馬可夫轉移測量誤差迴歸模型校正多階段類別與序位結果相關因子效應

Multistate Markov Transition Measurement Error Regression Model for Calibrating Biased Effect Size of Categorical and Ordinal Outcome

蘇秋文(Chiu-Wen Su)

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(2016年)

https://doi.org/10.6342/NTU201602191

摘要

研究背景
過去已有許多統計方法針對流行病學研究中常見測量誤差進行研究，然而測量誤差對於所關心的危險因子在疾病相關性上之影響程度仍有許多方面值得探究。首先測量誤差對重覆性測量資料的影響，特別是在多階層及長期追蹤性資料，甚少被提出討論。其次，當二元測量結果擴展至多階段結果，包含類別及序位資料，或是多階段結果伴隨有時間性的多階段疾病進程性質時，過去傳統的統計方法往往有所限制而無法具體適用。因此發展適合之統計評估方法有其必要性。

研究目的
本論文研究目的在統計方法發展上包含
應用貝氏向非循環圖模型發展非模型基礎及多階層廻歸測量誤差模型，針對兩階段結果重覆測量資料進行危險因子影響程度校正;
應用貝氏向非循環圖模型發展馬可夫廻歸測量誤差模型，針對多階段類別結果資料進行危險因子影響程度校正;
應用貝氏向非循環圖模型發展等比例勝算馬可夫測量誤差模型，針對多階段序位結果資料進行危險因子影響程度校正;
應用貝氏向非循環圖模型發展部分隱藏型馬可夫測量誤差廻歸模型，針對多階段具潛伏階段特性(例如大腸腺腫、以及無介入計劃下無法觀察之疾病臨床症前期)結果資料進行危險因子影響程度校正;
再者，本論文以上述所提及之統計方法，應用於社區牙周指數及附連指數測量結果為主之社區牙周病早期偵測與大腸癌糞便潛血篩檢，針對危險因子受影響程度分別利用所提不同模型進行驗證及比較研究。
利用研究目的(1)所提統計模型，對於社區牙周指數及附連指數具測量誤差下，探討錯誤分組下牙周病兩階段危險因子，進行個別危險因子校正，並探究其效應為差別性錯誤分組(無校正時危險性被高估)或無差別性錯誤分組(無校正時危險性被低估)。
利用研究目的(2)及(3)所提統計模型，對於社區牙周指數被視為類別或序位測量結果下，探討錯誤分組下進行牙周病個別危險因子校正及並探究其效應為差別性錯誤分組或無非差別性錯誤分組。
對大腸癌篩檢資料應用為
利用研究目的所提統計模型，在糞便潛血檢測存在可能測量誤差之下，其評估是否為一好的替代終點，用以預測大腸腺腫及大腸癌發生(通常需要長期追蹤)，並評估大腸腺腫及大腸癌危險因子校正及其相關效應大小;
考量大腸癌多階段疾病進程之多階段結果包含正常、腺腫、篩檢偵測癌及臨床偵測癌，以及相對應各階段糞便潛血檢測之測量誤差(敏感度及特異度)下，進行如同研究目的(7)所欲進行之評估。

材料與方法　
研究設計與資料來源
本研究第一個應用為社區牙周病篩檢資料，針對該研究所收集之相關風險因子，以本研究應用發展之方法探討測量誤差校正風險因子對於疾病影響之效果。該研究為兩階段設計。在校準研究資料(validation study)中收集包含不同區域共31位受試者之牙周評估資料，並與資深牙周病醫師(作為黃金標準)比較，估計社區牙周指數(CPI)及附連(LA)指數對於牙齒六分區(sextant)層級之敏感度與特異度。此敏感度與特異度資訊繼而運用於台灣全國性篩檢(主要研究資料, main study)，該研究共計納入4016位18歲以上研究對象，評估各風險因子透過貝氏階層模型引入敏感度與特異度校準後在考量同一個研究對象在牙齒六分區層級間之相關性後對於疾病之影響。
本研究第二個應為利用糞便潛血免疫法檢查(FIT)為工具進行社區大腸直腸癌篩檢資料進行糞便潛血濃度(f-Hb)之檢查。此一實證資料之運用顯現了以糞便潛血濃度作為大腸腺腫以及大腸直腸癌之替代終點之表現。所收集資料中主要藉由病理確診之篩檢偵測以及臨床偵測之大腸直腸癌與大腸直腸腺腫作為黃金標準(大腸直腸癌與腺腫之觀察疾病狀態)。藉由追蹤篩檢族群得到之篩檢間隔個案以及後續篩檢偵測之大腸直腸癌與大腸腺腫之資訊進行敏感度與特異度之估計，繼而用以得到各風險因子對於大腸腺腫與大腸直腸癌於校正後之影響，並評估以糞便潛血濃度作為疾病替代終點之表現。
統計方法
本研究發展一系列之統計方法並運用於上述牙周病以及大腸直腸癌實證資料。研究中藉由發展貝氏階層測量誤差迴歸模型，將長期追蹤資料中重複測量以及階層特性納入模型考量。研究中基於離散狀態(discrete-state)馬可夫過程發展貝氏階層測量誤差迴歸模型並運用於多階段類別性質以及序位性質資料。本研究亦在貝氏架構下發展離散狀態與連續時間(discrete-state, continuous-time)之多階段模型。運用所發展之模型建構部分潛藏馬可夫測量誤差模型，運用於族群大腸直腸癌篩檢實證資料。

