Department of Biostatistics, Boston University School of Public Health, Boston, Massachusetts, USA.
Early Development Analytics, Novartis Pharmaceuticals Corporation, East Hanover, New Jersey, USA.
Stat Med. 2022 Dec 30;41(30):5810-5829. doi: 10.1002/sim.9595. Epub 2022 Oct 28.
Given their improvements in bias reduction and efficiency, joint models (JMs) for longitudinal and time-to-event data offer great potential to clinical trials. However, for JM to become more widely used, there is a need for additional development of design considerations. To this end, Chen et al previously developed two closed-form sample size formulas in the JM setting. In this current work, we expand upon this framework by utilizing the time-dependent slopes parameterization, where the change in the longitudinal outcome influences the hazard, in addition to the current value of the longitudinal process. Our extended formula for the required number of events can be used when testing significance of the association between the longitudinal and time-to-event outcomes. We find that if the data indeed are generated such that not only the current value, but also the slope of the longitudinal outcome influence the hazard of the time-to-event process, it is advisable to use the current formula developed utilizing the time-dependent slopes parameterization. In this setting, our proposed formula will provide a more accurate estimate of power compared to the method by Chen et al. To illustrate our proposed method, we present power calculations of a biomarker qualification study for Hutchinson-Gilford progeria syndrome, an ultra-rare premature aging disease.
鉴于联合模型（JMs）在减少偏差和提高效率方面的改进，它们为临床试验提供了巨大的潜力。然而，为了使 JM 得到更广泛的应用，需要进一步开发设计考虑因素。为此，Chen 等人之前在 JM 环境中开发了两个闭式样本量公式。在当前这项工作中，我们通过利用时变斜率参数化扩展了这个框架，其中纵向结果的变化不仅会影响风险，还会影响纵向过程的当前值。我们扩展的所需事件数量公式可用于检验纵向和生存结局之间关联的显著性。我们发现，如果数据确实是这样生成的，即不仅当前值，而且纵向结果的斜率都会影响生存事件过程的风险，那么使用利用时变斜率参数化开发的当前公式是明智的。在这种情况下，与 Chen 等人的方法相比，我们提出的公式将提供更准确的功效估计。为了说明我们提出的方法，我们展示了 Hutchinson-Gilford progeria 综合征（一种超罕见的早衰疾病）的生物标志物资格研究的功效计算。
