分层单双边配对数据优势比的同质性检验及样本量的确定

Homogeneity Test and Sample Size Determination of Odds Ratios for Stratified Unilateral and Bilateral Paired Data

摘要: 在临床试验中，会对成对身体器官或部位进行试验，获得单边或双边的配对数据；同时，由于患者年龄、性别等混杂因素的影响，相同的治疗方法可能会产生不同的治疗效果。因此，本文基于优势比这一衡量治疗效果的指标对分层单双边混合配对数据进行研究。在Donner模型下提出对分层两组的单双边混合数据中各层优势比的同质性假设。利用迭代算法得到最大似然估计量；构造似然比检验统计量(T_LR)、Wald检验统计量(T_W)和拉格朗日乘数检验统计量(T_SC)进行同质性检验；基于第一类错误率和功效比较三种检验统计量的效果。为临床试验设计和试验数据的检验方法选择提供建议，以提高检验效果。本文还通过对比各检验方法，预测在固定的显著性水平下达到目标功效所需的最小样本量，既减少临床试验成本，又使后续进行的试验有更稳健的第一类错误率和更好的功效。蒙特卡洛模拟结果显示：在同质性假设下，T_W在三个检验统计量中表现最为冒进；T_LR相对冒进，总体表现较为稳健；而T_SC在各种情况下均表现稳健，且功效较高，因此最为推荐使用。对于试验样本量的确定，为了达到相同的功效，T_W所需样本量较小；随着层数的增加，三个检验统计量所需样本量差异逐渐减小；随着优势比增加，越来越接近于1，三个检验统计量所需样本量也会逐渐增加。

Abstract: In clinical trials, pairs of body organs or parts are tested to obtain unilateral or bilateral paired data. At the same time, due to the influence of confounding factors such as patient age and gender, the same treatment method may produce different therapeutic effects. Therefore, this paper studied stratified unilateral and bilateral paired data based on the odds ratio which is an index to measure the treatment effect. In the Donner model, the homogeneity hypothesis of the odds ratios of each stratum in the stratified unilateral and bilateral paired data in two groups is proposed. The maximum likelihood estimator is obtained by iterative algorithm. The likelihood ratio test statistic (T_LR), Wald test statistic (T_W) and Lagrange multiplier test statistic (T_SC) are constructed for homogeneity test. The effects of the three test statistics are compared based on the type I error rate and power, to provide suggestions for clinical trial design and test method selection of test data, so as to improve test results. This paper also predicts the minimum sample size required to achieve the target power at a fixed significance level by comparing these testing methods, which not only reduces the cost of clinical trials, but also enables the subsequent trials to have a more robust type I error rate and better power. Monte Carlo simulation results show that T_W is the most aggressive among the three test statistics under the homogeneity hypothesis. T_LR is relatively aggressive, the overall performance is relatively stable; T_SC is robust in all situations and has high power, so it is most recommended. For the determination of the sample size of the test, in order to achieve the same power, the sample size required by T_W is small. With the increase of the number of stratums, the difference of sample size required for the three test statistics gradually decreases. As the odds ratio increases and gets closer to 1, the sample size required for the three test statistics will gradually increase.