Heterogeneity in the Population Explains Many Phenomena

HETEROGENEITY IN THE POPULATION EXPLAINS MANY PHENOMENA

High and increasing health care costs have attracted considerable interest from academics and policy makers in the decades leading up to this account, particularly in the United States. According to the Centers for Medicare and Medicaid Services, U.S. health care spending grew 4.6 percent in 2019, reaching $3.8 trillion, or $11,582 per person. As a share of the nation’s Gross Domestic Product (GDP), health spending accounted for 17.7 percent.[70]

Many studies have attempted to explain why health expenditures are so high in the United States. One key fact that many of these studies tried to unpack is that we don’t all spend the same amount on health care. In other words, there is heterogeneity in health care spending. Indeed, an important finding from these studies is that expenditures vary widely for individuals, tending to rise with age, and also across individuals in a cohort; that is, some people spend much more than others over a lifetime.

Understanding this heterogeneity is key to the design of sensible health policies. For example, a policy that treats all individuals in the same way (for example, by increasing insurance premiums to try to discourage people from accessing unnecessary medical care) is unlikely to reduce overall health care expenditures. On the other hand, a policy that focuses on chronic disease – the estimates cited here put chronic disease prevalence at about half of the U.S. population and attribute 86 percent of health care costs to it – would encourage interventions that could reduce the percent of people with chronic diseases or improve the cost-effectiveness of spending devoted to people with chronic diseases.[71] This is a more promising approach. In the 1950s, when acute diseases were more common than chronic diseases, this approach would not have been as effective.[72]

Chris Zook, a former PhD student of Richard’s, wrote his dissertation in the 1970s about the high-cost users of medical care. He used this maxim and data to show that the highest-cost users were people with specific chronic conditions. He said that one of the principles he learned from Richard was the idea that “average behavior” was rarely the norm in large groups. To understand group behaviors, the key was to identify the right relatively homogeneous segments of people who behaved similarly with regard to the phenomenon you were studying. After doing this, you could productively analyze the behaviors of each segment separately. Once that was done, you could reassemble the population to understand its aggregate behavior.

Chris went on to a career in business strategy and became a best-selling author on the subject. He credits this heterogeneity idea as “central to understanding the micro-economics of business strategy in study after study, ranging from the turnaround of LEGO (where an incredibly small percentage of obsessive users bought a huge share of LEGOs and were critical to understand separately and in a segmented way) to strategy work for a rental car company (where, again, the key was to understand the relatively homogeneous segments of renters in order to plan and market in a way that would optimize car utilization). I recall a healthcare study for a medical supplier that was trying to understand the enormous differences we were observing in the use of IV fluids across patients in intensive care units. It wasn’t until we got the homogeneous segments exactly right, involving some unexpected twists and dimensions, that we could uncover whether the differences were due to the underlying populations, or due to different medical practices. The list goes on and on through my life, across so many vexing problems of trying to understand and predict group behaviors.”

An example from the early pandemic relates to contagion. As many of us learned when following the news about COVID-19, the basic reproductive number, R0, is widely used to predict the spread of a disease. This number represents the average number of people an infected individual would infect in a fully susceptible population under specified conditions. Reproduction estimates under current conditions can differ, and neither kind of average captures all variation between groups. Not every sick person will infect the same number of additional people. “Superspreaders” are people who for several reasons are much more likely to infect others, and superspreading events generate a disproportionally large number of infections (as, for example, a February 2020 Biogen convention in Boston).[73]

Lee Hsien Loong, Singapore’s prime minister during the early pandemic and a former student of Richard’s, credits understanding the heterogeneity in rates of transmission and in the infected population as important to understand Singapore’s early experience with COVID around May 2020.

Heterogeneity in COVID transmission Lee Hsien Loong “The COVID-19 pandemic offers two vivid examples of the importance of understanding heterogeneity. Countries and cities are tracking their R0, the reproduction rate of the virus, and the death rate. These global parameters gloss over important heterogeneity in the population. Singapore started having COVID-19 cases in January 2020. As the outbreak continued, our R0 stayed well below 1. We took some comfort in this, and attributed it to assiduous contact tracing. But we were also acutely aware that this was a global figure for Singapore, and that the R0 could be much higher in specific settings if the virus spread there. And so it turned out. We have 300,000 migrant workers living in communal dormitories, where the transmission potential is high. A few undetected cases there snowballed into a major outbreak. The R0 in the dormitories was estimated to be between 2 and 3. However, another heterogeneity has kept our death rates very low. As of the time of writing, our fatality rate is around 0.05 percent, 34 deaths out of about 60,000 COVID-19 cases so far. This may be because many of our cases were migrant workers, who are younger and healthier than our general population. The vast majority have had mild or no symptoms, and only a handful needed ICU care. A similar sized outbreak among our elderly population or nursing homes in those early days would have been quite a different story. Fortunately, now that we have vaccines, we have prioritized the vaccination of the elderly and vulnerable, which has hopefully reduced this risk.”

