Yousefi Ali, Dougherty Darin D, Eskandar Emad N, Widge Alik S, Eden Uri T
Department of Neurological Surgery, Massachusetts General Hospital and Harvard Medical School, Boston, MA.
Department of Mathematics and Statistics, Boston University, Boston, MA.
Comput Psychiatr. 2017 Oct 1;1:58-81. doi: 10.1162/CPSY_a_00003. eCollection 2017 Oct.
Censored data occur commonly in trial-structured behavioral experiments and many other forms of longitudinal data. They can lead to severe bias and reduction of statistical power in subsequent analyses. Principled approaches for dealing with censored data, such as data imputation and methods based on the complete data's likelihood, work well for estimating fixed features of statistical models but have not been extended to dynamic measures, such as serial estimates of an underlying latent variable over time. Here we propose an approach to the censored-data problem for dynamic behavioral signals. We developed a state-space modeling framework with a censored observation process at the trial timescale. We then developed a filter algorithm to compute the posterior distribution of the state process using the available data. We showed that special cases of this framework can incorporate the three most common approaches to censored observations: ignoring trials with censored data, imputing the censored data values, or using the full information available in the data likelihood. Finally, we derived a computationally efficient approximate Gaussian filter that is similar in structure to a Kalman filter, but that efficiently accounts for censored data. We compared the performances of these methods in a simulation study and provide recommendations of approaches to use, based on the expected amount of censored data in an experiment. These new techniques can broadly be applied in many research domains in which censored data interfere with estimation, including survival analysis and other clinical trial applications.
删失数据常见于试验结构的行为实验以及许多其他形式的纵向数据中。它们会导致后续分析中出现严重偏差并降低统计功效。处理删失数据的原则性方法，如数据插补和基于完整数据似然性的方法，在估计统计模型的固定特征方面效果良好，但尚未扩展到动态测量，如随时间对潜在潜变量的序列估计。在此，我们提出一种针对动态行为信号的删失数据问题的方法。我们开发了一个状态空间建模框架，在试验时间尺度上具有删失观测过程。然后我们开发了一种滤波算法，以使用可用数据计算状态过程的后验分布。我们表明，该框架的特殊情况可以纳入处理删失观测的三种最常见方法：忽略有删失数据的试验、插补删失数据值或使用数据似然性中的完整信息。最后，我们推导了一种计算效率高的近似高斯滤波器，其结构与卡尔曼滤波器相似，但能有效处理删失数据。我们在模拟研究中比较了这些方法的性能，并根据实验中预期的删失数据量提供了使用方法的建议。这些新技术可广泛应用于许多删失数据干扰估计的研究领域，包括生存分析和其他临床试验应用。
