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Copyeditor: Timi Santiago

ManagingOrganizational Complexity

JONA Volume 40, Number 11, pp 00-00 Copyright B 2010 Wolters Kluwer Health | Lippincott Williams & Wilkins

Flash Crashes, Bursts, and Black Swans Parallels Between Financial Markets and Healthcare Systems Bruce J. West, PhD, FAPS, FARL Thomas R. Clancy, PhD, MBA, RN As systems evolve over time, their natural tendency is to become increasingly more complex. Studies in the field of complex systems have generated new perspectives on management in social organizations such as hospitals. Much of this research appears as a natural extension of the cross-disciplinary field of systems theory. This is the 16th in a series of articles applying complex systems science to the traditional management concepts of planning, organizing, directing, coordinating, and controlling. In this article, Dr Clancy, the editor of this column, and coauthor, Dr West, discuss how the collapse of global financial markets in 2008 may provide valuable insight into mechanisms of complex system behavior in healthcare. Dr West, a physicist and expert in the field of Authors’ Affiliations: Chief Scientist (Dr West), The Mathematical and Informational Directorate of the US Army Research Office, Research Triangle Park, North Carolina; Clinical Professor (Dr Clancy), School of Nursing, University of Minnesota, Minneapolis. Corresponding author: Dr Clancy, School of Nursing, Weaver Densford Hall, 308 Harvard Ave South, University of Minnesota, Minneapolis, MN (clanc027@ umn.edu). DOI: 10.1097/NNA.0b013e3181f88a8b

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complex systems and network science, is author of a chapter in the book, On the Edge: Nursing in the Age of Complexity. On May 6, 2010, the DOW Jones Industrial Average (DJIA), a leading indicator of stock prices, plunged 999 points in less than 30 minutes. This unprecedented and unexpected drop in prices eliminated more than $800 billion in value to investors. As quickly as it plummeted, the DJIA regained $600 billion of its loss in just over 10 minutes, leaving investors reeling and Securities and Exchange Commissioners bewildered.2 Although analysts are still piecing together what happened on May 6, a number of underlying themes are surfacing. As the build-out of the intranet has matured, vast electronic communication networks between multiple, interdependent domestic and international financial markets have emerged. Collectively, the structure of the network is tightly coupled, and information regarding stock prices is communicated instantaneously to traders. Sophisticated computer models predict the direction of stock prices and automatically

activate large blocks of buy-andsell orders. Because of extremely complex financial products called derivatives, stock price fluctuations are amplified exponentially with sudden, unpredictable changes in the economic environment. Here we note the unpredictable nature of the changes and emphasize that although unpredictable, their occurrence was not entirely unexpected as foretold in Taleb’s3 book, The Black Swan. This kind of convergence of factors occurred on May 6, when unpredicted political unrest in Greece created a cascading series of sell orders across the markets, which sent stock prices plummeting. Now dubbed a Bflash crash,[ the wild volatility in the stock market on May 6, has eerie parallels to today’s increasingly complex healthcare systems. Both financial and healthcare systems contain a connected web of subsystems that communicate through tightly coupled electronic networks. In healthcare systems, these networks are facilitated through electronic medical records linked by the intranet. As health systems have matured and become more complex, the flow of data has become progressively dependent on the structure of the network. In

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Managing Organizational Complexity

Figure 1. Percent occupancy for a medical nursing unit over a 1-year period.

complex networks that develop without design (such as the intranet), the distribution in the number of connections between elements often follows a power-law distribution; roughly 80% of the links to Web sites occur in less than 20% of them. Complex networks with power-law distribution are prone to black swans, a single unpredicted cumulative event of enormous impact. This may, in part, have contributed to the flash crash the financial markets experienced on May 6, 2010. Could this happen in your healthcare system?

Bursts The answer is a resounding yes, and it probably happens more often than we like to admit. Consider the probability that a nursing unit’s daily census suddenly jumps from its average occupancy of 60% to 100% of bed capacity. If we assumed the percent occupancy on the unit is normally distributed around a mean of 60% (Figure 1), the probability of this occurring is less than 0.3%. And that would be correct if we analyzed only the midnight census, the usual statistics hospitals report. In contrast, the interarrival rate of admissions to nursing units is usually stochastic (a mixture of both random and scheduled events). For

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example, Figure 2 presents a histogram representing the minutes between admissions for a typical medical nursing unit. Notice the significant difference in the patterns between the 2 distributions. Figure 1 is a normal distribution, whereas Figure 2 is apparently an exponential distribution with a very long right tail. Figure 2 suggests that there is a high frequency of admissions with a very short interarrival rate (the tall columns on the left) interspersed with long periods without an admission (the short columns on the far right). In other words, there are Bbursts[ of admissions (during the day and evening shifts) followed by long periods of few admissions (the night shift). One method of visualizing admission bursts is to use timeseries plots. Figure 3 presents the interarrival rate of admissions to the same nursing unit depicted in

Figures 1 and 2 over a 2-week period. Figure 4 shows how the census fluctuates with changes in the admission rate over the same period. Admission bursts are represented in Figure 3 as periods where a cluster of interarrival rates is near 0 minute. There are 2 bursts noted in Figure 3: the first is from admissions 12 to 26 (on the x-axis), and the second is from admissions 56 to 61.

