Existence of complementary pairs of proportionally balanced designs

Proportionally balanced designs (pi BDs) were introduced by Gray and Matters in response to a need for the allocation of markers of the Queensland Core Skills Test to have a certain property. Subsequent papers extended the theoretical results relating to such designs and provided further instances and general constructions. This work focused on designs comprising blocks of precisely two sizes, and when each variety occurs with one of precisely two possible frequencies. Two designs based on the set V of varieties are complementary if, whenever B is a block of one, then its complement with regard to the set V is a block of the other. Here we present necessary conditions for the existence of complementary pairs of such pi BDs and provide lists of some restricted parameter sets satisfying these necessary conditions. The lists are arranged according to the number of blocks. We demonstrate that not all of these parameter sets give rise to designs. However we establish by construction of the sets of blocks that, for every feasible number of blocks less than or equal to 100, with the possible exception of 63, there exists at least one pair of complementary pi BDs. We also investigate the conditions under which the complementary design can be isomorphic to the original design, and again provide a list of feasible parameters for pairs of such designs with at most 400 blocks.

Risks for ross river virus disease in tropical Australia

Background There are no analytical studies of individual risks for Ross River virus (RRV) disease. Therefore, we set out to determine individual risk and protective factors for RRV disease in a high incidence area and to assess the utility of the case-control design applied for this purpose to an arbovirus disease. Methods We used a prospective matched case-control study of new community cases of RRV disease in the local government areas of Cairns, Mareeba, Douglas, and Atherton, in tropical Queensland, from January I to May 31, 1998. Results Protective measures against mosquitoes reduced the risk for disease. Mosquito coils, repellents, and citronella candles each decreased risk by at least 2-fold, with a dose-response for the number of protective measures used. Light-coloured clothing decreased risk 3-fold. Camping increased the risk 8-fold. Conclusions These risks were substantial and statistically significant, and provide a basis for educational programs on individual protection against RRV disease in Australia. Our study demonstrates the utility of the case-control method for investigating arbovirus risks. Such a risk analysis has not been done before for RRV infection, and is infrequently reported for other arbovirus infections.