Tawiah Richard, McLachlan Geoffrey J, Ng Shu Kay
School of Medicine and Menzies Health Institute Queensland, Griffith University, Queensland, Australia.
Department of Mathematics, University of Queensland, Queensland, Australia.
Stat Methods Med Res. 2020 May;29(5):1368-1385. doi: 10.1177/0962280219859377. Epub 2019 Jul 11.
Many medical studies yield data on recurrent clinical events from populations which consist of a proportion of cured patients in the presence of those who experience the event at several times (uncured). A frailty mixture cure model has recently been postulated for such data, with an assumption that the random subject effect (frailty) of each uncured patient is constant across successive gap times between recurrent events. We propose two new models in a more general setting, assuming a multivariate time-varying frailty with an AR(1) correlation structure for each uncured patient and addressing multilevel recurrent event data originated from multi-institutional (multi-centre) clinical trials, using extra random effect terms to adjust for institution effect and treatment-by-institution interaction. To solve the difficulties in parameter estimation due to these highly complex correlation structures, we develop an efficient estimation procedure via an EM-type algorithm based on residual maximum likelihood (REML) through the generalised linear mixed model (GLMM) methodology. Simulation studies are presented to assess the performances of the models. Data sets from a colorectal cancer study and rhDNase multi-institutional clinical trial were analyzed to exemplify the proposed models. The results demonstrate a large positive AR(1) correlation among frailties across successive gap times, indicating a constant frailty may not be realistic in some situations. Comparisons of findings with existing frailty models are discussed.
许多医学研究得出了来自人群复发性临床事件的数据，这些人群中包含一部分已治愈患者以及多次经历该事件的未治愈患者。最近针对此类数据提出了一种脆弱性混合治愈模型，其假设是每个未治愈患者的随机个体效应（脆弱性）在复发性事件之间的连续间隔时间内是恒定的。我们在更一般的背景下提出了两个新模型，假设每个未治愈患者具有具有自回归（AR(1)）相关结构的多元时变脆弱性，并处理源自多机构（多中心）临床试验的多级复发性事件数据，使用额外的随机效应项来调整机构效应和机构与治疗的交互作用。为了解决由于这些高度复杂的相关结构导致的参数估计困难，我们通过基于广义线性混合模型（GLMM）方法的残差最大似然（REML）的EM型算法开发了一种有效的估计程序。进行了模拟研究以评估模型的性能。分析了来自一项结直肠癌研究和重组人脱氧核糖核酸酶多机构临床试验的数据集，以举例说明所提出的模型。结果表明，在连续间隔时间内的脆弱性之间存在很大的正AR(1)相关性，这表明在某些情况下恒定的脆弱性可能不现实。讨论了研究结果与现有脆弱性模型的比较。
