Multilevel and longitudinal studies are frequently subject to missing data. For example, biomarker studies for oral cancer may involve multiple assays for each participant. Assays may fail, resulting in missing data values that can be assumed to be missing completely at random. Catellier and Muller proposed a data analytic technique to account for data missing at random in multilevel and longitudinal studies. They suggested modifying the degrees of freedom for both the Hotelling-Lawley trace F statistic and its null case reference distribution. We propose parallel adjustments to approximate power for this multivariate test in studies with missing data. The power approximations use a modified non-central F statistic, which is a function of: 1) the expected number of complete cases, 2) the expected number of non-missing pairs of responses, or 3) the trimmed sample size, which is the planned sample size reduced by the anticipated proportion of missing data. The accuracy of the method is assessed by comparing the theoretical results to the Monte Carlo simulated power for the Catellier and Muller multivariate test. Over all experimental conditions, the closest approximation to the empirical power of the Catellier and Muller multivariate test is obtained by adjusting power calculations with the expected number of complete cases. The utility of the method is demonstrated with a multivariate power analysis for a hypothetical oral cancer biomarkers study. We describe how to implement the method using standard, commercially available software products and give example code.
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机译：多层次和纵向研究经常会缺少数据。例如，针对口腔癌的生物标志物研究可能涉及针对每个参与者的多种检测方法。化验可能会失败，从而导致丢失的数据值，可以认为这些数据值是随机完全丢失的。 Catellier和Muller提出了一种数据分析技术，以解决多层次和纵向研究中随机丢失的数据的问题。他们建议修改Hotelling-Lawley迹线F统计量及其无效案例参考分布的自由度。我们建议在数据缺失的研究中进行平行调整，以近似化此多元测试的功效。功效近似值使用修正的非中心F统计量，该统计量是以下函数：1）预期的完整案例数； 2）预期的无缺失对响应数；或3）修剪后的样本大小，即计划的样本量减少了丢失数据的预期比例。通过将理论结果与Catellier和Muller多元检验的蒙特卡洛模拟功效进行比较，可以评估该方法的准确性。在所有实验条件下，通过以预期的完整案例数调整功效计算，可以获得与Catellier and Muller多元检验的经验功效最接近的近似值。该方法的实用性通过一项假设的口腔癌生物标志物研究的多变量功效分析得到证明。我们描述了如何使用标准的市售软件产品来实现该方法，并给出示例代码。
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