以寇斯為導向之整合隨機模型評估族群篩檢效益

Consolidated Coxian Phase-type-based Stochastic Model for Evaluation of Effectiveness of Population-based Screening

任小萱(Hsiao-Hsuan Jen)

指導教授 ： 陳秀熙

國立臺灣大學/公共衛生學院/流行病學與預防醫學研究所/博士(2019年)

https://doi.org/10.6342/NTU201901194

摘要

研究背景
利用以族群為主的組織性服務篩檢計畫進行癌症篩檢效益評估雖然較利用實驗設計或類實驗設計困難，但往往可以提供較多的訊息。其難度除了缺乏適當的對照組之外，要將篩檢組織面(如涵蓋率)、過程面(轉介過程及等待時間)及結果面(疾病多階段進展過程)的因素考量在內將會牽涉複雜的過程，也因此需要一個完整且複雜的數學模式，才能有系統的將各項因子對篩檢成效的影響各別釐清。因此，本論文將以寇斯多相模式為基礎(描述轉介等候過程)，結合佇列過程(描述族群篩檢參與)、閾值模式(描述陽性個案轉介參與)及寇斯多相半馬可夫模式(描述疾病自然進展)成一個整合隨機模型，以進行族群篩檢效益之評估，並且評量篩檢組織面、過程面及結果面三類要素對效益之影響。
研究目的
(1) 擴展先前用來描述族群參與的佇列過程，加入機構因素及區域別因素；
(2) 結合寇斯多相模式及閾值模式評估轉介順從度及等候時間的多相樣態；
(3) 發展寇斯多相半馬可夫模式描述大腸直腸腺腫及不同階段大腸癌之進展；
(4) 結合以上兩個寇斯多相模式與佇列過程，發展適用於族群大規模篩檢評估之整合隨機模型；
(5) 發展電腦模擬程序，評估篩檢組織面、過程面及結果面三類要素在不同情境之下對組織性大規模篩檢效益之影響。
資料來源
本論文統計模型發展動機源自於臺灣大腸直腸癌大規模篩檢計畫之評估。臺灣自2004年開始由政府提供兩年一次的免疫化學糞便潛血檢驗做為大腸直腸癌篩檢之工具，本論文以2004年至2009年間篩檢的目標族群(50-60歲民眾共5,417,699人)做為研究世代。在2004-2014年間，共計3,072,164人參加過至少一次篩檢，篩檢涵蓋率為56.6%；參加第一次篩檢的個案中有211,531人檢查結果為陽性，陽性率為6.9%；陽性個案中完成轉介者計124,921人，轉介完成率為59%；參與篩檢者在2004-2014年間共偵測出88,730例大腸腺腫及51,145例大腸直腸癌個案(包括9,396例第一次篩檢發現個案及4,941例後續篩檢個案)，另有6,184人為間隔癌個案，而在未參加篩檢的族群中則有30,624人被診斷為大腸直腸癌(拒絕個案)。
方法
為了建構一個可以涵蓋族群組織性篩檢過程的完整架構，我們以佇列過程為出發點，考量機構因素及區域別因素的階層性資料結構描述族群的篩檢參與，在參與個案扺達篩檢計畫後，應用結合寇斯多相模式及閾值模式描述陽性個案接受轉介之順從度及等候時間的多相樣態，並且以另一寇斯多相半馬可夫模式描述大腸直腸腺腫及不同階段大腸癌之進展。據此，發展電腦模擬程序，評估篩檢組織面、過程面及結果面三類要素在不同情境之下對組織性大規模篩檢於轉介等候及篩檢效益之影響。
結果
1. 考量轉介面因素對篩檢涵蓋率之推估
結合佇列模式及閾值模式後，我們發現寇斯多相模式將轉介區分為兩個面相，若設定兩個月為轉介最大可容許等待時間，則可推定對一個三年一次的篩檢計畫而言，陽性率為7%且轉介順從度為60%，則篩檢涵蓋率可以達到90%。本模式可應用於考量篩檢涵蓋率、陽性率及轉介順從度等結構面變項之聯合分佈下之推估。
2. 篩檢對晚期癌症比例降低之推估效益
本論文利用臺灣大腸直腸癌篩檢實證資料對疾病自然史進行進展參數之估計，並結合上述發展之整合隨機模型據以發展一系列電腦模擬評估篩檢對晚期大腸直腸癌效益之評估，結果如下：
(1) 在現行篩檢情境相似參數之下(陽性率7%及轉介順從度60%)，兩年一次且篩檢涵蓋率達50%可以降低20%晚期大腸直腸癌；
(2) 與(1)相比，在陽性率7%及轉介順從度60%之下，當篩檢涵蓋率達20%, 50%, 80%及100%時，晚期大腸直腸癌降低效益分別為8%, 20%, 30%及36%。
(3) 與(1)相比，在陽性率7%及篩檢涵蓋率50%之下，當轉介順從度達20%, 50%, 80%及100%時，晚期大腸直腸癌降低效益分別為7%, 18%, 26%及31%。
(4) 陽性率降低(提高轉介標準)或篩檢間隔變長將會滅少篩檢效益。
結論
本論文結合佇列過程(描述族群篩檢參與)、閾值模式(描述陽性個案轉介參與)及寇斯多相半馬可夫模式(描述疾病自然進展)並建構一個整合隨機模型發展族群篩檢評估之架構，並將此模式應用於臺灣大腸直腸癌篩檢計畫進行相關參數估計，此整合隨機模型可用來監測篩檢計畫的結構及過程面，並做為各面向因素對結果面(篩檢效益)之預測。