結果　
兩階段牙周病測量誤差校正
研究結果顯示牙周病測量誤差存在地域性差異，牙周社區指數的陽性概似值介於1.12至7.71間，附連指數介於0.92至5.71間，合併兩項指數則介於0.83至18.62間。吸菸校正後之勝算比較無校正之勝算比有顯著性改變，吸菸對於牙周指數≥3的危險性由無校正之2.02倍 (95% CI:1.63 - 2.52)，改變至校正後2.75倍(95% CI:2.01-3.77)，附連指數≥1的危險性由無校正之1.93倍(95% CI: 1.47- 2.54)，改變至校正後約3.85倍(95% CI: 2.44 - 6.13)，就牙周病歸因於吸菸危害，在牙周指數≥3而言，吸菸的歸因比由無校正之18%，改變至校正後的28%，附連指數≥1的歸因比則由無校正之17%，改變至校正後的39%。並比較校正結果與無校正結果在接受作業特徵曲線上之差異。

多階段牙周病測量誤差校正
運用等比例馬可夫廻歸測量誤差模型，針對多階段類別結果資料(正常、輕度、中度及重度)進行牙周病危險因子影響程度校正(實際無牙周病而檢測為輕度牙周病之測量誤差為30%，實際為輕度牙周病而檢測為中度牙周病之測量誤差為12%，實際為中度牙周病而檢測為輕度牙周病之測量誤差為42%，實際為中度牙周病而檢測為重度牙周病之測量誤差為10%，實際為重度牙周病而檢測為輕度牙周病之測量誤差為27%，實際為重度牙周病而檢測為中度牙周病之測量誤差為32%)。考量測量誤差下危險因子之淨危險性大幅增加。糖尿病在疾病進程上有2.15倍的危險性。吸菸影響早期牙周病，其危險性較無糖尿病者高，危險比為2.54(95 CI: 0.72-9.5)，影響中度牙周病危險比降為1.57 (95% CI: 1.17-2.14)，而重度牙周病危險比再降為0.89 (95% CI: 0.55-1.44)。模型比較之結果顯示，所有因子在牙周病多階段進展具同質性，宜以部分等比例馬可夫模型評估其對於疾病惡化之影響效果。

兩階段大腸直腸腺癌測量誤差校正
未考量測量誤差校正之危險因子對大腸腺腫危險對比值，年齡為1.27 (95% CI: 1.18-1.36)，BMI為1.16 (95% CI: 1.08-1.24)，代謝症候群為1.28 (95% CI: 1.17-1.39)、抽菸為1.4 (95% CI: 1.29-1.52)、飲酒為1.35 (95% CI: 1.24-1.46) 所有危險因子影響皆為低估。考量測量誤差校正時，特別是年齡及性別因子校正後會比未校正的危險對比值放大許多，且接近觀測腺腫之危險對比值。例如高BMI的危險對比值在未校正前為1.16 (95% CI: 1.08-1.24)，校正後升高到1.41 (95% CI: 1.19-1.68)，非常接近直接由資料觀察到的1.40 (95% CI: 1.25-1.58)。除性別外，年齡、代謝症候群、抽菸、飲酒等在發生腺腫的危險對比值的影響亦有相同的發現。多變量分析結果建議，年齡、性別及BMI應考量測量誤差校正，當考慮這些因子下，代謝症候群、抽菸、飲酒因子即無進行校正之必要。然而這些危險因子在大腸直腸癌的危險性上之校正結果與大腸腺腫不同，校正後的危險對比值並不接近觀測大腸直腸癌之危險對比值。

