在有訊息審查情況下利用廣義動差法提升重複事件資料分析的效率

Abstract

復發事件資料廣泛應用於醫學研究、保險精算等領域，常見於疾病再發生、保險重複理賠等情況。在縱向追蹤研究中，復發事件的觀察過程經常因資訊性審查而終止，使得傳統假設獨立審查的統計方法不再適用。Wang et al. (2001) 提出透過潛在變數描述資訊性審查機制，並建構乘法強度模型來處理此問題。此方法利用潛在變數有效處理個體異質性並允許審查機制與復發事件過程的相依性，提供了靈活且實用的模型框架。然而，在此假設下，Wang et al. (2001) 採用條件概似估計法時，由於將潛在變數和審查時間分布視為干擾參數，可能導致估計效率的損失。為改善此問題，本研究提出利用Hansen(1982)所發展的廣義動差估計法（GMM）來提升參數估計效率。本研究考慮不同權重函數的選擇，透過構造最優化估計方程式，期望獲得更有效率的參數估計結果。GMM方法在適當權重選擇下能達到更佳的漸近效率，且具有假設較少的優點。本研究將通過蒙地卡羅模擬實驗來評估所提出方法的表現。模擬設計將考慮多種不同的權重函數選擇，並評估將這些權重函數合併使用是否能真正帶來估計效率的改善，驗證GMM方法在效率提升上的實際效果。

Recurrent event data are widely applied in medical research, actuarial science, and other fields, commonly encountered in situations such as disease recurrence and repeated insurance claims. In longitudinal follow-up studies, recurrent event processes are often terminated due to informative censoring, rendering traditional statistical methods that assume independent censoring no longer applicable. Wang et al. (2001) proposed using latent variables to characterize the informative censoring mechanism and constructed a multiplicative intensity model to address this problem. This approach handles individual heterogeneity using latent variables and allows for dependence between the censoring mechanism and the recurrent event process, providing a flexible and practical modeling framework. However, Wang et al. (2001)'s estimation approach may not achieve optimal statistical efficiency. To improve this issue, this study proposes utilizing the Generalized Method of Moments (GMM) developed by Hansen (1982) to enhance parameter estimation efficiency. This study considers different weight functions to obtain more efficient parameter estimation results. The GMM method can achieve better asymptotic efficiency under appropriate weight selection and has the advantage of requiring fewer assumptions. The study will evaluate the performance of the proposed method through Monte Carlo simulation experiments. The simulation design will consider various different weight function selections and assess whether combining these weight functions can truly bring about improvements in estimation efficiency, thereby verifying the actual effectiveness of the GMM method in efficiency enhancement.