Institute of Biostatistics and Registry Research, Brandenburg Medical School Theodor Fontane, Fehrbelliner Straße 39, 16816, Neuruppin, Germany.
Leibniz Centre for Agricultural Landscape Research (ZALF), Müncheberg, Germany.
Sci Rep. 2024 Jun 20;14(1):14232. doi: 10.1038/s41598-024-64573-9.
Predictive biomarkers are essential for personalized medicine since they select the best treatment for a specific patient. However, of all biomarkers that are evaluated, only few are eventually used in clinical practice. Many promising biomarkers may be erroneously abandoned because they are investigated in small studies using standard statistical techniques which can cause small sample bias or lack of power. The standard technique for failure time endpoints is Cox proportional hazards regression with a multiplicative interaction term between binary variables of biomarker and treatment. Properties of this model in small studies have not been evaluated so far, therefore we performed a simulation study to understand its small sample behavior. As a remedy, we applied a Firth correction to the score function of the Cox model and obtained confidence intervals (CI) using a profile likelihood (PL) approach. These methods are generally recommended for small studies of different design. Our results show that a Cox model estimates the biomarker-treatment interaction term and the treatment effect in one of the biomarker subgroups with bias, and overestimates their standard errors. Bias is however reduced and power is increased with Firth correction and PL CIs. Hence, the modified Cox model and PL CI should be used instead of a standard Cox model with Wald based CI in small studies of predictive biomarkers.
预测生物标志物对于个性化医学至关重要，因为它们为特定患者选择最佳治疗方法。然而，在所有评估的生物标志物中，最终只有少数用于临床实践。许多有前途的生物标志物可能会被错误地放弃，因为它们是在使用标准统计技术的小型研究中进行研究的，这可能会导致小样本偏差或缺乏效力。用于失效时间终点的标准技术是 Cox 比例风险回归，其中包含生物标志物和治疗的二进制变量之间的乘法交互项。到目前为止，尚未评估该模型在小型研究中的特性，因此我们进行了模拟研究以了解其小样本行为。作为补救措施，我们对 Cox 模型的得分函数应用了 Firth 校正，并使用似然比（PL）方法获得了置信区间（CI）。这些方法通常被推荐用于不同设计的小型研究。我们的研究结果表明，Cox 模型会以有偏差的方式估计生物标志物-治疗交互项和生物标志物亚组中的治疗效果，并高估其标准误差。但是，Firth 校正和 PL CI 可以减少偏差并提高功效。因此，在预测生物标志物的小型研究中，应使用修正的 Cox 模型和 PL CI 代替基于 Wald 的标准 Cox 模型和 CI。