多階段大腸直腸癌及腺腫測量誤差校正
在兩階段校正後，利用部分五階段隱藏型馬可夫模型，將糞便潛血檢測結果視為一個階段，以驗證糞便潛血是否為大腸腺腫之替代終點。由兩階段校正所發現具意義的年齡、性別及BMI，在多階段測量誤差校正後，其影響程度較兩階段校正更大。男性相對危險性為2.26(95% CI: 2.01-2.55)、高齡者相對危險性為2.12(95% CI: 1.88-2.39)，高BMI相對危險性為1.23 (95% CI: 1.10-1.39)。值得注意的是年齡、性別及BMI危險因子之影響程度在多階段疾病進程上自糞便潛血至腺腫、腺腫至臨床前期、臨床前期至臨床前各段皆小於1或接近於1，這樣的結果無法自兩階段模型上得到。改變糞便潛血試驗陽性的切點值對估計結果影響不大。
應用四階段部分隱藏型馬可夫測量誤差回歸模型於全國大腸直腸癌篩檢資料，可估得糞便潛血檢驗特異度約為96%，其對大腸腺腫及大腸癌的敏感度則分別為63%及82%。考慮測量誤差校正後，性別(男性相較於女性)作用於腺腫發生、腺腫至臨床症前期大腸直腸癌及臨床症前期至症狀期大腸直腸癌的相對危險性(Relative Risk, RR)分別為1.80 (95% CI: 1.35-2.35)、0.77 (95% CI: 0.59-0.99)及0.98 (95% CI: 0.76-1.27)；年齡層(60歲以上相對於60歲以下)的相對危險性則分別為1.79 (95% CI: 1.39-2.34)、1.07 (95% CI: 0.83-1.36) 及0.88 (95% CI: 0.69-1.13)，與五階段部分隱藏型馬可夫測量誤差回歸模型結果相似。

結論　本論文運用貝氏馬可夫鏈蒙地卡羅-吉布斯抽樣法發展多階段馬可夫測量誤差迴歸模型，並據以提出多項統計上嶄新的突破性想法如下：
發展貝氏多階段測量誤差迴歸模型應用於多階段重複測量資料之長期追蹤;
以離散型馬可夫過程和等比例勝算馬可夫模型發展貝氏多階段測量誤差迴歸模型應用於類別與序位多階段資料結果;
發展部分隱藏型馬可夫測量誤差迴歸模型應用於癌症或慢性病之疾病多階段進展;
，並利用牙周病檢查與大腸癌糞便潛血篩檢兩種資料以上述統計模型進行創新的應用，包含
利用牙周病診斷誤差校正研究探討錯誤分組下牙周病兩階段危險因子，進行個別危險因子或考量其他干擾因子之校正及其效應大小；
利用貝氏測量誤差迴歸模型同時針對個別危險因子或考量其他干擾因子下，探討牙周病從正常到嚴重四階段危險因子校正及其效應大小；
以兩階段模型校正在糞便潛血濃度具測量誤差下大腸腺腫及大腸癌之相關危險因子及其效應大小，並評估糞便潛血濃度是否可用於預測大腸腺腫及大腸癌發生長期追蹤之替代工具;
以多階段模型校正大腸腺腫及大腸癌之相關危險因子及其效應大小，並評估糞便潛血濃度是否為預測大腸腺腫及大腸癌發生長期追蹤之替代工具。

重要的發現包含
貝氏多階段測量誤差迴歸模型結果顯示校正前之牙周病所有相關危險因子之效應大小皆低估，校正後將提高其效應(無偏差錯誤分組)，建議在未考慮錯誤分組下，應加強生活型態改善之預防工作；
等比例勝算馬可夫模型校正後之效應也比較大，本研究發現除了身體質量指數外每個變數之效應大小，在控制起始的轉移機率後與各階段轉移機率是互相獨立的；
同時考慮年齡、性別、身體質量指數、代謝症候群、抽菸和喝酒後，校正後之糞便潛血濃度顯示對於大腸腺腫是好的長期追蹤替代工具，但在大腸癌表現上則適中；
在多變量分析中同時考慮所有因子後，效應大小可能只需要校正考慮年齡、性別及身體質量指數，而代謝症候群、抽菸和喝酒後則不需要進行校正；
利用四階段部分隱藏馬可夫模型考量糞便潛血濃度之敏感度與特異度測量誤差，當控制大腸癌多階段疾病進程時，年齡及性別之大腸癌腫瘤及大腸癌危險因子，及其效應大小因予以校正。

