The Tough Math Behind Humanitarian Aid

Northern Mali, wracked by drought and by the occupation of Islamic jihadists, now faces mass starvation. The United Nations estimates that 585,000 need “immediate food relief.” But as of late February, international donors had come up with only $17 million in emergency assistance, a tiny fraction of the money that relief groups say is necessary to prevent widespread death.

Mali is hardly alone. The cruel truth is international relief groups are routinely forced to ration scarce supplies of high-powered, ready-for-use therapeutic foods.

If 5,000 children are undernourished, but there isn’t enough emergency nutrition to go around, who gets top priority? It’s a question of triage. The standard policy today is to spread the food as widely as possible, even if very few children get a full dose.

In a provocative new paper this week, however, researchers at Stanford’s Graduate School of Business and the University of Bergen in Norway argue that an ‘all-or-nothing” approach would save more lives.

If relief workers are forced to practice triage, they say, the best approach is to concentrate all the available relief on the children closest to death’s door.

The findings run counter to current practices at most relief organizations. They may not sit well with humanitarian groups either, as relief workers could be forced to make wrenching distinctions among children who are all undernourished.

The researchers — Lawrence M. Wein, Jeffrey S. Skoll Professor of Management Science at Stanford’s Graduate School of Business; Yan Yang, a former graduate student at Stanford’s Institute for Computational and Mathematical Engineering; and Jan Van den Broeck at the University of Bergen — published their findings March 4 in Proceedings of the National Academy of Sciences.

The team based its findings on mathematical analysis of data on thousands of undernourished children aged 5 or younger in the Democratic Republic of Congo and in Niger. Their conclusion: An “all-or-nothing” approach, combined with a more comprehensive measure of undernourishment, could reduce deaths and life-limiting disabilities by 9%, compared with current policies. Alternatively, they estimate, relief groups could get the same health results as today but reduce the cost by 61%.

The researchers cautioned that their findings need more testing, because the available data has limitations. But the study may be more important as an example of creatively applying mathematical tools to humanitarian relief.

At Stanford, Wein has already made headlines by using mathematical models to analyze challenges in health care, such as quantifying the modes of influenza transmission, as well as in handling terrorist threats.

After the terrorist attacks on Sept. 11, 2001, for example, Wein and his colleagues used mathematical modeling to devise novel responses to potential attacks involving anthrax, smallpox, and botulinum toxin. Some of their proposals are now government policy. In the case of anthrax, for example, President Obama has approved Wein’s recommendation of using U.S. postal carriers to deliver powerful antibiotics door to door. Likewise, Wein used mathematical analysis to show that terrorists could easily kill legions of people by slipping minute amounts of botulism into the nation’s dairy supplies — but that the threat could be greatly reduced by requiring dairies to pasteurize more intensively and by making simple improvements in security. When Wein wrote an op-ed entitled “Got Toxic Milk?” for The New York Times, the Bush administration and the dairy industry temporarily blocked publication of his peer-reviewed study.

The common thread through much of Wein’s work stems from his mathematical analysis of manufacturing. In the 1980s and 1990s, he wrote heavily about “queuing” and dynamic scheduling in semiconductor production. He then applied similar mathematical tools to analyze a host of other questions: the best way to allocate kidneys for transplant, the best “cocktails” of antiretroviral drugs for treating AIDS, and the best strategy to eradicate smallpox after a bioterrorist attack.

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MANA, 2013

In the new paper, Wein, Yang, and Van den Broeck focus on getting the most out of “ready-for-use therapeutic foods,” or RUTFs, in famine situations. RUTFs are essentially protein-rich pastes, often made from peanuts, which are packed with a balance of vitamins, carbohydrates, and other nutrients. They don’t need to be heated or cooked, can be stored without refrigeration, and can dramatically reverse the effects of starvation.

Using advanced statistical regressions, the researchers analyzed the impact of different doses of RUTFs on children with different degrees of undernourishment. The two main gauges of undernourishment are “wasting,” based on weight-height ratios or “WHZ” scores, and “stunting,” based on height and age or “HAZ” scores.

In practice, relief organizations screen children primarily by WHZ scores for acute wasting. But the researchers found that the best predictor of early death and life-shortening disabilities was a combination of both the stunting and wasting measures. Stunting, they found, significantly aggravates the impact of wasting as a cause of early death.

The second big finding was that an “all-or-nothing” distribution of ready-for-use food saves more lives. It would be more effective, for example, to give full doses of RUTF to the 25% of children who are the most severely undernourished than to give half doses to the 50% who are the worst off.

The researchers acknowledge that their approach may be politically or culturally unacceptable in some areas, and they caution that empirical issues remain. But Wein said their approach shouldn’t pose new moral or ethical issues. That’s because most current approaches already practice a form of triage by defining severe undernourishment as a WHZ score of less than -3. Children with slightly milder symptoms are given less-powerful “supplements.”

“If you believe our results, which appear to be reasonably robust, one would say that blanket distribution poses a bigger ethical problem than an all-or-nothing approach,” Wein said.