# Clusters, Gaps, and RandomnessVasovagal Syncope Recurrence Patterns

## Author + information

- Received September 27, 2016
- Revision received February 2, 2017
- Accepted February 16, 2017
- Published online September 18, 2017.

## Article Versions

- previous version (April 26, 2017 - 11:00).
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## Author Information

- Inderjeet S. Sahota, MSc,
- Connor Maxey, BSc,
- Payam Pournazari, MD, MSc and
- Robert S. Sheldon, MD, PhD
^{∗}(sheldon{at}ucalgary.ca)

- ↵∗
**Address for correspondence:**

Dr. Robert S. Sheldon, Libin Cardiovascular Institute of Alberta, University of Calgary, 3280 Hospital Drive NW, Calgary, Alberta T2N 4Z6, Canada.

## Graphical abstract

## Abstract

**Objectives** This study elucidated the temporal recurrence patterns of syncope in patients with frequent vasovagal syncope (VVS).

**Background** Understanding the temporal distribution of fainting spells in syncope patients may illuminate biological processes and inform decision making.

**Methods** Patients from the POST 2 (Prevention of Syncope Trial 2) were included; all had VVS and fainted ≥4 times in the study year, providing ≥3 interevent intervals (IEIs). Only fainting spells separated by ≥1 day were included. IEI distributions were analyzed using Poisson modeling and cumulative sum distributions.

**Results** Twenty-four patients (5 males, 19 females; mean 33 years of age) had a total of 286 syncopal events and 262 IEIs, with a median 6 IEI. They resembled excluded subjects in age and sex but fainted more often in their lives (median: 57 vs. 13 fainting spells, respectively; p < 0.0001) and in the previous year (median: 23 vs. 3 fainting spells, respectively; p < 0.0001). Subjects had a median IEI duration of 8 (interquartile range: 4 to 19) days. The IEI distributions were fit well by Poisson models with a median r^{2} of 0.94 (95% confidence interval: 0.91 to 0.97). The patients’ Poisson rate constant frequencies were 7 to 263 fainting spells/year with a median rate of 19 fainting spells/year. The modal syncope frequency was 10 to 15 fainting spells per year. Seven patients had biexponential distributions, and many patients fainted in clusters.

**Conclusions** Patients with frequent VVS have fainting spells that occur randomly in time. Clusters of syncope occur, and in this population, there is a central tendency to 10 to 15 fainting spells per year. This provides a quantitative measure of frequency and predictability that may afford individualized treatment goals.

We report the temporal distribution of recurrences of vasovagal syncope (VVS). This troublesome syndrome occurs in at least 35% to 40% of people and usually recurs. Young and middle-aged people have a median of 3 to 4 fainting spells in their lifetime, and the predilection to fainting can last decades (1). There is growing evidence that most people improve in the absence of specific treatments (2). Understanding and measuring these changes in syncope frequency may lead to improved risk stratification and treatment.

Syncope and supraventricular tachycardia events fluctuate within single days (3–5), but their longer fluctuations are unknown. The 3 main situations predisposing to a syncopal spell, prolonged orthostatic stress, exposure to blood, trauma, or acute pain, and heavy exercise, are not uncommon in many lives and usually do not provoke syncope. There also is speculation that VVS may occur in clusters. Understanding how people differ among themselves and over time is an important step.

One possibility is that the susceptibility to the reflex varies randomly over time, and differs among people. If so, the likelihood of remaining recurrence-free in each person should fit a Poisson distribution, known well as a monoexponential decay (6). The demonstration that recurrences fit the Poisson model would have implications for understanding the persistence of the trait and for establishing goals for treatment, using datasets of varying lengths and events and having patients serve as their own controls. We therefore aimed to demonstrate whether syncope events could be depicted as occurring randomly and whether these events appear to cluster. To begin, we modeled the distributions of the days with syncope recurrences in patients with frequent syncope in the POST 2 (Prevention of Syncope Trial 2) (7). To identify clusters, we depicted recurrence patterns with their cumulative distribution patterns.

## Methods

### Study subjects

Subjects were participants in the POST 2 trial (NCT00118482). This was a randomized, placebo-controlled, double-blind trial that compared the effect of fludrocortisone with that of placebo in preventing VVS (7). Institutional ethics committees at all sites approved the study. Patients were eligible for POST 2 if they had VVS according to the Calgary syncope score (8) and ≥3 lifetime syncopal spells. All subjects were free of cardiovascular disease, permanent pacemakers, carotid sinus hypersensitivity, and other major noncardiac medical conditions and had no other identifiable cause of syncope. POST 2 did not demonstrate significant benefit compared to placebo, although benefit was noted in patients after 2 weeks of treatment.

