Inferences for Selected Location Quotients with Applications to Health Outcomes.

Location quotient (LQ) is an index frequently used in geography and economics to measure the relative concentration of activities. This quotient is calculated in a variety of ways depending on which group to use as a reference. Here, we focus on simultaneous inference for the ratios of the individual proportions to the overall proportion based on binomial data. Apparently, this is a multiple comparison problem and multiplicity adjusted location quotients have not been addressed up to now. In fact, there is a negative correlation between the comparisons. The quotients can be simultaneously tested against unity and simultaneous confidence intervals can be constructed for the LQs based on existing probability inequalities and by directly using the asymptotic joint distribution of the associated z-statistics. The proposed inferences are appropriate for analysis based on sample surveys. A real data set is used to demonstrate the application of multiplicity adjusted LQs. A simulation study is also carried out to assess the performance of the proposed methods in terms of achieving a nominal coverage probability. It is observed that the coverage of the simple Bonferroni adjusted Fieller intervals for LQs is just as good as the coverage of the method which directly takes the correlations into account.