應用閾值相依之失能與死亡統計模型於介入效益評估

Abstract

背景：儘管失能與死亡模型(disability and death model, DDM)已經被廣泛的使用在分析以中止事件為特徵的事件歷史資料，對於中繼事件如何在不同失能與死亡模型中影響到對於介入效益之評估往往未能妥適的加以考量，且受限於中繼事件的狀態是具有持續時間相依性，且中繼狀態本身來自於事件歷史資料，過去在分析上中繼狀態的影響經常運用未考慮此一時間相關特性之方法而未能得到適當的效益估計。時間相依寇斯等比例風險回歸模式與半馬可夫模式為可以用來處理前述時間相依性之評估方法，但過往此兩個分析方法尚未廣泛的運用於此類資料結構中以適當的評估介入效益。 目的：藉由使用腦中風世代資料，包含中風死亡與復發時間，來達到以下的目的 (1)評估在失能模型中具有時間相依性的中繼狀態如何影響中止事件的進展，藉由使用與比較時間相依寇斯模型與非時間相依寇斯模型，並將中繼事件狀態作為解釋變項 (2)藉由使用半馬可夫模式，評估持續時間相依的中繼狀態如何影響中止事件的進展 (3)根據Clayton copular模擬失能模型結構下之相關結構時間資料 (4)藉由(1)到(3)評估失能模型中之時間相關性對於時間相依寇斯模型與半馬可夫模式評估方法之表現影響。 材料：本研究的資料來源為1992-1995所執行的臨床隨機雙盲試驗，共納入466位第一次非心源性腦梗塞的中風患者，並將其隨機分派接受aspirin (n=222)治療或nicametate (n=244)治療。臨床試驗的患者追蹤是否發生腦中風復發，以及進一步追蹤死亡資訊至2010年九月。 方法：提出以轉換時間相依變數為基礎之寇斯迴歸模型，用來考慮中風復發時間。此外，馬可夫過程與半馬可夫模式也同樣用來分析此資料集。在半馬可夫模式中，等候時間分布(此為半馬可夫模式之語言)上則是透過韋伯分布來描述。 結果：在應用時間相依寇斯模型分析中風世代資料時，nicametate治療增加復發的風險(HR: 1.65, 95% CI: 0.91-2.98)，而nicametate對於預防腦血管疾病死亡則有顯著的影響(HR: 0.63, 95% CI: 0.41-0.97)。Nicametate治療的機制進一步藉由半馬可夫失能風險模式來說明，顯示nicametate治療增加復發風險(HR: 1.72, 95% CI: 0.98-3.67)，主要是由於降低第一次中風後的競爭死因風險(HR: 0.72, 95% CI: 0.45-1.14)。運用半馬可夫模式評估 nicametate對於死亡所達到之保護結果則為0.68(0.37-0.9995)。時間相依性對於運用時間相依寇斯模型評估介入效益具有高估之影響，而以半馬可夫失能風險模式進行效益評估在不同相關性之情境下則可有一致之表現。 結論：本論文提出時間相依寇斯模型與半馬可夫模式，來處理實證資料具有持續時間相依特性的失能模型。這兩種模式都可以用來校正由於忽略疾病時間相依(中繼狀態)具有偏差的估計，在應用上兩種模式各有其優缺點。這兩種模式對於健康照護決策模式與治療或介入效益的經濟評估是非常有用，尤其是疾病的持續時間相依納入考量。

Background Although the disability and death model (DDM) has been widely used in modelling event history data characterized by first intermediate state and then the subsequent terminal, how the effect of intermediate state affects the evaluation of intervention inherent from such a kind of data has been often inadvertently analyzed by using a naïve statistical approach without considering the duration staying in the intermediate state. The time-dependent Cox proportional hazards regression method or the semi-Markov model can be applied to taking into account duration-dependent property, but the models have been barely applied to evaluating the efficacy of treatment and how the evaluation of the efficacy of treatment is affected by inter-correlated property between time to intermediate state and time to terminal event without passing through intermediate state has been elucidate as yet. Aims By making use of stroke cohort data including the recurrence time and survival time, the objectives of this thesis are therefore (1)to assess how duration-dependent intermediate state in the DDM affects the prognosis of terminal event using the Cox time-dependent model in comparison with time-independent Cox model when intermediate state is treated as a covariate; (2)to assess how duration-dependent intermediate state affects the prognosis of terminal event using the Semi-Markov model; (3)to simulate inter-correlated time-to-intermediate and time-to-terminal events by using the Copular approach; (4)to evaluated the effect of correlation on the estimated results on intervention effect size based on (1) to (3). Data Sources The source of data used in this study were derived from the cohort based on a multicenter randomized double-blind controlled trial during 1992 to 1995 with the enrollment of a total of 466 patients with first-time non-cardioembolic ischemic stroke who were randomly allocated to receive aspirin (n=222) or nicametate (n=244). The trial cohort was followed up over time to ascertain the date of recurrence and death until September 2019. Methodology The switched time-dependent-covariate (namely the intermediate state of the DDM)-based Cox regression model was proposed to fit in with the stroke recurrence time. The semi-Markov model, using the distribution of duration (holding time in the language of Semi-Markov model) with the Weibull distribution, were proposed. Results Applying the time-dependent Cox model to the stroke cohort, while nicametate treatment led to an increased risk of recurrence (HR: 1.65, 95% CI: 0.91-2.98) the significant effect of nicametate treatment on the prevention of cerebrovascular death was revealed (HR: 0.63, 95% CI: 0.41-0.97). The mechanism of the nicametate treatment was further elucidate using the semi-Markov DDM. While the nicametate treatment resulted in higher risk of recurrence (HR: 1.72, 95% CI: 0.98-3.67), which is mainly due to the reduced risk of competing death after first-time stroke (HR: 0.72, 95% CI: 0.45-1.14). The efficacy of nicametate in terms of averting CVD was estimated as 0.68 (95% CI: 0.37-0.9995) derived from the estimated results of semi-Markov model. The correlation between three succesive times under the DDM structure results in an overestimated result for time-dependent Cox regression on the evaluation of intervention efficacy while that for semi-Markov DDM remain consistent. Conclusion This thesis proposes time-dependent Cox regression model and semi-Markov model to deal with empirical data characterized by duration-dependent DDM. While both models can be used to rectify the biased estimate due to the neglected aspect of duration of disease (intermediate state) the application of two models have respective merits and weaknesses.