Bayesian Condom Use
What do you do when you see the word “condom” in the title of a new arXiv entry?! You click with wild excitement of course! And you end up reading
Not only is it the only article on arXiv with “condom” in the title (note: there are none with “condom” in the authors’ names), but it also happens to be a very interesting read; it’s about using the methodology developed in this paper by some of the same authors to the problem of validating a large-scale intervention to promote condom use among female sex workers in southern India (funded by the Gates foundation and also presented here).
In short and as far as I understood, the data describes HIV prevalence in the population of sex workers and their clients in a specific region. One part of the intervention was about providing condoms to susceptible “high-risk” people. However one doesn’t necessarily know whether the condoms are used or “properly” used, or if they are actually used by the targeted high-risk people. Moreover the authors write that
[...] directly observed quantities as HIV prevalence do not provide straightforward indications on the impact of an intervention. Indeed, an epidemic has an intrinsic dynamic, which can cause the prevalence to grow although an efficient intervention is being led if the intervention is introduced early in an epidemic. Alternatively, in a mature epidemic the prevalence can decrease even though on-going interventions are inefficient [...]
Hence the goal is to assess the impact of the intervention. A proposed state space model [note: the wikipedia pages on SSMs and HMMs are terrible, let's fix that some time] explains the observed time series of HIV prevalence given unobserved parameters and hidden time series like condom use (see the diagram above taken from the paper; CU(t) represents condom use at time t); see the paper for the full model expressed a system of differential equations. Computational methods (particle MCMC here) allow to estimate the hidden quantities of interest, and to establish a positive increase of condom use among the studied population (again, without direct reports on condom use); see the figure below, again taken from the paper.
It’s good to see cutting-edge Monte Carlo methods being helpful for such important problems (along with recent promising applications in ecology here and here)! It also shows that when a new algorithm really rocks, it catches on really fast; kudos to applied scientists of various fields who are very responsive, particle MCMC having only been introduced in a 2010 JRSS B paper.