含结构零的2×2列联表的统计推断

1、含结构零的2X2列联表的统计推断摘要随着生物医学、社会学、经济学和教育心理学等学科的快速发展，分类数据 的研究越来越受到国内外相应领域的理论研究者和实际应用工作者的高度重视。 利用分类数据来研究两种处理方法的等价性（或非劣性）是生物医学研究中的一 个重要课题。结合生物医学统计研究的最新进展，本文研究分类数据中含结构零 的2X2列联表，研究其具有生物医学意义和数学意义的基于风险差（RD ）或 风险比（RR ）的等价性（或非劣性）评价问题。目前国内外对含结构零2X2 列联表的研究主要基于风险差或风险比等于某一固定值的双边假设检验及其置 信区间等问题，然而关于RD或RR的区间假设检验、齐性检验以及相

2、应的等价 性评价等问题，目前国内外尚未见有相关报道，本文将系统全面地研究这些问题。 本文具体研究内容如下：对含结构零的2X2列联表，首次研究了风险差（RD ）的形如“ H0 : RD 8 H1： RD A 或RR 气 H : A RR 气”的区间假设，其中0 80 H : |RD| A or RR A H : A RR A for the first time, where A and A are pre-defined thresholds which satisfy 0 A A . In order to test this hypothesis, we consider two meas

3、urements: the Wald type and its logarithmic transformation. For each measurement, sample-based estimation and CMLE-based estimation are presented. Altogether we get four testing statistics. For each statistic, corresponding significance test and sample size are given. The simulation shows the logari

4、thmic transformation statistic based on CMLE is the best one among the four.For K pairs of independent 2X2 tables with structural zero, we systematically study the homogeneity of RD s (or RR s) for the first time. We propose score tests (for both RD and RR), Wald,s tests (for both RD and RR ) and lo

5、garithmic transformation test (for RR only) to test whether the RD s (or RR s) are equal across strata. Powers and sample size formulae for testing the homogeneity of RD s (or RR s) are given. Through comparison, we draw conclusions that score tests (for RD and RR ) perform better and the logarithmi

6、c transformation test (for RR only) performs well relatively.For K pairs of independent 2X2 tables which contain structural zero, on the assumption that all RD s (or RR s) equal by strata, we study the hypothesis that whether the common RD (or RR ) equals a specified non-zero (or non-one) value. We

7、discuss both the significance test approach and the confidence interval approach with score statistics (for both RD and RR ), Wald,s statistics (for both RD and RR ) and logarithmic transformation statistic (for RR only). Corresponding approximate sample sizes required for a specific power or a spec

8、ific interval width are given out. Our simulation shows that for RD, score test outperforms Walds test, stratified test is better than unstratified one. For RR , with the significance test approach, score test is ideal in many occasions, logarithmic transformation test is good in some occasions and

9、Walds test performs poorly.In conclusion, a series of new results, which have never been seen in the literature, are obtained for the first time. These new results are useful for studying diseases such as SARS and AIDS etc. and new drugs, and also valuable for medical administrators and hospitals to make decisions.Key Words :2 x 2 contingency table with structur