Social Science Statistics Blog

December 12, 2006

Better Way To Make Cumulative Comparisons With Small Samples?

On July 15, 1971 the research vessel Lev Berg set sail from Aralsk (Kazakhstan) to survey the Aral Sea, then the 4th largest freshwater lake in the world. The Soviet Union had been steadily draining the Aral for agricultural purposes since the 1950s and the Lev Berg was to measure the ecological damage. This trip included passing by the island Vozrozhdeniye on the South side.

(Image Source: "The 1971 Smallpox Epidemic in Aralsk, Kazakhstan, and the Soviet Biological Warfare Program." Center for Nonproliferation Studies Occasional Paper No. 9, Jonathan B. Tucker and Raymand A. Zilinskas.)

Vozrozhdeniye was an ideal site for the main Soviet bioweapons field testing because itwas in a remote area, easily secured as an island, and had reliable winds from the Northto the South allowing ``safe'' testing and housing on the North end. The site was active from 1936 until 1990 when Yeltsin publicly denounced the program and
had it shut down. This is despite the Soviet Union having signed the 1972 Biological and Toxin Weapons Convention outlawing such research. Shortly after the Lev Berg returned to Aralsk, there was an unusual outbreak of smallpox there, starting with a young researcher who had been onboard. The following is the best
epidemiological data available:

Comparison Case: in 1972 a Muslim man from Kosovo went on a pilgrimage to Mecca, returning through Baghdad where he was infected with smallpox. This was the first reported smallpox case in Kosovo since 1930 and it apparently went undiagnosed for six weeks producing 175 cases and 35 deaths. A good comparison since rates of vaccination were similar as were socio-economic conditions.

Kaplan-Meier graph with time-to-event = onset of illness:

(Image Source: Ibid.)

Key difference: all three Aralsk deaths were from hemorrhagic smallpox and only five in Kosovo were. The baseline for naturally occurring smallpox: Rao's study in Madras, India had 10,857 cases with only 240 hemorrhagic. Only two possible explanations seem to remain for the differences:
- host conditions (nutrition, genetic resistance, environment) differ greatly.
- Aralsk strain was an unusual type.
Obviously, it would be nice to claim strong evidence that the Soviet case resulted from escaped smallpox. We know the extent of the bioweapons program from Yeltsin's opening of the files, but not the responsibility of this dissemination with 100% certainty.

This is just a motivating (and interesting) example; the real question is about testing really small samples, when exact inference doesn't seem appropriate. So what other approaches would readers suggest for making comparisons with these types of cumulative data besides simple Kaplan-Meier comparisons? Obviously typical
correlational analysis won't work (polychoric, multichoric, etc.) and standard tabular approaches are not going to be effective either.

Posted by Jeff Gill at 2:48 PM

Naming Conventions

This discussion came up yesterday in the Bayes course. There is a plethora of names for multilevel models. Sociologists seem to prefer "hierarchical," many statisticians say "mixed effects," and there is heterogeneity about usage in economics. It seems reasonable to standardize, but this is unlikely to happen. Maybe the most common comes from the following. Given two data matrices, x_{ij} for individual i in cluster j, and z_j for cluster j, there are perhaps four canonical models:

"Pooled:" y_{ij} = \alpha + x_{ij}'\beta + z_j'\gamma + e_{ij}

"Fixed Effect:" y_{ij} = \alpha_j + x_{ij}'\beta + e_{ij}

"Random Effect:" y_{ij} = \alpha_j + x_{ij}'\beta + z_j'\gamma + e_{ij}

"Random Intercept and Random Slope:" y_{ij} = \alpha_j + x_{ij}'\beta_j + z_j'\gamma + e_{ij}

Some prefer "random intercepts" for "fixed effects" and perhaps we can consider these all to be members of a larger family where indices are turned-on turned-off systematically. On the other hand maybe it's just terminology and not worth worrying about too much. Thoughts?

Posted by Jeff Gill at 10:23 AM

September 24, 2006

Fundamental Changes in Methodology Labor Market?

Last Fall I counted 51 faculty methods jobs posted in political science. I paid close attention because I was on a relevant search committee. This was particularly interesting because equilibrium in past years was about five or so. Right now there are 39 methods jobs posted (subtracting non-tenure/tenure track positions). Now some of these are listed as multiple fields, but one has to presume that listing the ad on the methods page is a signal.

Apparently we have US News and World Report to thank for fundamentally changing the labor market by making methodology the fifth "official" field of the discipline. A number of (non-methodologist) colleagues believed that I must be exaggerating since an order of magnitude difference seems ridiculous. Actually, it turns out that I was underestimating as Jan Box-Steffensmeier (president of the Society for Political Methodology and the APSA methods section) recently got a count of 61 from the APSA. I think their definition was a little broader than mine (perhaps including formal theory and research methods jobs at undergraduate-only institutions).

So an interesting question is how quickly does supply catch up to demand here? My theory is that it will occur rather slowly since the lead time for methods training seems to be longer than the lead time for other subfields. This is obviously good news for graduate students going on the market soon in this area. I'm curious about other opinions, but I think that this is a real change for the subfield.

Posted by Jeff Gill at 10:05 AM

August 16, 2006

The Poincaré Conjecture

While I'm sure that many readers of this blog saw this article in the August 15 NYT science section, it's worth noting anyway as an insight into the sociology of mathematics and a look at some interesting pure mathematics as well (plus the graphics therein were really cool).

It seems that Perelman solved a 102 year old mathematical question of huge importance but wants to have nothing to do with the affect on the field and the resulting acclaim (including an almost certain Fields Medal) since he's disappeared into the Russian forest. Nonetheless, other mathematicians have taken on the task of writing up his results producing proofs in three books that are now available online. These are fascinating to read, even though much of the discussion is at the highest mathematical level, since some of the principles are familiar to us (Cauchy-Schwartz, gradients, Hessians, etc.) from routine work, but obviously appearing in wildly different contexts.

So here's the related question. Suppose, like mathematics, we could list the "big" unsolved problems in political science. What would this list look like? Personally, I'd love to see such a thing. Of course it is unclear whether we have a David Hilbert-like figure to say "As long as a branch of science offers an abundance of problems, so is it alive" and then to go on and identify the 23 most important unsolved problems (the 1900 "Hilbert Challenge":). In this vein, my list of unsolved problems would start with why does the discipline cling to the bankrupt NHST and continue to worship "stars"?

Posted by Jeff Gill at 10:34 PM