Borkhoff Cornelia M, Johnston Patrick R, Stephens Derek, Atenafu Eshetu
Division of Pediatric Medicine and the Pediatric Outcomes Research Team (PORT), Department of Pediatrics and Child Health Evaluative Sciences, The Hospital for Sick Children, Peter Gilgan Centre for Research and Learning, 686 Bay St., Toronto, Ontario, M5G 0A4, Canada; Women's College Research Institute, Women's College Hospital, 7th Floor, 790 Bay St., Toronto, Ontario, M5G 1N8, Canada; Institute of Health Policy, Management and Evaluation, University of Toronto, 155 College St., Suite 425, Toronto, Ontario, M5T 3M6, Canada.
Clinical Research Program, Children's Hospital Boston, 300 Longwood Avenue, Boston, MA 02115, USA.
J Clin Epidemiol. 2015 Jul;68(7):733-9. doi: 10.1016/j.jclinepi.2014.09.025. Epub 2014 Nov 13.
Aligning the method used to estimate sample size with the planned analytic method ensures the sample size needed to achieve the planned power. When using generalized estimating equations (GEE) to analyze a paired binary primary outcome with no covariates, many use an exact McNemar test to calculate sample size. We reviewed the approaches to sample size estimation for paired binary data and compared the sample size estimates on the same numerical examples.
We used the hypothesized sample proportions for the 2 × 2 table to calculate the correlation between the marginal proportions to estimate sample size based on GEE. We solved the inside proportions based on the correlation and the marginal proportions to estimate sample size based on exact McNemar, asymptotic unconditional McNemar, and asymptotic conditional McNemar.
The asymptotic unconditional McNemar test is a good approximation of GEE method by Pan. The exact McNemar is too conservative and yields unnecessarily large sample size estimates than all other methods.
In the special case of a 2 × 2 table, even when a GEE approach to binary logistic regression is the planned analytic method, the asymptotic unconditional McNemar test can be used to estimate sample size. We do not recommend using an exact McNemar test.
使估计样本量的方法与计划的分析方法保持一致，可确保获得实现计划效能所需的样本量。在使用广义估计方程（GEE）分析无协变量的配对二元主要结局时，许多人使用精确的 McNemar 检验来计算样本量。我们回顾了配对二元数据样本量估计的方法，并在相同的数值示例上比较了样本量估计值。
我们使用 2×2 表的假设样本比例来计算边缘比例之间的相关性，以基于 GEE 估计样本量。我们根据相关性和边缘比例求解内部比例，以基于精确 McNemar、渐近无条件 McNemar 和渐近条件 McNemar 估计样本量。
渐近无条件 McNemar 检验是 Pan 的 GEE 方法的良好近似。精确 McNemar 过于保守，与所有其他方法相比，会产生不必要的大样本量估计值。
在 2×2 表的特殊情况下，即使计划的分析方法是二元逻辑回归的 GEE 方法，也可使用渐近无条件 McNemar 检验来估计样本量。我们不建议使用精确 McNemar 检验。
