NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, 21 Lower Kent Ridge, Singapore, 119077, Singapore.
Yong Loo Lin School of Medicine, Department of Surgery, National University of Singapore and National University Health System, 10 Medical Dr, Singapore, 117597, Singapore.
BMC Med Res Methodol. 2020 Jun 6;20(1):145. doi: 10.1186/s12874-020-01027-6.
The change in two measurements of a continuous outcome can be modelled directly with a linear regression model, or indirectly with a random effects model (REM) of the individual measurements. These methods are susceptible to model misspecifications, which are commonly addressed by applying monotonic transformations (e.g., Box-Cox transformation) to the outcomes. However, transforming the outcomes complicates the data analysis, especially when variable selection is involved. We propose a robust alternative through a novel application of the conditional probit (cprobit) model.
The cprobit model analyzes the ordered outcomes within each subject, making the estimate invariant to monotonic transformation on the outcome. By scaling the estimate from the cprobit model, we obtain the exposure effect on the change in the observed or Box-Cox transformed outcome, pending the adequacy of the normality assumption on the raw or transformed scale.
Using simulated data, we demonstrated a similar good performance of the cprobit model and REM with and without transformation, except for some bias from both methods when the Box-Cox transformation was applied to scenarios with small sample size and strong effects. Only the cprobit model was robust to skewed subject-specific intercept terms when a Box-Cox transformation was used. Using two real datasets from the breast cancer and inpatient glycemic variability studies which utilize electronic medical records, we illustrated the application of our proposed robust approach as a seamless three-step workflow that facilitates the use of Box-Cox transformation to address non-normality with a common underlying model.
The cprobit model provides a seamless and robust inference on the change in continuous outcomes, and its three-step workflow is implemented in an R package for easy accessibility.
连续结果的两个测量值的变化可以直接通过线性回归模型建模，也可以通过个体测量的随机效应模型（REM）间接建模。这些方法容易受到模型设定不当的影响，通常通过对结果应用单调变换（例如 Box-Cox 变换）来解决。然而，对结果进行变换会使数据分析变得复杂，尤其是在涉及变量选择时。我们通过对条件概率（cprobit）模型的新颖应用，提出了一种稳健的替代方法。
cprobit 模型分析每个受试者内的有序结果，使估计值对结果的单调变换不变。通过对 cprobit 模型的估计进行缩放，我们可以获得暴露对观测结果或 Box-Cox 变换结果变化的影响，前提是原始或变换尺度上的正态性假设是充分的。
使用模拟数据，我们展示了 cprobit 模型和 REM 在有或没有变换的情况下的相似良好性能，除了当应用于小样本量和强效应的情况时，两种方法都存在一些偏差。只有在使用 Box-Cox 变换时，cprobit 模型才对偏态个体特定截距项具有稳健性。使用来自乳腺癌和住院患者血糖变异性研究的两个真实数据集，这些数据集利用电子病历，我们说明了我们提出的稳健方法的应用，作为一个无缝的三步工作流程，该流程使用 Box-Cox 变换来解决非正态性问题，同时使用共同的基本模型。
cprobit 模型为连续结果的变化提供了无缝和稳健的推断，其三步工作流程在 R 包中实现，便于使用 Box-Cox 变换解决非正态性问题。