All patients in both the control and the experimental groups were eligible for this analysis because there were no significant treatment benefits in the population as a whole, and populations in both arms showed substantial improvement. Patients were followed for 1 year, and the dates of subsequent fainting spells in the follow-up year were recorded for each individual. The POST 2 adjudication committee reviewed and approved all syncope events. Patients were eligible for inclusion in this substudy if they had experienced at least 4 syncopal spells in the follow-up year, providing a minimum of 3 interevent intervals (IEIs).

### Data analysis

The primary unit of analysis was any day with at least 1 syncopal spell in the follow-up year, recognizing and accepting the diurnal variability of VVS and the potential for multiple spells within 1 day due to a persistent state that day. IEIs were the number of calendar days between adjacent syncopal spells. There were 2 analyses: the first analysis assessed whether syncope days occurred randomly and therefore had a rate constant, and the second analysis assessed whether syncope may occur in clusters.

### Assessment of randomness

The IEIs for each patient were plotted as Kaplan-Meier distributions, and Poisson (monoexponential decay) models were applied to each to determine their fit. Constraints on the modeled data included a K value (rate constant, syncope days/year) >0 and plateau = 0. Recurrent syncopal spells that were randomly distributed in time should have provided a good fit to the Poisson model. Note as well that the Poisson rate constant was the arithmetic mean syncope frequency of the events and that confidence intervals were estimated. To search for evidence of multiple frequencies, we also tested biexponential models for all patients. Higher order modeling was not conducted because of the limited sizes of the data sets. As well, this method only demonstrates that rates of individual recurrences share a common rate constant and does not address whether they occur contiguously or discontinuously. We defined a better biexponential fit if the improvement in fit was at least an r^{2} value of >0.01 and the higher rate constant was at least twice the lower rate constant. Syncope recurrence rate constants are expressed as syncope days/year.

### Assessment of clustering

Most available statistical techniques for estimating clustering require data sets far larger than those reported here (9–12). However, a plot of the cumulative sum of events relative to time is useful (9). If events are randomly distributed, the events should be linearly and tightly distributed. Clusters, which were defined by stable changes in syncope frequency, usually will appear as abrupt increases in the slope, whereas gaps will appear as breaks in the curve. Figure 1 illustrates the analysis of a theoretical patient. An initial cluster terminates in an asymptomatic gap, followed by a second cluster, which is followed immediately by a third cluster with a slower rate of syncope recurrences.

### Statistical analysis

Statistical analyses were performed using Prism 6 for Macintosh (Graphpad Software, Inc., La Jolla, California). All data are medians with interquartile ranges (IQRs) and categorical data as counts and percentage, unless otherwise stated. The statistical significance of differences were assessed using the Mann-Whitney *U* and Kruskal-Wallis tests and the chi-square statistic. The goodness of fits of the Poisson models were expressed as the statistical significance of the correlation coefficient.

## Results

### Study population

Twenty-four subjects met the inclusion criteria for this study, of whom 5 were males (Table 1). The median (with IQR) age at the time of entry into POST 2 was 33 (IQR: 22 to 48) years of age. Compared to the excluded subjects, they were of similar ages and sex distribution and had been fainting for a similar number of years. However the included subjects had fainted more often in their lives (median: 57 vs. 13 fainting spells, respectively; p < 0.0001) and more frequently in the previous year (median: 23 vs. 3 fainting spells, respectively; p < 0.0001). The frequencies of syncope in the distant history were similar in the 2 populations (median: 1.22 vs. 0.82 fainting spells per year, respectively).

### Interevent intervals

The 24 subjects had a total of 286 syncopal episodes and 262 IEIs. Subjects had a median of 6.5 (IQR: 4.0 to 18.0) fainting spells and a median of 5.5 (IQR: 3.0 to 18.0) IEIs and median IEI durations of 8 (IQR: 4 to 19) days (Figure 2). The actuarial distributions of the IEIs for each of the 24 patients were subjected to monoexponential Poisson modeling analysis.

### Outcome syncope frequencies

The rate constant, k, in the Poisson distribution is also the mean frequency. Therefore, the Poisson equation can be used to estimate outcome frequencies with confidence intervals in datasets that are both less than a full year and bounded on either side by a syncopal spell. Such outcome patterns are otherwise difficult to analyze. The distributions of all individuals were fit well by monoexponential Poisson models (Table 2). Most individuals (19 of 24 [79%]) had r^{2} values ≥0.9. The lower values were 0.61, 0.78, 0.84, 0.87, and 0.89. The rate constants, which are the mean syncope recurrence frequencies, ranged from 7 to 263 syncope days per year.

