離散時間多階段隨機過程於社區高血壓篩檢之應用

Application of Discrete-Time Multistate Stochastic Process to Community-based Screening for Hypertension

王韋之(Wei-Jhih Wang)

指導教授 ： 陳秀熙 教授

共同指導教授 ： 張淑惠 教授

國立臺灣大學/公共衛生學院/流行病學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.02254

摘要

研究動機與目的
過去研究中，隨機過程廣泛地被應用於生物醫學領域中，如：慢性病或癌症等定期追蹤資料。但其大多是利用連續時間的隨機過程來探討事件發生的時間，較少用離散隨機過程來探討篩檢次數等相關問題。而篩檢次數之估計和後續成本的計算有相當大的關連，但在實際應用面上會存有設限問題，並不能夠觀察到所有人的檢查次數，因此篩檢出疾病之前需經過多少次檢查為本研究有興趣探討的問題。

資料來源與方法
本文以基隆市社區篩檢中高血壓為例，以連續時間和離散時間隨機過程做連結。在僅將高血壓分為有無的二階段情況下，討論指數分佈和幾何分佈之關係，其想法為當指數分佈切割成數段時間區間，可視為離散，若每一區間視為一個事件，當在某區間中發生一個成功事件，經過 個時間區間，可看成在幾何分佈中，當第一個成功發生之前有 次失敗。將此概念延伸至三階段推導出離散時間隨機過程，欲探討階段轉移之前所需的篩檢次數。而可逆多階段討論正常到高血壓前期的往返次數，則使用負二項分佈來討論多次往返之前需要多少篩檢次數。而分別就此三種情況探討篩檢出高血壓前所需的平均篩檢次數，並依照年齡、性別、糖尿病等變項分層後來討論。

估計結果
以二階段來看，平均一個人需篩檢3.94次才能夠觀察到高血壓出現，而依各變項分層之後，在二階段中，每一個變項都有顯著差異，即不論是男女、五十歲以上或以上、是否患有糖尿病、是否肥胖以及教育程度高低都會影響到在偵測到疾病之前所需的篩檢次數。在多階段的情況下，目前尚未發展出離散型概似函數，若用連續時間來進行估計可得知從平均一個正常至第二期高血壓需要約19人年。將此估計值帶入離散時間隨機過程，從正常到第二期高血壓需要2.33篩檢,從第一期高血壓到第二期高血壓則需要3.47次篩檢。若考慮分層，從正常觀察到第一期高血壓時，每一個變項亦為顯著，代表各變項皆會影響到平均篩檢時間，但若從第一期高血壓觀察第二期高血壓時，僅有年齡和性別對於平均篩檢時間有顯著差異。以負二項分佈在討論正常到前期高血壓往返次數時，若不進展到高血壓，看到一次前期高血壓需經過8.64次篩檢，觀察到兩次前期高血壓需經過17.28次，若從前期高血壓進展到第一期高血壓或第二期高血壓需3.09次，一旦觀察到高血壓則過程停止。

結論
離散型隨機時間模型可用以估計偵測到疾病之前所需的平均篩檢次數，在多階段部分，目前僅推導出離散時間模型之轉移機率，仍未發展出概似函數，但此概念亦可以應用於其他多階段轉移的資料上。未來是否可利用廣義線性模式來進行估計離散時間模式，或者是否可以利用其他估計方法，如：貝氏估計等，在未來的研究中可進一步討論。

關鍵字

平均篩檢次數 ； 幾何分佈 ； 負二項分佈 ； 離散時間隨機過程 ； 高血壓

並列摘要

Introduction
The application of stochastic process to chronic disease or cancer has been widely used in biomedical field. However, the majority of models have the emphasis on modeling occurrence of event been based on a continuous -time stochastic process. Very few studies have focused on the use of discrete-time stochastic process. In the realm of economic evaluation of cancer or chronic disease screening, it is customary to ask the question like the following “How many examinations, on average, should be taken in order to detect first occurrence of disease”.

Objective
The aim of this study was to model the average number of screens, using geometric model or negative binomial_based multistate model, to detect disease.

Resource and Method
We use community based screening data in Keelung, focus on hypertension. In order to make continuous-time model with the discrete-time stochastic process, we demonstrated how exponential distribution can be connected to geometric distribution with binary outcome, i.e: hypertension or not. The concept was also extended to develop multistate model for estimating the screening times before occurrence of disease. To transform the exponential distribution into discrete time with small interval, we divide a time period into several epochs, and regard every epoch commensurate whether to have an event. When the first success event occurs after y epochs, we can regard y times failure before a success event given geometric distribution. In addition, we also took into account the reversible process of three-state model by using negative binomial distribution. Besides, we assess the effect of covariates on different situations.

Estimated result
On average, person will be detected first hypertension after 3.94 screening times in two-state model, and every covariate (sex, age, diabetes, obesity, and education level) was significant. Using mean sojourn time, we inferred normal to stage 2 hypertension would take 19 person years. It’s 2.33 times detect stage 2 hypertension, and 3.47 times from stage 1 to stage 2 hypertension on average. Regarding covariates, every covariate plays a significant role in the occurrence of stage 1 hypertension. Sex and age affected transition from stage 1 to stage 2 hypertension. Without hypertension, first pre-hypertension was after 8.64 screening times, and second pre-hypertension after 17.28 times. Progressing to hypertension, it took 3.09 times of screening, from pre-hypertension to hypertension.

Discussion
In conclusion, we developed the discrete time stochastic multistate model to estimate expected number of screening times before detecting pre-hypertension or hypertension. The generalize linear models can be further developed to make the generalize discrete time models. The alternative can be considered by using Bayesian method.

並列關鍵字

expected screening times ； geometric distribution ； negative binomial distribution ； discrete time stochastic process ； hypertension

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