Joint models for a longitudinal biomarker and a terminal event have gained interests for evaluating cancer clinical trials because the tumor evolution reflects directly the state of the disease. A biomarker characterizing the tumor size evolution over time can be highly informative for assessing treatment options and could be taken into account in addition to the survival time. The biomarker often has a semicontinuous distribution, i.e., it is zero inflated and right skewed. An appropriate model is needed for the longitudinal biomarker as well as an association structure with the survival outcome. In this article, we propose a joint model for a longitudinal semicontinuous biomarker and a survival time. The semicontinuous nature of the longitudinal biomarker is specified by a two-part model, which splits its distribution into a binary outcome (first part) represented by the positive versus zero values and a continuous outcome (second part) with the positive values only. Survival times are modeled with a proportional hazards model for which we propose three association structures with the biomarker. Our simulation studies show some bias can arise in the parameter estimates when the semicontinuous nature of the biomarker is ignored, assuming the true model is a two-part model. An application to advanced metastatic colorectal cancer data from the GERCOR study is performed where our two-part model is compared to one-part joint models. Our results show that treatment arm B (FOLFOX6/FOLFIRI) is associated to higher SLD values over time and its positive association with the terminal event leads to an increased risk of death compared to treatment arm A (FOLFIRI/FOLFOX6).

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纵向半连续标记和终末事件的两部分联合模型应用于转移性结直肠癌数据

纵向生物标志物和终末事件的联合模型在评估癌症临床试验方面引起了人们的兴趣，因为肿瘤的演变直接反映了疾病的状态。表征肿瘤大小随时间变化的生物标志物对于评估治疗方案可以提供大量信息，并且除了生存时间之外还可以考虑在内。生物标志物通常具有半连续分布，即，它是零膨胀且右偏的。纵向生物标志物以及与生存结果的关联结构需要适当的模型。在本文中，我们提出了纵向半连续生物标志物和生存时间的联合模型。纵向生物标志物的半连续性质由两部分模型指定，该模型将其分布分为由正值与零值表示的二元结果（第一部分）和仅具有正值的连续结果（第二部分）。生存时间是用比例风险模型建模的，我们提出了与生物标志物的三种关联结构。我们的模拟研究表明，假设真实模型是由两部分组成的模型，当忽略生物标志物的半连续性质时，参数估计可能会出现一些偏差。对 GERCOR 研究的晚期转移性结直肠癌数据进行了应用，将我们的两部分模型与部分联合模型进行了比较。我们的结果表明，与治疗组 A (FOLFIRI/FOLFOX6) 相比，治疗组 B (FOLFOX6/FOLFIRI) 随着时间的推移与较高的 SLD 值相关，并且其与终末事件的正相关导致死亡风险增加。