O'Brien Peter C, Zhang David, Bailey Kent R
Division of Biostatistics, Mayo Clinic, 200 First Street SW, Rochester, MN 55905, USA.
Stat Med. 2005 Feb 15;24(3):341-58. doi: 10.1002/sim.1963.
Last observation carried forward (LOCF) and analysis using only data from subjects who complete a trial (Completers) are commonly used techniques for analysing data in clinical trials with incomplete data when the endpoint is change from baseline at last scheduled visit. We propose two alternative methods. The semi-parametric method, which cumulates changes observed between consecutive time points, is conceptually similar to the familiar life-table method and corresponding Kaplan-Meier estimation when the primary endpoint is time to event. A non-parametric analogue of LOCF is obtained by carrying forward, not the observed value, but the rank of the change from baseline at the last observation for each subject. We refer to this method as the LRCF method. Both procedures retain the simplicity of LOCF and Completers analyses and, like these methods, do not require data imputation or modelling assumptions. In the absence of any incomplete data they reduce to the usual two-sample tests. In simulations intended to reflect chronic diseases that one might encounter in practice, LOCF was observed to produce markedly biased estimates and markedly inflated type I error rates when censoring was unequal in the two treatment arms. These problems did not arise with the Completers, Cumulative Change, or LRCF methods. Cumulative Change and LRCF were more powerful than Completers, and the Cumulative Change test provided more efficient estimates than the Completers analysis, in all simulations. We conclude that the Cumulative Change and LRCF methods are preferable to LOCF and Completers analyses. Mixed model repeated measures (MMRM) performed similarly to Cumulative Change and LRCF and makes somewhat less restrictive assumptions about missingness mechanisms, so that it is also a reasonable alternative to LOCF and Completers analyses.
末次观察值结转（LOCF）以及仅使用完成试验的受试者（完成者）的数据进行分析，是在临床试验数据不完整且终点为末次计划访视时相对于基线的变化时，常用于分析数据的技术。我们提出了两种替代方法。半参数方法累积连续时间点之间观察到的变化，在概念上类似于当主要终点为事件发生时间时熟悉的寿命表方法和相应的Kaplan-Meier估计。通过结转每个受试者在最后一次观察时相对于基线变化的秩而非观察值，可得到LOCF的非参数类似方法。我们将此方法称为LRCF方法。这两种方法都保留了LOCF和完成者分析的简单性，并且与这些方法一样，不需要数据插补或建模假设。在没有任何不完整数据的情况下，它们简化为通常的两样本检验。在旨在反映实际中可能遇到的慢性病的模拟中，当两个治疗组的删失情况不相等时，观察到LOCF会产生明显有偏的估计和明显膨胀的I型错误率。这些问题在完成者、累积变化或LRCF方法中不会出现。在所有模拟中，累积变化和LRCF比完成者更具检验效能，并且累积变化检验比完成者分析提供了更有效的估计。我们得出结论，累积变化和LRCF方法优于LOCF和完成者分析。混合模型重复测量（MMRM）的表现与累积变化和LRCF相似，并且对缺失机制的假设限制较少，因此它也是LOCF和完成者分析的合理替代方法。
