Research Ideas

[TheCedarPrince]

These are some research ideas that us in JuliaHealth have been mulling over and discussing to leverage the composition of IPUMS.jl with the rest of the Julia ecosystem.

[TheCedarPrince]

From discussion with @00krishna:

Oh yeah, and there is also some really interesting work happening in applied math and stats on how to deal with analysis of geospatial data when the geometry sizes are so different. Like if you have a bunch of counties or MSAs or census tracks of different size. The usual geostats thing to do is to look at the centroid of the geometry, but that leads to all kinds of weird estimation problems. It comes about from this paper: https://arxiv.org/abs/1902.05911

There could be counties that are rural and very large. So their centroids are located really far from other adjacent counties that are also big. But in reality, the distance metric is wrong. Those counties are probably closer or more similar than the distance between centroids would lead us to believe.

So say you are looking at birthweight by census tract. So all being being equal, you could look at babies in each tract today and babies in each tract 20 years ago, and see if there is a statistically significant change in average birthweight between the two samples. But, if the boundaries of the census tract change over that time frame, then what do you do? Now you have two sources of variation, both the time and the space. You probably throw out those tracts that have changed, and have a smaller sample. So the idea that this paper is getting at, is whether you can preserve some of the information from those census tracts that you would otherwise have to throw out.

[TheCedarPrince]

As a follow-up to this, I spoke with a friend of mine from Northeastern University, Tony Xiao, who is a much better topologist than I am. We took a look together at this paper and the mathematics in this are not as actually challenging as I thought or would imagine. In fact, things like a Vietoris–Rips complex or a Simplical Complex are not too bad at all. Tony then suggested what might be a useful place to look is also within Topological Data Analysis methods -- which, as luck would have it, I came across a Julia Discourse talking about this just recently: TDA discussion. Additionally, there is a professor at my university who is doing some really exciting and pioneering work in TDA that I could pester named Dr. Jose Perea (I run into him not infrequently in the halls 😂 )

I also spoke with another Northeastern University friend, Connor Anderson, about this and he thought the idea held merit from his view as a pure algebraic topologist. He thought the ideas of using structure preserving homologies would be great. The trick would be cementing it against a time series is what he was considering and then not double counting persons.

P.S. I should also mention that although Tony and Connor are on the pure maths side, they did help with a sanity check in that this paper's application of the structure preserving is a "good idea".

[TheCedarPrince]

From discussion with @00krishna:

Another interesting angle would be to look at IPUMS usage within economics. There is a lot of work in economics these days on Heterogeneous Agent models for understanding Macroeconomics. But those models look at distributions of economic agents in the population, whereas traditional Macroeconomic models assume that everyone is identical--a representative agent. So with the IPUMS data, we can uniquely model those agent distributions.

Then we could connect the econ model back to the health models. I think a lot of the econ-health connection is done in a statistical way. Like bad economic outcomes are correlated with bad health. That is important, but I find it kinda unstatisfying. So it seems like are are questions of what to do about it. Like we would use something like SciML to determine what the benefit of an additional hospital, or additional clinics might be.

NOTE: Actually, some of the folks on the Julia economics channel would be good resources to talk to, like David Childers and Jesse Perla.