Recurrent composite events

1967 ◽  
Vol 4 (1) ◽  
pp. 34-61 ◽  
Author(s):  
R.T. Leslie

On a sequence of Bernoulli trials, the definition of a recurrent event ε involves the occurrence of a unique pattern of successes (S) and failures (F), the final element of which is the result of the nth trial. Success runs are the best known of such recurrent events, but Feller (1959, §13.8) mentions more complicated patterns, among which two types may be distinguished. The simpler involves a single more complex pattern such as SSFFSS; the second type involves a set of alternative events defining ε, which is said to occur when any one of the alternatives occurs at trial number n. Thus if ε stands for “either a success run of length r or a failure run of length ρ”, there are two alternatives in the set; the problem is elementary because the component events are “non-overlapping”.

1967 ◽  
Vol 4 (01) ◽  
pp. 34-61 ◽  
Author(s):  
R.T. Leslie

On a sequence of Bernoulli trials, the definition of a recurrent event ε involves the occurrence of a unique pattern of successes (S) and failures (F), the final element of which is the result of the nth trial. Success runs are the best known of such recurrent events, but Feller (1959, §13.8) mentions more complicated patterns, among which two types may be distinguished. The simpler involves a single more complex pattern such as SSFFSS; the second type involves a set of alternative events defining ε, which is said to occur when any one of the alternatives occurs at trial number n. Thus if ε stands for “either a success run of length r or a failure run of length ρ”, there are two alternatives in the set; the problem is elementary because the component events are “non-overlapping”.


1974 ◽  
Vol 11 (1) ◽  
pp. 190-192 ◽  
Author(s):  
M. B. Rajarshi

Success runs of a fixed length in a two-state Markov chain are discussed. The results are analogous to those in the case of independent Bernoulli trials. The generating function of the waiting time for the first occurrence of a success run is obtained from the theory of recurrent events. Under certain conditions, the distribution of the number of long runs in a large number of trials is shown to be Poisson.


1974 ◽  
Vol 11 (01) ◽  
pp. 190-192 ◽  
Author(s):  
M. B. Rajarshi

Success runs of a fixed length in a two-state Markov chain are discussed. The results are analogous to those in the case of independent Bernoulli trials. The generating function of the waiting time for the first occurrence of a success run is obtained from the theory of recurrent events. Under certain conditions, the distribution of the number of long runs in a large number of trials is shown to be Poisson.


1962 ◽  
Vol 88 (3) ◽  
pp. 360-366 ◽  
Author(s):  
M. T. L. Bizley

In a series of trials with constant probability p of ‘success’ (S) and q ( = I–p) of ‘failure’ (F), the problems arise of determining the expected number of trials required to obtain a specified pattern of results (e.g. SSFSFFSSSFF), and of calculating the probability that such a pattern will appear in a given number of trials. We are here concerned essentially with ‘general’ patterns which may exhibit no clear regularity; many methods are available, and well known, for dealing with regular patterns (e.g. SSSSSS or SFSFSF), which do not apply to irregular ones. Feller, has shown how to solve the problems for general patterns, using an ingenious definition of the event corresponding to the appearance of the pattern whereby it becomes a recurrent event; his powerful general theory of recurrent events then applies and yields the required information by means of generating functions. A different method is given on page 171 of Bizley for finding the expected number of trials required to obtain a general pattern; this uses only the simplest mathematical tools but involves rather a lot of work for long patterns. Under each of these methods, however, every given pattern has to be treated individually and a separate calculation performed.


2020 ◽  
Vol 91 (4) ◽  
pp. 352-357
Author(s):  
Jessica Tedford ◽  
Valerie Skaggs ◽  
Ann Norris ◽  
Farhad Sahiar ◽  
Charles Mathers

INTRODUCTION: Atrial fibrillation (AF) is one of the most common cardiac arrhythmias in the general population and is considered disqualifying aeromedically. This study is a unique examination of significant outcomes in aviators with previous history of both AF and stroke.METHODS: Pilots examined by the FAA between 2002 and 2012 who had had AF at some point during his or her medical history were reviewed, and those with an initial stroke or transient ischemic attack (TIA) during that time period were included in this study. All records were individually reviewed to determine stroke and AF history, medical certification history, and recurrent events. Variables collected included medical and behavior history, stroke type, gender, BMI, medication use, and any cardiovascular or neurological outcomes of interest. Major recurrent events included stroke, TIA, cerebrovascular accident, death, or other major events. These factors were used to calculate CHA2DS2-VASc scores.RESULTS: Of the 141 pilots selected for the study, 17.7% experienced a recurrent event. At 6 mo, the recurrent event rate was 5.0%; at 1 yr, 5.8%; at 3 yr 6.9%; and at 5 yr the recurrent event rate was 17.3%. No statistical difference between CHA2DS2-VASc scores was found as it pertained to number of recurrent events.DISCUSSION: We found no significant factors predicting risk of recurrent event and lower recurrence rates in pilots than the general population. This suggests CHA2DS2-VASc scores are not appropriate risk stratification tools in an aviation population and more research is necessary to determine risk of recurrent events in aviators with atrial fibrillation.Tedford J, Skaggs V, Norris A, Sahiar F, Mathers C. Recurrent stroke risk in pilots with atrial fibrillation. Aerosp Med Hum Perform. 2020; 91(4):352–357.


