angioplasty or reoperative CABG). Results: There were 3072 deaths to mid 1999. 30 day and long term survival were significantly better in patients treated in the first five years than during the following decade. The age of the patients, proportion of female patients, and number of grafts increased over time. An urgent procedure (odds ratio 3.3), older age (9% per year) and female sex (odds ratio 1.5) were associated with increased risk for 30 day mortality, while age (7% per year) and a recent myocardial infarction (odds ratio 1.16) influenced long term survival. Internal mammary artery grafts were followed by better short and long term survival, though there was an obvious selection bias in favour of younger male patients. Conclusions: This study shows worsening crude mortality at 30 days after CABG from the mid 1980s, associated with the inclusion of higher risk patients. Older age, an acute myocardial infarction in the year before surgery, and the use of sephenous vein grafts only were associated with poorer long term survival and greater risk of a recurrent cardiac event. Female sex predicted recurrent events but not long term survival.

A propensity score-matched comparison between Cardia and Amplatzer PFO closure devices - insights from the SOLUTION registry (Swiss percutaneOus patent foramen ovale cLosUre in recurrent clinical events prevenTION)

Aims: To compare clinical outcome of Amplatzer PFO (APFO) to Cardia PFO (CPFO) occluder. Percutaneous patent foramen ovale (PFO) closure prevents stroke recurrence in stroke due to paradoxical embolism. Methods and results: The primary endpoint was a composite of stroke, TIA, or peripheral embolism at follow-up. The secondary endpoint was residual shunt. Outcome was compared among 934 (APFO: 712; CPFO: 222) patients, and in 297 propensity score-matched patients. The primary endpoint occurred in 29 patients (0.71/100 patient-years): four (2%) with the CPFO (0.31/100 patient-years), and 25 (4%) with the APFO (0.89/100 patient-years) (p=0.20). Residual shunt at six months was more frequent with the CPFO (31% versus 9%, p<0.001). No differences in residual shunts were seen at the last available echocardiographic follow-up (9±18 months): APFO 11%, CPFO 14%, p=0.22. Conclusions: This study suggests that PFO closure with APFO or CPFO is equally effective for the prevention of recurrent events. Residual shunt was more frequent at six months with CPFO, but was similar to APFO at later follow-up.

Long-term risk of first recurrent stroke in the Perth Community Stroke Study

Background and Purpose-Few community-based studies have examined the long-term risk of recurrent stroke after an acute first-ever stroke. This study aimed to determine the absolute and relative risks of a first recurrent stroke over the first 5 years after a first-ever stroke and the predictors of such recurrence in a population-based series of people with first-ever stroke in Perth, Western Australia. Methods-Between February 1989 and August 1990, all people with a suspected acute stroke or transient ischemic attack of the brain who were resident in a geographically defined region of Perth, Western Australia, with a population of 138 708 people, were registered prospectively and assessed according to standardized diagnostic criteria. Patients were followed up prospectively at 4 months, 12 months, and 5 years after the index event. Results-Three hundred seventy patients with a first-ever stroke were registered, of whom 351 survived >2 days. Data were available for 98% of the cohort at 5 years, by which time 199 patients (58%) had died and 52 (15%) had experienced a recurrent stroke, 12 (23%) of which were fatal within 28 days. The 5-year cumulative risk of first recurrent stroke was 22.5% (95% confidence limits [CL], 16.8%, 28.1%). The risk of recurrent stroke was greatest in the first 6 months after stroke, at 8.8% (95% CL, 5.4%, 12.1%). After adjustment for age and sex, the prognostic factors for recurrent stroke were advanced, but not extreme, age (75 to 84 years) (hazard ratio [HR], 2.6; 95% CL, 1.1, 6.2), hemorrhagic index stroke (HR, 2.1; 95% CL, 0.98, 4.4), and diabetes mellitus (HR, 2.1; 95% CL, 0.95, 4.4). Conclusions-Approximately 1 in 6 survivors (15%) of a first-ever stroke experience a recurrent stroke over the next 5 years, of which 25% are fatal within 28 days. The pathological subtype of the recurrent stroke is the same as that of the index stroke in 88% of cases. The predictors of first recurrent stroke in this study were advanced age, hemorrhagic index stroke, and diabetes mellitus, but numbers of recurrent events were modest. Because the risk of recurrent stroke is highest (8.8%) in the first 6 months after stroke, strategies for secondary prevention should be initiated as soon as possible after the index event.

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.

