Applied Approximate Counting: Malaria

My first first-authored global health paper came out today (I consider it my first “first-authored” paper ever, since the mathematicians I’ve worked with deviantly list authorship in alphabetical order regardless of seniority and contribution). It’s a bit of a mouthful by title: Rapid Scaling Up of Insecticide-Treated Bed Net Coverage in Africa and Its Relationship with Development Assistance for Health: A Systematic Synthesis of Supply, Distribution, and Household Survey Data.

What I find really pleasing about this research paper is the way it continues research I worked on in graduate school, but in a completely different and unexpected direction. Approximate counting is something that my advisor specialized in, and he won a big award for the random polynomial time algorithm for approximating the volume of convex bodies. I followed in his footsteps when I was a student, and I’m still doing approximate counting, it’s just that now, instead of approximating the amount of high-dimensional sand that will fit in an oddly shaped high-dimensional box, I’ve been approximating the number of insecticide-treated bednets that have made it from manufacturers through the distribution supply-chain and into the households of malaria-endemic regions of the world. I’m even using the same technique, Markov-chain Monte Carlo.

I’ve been itching to write about the computational details of this research for a while, and now that the paper’s out, I will have my chance. But for today, I refer you to the PLoS Med paper, and the technical appendix, and the PyMC code on github.

4 Comments

Filed under MCMC, global health

4 responses to “Applied Approximate Counting: Malaria

  1. Anand Patil

    Abie,

    Very nice! This is a great example of the benefits of thoughtful, coherent data fusion in large-scale health assessments. And I’m sure it wasn’t easy to fit… congratulations!

    I think I understand everything except the \eta parameter. What does it mean if it’s less than one? Also, why aren’t the household surveys on LLIN stocks affected by it?

    Anand

  2. Thanks Anand!

    \eta and \alpha parameterize my mapping from stock to ownership coverage. It comes from a negative binomial model (and uses the PyMC-preferred parameters). \eta has an interpretation as a sort of “household size factor”, so a value less than one would indicate that something is wrong… I expect posterior values between 3 and 6.

    The \alpha parameter is interesting from an inequality perspective. It says something about how closely the nets-per-household matches a Poisson distribution. But I think it’s not safe to draw any conclusions from the data currently available.

    Of course, if you really want to know what I’m doing with \eta, you can use the source. It’s here, in the formula for a negative binomial r.v. being non-zero.

  3. So pretty Abie. I still owe you a drink for a proper toast to your first first authorship!

  4. Pingback: World Malaria Report and MCMC | Healthy Algorithms