佇列閾值及寇斯多相統計模型探討與大腸直腸癌早期發現和住院之相關時間分布

背景台灣大腸直腸癌的發生率逐年增加，對於大腸直腸癌的早期發現可以先透過糞便潛血檢查再進一步地接受大腸鏡來進行確診，在確診為大腸直腸癌病人後，後續的住院治療這些都是不容忽視的問題。然而為了考慮民眾的篩檢到達率、未接受大腸鏡確診者的特性、等待接受大腸鏡確診的時間以及大腸直腸癌病人接受後續住院治療的住院天數，傳統的佇列模型是無法實行的。研究目的本論文的研究目的是將佇列過程、閾值模型以及寇斯多相模型整合為一個統計方法，並將此方法應用在分析台灣全國大腸直腸癌篩檢之陽性個案所需進行大腸鏡確診的等待時間以及大腸直腸癌病人的住院天數。研究方法閾值模型由邏輯斯迴歸以及截尾卜瓦松迴歸模型所組成，邏輯斯迴歸用來研究未接受大腸鏡確診者的特性，截尾卜瓦松模型則用來分析等待接受大腸鏡確診的時間分布。而寇斯多相模型可以探討等待時間的最佳隱藏階段，處理接受轉介民眾之間的異質性。為了可以更進一步地考慮民眾的篩檢到達率，我們結合了卜瓦松過程、閾值模型以及寇斯多相模型進而發展出一個佇列閾值寇斯多相模型。在住院治療方面，我們利用寇斯多相模型對178位大腸直腸癌病人的住院天數進行分析，探討其最佳的隱藏階段個數。結果第一部份：在篩檢前期（2004-2009年），閾值模型的結果顯示女性、年齡較高者、居住在東部、離島或非都會區民眾、在醫院進行篩檢的民眾或是盛行篩檢個案（首次參與篩檢）有較高的機率不接受後續轉介，而居住在中部或大都會地區、在衛生所或健康服務中心接受篩檢的民眾或是非首篩個案其所需等待接受大腸鏡確診的時間較短。第二部份：在佇列閾值二階段寇斯多相階段模型中，等待大腸鏡確診的時間可被分類為等待時間較短階段以及等待時間較長階段，其結果顯示民眾的篩檢到達率每人天為0.00021，不接受後續確診的機率為0.26，一年大約有15% 的民眾對於後續大腸鏡的確診會猶豫不決而陷入等待時間較長的階段。在等待時間較短階段的平均等待時間為32天而在等待時間較長階段的平均等待時間為169天。當我們將危險分數考慮到模型中進行分析時，佇列閾值二階段寇斯多相階段模型顯示低分群在等待時間較短階段的平均等待時間為36天而高分群為30天，在等待時間較長階段，兩群的平均等待時間皆為167天。第三部份：在住院治療方面，我們利用三階段寇斯多相模型對178位大腸直腸癌病人的住院天數進行分析，住院天數可被分為短期停留階段、中期停留階段及長期停留階段。在短期停留階段中，平均住院天數為10天，而中期停留階段及長期停留階段的平均住院天數均為49天。當我們將性別放入模型中考量時，可利用二階段寇斯多相模型對住院天數進行分析，住院天數可被分為短期停留階段及長期停留階段。二階段寇斯多相模型的結果顯示男性會比女性較早出院或死亡。若將年齡放入模型中考量時，年長者相對於年輕的病人較早出院或死亡。結論這是一個新的佇列閾值寇斯多相模型，它被用來解決佇列過程、陽性個案不接受後續轉介的閾值問題以及針對等待接受大腸鏡轉介的時間和大腸直腸癌病人接受後續住院治療的住院天數來探討其最佳的隱藏階段數。

關鍵字

寇斯多相模型；閾值模型；等候時間；大腸直腸癌；大腸直腸癌篩檢

並列摘要

Background As the incidence rate of colorectal cancer (CRC) has been increasing in Taiwan, early detection of CRC through fecal immunochemical test (FIT) screening first and then colonoscopy examination and hospitalization of CRCs cannot be overemphasized. However, the arrival rate of screenees, the non-compliers of undergoing colonoscopy, the waiting time (WT) for undergoing colonoscopy, and the length of stay (LOS) for CRCs has rendered the conventional queue model infeasible. Aims The objective was to integrate the queue process, hurdle model, and Coxian phase-type model into a unifying framework that was applied to two empirical datasets, one relating to the WT of undergoing colonoscopy from Taiwanese nationwide screening program, and the other pertaining to the LOS on hospitalized CRCs enrolled from one medical centre. Methods The hurdle model was developed in combination with a mixture of the logistic regression model that dealt with the non-compliance part and the truncated Poisson regression model pertaining to the WT distribution. The Coxian phase-type was further developed to identify the optimal hidden phase of WT. To further consider the arrival rate of screenees, we developed the queue hurdle Coxian phase-type model which is the combination of the Poisson process, hurdle model and Coxian phase-type model. Data on the LOS of 178 CRCs were modelled by the Coxian phase-type model to identify the optimal number of hidden phases. Results Part I : From 2004 to 2009, the results of the hurdle model indicate the factors associated with non-compliance for colonoscopy included female, older age group, eastern Taiwan or offshore islands area, rural area, hospital screening unit and prevalent screening rounds, and the factors associated with shorter WT for colonoscopy included middle Taiwan area, main urban area, public health centers screening unit and subsequent screening rounds. Part II : The queue hurdle 2-phase Coxian phase-type model was classified as short- and long waiting phase. The arrival rate was 0.00021 per person-days and the probability of non-compliance with colonoscopy was 0.26. Annually, around 15% subjects were so hesitant to be referred to undergo colonoscopy that they were trapped in long waiting phase. The mean WT of short waiting phase and long waiting phase were 32 days and 169 days, respectively. Further to consider the effect of risk score on the model, the queue hurdle 2-phase Coxian phase-type model indicates the mean WT in short waiting phase were 36 days and 30 days for the low score group and the high score group, separately and 167 days in longer waiting phase among these two groups. Part III : For hospitalization, the LOS with 178 CRCs was modelled by the 3-phase Coxian phase-type model classified as short-stay, medium-stay and longer-stay phase. In the short-stay phase, the expected LOS was 10 days whereas both the medium- and longer-stay phases were 49 days. When gender was taken into account, the LOS was modelled as a 2-phase Coxian phase-type model, short- and long-stay care. It shows that male would discharge or die earlier than female. Regarding age, it shows the elderly would discharge or die earlier than the young. Conclusions A new queue hurdle Coxian phase-type model was developed to solve the queue process, the hurdle issue in relation to the problem of non-compliance with the referral of positive results of screenees to have confirmatory diagnosis, and to identify hidden phases during the WT for undergoing colonoscopy among the referrals and LOS in hospitalization for the treated CRCs.

並列關鍵字

Coxian phase-type ； the hurdle model ； waiting time ； colorectal cancer ； colorectal cancer screening

參考文獻

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佇列閾值及寇斯多相統計模型探討與大腸直腸癌早期發現和住院之相關時間分布

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