While most adults adjust fairly well to hospital settings, children are much more unstable. In the 1980s, children in hospitals were dying because doctors and nurses couldn’t quickly obtain the necessary approval to take medical action. As a result, hospitals employed rapid-response teams (RRTs) that allowed medical personnel to act without first seeking approval. Then in 2005, hospitals introduced the Pediatric Early Warning Score (PEWS) to ensure that pediatric patients received critical care in a timely manner, before their conditions rose to emergency level. Originally developed to identify pediatric patients who were at risk of cardiac arrest, the system now models any type of clinical deterioration.
Scoring systems for PEWS vary by hospital. While the system has substantially lowered the rate of pediatric cardiac arrest outside of the intensive care unit (ICU), it is not without its flaws. The current PEWS analyzes only the most recent patient observations, rather than an accumulation of existing ones. As a result, it completely misses an estimated 15% of deteriorating patients. Additionally, it provides only a 30-minute warning window before cardiac arrest, which is too short a time period to prepare the ICU and execute an effective preventive response. During a minisymposium presentation at the 2017 SIAM Conference on Applications of Dynamical Systems, Andrew Roberts of Cerner Math presented a predictive model for an improved early warning system that identifies at-risk patients more quickly. His system improves cardiac arrest warning time and lessens physiological decline in children.
Roberts began by re-emphasizing the particular vulnerability of children in hospital settings. “Kids are at an extremely high risk of deteriorating quickly in a hospital,” he said. “They get unexpectedly sick, and there’s very little warning time.” Given the high demand for attention in hospitals, practitioners rarely check on patients as frequently as they should. “Initially, when a patient comes into a hospital, they only get looked every four-six hours, which is not very much,” Roberts said. Nurses assess patients with high PEWS scores more often, generally every two-four hours. Even so, many patients go longer than four hours without an evaluation. Such sparse data collection complicates the predictive process. “The clinical problem of pediatric cardiac arrest produces a mathematical problem,” Roberts said. “How do you make a prediction without much data?”
Roberts chose to base his model on six to 10 observations — the number of times hospital staff is likely to check on a risky patient within a 24-hour window. He also utilized prior patient observations, rather than only the most recent check-in. “PEWS quantifies what nurses are seeing and convinces doctors to come take action,” Roberts said. “But it doesn’t work as an effective early warning system.” Because it is based on nurses’ observations, the current PEWS system is subjective. Nurses switch shifts and interpret symptoms—such as skin color or irritability—in different ways, resulting in a lack of scoring consistency. Roberts used multiple data points to objectify the scoring system. “We want this to be nurse-independent,” he said. Instead, he based his system on regularly-collected vitals, such as heart rate.
Pediatric Early Warning Score at the Royal Alexandra Hospital for Sick Children in Brighton. Image courtesy of Andrew Roberts.
Unfortunately, nurses often record vitals—now acting as variables—at different times, rather than all at once. “You don’t even have the same time stamps for all the data observations you’re looking at,” Roberts said. To combat this inconsistency, he developed a ratio of deviations (RoD) that relates two measures of dispersion and can be used with low-frequency observations. “It’s basically the ratio of the root mean square of successive differences (RMSSD) and the standard deviation (SD),” he said. RMSSD is a local measure of dispersion, while SD is a global measure. Roberts’ proposed system will alert users if the RoD, or either parts of the ratio, increase. “An increasing RoD corresponds to a decreasing autocorrelation in some asymptotic sense,” he said. And a decreasing autocorrelation may indicate a Hopf bifurcation, or tipping point at which a system’s stability switches. Although Hopf bifurcations are usually considered reversible and thus not known as tipping points, in this case the delayed bifurcation has a hysteresis effect. Therefore, it makes sense to consider the bifurcation as a tipping point.
The RoD in Roberts’ predictive algorithm detects a change in the nature of jumps in a time series. The result is a synthesized data system. “It’s basically a Van der Pol oscillator with some extra variables,” he said. At this point, Roberts reminded his audience of the dangerous instability of children. “When either your heart rate or respiratory rate goes up, the other goes up to deal with it,” he said. “If you’re healthy, these things will stabilize.” The same is true of blood pressure. However, if conditions fail to stabilize, cardiac arrest occurs. “This is the physical reason for a Hopf bifurcation,” Roberts added. “And a Van der Pol oscillator is a good way to deal with it.”
Roberts conducted 100 control runs and 100 runs with a ramped parameter (with different sigmas) to test his model. After prescribing a mean sample time, generating 100 samples of each realization, and evaluating the RoD on each sample, he had nearly half a million samples. “The fewer samples I have, the less true positives I have, but that’s kind of expected,” he said. “The false positive rates are a little high, but if you only have six to 10 observations, you can’t expect to do much better.” He noted that the number of false negatives is not dependent on noise. This is not true of false positives, as noise can sometimes trigger them. Ultimately, Roberts learned that a noisier system performs better, with superior detection before bifurcation. “This is good, because sick kids tend to be noisy,” he said.
In a clinical setting, Roberts’ improved PEWS system identifies 10% more patients than a standard PEWS; its success rate is 95% rather than 85%. It also typically provides two to six hours of warning, rather than merely 30 minutes. Fundamentally, his system has the potential to advance pediatric cardiac care. “Movement to the emergency room becomes less emergent,” Roberts said. “They can do more to calm these kids down before things get too bad.”
||Lina Sorg is the associate editor of SIAM News.