The odds of survival

A mathematical dabbler is looking to find the odds. The chances of finding a donor. Of anyone in need of a donor
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First Published: Thu, Apr 11 2013. 06 35 PM IST
A file photo of a hospital in New Delhi. Photo: HT
A file photo of a hospital in New Delhi. Photo: HT
Updated: Thu, Apr 11 2013. 08 07 PM IST
In recent weeks, several of us have been trying ways to increase the odds. You’ve heard that phrase, for sure. Here, I’m not talking about a cricket fantasy league or a horse race. Instead, this is about what dabblers in mathematics don’t often have the chance to attempt and then write about: increasing the odds for someone’s very survival.
This is a story about odds.
My friend Nalini Ambady is an eminent and greatly loved professor of psychology who got her PhD and first taught at Harvard. Her research into thin-slice knowledge—how the swift first impressions we make can be surprisingly accurate—is path-breaking and innovative enough that Malcolm Gladwell wrote about it in Blink.
In 2004, Nalini was teaching at Tufts University outside Boston, where she lived with her husband, Raj Marphatia, and their daughters, Maya and Leena. That July, she was diagnosed with leukaemia. Amazingly, this happened just weeks after Raj—a respected lawyer and, incidentally, my school buddy—had a bout with cancer himself.
What are the odds, you’d think.
Nalini and Raj were treated, their disease went into remission and they’ve had a healthy, happy nine years. The girls are today on the threshold of college. In 2011, Nalini was offered a prestigious position at Stanford University, heading her own research lab. The family moved to California that year.
Last November, Nalini’s leukaemia returned. She went through chemotherapy, but it was soon clear that her only option for recovery, really, was a stem cell transplant.
If you know something about such transplants, you know that you need a donor to give you a batch of robust cells to replace dysfunctional ones. Across the world, there are databases of potential donors, about 20 million generous people who have agreed to donate their healthy cells to those in need. Only, you can’t simply pick one of these folks at random. Analogous to the way blood donation works, your cell characteristics must match the donor’s. Nalini’s doctors thus started a search for her specific cell type in the US databases, which are linked to many others around the world.
This is where Nalini came up against odds, in different ways.
The best chance of a match is a person who shares the same ethnicity, defined as narrowly as possible, as you. The odds decline as you move further out, ethnically. So Nalini’s best hope would be with a donor from her community in her home state of Kerala; failing that, an Indian or South Asian donor; failing that, somebody else altogether.
Yet so few Indians have signed up as donors that an Indian like Nalini has about a 5% chance of finding a match in these databases. Compare to the 75% chance a Caucasian has. Even so, the initial news was good for Nalini. The search found a dozen potential matches, though of course we don’t know what their ethnicity is. Unfortunately, on further testing, none of them was a good enough match for her.
Twelve potential matches. All fell through. What are the odds?
And now her family and friends are searching in India. There are Indian databases (DATRI, MDRI and others), at least one of which is also linked internationally. Now these are populated almost entirely by Indian names, so you’d think the odds of a match would be good. Yet here’s the thing: taken as a whole, the Indian databases have no more, as far as I can tell, than about 50,000 donors.
In the international databases, there were two reasons for the low chance of a match: one, Indians form a small fraction of the registered donors, and two, the odds of finding a match for Nalini are lower among non-Indians. In the Indian databases, Indians form a large fraction of the names, but chances of a match remain low anyway—because there are so few names registered.
Sure enough, Nalini has still not found a match in India. Neither has Karthik Shankaran, a 35-year-old executive in Chennai who needs a donor too. Neither have some others I know about.
And this is why many of us, here and abroad, are trying to increase the odds for Karthik, Nalini and others like them. We are entering names into those databases as fast as possible, because both need donors in the next six or seven weeks. Imagine if we could double that Indian number of 50,000: we’d have doubled their chances of finding a match. Of anyone in need finding a match.
Of you finding a match.
And this is where a mathematical dabbler like me takes the chance, the liberty if you will, of urging readers like you to sign up as donors. (What are the odds, I want to know?)
Help us increase the odds that Nalini and Karthik will live. Take a chance on life itself.
(There’s little risk in being a donor, or a potential donor. Visit helpnalininow.org and swab4karthik.com for all the information you need. Or send us a note: helpnaliniindia@gmail.com).
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers will explore the joy of mathematics, with occasional forays into other sciences. To read Dilip D’Souza’s previous columns, go to www.livemint.com/dilipdsouza-
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First Published: Thu, Apr 11 2013. 06 35 PM IST
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