具空間變化係數的 Cox 比例風險模型之懲罰性估計

Abstract

在流行病學長期追蹤研究中，某些疾病的發生和/或死亡可能會受到地理分布的影響。舉例而言，由於空氣汙染為公共衛生中最重要的議題之一，某些疾病的發生和/或死亡與不同地區的汙染物來源和濃度之間的相關性倍廣泛研究。在空間流行病學研究中，建立包含與地理分布有關的空間因子之統計模型是很重要的。因此，我們提出納入空間變數之比例風險模型，並允許其共變數效應可為隨空間變化和不隨區域而改變。在我們提出的模型中，欲估計的參數個數將隨區域與共變數增加而增長。為了解決過多的參數與空間稀疏性的問題，我們在所有區域之參數絕對值總和中引入懲罰項，並藉由核函數在部分概似中使用某區域之鄰近區域之資訊來發展一種估計方法。最後以台灣地區為架構進行模擬分析檢驗所提出估計式之有限樣本表現量，並比較不同懲罰力度、核函數下之估計表現。

In epidemiologic follow-up studies, the occurrence and/or death of certain disease may be influenced by geographic distribution. For example, the association patterns between the occurrence and/or death of certain disease and the pollutant sources and concentrations in different areas has been widely studied since air pollution is one of the most important issues in public health. In spatial epidemiology studies, it is important to establish statistical models including the spatial factors related to geographic distribution. Therefore, we propose a proportional hazards model that not only incorporates spatial covariates but also allows the covariate effects to be spatially varying and invariant across areas. In the proposed model, the number of parameters to be estimated increases as the number of areas and covariates increases. For tackling the issues of the large number of parameters and spatial sparseness, we develop an estimation method by introducing the penalty term in sum of absolutely values of parameters across all areas and a kernel function using the information of neighboring regions in an area into the partial likelihood. In the finite-sample simulation study, the Taiwan regions are used as the spatial framework to examine the performance of the proposed estimates with different penalty levels and kernel functions.