Recognizing heterogeneity in the population can also help design policies for different segments of the population. For example, the Centers for Disease Control figures cited in this account reported that more than 90 percent of COVID deaths in the United States had occurred among those 55 years or older, and fewer than 1 percent among those younger than 25 years old.[74] This suggests that nursing homes are in a dramatically different risk category than are schools.

Richard argued from the early days of the pandemic that the failure to attend sufficiently to heterogeneity in risk had profound negative consequences in the United States and other nations. In the early days, we took woefully inadequate measures to protect elderly citizens, particularly those in long-term care facilities. At the opposite end of the spectrum, given the severe learning and mental-health consequences to young students from being out of school, and the relatively low risks to those students, Richard believes that we were far too reluctant to open schools, particularly to younger students and to those from families whose children would suffer more from online versus in-person education.

Understanding heterogeneity frequently helps to diagnose problems where behavior changes over time. Early in 2021, COVID-19 infection rates started dropping precipitously in many developed countries. The most frequent explanations were better social distancing, developing herd immunity, and vaccines getting into arms. Heterogeneity, an additional factor, got little attention.

To see how heterogeneity in risk might explain declining COVID infection rates, you can use a very simple hypothetical example and assume that half of the population has a high risk of contracting COVID (say 20 percent) and the other half a low risk (say 1 percent). These differences in risk of infection could be driven by people’s behavior, housing conditions, employment, the virus strains in their locale, etc. Initially the infection rates will be high because a lot of high-risk people would get infected, but as time passes fewer of these people remain at risk under the model’s assumption that infection removes someone from the susceptible pool for the period being considered, and the overall infection rate starts approximating the infection rate of the low-risk group (1 percent). This simplified example reveals the mechanism behind the phenomenon: high-risk people make the overall infection rate high at the beginning but as time goes by they become less prevalent in the population at risk of getting infected. This drives the overall infection rate down over time.[75]

The above pattern applies to many areas beyond COVID-19. In fact, Richard has documented heterogeneity in risk as a reason why hernia recurrences, smoking relapse rates, and criminal recidivism rates decline over time.[76] This does not eliminate other factors as well – but heterogeneity is important and often neglected.

One of the most interesting settings in which heterogeneity is important is college admissions. In a landmark book, The Early Admissions Game, Richard and his coauthors argue that early admissions, a process by which many applicants gain access to elite colleges in the United States, provides benefits to some students by boosting their chances of admissions, but is not appropriate for everyone.[77]

Some have argued that because applicants from high-income families tend to apply through early admissions (since they are more likely to have the information and resources needed to do so), it offers an unfair advantage to them. “Early-admission programs tend to advantage the advantaged,” Derek Bok, former president of Harvard, said in 2006 when Harvard dropped early admissions (it was later reinstated).[78] Barry Nalebuff, a professor at Yale School of Management and one of Richard’s coauthors, shows how heterogeneity matters when comparing applicants at the admissions cutoff. This comparison tests the stated argument about qualifications; fairness can also involve criteria beyond test scores.

Heterogeneity in college admissions Barry Nalebuff Richard likes giving people puzzles to solve. These puzzles aren’t just brainteaser exercises but ways of understanding policy problems. The trick to solving his puzzles is often a combination of marginal analysis combined with understanding heterogeneity in the population. I particularly remember a puzzle I struck out on. At the time, colleges were debating the fairness of early admissions. Richard noted that Stanford University’s president Hennessy defended the fairness of early admissions by emphasizing that the average SAT score of those admitted early was 210 points higher than the average SAT score of those admitted in the regular pool. This suggested that applicants admitted under early admissions were more qualified than those admitted under regular admissions. Was that a valid argument? I focused on the fact that early applicants were more likely to come from better schools with better counselors and better test preparation. Thus, the scores of early applicants might be more inflated relative to their innate ability. Too complicated, replied Richard. He provided the key insight that showed the failure of the Stanford president’s argument: To determine if early admission is fair, we need to know if the worst person admitted under early admission is better than the best person denied under regular admission. Think about the margin, not the average! The early action pool has many students with perfect SAT scores, so the high average might be hiding other early admission students who have much lower scores – lower than those of some students who might be rejected under regular admission. Like so many of Richard’s lessons, the answer is obvious – but only in hindsight.

Yair Tauman, a coauthor with Richard on papers about games involving espionage and deterrence, notes that heterogeneity, combined with imperfect information, can lead to counterintuitive results. He observes that “Russia has a number of ways it could try to disrupt U.S. intelligence efforts.” Intriguingly, he then notes that in some plausible situations, “Russia should deliberately employ less effective disruptive measures. Both countries will take less hostile actions if the signal on Russian capabilities is more reliable.”[79]