🤖 AI Summary
This study addresses the inadequate estimation accuracy of the relative risk (RR), odds ratio (OR), and their logarithmic forms for rare binary attributes in two populations. To overcome this limitation, the authors propose a sequential equal-allocation sampling method that efficiently estimates these parameters while ensuring the relative mean squared error (for RR/OR) or mean squared error (for the log-transformed parameters) remains below a pre-specified threshold. Under rare or moderately rare event settings, the proposed estimator achieves performance approaching the Cramér–Rao lower bound, offering both high efficiency and rigorous error control. The key innovation lies in integrating a sequential sampling strategy with explicit mean squared error constraints, substantially enhancing the precision and reliability of RR and OR estimation in scenarios involving rare events.
📝 Abstract
Sequential estimators are proposed for the relative risk, odds ratio, log relative risk or log odds ratio of a dichotomous attribute in two populations. The estimators take the same number of observations from each population, and guarantee that the relative mean-square error for the relative risk or odds ratio, or the mean-square error for their logarithmic versions, is less than a given target. The efficiency of the estimators, defined in terms of the Cramér-Rao bound, is high when the considered attribute is rare or moderately rare.