Given two populations from which independent binary observations are taken with parameters $p_1$ and $p_2$ respectively, estimators are proposed for the relative risk $p_1/p_2$, the odds ratio $p_1(1-p_2)/(p_2(1-p_1))$ and their logarithms. The sampling strategy used by the estimators is based on two-stage sequential sampling applied to each population, where the sample sizes of the second stage depend on the results observed in the first stage. The estimators guarantee that the relative mean-square error, or the mean-square error for the logarithmic versions, is less than a target value for any $p_1, p_2 \in (0,1)$, and the ratio of average sample sizes from the two populations is close to a prescribed value. The estimators can also be used with group sampling, whereby samples are taken in batches of fixed size from the two populations simultaneously, each batch containing samples from the two populations. The efficiency of the estimators with respect to the Cramér-Rao bound is good, and in particular it is close to $1$ for small values of the target error.

翻译：给定两个总体，分别从其中独立抽取二元观测值，其参数分别为 $p_1$ 和 $p_2$。本文提出了相对风险 $p_1/p_2$、比值比 $p_1(1-p_2)/(p_2(1-p_1))$ 及其对数的估计量。估计量采用的抽样策略基于对每个总体应用的两阶段序贯抽样，其中第二阶段的样本量取决于第一阶段观测到的结果。这些估计量保证，对于任意 $p_1, p_2 \in (0,1)$，其相对均方误差（或对数版本的均方误差）小于目标值，且两个总体的平均样本量之比接近预设值。这些估计量也可用于分组抽样，即同时从两个总体中以固定批量大小抽取样本，每批包含来自两个总体的样本。估计量相对于克拉默-拉奥下界的效率良好，尤其当目标误差值较小时，效率接近 $1$。