Power-Law Distributions Notice in Figure 4 that immediately following a burst, the census jumps to more than 100% of bed capacity (25 beds). When the census spikes more than 100% capacity, the difference represents those patients admitted to the unit but are waiting for a bed to open. Clearly, the census peaks at 100% or greater far more frequently than the histogram calculated from the midnight census suggests (0.3%). These sharp spikes in census correlate highly with nonlinear increases in nursing workload and represent healthcare’s equivalent of a flash crash. In fact, Figure 2 can be transformed (Figure 5) to show that the admission interarrival rate follows a power-law distribution similar to those seen in the financial markets prior to their crash on May

Figure 2. Minutes between admissions onto a medical nursing unit fit by an exponential distribution (solid curve).

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Managing Organizational Complexity

Figure 3. Time-series plot of minutes between admissions over a 2-week period.

6, 2010. Figure 5 is a log-log graph of Figure 2, and the solid curve represents the best fit to the histogram data (a hyperbolic distribution) and asymptotically becomes inverse power law. Like the stock market, the frequency of the occurrence of an earthquake of a given magnitude also has the form shown in Figure 5, and the challenge is to design a building to withstand the 100-year earthquake, or a financial system that has safeguards to minimize the damage of the flash crash or a healthcare system with the same protections. Flash crashes are indicative of the increasingly interdependent nature of interactions woven into the electronic and social net-

works of health systems today. A flash crash occurs when multiple factors converge simultaneously to unpredictably and rapidly increase nursing workload. These factors may include a burst in admissions, electronic order transactions, or patient acuity. If these factors were simply random, the probability of them all occurring simultaneously would be very small. However, as shown in Figures 2, 3, and 4, these bursts in census and workload spike quickly but are never captured in the midnight census. Power-law distributions are suggestive of a complex mix of underlying random and nonrandom mechanisms that drive system behavior. In the case of admission bursts, new evidence suggests

that this mechanism might result from simply setting priorities. The flow of entities (people, information, things) in human and other complex systems has a natural rhythm that is Bbursty.[ Whether it is the frequency of e-mails, handwritten letters, or patients arriving at an emergency room, human activity usually occurs in bursts. And these busts are described statistically by a power-law distribution. In his new book, Bursts: The Hidden Pattern Behind Everything We Do, Barabasi4 suggests that these bursts result from having to prioritize activities. For example, if there are a limited number of vacant beds on a nursing unit, those patients with the most critical needs are admitted first, whereas

Figure 4. Time-series plot of a medical unit’s census after every admission over a 2-week period.

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Managing Organizational Complexity

Figure 5. Log-log graph for the time interval between admissions on a medical unit for 1 year of data.

those with less critical needs must wait. This results in busts of activities (critical admissions) with long periods without activity (no admissions). What is most amazing about this phenomenon is the frequency of power-law distributions, regardless of the area. There seems to be an underlying principle at work when prioritization takes place in complex human systems (such as hospitals).

Black swans The presence of power-law distributions in complex systems has important implications for measuring performance in healthcare system behavior. For example, performance improvement methodologies that assume events are random, independent, and nor-

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mally distributed underestimate the frequency of Bbursts[ as well as unpredicted events of enormous impact (black swans). In nursing systems, these busts might result in sudden spikes in workload or flash crashes. If flash crashes converge on multiple units simultaneously, the result may be a black swan such as a patient death from a medical error. In the financial markets, computer models predicted that the probability of multiple markets crashing simultaneously was virtually impossible, then it happened in the fall of 2008 when the US suffered the worst financial crisis since 1929. However, this highly improbable event was not entirelyunexpected;scientistsworking in econophysics had uncovered

an inverse power law predicting the existence of flash crashes and black swans. But because such Blaws[ did not predict precisely when flash crashes would occur, they were systematically ignored by the global economics community and not included in their dynamic models. No strategy was developed to mitigate their effect, and we are now suffering the consequences of that oversight. We believe this, to some extent, can and is happening in healthcare systems today. In future articles, we plan to investigate various methods to identify power-law distributions in critical healthcare processes and discuss strategies to anticipate and reduce the effect of and recover from flash crashes and black swans.

REFERENCES 1. Lindberg C, Nash S, Lindberg C. On the Edge: Nursing in the Age of Complexity. Bordentown, NJ: Plexus Press; 2008. 2. Krantz M. Cause of Fflash crash_ still unknown but knowledge can help protect you. Available at http://www.usatoday. com/money/perfi/columnist/krantz/ 2010-05-11-flash-crash_N.htm. Accessed July 12, 2010. 3. Taleb NN. The Black Swan. New York, NY: Random House; 2007. 4. Barabasi AL. Bursts: The Hidden Pattern Behind Everything We Do. New York, NY: Penguin Publishing; 2010.

JONA  Vol. 40, No. 11  November 2010

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