Stroke ◽  
2012 ◽  
Vol 43 (suppl_1) ◽  
Author(s):  
LAURA EVENSEN ◽  
Nan Liu ◽  
Yijun Wang ◽  
Bernadette Boden-Albala

Objective: To describe the relationship between sleep problems, measured by the Medical Outcomes Sleep scale (MOS) at baseline, in ischemic stroke and TIA (IS/TIA) patients and the likelihood of having a recurrent event, leading to vascular death. Background: Among IS/TIA patients, there is increased risk for recurrent vascular events, including stroke, MI and vascular death. While history of stroke is a major predictor of recurrent events, there may be unidentified factors in play. Sleep quality may predict recurrent vascular events, but little is known about the relationship between sleep and recurrent events in IS/TIA patients. Methods: The Stroke Warning Information and Faster Treatment (SWIFT) Study is an NINDS SPOTRIAS funded randomized trial to study the effect of culturally appropriate, interactive education on stroke knowledge and time to arrival after IS/TIA. Sleep problems and recurrent event information were collected among consentable IS/TIA patients. Cox proportional hazards models were used to describe relationships between sleep and recurrent vascular events in IS/TIA patients. The MOS, a 12 item sleep assessment, measures 6 dimensions of sleep: initiation, maintenance, quantity, adequacy, somnolence and respiratory impairment. Results: Over 5 years, the SWIFT study cohort of 1198 [77% IS; 23% TIA] patients were prospectively enrolled. This cohort was 50% female; 50% Hispanic, 31% White and 18% Black, with a mean NIHSS of 3.2 [SD ±3.8]. 750 subjects completed the MOS scale at baseline. In a multivariate analysis, after adjusting for demographics and vascular risk factors: gender, age, race ethnicity, NIHSS, stroke history, qualifying event type, hypertension, diabetes, smoking and family stroke history, longer sleep initiation is associated with combined outcome of IS/TIA, MI and vascular death [p=0.1, HR=1.09]. Significant predictors of vascular death included: trouble falling asleep (initiation) [p=0.05, HR=1.15]; not ‘getting enough sleep to feel rested’ and not ‘getting the amount of sleep you need’ (adequacy) [p=0.06, HR=1.18 and p=0.03, HR=1.18, respectively]; shortness of breath or headache upon waking (respiratory impairment) [p=0.003, HR=1.33]; restless sleep [p=0.07, HR=1.15] and waking at night with trouble resuming sleep [p=0.004, HR=1.23] (maintenance); daytime drowsiness [p=0.05, HR=1.18] and trouble staying awake [p=0.01, HR=1.25] (somnolence); and taking naps (quantity) [p=0.03, HR=1.22]. Conclusions: Sleep problems represent diverse, modifiable risk factors for secondary vascular events, particularly vascular death. Exploring sleep dimensions may yield crucial information for reduction of secondary vascular events in IS/TIA patients. Further investigation is needed to fully understand the effects of sleep on secondary vascular event incidence.


2015 ◽  
Vol 26 (4) ◽  
pp. 1969-1981 ◽  
Author(s):  
Jing Ning ◽  
Mohammad H Rahbar ◽  
Sangbum Choi ◽  
Jin Piao ◽  
Chuan Hong ◽  
...  

In comparative effectiveness studies of multicomponent, sequential interventions like blood product transfusion (plasma, platelets, red blood cells) for trauma and critical care patients, the timing and dynamics of treatment relative to the fragility of a patient’s condition is often overlooked and underappreciated. While many hospitals have established massive transfusion protocols to ensure that physiologically optimal combinations of blood products are rapidly available, the period of time required to achieve a specified massive transfusion standard (e.g. a 1:1 or 1:2 ratio of plasma or platelets:red blood cells) has been ignored. To account for the time-varying characteristics of transfusions, we use semiparametric rate models for multivariate recurrent events to estimate blood product ratios. We use latent variables to account for multiple sources of informative censoring (early surgical or endovascular hemorrhage control procedures or death). The major advantage is that the distributions of latent variables and the dependence structure between the multivariate recurrent events and informative censoring need not be specified. Thus, our approach is robust to complex model assumptions. We establish asymptotic properties and evaluate finite sample performance through simulations, and apply the method to data from the PRospective Observational Multicenter Major Trauma Transfusion study.


2002 ◽  
Vol 39 (3-4) ◽  
pp. 309-332 ◽  
Author(s):  
K. Sen ◽  
Manju L. Agarwal ◽  
S. Chakraborty

In this paper, joint distributions of number of success runs of length k and number of failure runs of length k' are obtained by using combinatorial techniques including lattice path approach under Pólya-Eggenberger model. Some of its particular cases, for different values of the parameters, are derived. Sooner and later waiting time problems and joint distributions of number of success runs of various types until first occurrence of consecutive success runs of specified length under the model are obtained. The sooner and later waiting time problems for Bernoulli trials (see Ebneshahrashoob and Sobel [3]) and joint distributions of the type discussed by Uchiada and Aki [11] are shown as particular cases. Assuming Ln and Sn to be the lengths of longest and smallest success runs, respectively, in a sample of size n drawn by Pólya-Eggenberger sampling scheme, the joint distributions of Ln and  Sn as well as distribution of M=max(Ln,Fn)n, where Fn is the length of longest failure run, are also  obtained.


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