關鍵字

大腸癌篩檢 ； 寇斯多相模型 ； 篩檢效益評估 ； 疾病自然史

並列摘要

Background
Evaluation of efficacy and effectiveness of population-based organized service screening is more intractable but informative than that of population-based experimental and quasi-experimental program. In addition to lacking of an adequate control group, elucidating a constellation factors implicated in population-based service screening program, including structure in relation to coverage rate, process resulting from referral process and waiting time for confirmatory diagnosis, and outcomes pertaining to multi-state disease natural history is a complex process that requires a comprehensive mathematical model to quantify relative contributions of each factor to the effectiveness of screening. To this end, this thesis proposes the consolidated Coxian-phase type model in conjunction with Queue process to develop a novel mathematical model for evaluating the impact of three-aspect factors on the effectiveness of population-based service screening program.
Aims
The aims of thesis are therefore to
(1) extend the previously proposed Queue process to model the arrival rate of eligible screenees by different settings of institution and geographic areas;
(2) apply the Coxian-phase type process in conjunction with Hurdle regression model to estimate the compliance rate and different phases of waiting time for confirmatory diagnosis;
(3) develop Coxian-phase Markov process and Semi-Markov process to elucidate and quantify the occult progression of multi-state disease process with the incorporation of AJCC tumour stage information;
(4) consolidate two Coxian-phase type processes in (2) and (3) in conjunction with the Queue process as a unifying quantitative system of population-based screening model; and
(5) project the effectiveness of population-based organized service screening program by changing various scenarios of underlying factors related to population-based organized service screening program.
Data
This thesis is motivated by population-based screening program for colorectal cancer (CRC) with biennial fecal immunochemical test (FIT) in Taiwan. A total of 5,417,699 eligible population (aged 50-69 years in 2004-2009) composed our study cohort. In 2004-2014, the program covered 56.6% (n=3,067,853) eligible population attending at least one FIT. The positive rate was 6.9% (n=211,531) in the first round. Among them, 59% (n=124,921) underwent confirmatory examination. Data on all screening history together with screening findings were prospectively collected in the central screening monitor system. A total of 88,730 subjects were detected as adenoma. There were 51,145 CRC diagnosed upon screening, including 9,396 and 4,941 screen-detected cases in the first and subsequent rounds of screen, respectively, 6,184 interval cancers, and 30,624 refusers among those never attended. Data on the distribution of AJCC staging were available.
Methods
To build up a unifying framework for modelling the whole process of population-based organized service screening, we began with the Queue process to capture the arrival rate of eligible screenees given hierarchical institute setting and geographic area. After the arrival of attending screening, we then applied the Coxian-phase type process in conjunction with Hurdle regression model to model the compliance and waiting time in relation to the referral process of confirmatory diagnosis for screen-positive subjects. Another Coxian-phase Markov process and Semi-Markov process was further developed to elucidate and quantify the occult progression of multi-state disease process with the incorporation of adenoma and AJCC tumour stage information. A series of simulation consolidating these two Coxian-phase type processes and the Queue process as a unifying quantitative system of population-based screening model was used to (1) elucidate the distribution of waiting time, and (2) project the effectiveness of population-based organized service screening program in terms of the reduction of advanced staged CRC with various scenarios of underlying factors related to population-based organized service screening program, including attendance rate, positive rate, and referral rate.
Results
1. Projection related to coverage rate and referral process
While the Queue process and the hurdle two-phase Coxian type model (abbreviated as QH-CPH model) were identified, the projection with the application of estimated parameters based on QH-CPH model indicates that if two-month waiting time is the maximum allowable clinical capacity, a three-year FIT screening program can be provided to cover 90% population given 7% positive rate, and 60% compliance rate. Other similar projections for the joint distribution of these parameters relevant to structure and process were derived in a similar manner.
2. Projected effectiveness of reducing advanced cancer
We estimated the transition parameters governing the disease natural history modelled by a series of Coxian-phase type Markov process to project the following results on the effectiveness of reducing advanced cancer.
(1) With parameters similar to the current situation (7% positive rate, and 60% referral rate), biennial screening with 50% coverage rate could yield the reduction of advanced CRC by 20%.
(2) Compared with (1), the corresponding figures for 20%, 50%, 80%, and 100% coverage rate were 8%, 20%, 30%, and 36%, respectively, given 50% referral rate and 7% positive rate.
(3) Compared with (1), the corresponding figures for 20%, 50%, 80%, and 100% referral rate were 7%, 18%, 26%, and 31%, respectively, given 50% coverage rate and 7% positive rate.
(4) The effectiveness reduced with lower positive rate and longer inter-screening interval.
Conclusion
The consolidated Coxian-phase-type-based stochastic process was constructed in commensuration with a unifying framework of population-based organized service screening. Its relevant parameters governing the whole process from the arrival to the outcomes of disease status were estimated on the basis of Taiwanese biennial nationwide colorectal cancer screening program. It is very useful for projecting the performance in relation to structure and process of screening program and also play an important role in the projection of effectiveness of screening program such as the reduction of advanced cancer.

並列關鍵字

Colorectal Cancer Screening ； Coxian phase-type model ； Evaluation of Effectiveness of Population-based Screening ； Natural history

參考文獻

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