Asymptotic conditional test procedures for relative difference under inverse sampling
For measuring the excess harmful effect of a risk factor, Sheps (New England J. Med. 259 (1958) 12101214; Biometrics 15 (1959) 8797) suggests use of the relative difference (RD), defined as the ratio between the difference in morbidity (or mortality) rates in the exposed and the unexposed and the underlying proportion of the people who would not have the disease otherwise in the unexposed. Recently, Lui (Biometrical J. 39 (1997) 215225) derives estimation and exact test procedures for the RD under a stratified negative binomial sampling. However, when the number of index subjects or the number of strata is large, calculation involved in application of the exact test and the exact interval estimation for the RD can be quite tedious and difficult. This paper provides an alternative by developing the asymptotic procedures in closed form for testing if the underlying relative difference equals any given specified value in a series of independent 22 tables and the corresponding asymptotic procedure for interval estimation. To evaluate the finite-sample performance of these asymptotic test procedures, this paper applies Monte Carlo simulation. This paper shows that these asymptotic procedures can be useful even when the number of index subjects per comparison group per stratum is not large.
relative difference inverse sampling negative binomial asymptotic test confidence limits