本研究利用統合性分析（Meta-analysis）探討物理活動（Physical activity, PA）和心血管疾病（Cardiovascular disease, CVD）之間的關聯性，並將其應用於外溢型保險商品的定價和回饋機制。通過 PM 二階動差改良法，改善隨機效應模型（Random-effect model）下對於研究間變異的估計，並利用模擬結果比較不同動差與不同估計方法之間的準確性。結合大量研究數據，包括受試者年齡、觀測區間、活動水平和心血管健康等因素，開發一種評估死亡風險的模型。透過統合性分析，本研究取得無運動狀況及有運動狀況對於心血管疾病死亡率的勝算比（Odds ratio, OR）為 0.560，再考慮不同類別設計，結合網絡式統合性分析（Network meta-analysis）計算出勝算比為 0.617，且得到活動強度超過特定水準後無助於死亡率改善的推論。根據上述結果，保險公司能夠更準確地針對不同物理活動強度進行定價，並設計了一套外溢回饋機制，通過激勵被保險人提升物理活動來降低保費。然而，該領域仍處於研究和開發階段，需要進一步的理論研究和實踐。

This study employs meta-analysis to investigate the association between physical activity (PA) and cardiovascular disease (CVD), and applies it to the pricing and feedback mechanism of a spillover insurance product. By utilizing the PM 2nd-moment difference method to enhance the estimation of between-study variance in the random-effects model, we compare the accuracy of different moments and estimation methods through simulation results. Integrating a substantial amount of research data, including factors such as subject age, observation period, activity levels, and cardiovascular health, a model for assessing mortality risk is developed. Through meta-analysis, this study obtains an odds ratio (OR) of 0.560 for the comparison between no exercise and exercise conditions regarding cardiovascular disease mortality rate. Further considering different category designs and incorporating network meta-analysis, the calculated odds ratio is 0.617, suggesting no significant improvement in mortality rate beyond a certain threshold of activity intensity. Based on these findings, insurance companies can more accurately price different levels of physical activity and design a feedback mechanism that incentivizes policyholders to increase their physical activity and reduce premiums. However, this field is still in the research and development stage, requiring further theoretical investigation and practical implementation.

1. 緒論 (Page 1)
2. 文獻回顧 (Page 2)
3. 研究方法 (Page 4)
4. 模擬結果 (Page 15)
5. CVD 與 PA 強度之實證 (Page 17)
6. 外溢商品的設計與評價 (Page 23)
7. 結論 (Page 26)
References (Page 28)

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