# 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.

Filed under global health, MCMC

### 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!