评论：当预期计数为零时，使用MCPMod分析二进制数据
Commentary: analyzing binary data using MCPMod when zero counts are expected
摘要：
Bretz et al（2005）提出了多重比较程序和建模（MCPMod）方法来设计和分析剂量探索研究。Pinheiro（2014）随后将其推广到各种类型的终点，包括但不限于二元终点、生存终点、计数数据和纵向数据。Pinheiro（2013）建议使用来自观察数据的估计协方差阵重新计算最佳对比度和检验临界值。对于许多II期研究，每组样本量较小且安慰剂应答率较低是常见的。在这种情况下，不能排除观察到零计数。例如，当安慰剂应答率为10%时，在安慰剂组或与安慰剂具有相似应答率的其他剂量组中观察到零应答者的可能性约为4%。在这篇手稿中，我们想用案例研究和模拟来说明Pinheiro（2013）的潜在问题。评价了使用Firth逻辑斯谛回归的替代方法，以获得每个剂量组的反应稳定估计值。此外，我们评估了两个选项，以解决有问题的对比度系数的问题。
英文摘要：
Bretz et al (2005) proposed multiple Comparison Procedure and Modeling (MCPMod) method to design and analyze dose-finding study. Pinheiro (2014) then generalized it to various types of endpoint, including but not limited to binary endpoint, survival endpoint, count data, and longitudinal data. Pinheiro (2013) recommended to use the estimated covariance matrix from the observed data to recalculate the optimal contrast and the critical value of the test For many phase II studies it is common to have small sample sizes per arm with low placebo response rates jointly. Under such circumstances, it cannot be excluded to have a zero count observed. For example, when the placebo response rate is 10%, there is about 4% chance to observe zero responders in the placebo group, or other dose group(s), which has a similar response rate as placebo. In this manuscript, we would like to illustrate the potential problem of Pinheiro (2013) using a case study and simulations. An alternative method using Firth's logistic regression was evaluated to get a stable estimate of response for each dose group. In addition, we evaluated two options to address the issue with problematic contrast coefficients.
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