The direct integral method for confidence intervals for the ratio of two location parameters.
In a relative risk analysis of colorectal caner on nutrition intake scores across genders, we show that, surprisingly, when comparing the relative risks for men and women based on the index of a weighted sum of various nutrition scores, the problem reduces to forming a confidence interval for the ratio of two (asymptotically) normal random variables. The latter is an old problem, with a substantial literature. However, our simulation results suggest that existing methods often either give inaccurate coverage probabilities or have a positive probability to produce confidence intervals with infinite length. Motivated by such a problem, we develop a new methodology which we call the Direct Integral Method for Ratios (DIMER), which, unlike the other methods, is based directly on the distribution of the ratio. In simulations, we compare this method to many others. These simulations show that, generally, DIMER more closely achieves the nominal confidence level, and in those cases that the other methods achieve the nominal levels, DIMER has comparable confidence interval lengths. The methodology is then applied to a real data set, and with follow up simulations.
Department of Biostatistics, Fred Hutchinson Cancer Research Center, Seattle, Washington, 98109, U.S.A.
Yanqing
Y
Wang
Department of Statistics, Texas A&M University, 3143 TAMU, College Station, Texas, 77843-3143, U.S.A.
Suojin
S
Wang
Department of Statistics, Texas A&M University, 3143 TAMU, College Station, Texas, 77843-3143, U.S.A.|Department of Mathematics and Statistics, University of Technology, Sydney, Australia.
Raymond J
RJ
Carroll
D000465:Algorithms; D015179:Colorectal Neoplasms / Q000453:epidemiology*; D003198:Computer Simulation; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D004032:Diet / Q000706:statistics & numerical data*; D005260:Female; D006801:Humans; D015994:Incidence; D008297:Male; D015233:Models, Statistical; D016017:Odds Ratio; D015203:Reproducibility of Results; D018570:Risk Assessment / Q000379:methods; D012680:Sensitivity and Specificity; D017678:Sex Distribution
Confidence interval; DIMER; Direct Integral Method for Ratios; Fieller's interval; Hayya's method; Ratios of location parameters