含結(jié)構(gòu)零的2×2列聯(lián)表的統(tǒng)計推斷

1、含結(jié)構(gòu)零的2X2列聯(lián)表的統(tǒng)計推斷摘要隨著生物醫(yī)學、社會學、經(jīng)濟學和教育心理學等學科的快速發(fā)展，分類數(shù)據(jù) 的研究越來越受到國內(nèi)外相應領(lǐng)域的理論研究者和實際應用工作者的高度重視。 利用分類數(shù)據(jù)來研究兩種處理方法的等價性（或非劣性）是生物醫(yī)學研究中的一 個重要課題。結(jié)合生物醫(yī)學統(tǒng)計研究的最新進展，本文研究分類數(shù)據(jù)中含結(jié)構(gòu)零 的2X2列聯(lián)表，研究其具有生物醫(yī)學意義和數(shù)學意義的基于風險差（RD ）或 風險比（RR ）的等價性（或非劣性）評價問題。目前國內(nèi)外對含結(jié)構(gòu)零2X2 列聯(lián)表的研究主要基于風險差或風險比等于某一固定值的雙邊假設(shè)檢驗及其置 信區(qū)間等問題，然而關(guān)于RD或RR的區(qū)間假設(shè)檢驗、齊性檢驗以及相

2、應的等價 性評價等問題，目前國內(nèi)外尚未見有相關(guān)報道，本文將系統(tǒng)全面地研究這些問題。 本文具體研究內(nèi)容如下：對含結(jié)構(gòu)零的2X2列聯(lián)表，首次研究了風險差（RD ）的形如“ H0 : RD 8 H1： RD A 或RR 氣 H : A RR 氣”的區(qū)間假設(shè)，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