Kalish L A
Department of Biostatistics, Dana-Farber Cancer Institute, Harvard School of Public Health, Boston, Massachusetts 02115.
Biometrics. 1990 Jun;46(2):493-9.
The standard estimator of the common odds ratio for pair-matched case-control studies, the stratified estimate, is consistent but it ignores all information from the concordant pairs. At the other extreme, the pooled estimator is more efficient as it uses all the data, but is not consistent. In order to trade between bias and precision, Liang and Zeger (1988, Biometrics 44, 1145-1156) proposed an estimator that is a compromise between the stratified and pooled estimates. In the current paper, the possibility of optimizing the trade-off is explored. Specifically, the family of weighted averages of the stratified and pooled estimates is considered, and the weight that minimizes an asymptotic approximation of mean squared error is derived. In practice, the optimal weight must be estimated from the data so that the estimator is only approximately optimal. Small-sample properties are evaluated via simulations.
配对病例对照研究中共同比值比的标准估计量，即分层估计量，是一致的，但它忽略了所有来自一致对的信息。在另一个极端情况下，合并估计量更有效，因为它使用了所有数据，但不一致。为了在偏差和精度之间进行权衡，Liang和Zeger（1988年，《生物统计学》44卷，1145 - 1156页）提出了一种估计量，它是分层估计量和合并估计量之间的折衷。在本文中，探讨了优化这种权衡的可能性。具体而言，考虑了分层估计量和合并估计量的加权平均族，并推导了使均方误差的渐近近似最小化的权重。在实际中，最优权重必须从数据中估计出来，因此该估计量只是近似最优的。通过模拟评估了小样本性质。