Of the 24 subjects, datasets were too small to test a biexponential model in 9 subjects, the improvement in fit was <1% in 5, and the rate constants were different in <10% in 6, leaving 5 subjects with an improvement in fit of >1% and rate constants of >10% apart (Table 3). Figure 3 depicts the syncope-free survivals for 2 patients whose rates were best fitted by monoexponential models and 2 patients whose rates were best fitted by biexponential models. Note the poorness of fit by the monoexponential models due to the prolonged tails of the curves. Two more patients had fits equivalent to both models, but the higher biexponential rate constants were at least double the slower rate constants. In total, at least 7 of 24 subjects had reasonable evidence of 2 syncope frequencies.

Figure 4 depicts the modelled frequency of syncope days per year. Figure 4 top left panel depicts the total population, except for 1 subject with a frequency of 262 days/year. There is a skewed distribution with a clear modal frequency of 10 to 15 days per year. Figure 4 top right panel depicts the population of 17 patients with evidence of only 1 syncope frequency. There is a similar skewed distribution with a modal frequency of 10 to 15 days per year. Figure 4 bottom panels depict the lower (left) and higher (right) modelled frequencies for the 7 patients who fit biexponential models. Fully 6 of 7 subjects had lower frequency rates of 10 of 14 days per year.

The overall monoexponential rate constants and therefore the outcome syncope frequencies did not vary with age or sex or lifetime syncope number, duration, or frequency (p = 0.10 to 0.66).

Knowing the rate constants derived from individual events does not establish that the events occur together; they simply represent the probabilities that each event will recur. To establish how events occur in time we assessed the cumulative sum of recurrences in the observation period for each patient.

### Distribution of recurrences in time

Figure 5 illustrates 9 examples (and not exemplary results) of recurrence distributions. Patients with a single model throughout time should fit closely to the linear regression line, and most patients deviated from the linear regression line of best fit. Figure 5 patients 20 and possibly 21 appear to fit the line best and have single processes. In contrast, Figure 5 patients 7 and 16 have 2 clusters with interposed gaps. Figure 5 patients 15 and 17 have obvious gaps at the start of observation periods before clusters, and both clusters are followed by epochs with slower rates.

## Discussion

Our main findings are that the days when VVS occurs are distributed randomly in time with easily identifiable rate constants and that some appear to exist in clusters with distinct starts and stops. These findings provide quantitative measurements for studying biological mechanisms and providing patient-specific care.

### Syncope usually recurs

Numerous studies have reported that many patients have recurrent VVS and that the tendency to have syncope can last for decades (2). For example, in POST 2, patients had a median 15 fainting spells over 9 years before enrolment and a median 4 fainting spells in the immediately preceding year (7). In a meta-analysis of 15 cohort studies and randomized trials of syncope and over 2,000 patients, the mean number of fainting spells in the year before enrollment was 2.6. In the year after randomization approximately half of subjects fainted. Baron-Esquivias et al. (13) reported that 30% of patients without specific treatment fainted in follow-up, with a higher likelihood of recurrence higher in patients with more previous episodes of syncope. Malik et al. (14) studied a smaller cohort of 46 patients with VVS up to 6.5 years with a mean follow-up period of 2 years and reported that 87% of patients had recurrent syncope with a median of 8 recurrent syncopal spells in the follow-up period. The time to first recurrence significantly predicted future frequency of spells, and the time to second recurrence had even greater predictive power (R = −0.92; p < 0.001). These reports suggest that patients can enter and persist in a state of elevated predilection to syncope.

Here we directly demonstrate that patients enter discretely bounded states of predilection to fainting and that the ability to fit the data to a Poisson distribution indicates that the characteristics of the state persist stably for months. Understanding how recurrences are distributed in time may afford individualized goals for therapy and novel approaches to biological understanding.

### Personalized medicine

Demonstrating the randomness of syncope recurrences and the fit of the data to a Poisson model may permit personalized targets for judging the effectiveness of therapeutic interventions. Similarly, it may provide a tool for establishing the significance of the beginning and end of apparently clustered events. Poisson modeling was first developed to assess the significance of clustering of infrequent events such as wrongful convictions in post-Napoleonic France (15) and then used for, among other purposes, studying deaths from horse kicks in the Prussian army (16) and unguided missile strikes on London during World War II (17).

