我们开发了一个函数比例风险混合治愈模型，其中在基线处测量了标量和函数协变量。混合治愈模型可用于研究具有特定感兴趣事件的治愈分数的人群，并扩展到功能数据。我们采用期望最大化算法并开发了一种基于半参数惩罚样条的方法来估计发生率和延迟部分的动态函数系数。所提出的方法计算效率高，同时通过粗糙度惩罚将平滑度纳入估计的函数系数中。仿真研究表明该方法在准确估计模型参数和基线生存函数方面具有令人满意的性能。最后，该模型的临床潜力在两个真实数据示例中得到证明，这些示例将丰富的高维生物医学信号作为在基线测量的功能协变量，并构成在当代医疗情况下应用治愈生存模型的新领域。我们特别分析了 (i) 2003-2006 年国家健康和营养检查调查中的每分钟体力活动数据，以研究基线体力活动的昼夜模式与 2019 年所有癌症死亡率之间的关联，同时调整其他生物因素因素； (ii) 重症监护病房收集的疾病严重程度的日常功能测量对重症监护病房后康复和死亡事件的影响。我们的研究结果为日常身体活动模式与癌症死亡率之间的关联提供了新的流行病学见解。 R 中提供了软件实现和所提出的估计方法的说明。

We develop a functional proportional hazards mixture cure model with scalar and functional covariates measured at the baseline. The mixture cure model, useful in studying populations with a cure fraction of a particular event of interest is extended to functional data. We employ the expectation-maximization algorithm and develop a semiparametric penalized spline-based approach to estimate the dynamic functional coefficients of the incidence and the latency part. The proposed method is computationally efficient and simultaneously incorporates smoothness in the estimated functional coefficients via roughness penalty. Simulation studies illustrate a satisfactory performance of the proposed method in accurately estimating the model parameters and the baseline survival function. Finally, the clinical potential of the model is demonstrated in two real data examples that incorporate rich high-dimensional biomedical signals as functional covariates measured at the baseline and constitute novel domains to apply cure survival models in contemporary medical situations. In particular, we analyze (i) minute-by-minute physical activity data from the National Health And Nutrition Examination Survey 2003-2006 to study the association between diurnal patterns of physical activity at baseline and all cancer mortality through 2019 while adjusting for other biological factors; (ii) the impact of daily functional measures of disease severity collected in the intensive care unit on post intensive care unit recovery and mortality event. Our findings provide novel epidemiological insights into the association between daily patterns of physical activity and cancer mortality. Software implementation and illustration of the proposed estimation method are provided in R.