Key Takeaway: The developed test has slightly higher power and simpler calculation than the Mathen statistic for detecting household clustering of disease cases, making it more suitable for diseases with unknown natural history.

Abstract

A test has been developed to detect the clustering of cases of a disease within households. An example of the calculations on some data from a filariasis survey is given, but the test could more generally be applied to any disease whose natural history is unknown, and where a test of space-time interaction is impractical. The test is compared to that of Mathen and Chakraborty. The pair statistic used was shown to have slightly higher power than the Mathen statistic for some simulated epidemics using alternative hypotheses with a probability of infection which was linear in the number of cases currently in the household. This power difference might be expected to increase with alternatives having a more extreme form of clustering than that with the linear infection probability function. The calculation of the moments of the pair statistic under the null is considerably simpler than for the Mathen statistic; this is particularly true with unequal house sizes. Further, the pair statistic has a distribution which is in general at least as well approximated by the normal as is the Mathen statistic.