The use of Poisson modeling shows promise for estimating patient-specific changes in time, provided that the distributions have first been shown to be random. They permit calculation of patient-specific rates and address a critical issue in clinical trials of paroxysmal events. This is the common lack of datasets that extend through a previously defined observation period and the situation in which patients withdraw after the final of several events. The Poisson distribution permits the calculation of a mean frequency in datasets bounded on either side by an event and specifically does not require a full observation period. Knowing that recurrences occur in Poisson distributions allows one to predict the likelihood of recurrences and also the statistical significance of periods of time without events. The confidence intervals around the distribution therefore permit personalized targets for syncope-free survival. Furthermore, few events are necessary to establish a baseline frequency, again permitting all patients to have personalized targets. Finally, many patients may not need to be followed for a full year, as the rate constants for frequent syncope establish the lengths of time of event-free survival to reach specified targets of statistical significance.

### Source of idiosyncratic rates

The ability to derive rate constants from events recurring over periods up to months long suggests that patients are in stable states characterized by constant probabilities of syncope. These states in turn appear to be idiosyncratic, with rate constants differing among subjects. We can only speculate on the source of the rate constants. First, it might be that the threshold for syncope is similar in all patients, but provoked by extraordinary events that occur at idiosyncratic rates manifested in idiosyncratic rate constants. Given the mundane situations in which much syncope occurs, such as quietly sitting or standing, this seems unlikely. Second, it may be that each subject has an idiosyncratic threshold for the vasovagal reflex, with some more prone than others to responding to daily situations. Finally, it may be that there is an event, either centrally or peripherally, that sets the threshold for the vasovagal reflex but varies, recurring at idiosyncratic rates, again manifested in idiosyncratic rate constants.

Importantly, the rates are defined from the probability of recurrence of individual fainting spells in each subject but do not address whether events with similar probabilities occur contiguously. For this, we performed a cluster analysis using the cumulative sum method (9).

### Cluster analysis

Clusters of syncope events with similar rate constants occurred in at least 5 of 24 subjects and possibly many more. They are bounded on either side by either asymptomatic gaps or by epochs with lower rate constants. As with heart rate, a gap (or asystole) is a gap only until the next event, and this interval itself defines a lower rate. For example, a gap of 30 days (or 3 s) is equivalent to a rate of 12 syncope days per year (or 20 beats/min). Similar clusters may exist in drug-refractory epilepsy, although the evidence for them generally is statistical (9–12). There appears to be a central tendency for lower frequency syncope to cluster around 10 to 15 syncopal spells per year, whereas the higher frequency clusters are more dispersed. These data are limited by their having been identified in a highly symptomatic population of very frequent fainters. For example, patients in clinics might have much longer clusters that could not be identified in this brief observation period. However the important point is that syncope of defined and stable frequency occurs in clusters in at least a sizeable minority of patients.

### Study limitations

The subjects in this substudy were highly selected from those who agreed to participate in a randomized clinical trial and may not be representative of the larger population. Indeed, most patients have recurrence rates far lower than those reported here, and whether syncope occurs randomly in time at these low rates was not addressed here. The sampling event was the day of that syncope occurred and not the specific time, and therefore, there will be some error on the scale of hours but not days. Similarly, we cannot comment on diurnal fluctuations in the likelihood of syncope (3–5). We also measured only days with frank syncope, and doubtless, there were other days during which patients had pre-syncope without progression to loss of consciousness. We did not separately analyze patients taking placebo or treatment, as this is the subject of ongoing study.

## Conclusions

The results do not allow us to address directly whether syncope occurs in clusters, although it does provide a methodology for determining the statistical significance of the edge of a cluster.

**COMPETENCY IN MEDICAL KNOWLEDGE:** Frequent VVS occurs randomly when measured over intervals of at least 1 day and, in many patients, occurs in clusters.

**TRANSLATIONAL OUTLOOK:** Poisson distribution provides a standardized measurement of recurrence likelihood, presumably reflecting a biological process. It also may inform reasonable estimates for when improvement can be judged, and ultimately define whether syncope occurs in clusters.

## Footnotes

All authors have reported that they have no relationships relevant to the contents of this paper to disclose.

All authors attest they are in compliance with human studies committees and animal welfare regulations of the authors’ institutions and Food and Drug Administration guidelines, including patient consent where appropriate. For more information, visit the

*JACC: Clinical Electrophysiology*author instructions page.

- Abbreviations and Acronyms
- IEI
- interevent interval
- VVS
- vasovagal syncope

- Received September 27, 2016.
- Revision received February 2, 2017.
- Accepted February 16, 2017.

- 2017 American College of Cardiology Foundation

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