Department of Statistics and Data Science, Pukyong National University, Busan, Republic of Korea.
Department of Public Health Sciences, Graduate School of Public Health, Seoul National University, Seoul, Republic of Korea.
Pharm Stat. 2024 Nov-Dec;23(6):1117-1127. doi: 10.1002/pst.2423. Epub 2024 Jul 16.
Finding an adequate dose of the drug by revealing the dose-response relationship is very crucial and a challenging problem in the clinical development. The main concerns in dose-finding study are to identify a minimum effective dose (MED) in anesthesia studies and maximum tolerated dose (MTD) in oncology clinical trials. For the estimation of MED and MTD, we propose two modifications of Firth's logistic regression using reparametrization, called reparametrized Firth's logistic regression (rFLR) and ridge-penalized reparametrized Firth's logistic regression (RrFLR). The proposed methods are designed by directly reducing the small-sample bias of the maximum likelihood estimate for the parameter of interest. In addition, we develop a method on how to construct confidence intervals for rFLR and RrFLR using profile penalized likelihood. In the up-and-down biased-coin design, numerical studies confirm the superior performance of the proposed methods in terms of the mean squared error, bias, and coverage accuracy of confidence intervals.
通过揭示剂量-反应关系来找到合适的药物剂量是非常关键的，也是临床开发中的一个具有挑战性的问题。在剂量发现研究中，主要关注点是在麻醉研究中确定最小有效剂量（MED），在肿瘤临床试验中确定最大耐受剂量（MTD）。为了估计 MED 和 MTD，我们提出了两种使用重参数化的 Firth 逻辑回归的修改，称为重参数化的 Firth 逻辑回归（rFLR）和脊惩罚重参数化的 Firth 逻辑回归（RrFLR）。所提出的方法通过直接减少感兴趣参数的最大似然估计的小样本偏差来设计。此外，我们开发了一种使用轮廓惩罚似然来构建 rFLR 和 RrFLR 置信区间的方法。在上下偏倚硬币设计中，数值研究证实了所提出的方法在均方误差、偏差和置信区间覆盖准确性方面的优越性能。
