Recently, Thomadakis et al. quantified potential sources of bias that can occur when shared parameter (SP) models are used to jointly model longitudinal trends of a biomarker over time (e.g., a slope) and time-to-dropout in an effort to address concerns over possible informative censoring. Although SP models induce no bias under a missingness completely at random dropout mechanism, the authors demonstrate that bias can occur under a missingness at random (MAR) dropout mechanism wherein dropout depends on the observed biomarker data. To address this, the authors propose including the most recent observed marker value within the hazard function for the time-to-dropout portion of an SP model. They demonstrate via a limited simulation that the proposed model minimizes bias under a specific MAR dropout mechanism and a specific missingness not-at-random dropout mechanism. In the present article, we compare and contrast their work with that of previous authors by illustrating via simulation and an example the degree of bias or lack thereof that can occur when applying SP models, particularly, in the presence of competing dropout mechanisms. We propose the use of a competing risk SP model as a means to minimize bias whenever competing dropout mechanisms are suspected assuming the competing mechanisms result from distinct observable causes of dropout.

中文翻译：

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在存在竞争辍学机制的情况下使用共享参数模型进行有偏估计

最近，Thomadakis等. 量化了在使用共享参数 (SP) 模型来联合模拟生物标志物随时间（例如，斜率）和退出时间的纵向趋势以解决对可能的信息审查的担忧时可能出现的偏差的量化潜在来源。尽管 SP 模型在随机丢失机制下完全没有偏差，但作者证明，偏差可能在随机丢失 (MAR) 丢失机制下发生，其中丢失取决于观察到的生物标志物数据。为了解决这个问题，作者建议在 SP 模型的退出时间部分的危险函数中包含最近观察到的标记值。他们通过有限的模拟证明，所提出的模型在特定的 MAR 退出机制和特定的缺失非随机退出机制下最小化了偏差。在本文中，我们通过模拟和示例说明应用 SP 模型时可能发生的偏差或缺乏偏差程度，特别是在存在竞争性 dropout 机制的情况下，将他们的工作与以前作者的工作进行比较和对比。我们建议使用竞争风险 SP 模型作为一种手段，以在怀疑竞争退出机制时最小化偏差，假设竞争机制是由不同的可观察到的退出原因引起的。