Analysis of recurrent failure times: A time-dependent Yule process approach

Analysis of recurrent events has been widely discussed in medical, health services, insurance, and engineering areas in recent years. This research proposes to use a nonhomogeneous Yule process with the proportional intensity assumption to model the hazard function on recurrent events data and the associated risk factors. This method assumes that repeated events occur for each individual, with given covariates, according to a nonhomogeneous Yule process with intensity function λx(t) = λ 0(t) · exp( x′β). One of the advantages of using a non-homogeneous Yule process for recurrent events is that it assumes that the recurrent rate is proportional to the number of events that occur up to time t. Maximum likelihood estimation is used to provide estimates of the parameters in the model, and a generalized scoring iterative procedure is applied in numerical computation. ^ Model comparisons between the proposed method and other existing recurrent models are addressed by simulation. One example concerning recurrent myocardial infarction events compared between two distinct populations, Mexican-American and Non-Hispanic Whites in the Corpus Christi Heart Project is examined. ^

The combined effect of pravastatin and aspirin on clinical cardiovascular events

The 3-hydroxy-3methylglutaryl coenzyme A (HMG-CoA) reductase inhibitors, or statins, can achieve significant reductions in plasma low-density lipoprotein (LDL)-cholesterol levels. Experimental and clinical evidence now shows that some statins interfere with formation of atherosclerotic lesions independent of their hypolipidemic properties. Vulnerable plaque rupture can result in thrombus formation and artery occlusion; this plaque deterioration is responsible for most acute coronary syndromes, including myocardial infarction (MI), unstable angina, and coronary death, as well as coronary heart diseaseequivalent non-hemorrhagic stroke. Inhibition of HMG-CoA reductase has potential pleiotropic effects other than lipid-lowering, as statins block mevalonic acid production, a precursor to cholesterol and numerous other metabolites. Statins' beneficial effects on clinical events may also thus involve nonlipid-related mechanisms that modify endothelial function, inflammatory responses, plaque stability, and thrombus formation. Aspirin, routinely prescribed to post-MI patients as adjunct therapy, may potentiate statins beneficial effects, as aspirin does not compete metabolically with statins but acts similarly on atherosclerotic lesions. Common functions of both medications include inhibition of platelet activity and aggregation, reduction in atherosclerotic plaque macrophage cell count, and prevention of atherosclerotic vessel endothelial dysfunction. The Cholesterol and Recurrent Events (CARE) trial provides an ideal population in which to examine the combined effects of pravastatin and aspirin. Lipid levels, intermediate outcomes, are examined by pravastatin and aspirin status, and differences between the two pravastatin groups are found. A modified Cox proportional-hazards model with aspirin as a time-dependent covariate was used to determine the effect of aspirin and pravastatin on the clinical cardiovascular composite endpoint of coronary heart disease death, recurrent MI or stroke. Among those assigned to pravastatin, use of aspirin reduced the composite primary endpoint by 35%; this result was similar by gender, race, and diabetic status. Older patients demonstrated a nonsignificant 21% reduction in the primary outcome, whereas the younger had a significant reduction of 43% in the composite primary outcome. Secondary outcomes examined include coronary artery bypass graft (38% reduction), nonsurgical bypass, peripheral vascular disease, and unstable angina. Pravastatin and aspirin in a post-MI population was found to be a beneficial combination that seems to work through lipid and nonlipid, anti-inflammatory mechanisms. ^

Clopidogrel: A CURE in acute coronary syndromes? (A Key Paper Evaluation)

The standard approach to preventing acute coronary syndromes (ACSs)has been to inhibit platelet aggregation with aspirin and to inhibit blood coagulation with low molecular-weight heparin (LMWH). Even with this combination there is still a substantial short and long-term cardiovascular risk. The Clopidogrel in Unstable angina to prevent Recurrent Events (CURE) trial [1] compared clopidogrel plus aspirin against aspirin alone in patients with ACSs. The clopidogrel regimen was a loading dose of 300 mg p.o. followed by 75 mg/day and the recommended dose of aspirin was 75 - 325 mg/day. The first primary outcome was a composite of death from cardiovascular causes, non-fatal myocardial infarction (MI) or stroke and this occurred significantly less often in the clopidogrel than the placebo group (9.3 vs. 11.4%). Although there were more clopidogrel patients with life-threatening bleeding (clopidogrel 2.2%, placebo 1.8%), this represented GI haemorrhages and bleeding at sites of arterial puncture rather than fatal bleeding. This trial suggests a role for clopidogrel in the long-term treatment of ACSs

Nonparametric estimation of the survival function for ordered multivariate failure time data: a comparative study

In longitudinal studies of disease, patients may experience several events through a follow-up period. In these studies, the sequentially ordered events are often of interest and lead to problems that have received much attention recently. Issues of interest include the estimation of bivariate survival, marginal distributions and the conditional distribution of gap times. In this work we consider the estimation of the survival function conditional to a previous event. Different nonparametric approaches will be considered for estimating these quantities, all based on the Kaplan-Meier estimator of the survival function. We explore the finite sample behavior of the estimators through simulations. The different methods proposed in this article are applied to a data set from a German Breast Cancer Study. The methods are used to obtain predictors for the conditional survival probabilities as well as to study the influence of recurrence in overall survival.

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

Dissertação de mestrado em Estatística