Social Science Statistics Blog

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.