關鍵字

測量誤差 ； 多階層資料結構 ； 馬可夫鍊模式 ； 牙周病篩檢 ； 大腸直腸癌篩檢

並列摘要

Background
Statistical methods for estimating misclassification error rates inherent from epidemiological studies have been well studied but their impacts on effect size regarding the relationship between the risk factor and the outcome of interest still leave some to be desired. First, how the effect size attributed to measurement errors made as a result of repeated outcomes, particularly implicated in hierarchical data structure, in longitudinal follow-up study has not been much researched. Second, when the binary outcome is extended to multistate outcome including categorical and ordinal data involving with the evolution of multistate disease progression with time, the applicability of these conventional statistical outcomes is limited. The development of complex statistical models and delicate estimation methods are therefore indispensable.
Aims
The purposes of this thesis are two-fold. The first attempts made to achieve statistical objectives include
(1) the development of non-model-based and hierarchical regression model for calibrating the effect size (in terms of odds ratio) of two-state outcome under the context of Bayesian directed acyclic graphic (DAG) model;
(2) the development of Markov regression model with measurement errors for calibrating the effect size of multistate categorical outcome under the context of Bayesian DAG model;
(3) the development of proportional odds Markov regression model for calibrating the effect size of multistate ordinal outcome under the context of Bayesian DAG model;
(4) the development of partially hidden-Markov model with measurement errors for calibrating the effect size of multistate outcome with partially latent states (such as adenoma and pre-clinical screen-detectable phase (PCDP) that are often unobservable in the absence of intervention program (such as early detection) under the context of Bayesian DAG model for calibrating the effect size of multistate outcome.
The second was the application of the proposed statistical methods as above to two datasets with different validation schemes, a community-based study on early detection of periodontal disease (PD) measured by community periodontal index (CPI) and loss attachment (LA), and a community-based screening for early detection of colorectal neoplasia with fecal immunochemical test (FIT), with different purposes. The specific aims for the first dataset (PD) were
(5) to examine whether the biased effect size caused by measurement errors of CPI and LA in the detection of PD was differential (overestimated effect size before calibration) or non-differential (underestimated effect size before calibration) using the statistical model proposed in the statistical aim of 1;
(6) to examine whether the biased effect size caused by measurement errors of CPI in detection of PD was differential or non-differential when categorical and ordinal multistate outcomes were considered by using the statistical model proposed in the statistical aims of 2 and 3;
and those for the second dataset (CRC) were
(7) to assess whether f-Hb obtained from FIT test for early detection of colorectal cancer and neoplasia with possible measurement errors is a good surrogate endpoint for colorectal cancer and adenoma (that requires long-term follow-up to identify) when the effect size related to certain risk factor was investigated by using the statistical model proposed in the statistical aim of (1) for the calibration of measurement errors;
(8) to assess the aim of (7) as above by considering multistate outcomes from Normal of neoplasia, adenoma, PCDP, and CP with the measurement errors (sensitivity and specificity of FIT) or with the positive result of f-Hb.

Study Design and Data Sources
The first illustration was based on a community-survey on periodontal disease and its risk factors to demonstrate how to calibrate effect size as a result of measurement errors. A two-stage validation study on calibration was first performed to estimate sensitivity and specificity of both CPI and LA measurements at sextant-level on 31 study subjects from different regions by comparing both outcomes between 13 well-trained dentists and a senior periodontist (gold standard). Afterwards, a Taiwanese nationwide survey (the main study) was conducted by enrolling 4016 participants aged 18 years or older to estimate effect sizes of each risk factor calibrated with both sensitivity and specificity by using a Bayesian hierarchical model with the incorporation of correlated sextant property within the same subject.
The second illustration was based on data on community-based colorectal cancer screening with fecal hemoglobin (f-Hb) concentration from the Taiwan nationwide colorectal cancer (CRC) screening with fecal immunochemical test (FIT) to demonstrate the role of FIT as the surrogate measurement for colorectal adenoma and colorectal cancer. The gold standard (true status of colorectal cancer) was pathological confirmation of CRC detected at screens and of clinically-detected interval CRC and also adenomas. Incident follow-up validation design to identify interval cancer between screens and adenoma at subsequent screens was used to estimate sensitivity and specificity that were used to calibrate the effects of risk factors on colorectal adenoma and cancer in order to verify the role of FIT as surrogate endpoint.

Statistical Models
A series of statistical methods were developed with two illustrations including periodontal disease and colorectal cancer. A Bayesian hierarchical measurement error regression model was developed to accommodate repeated outcomes and multilevel data in a longitudinal follow-up study. A Bayesian measurement error regression model for multistate categorical and ordinal outcome was established underpinning discrete-state Markov process and proportional odds Markov model. We also proposed a multistate Markov model in discrete-state and continuous time with the consideration of measurement error as well as treating the tool of detecting disease as a surrogate endpoint with a Bayesian underpinning. A partially-hidden Markov measurement error regression model for multistate progression of cancer or chronic disease was used to a large population-based colorectal cancer screening.

Results
Two-state calibration for periodontal disease
The results show that measurement errors for periodontal disease varied with regions indicated by a wide ranges of positive likelihood ratio (sensitivity/(1-specificity)) from 1.12 to 7.71 for CPI, from 0.92 to 5.71 for LA and from 0.83 to 18.62 for the combined use of CPI and LA. Adjusted odds ratios for all variables by comparing the uncalibrated estimates with the calibrated ones were inflated with the notable changes for smoking from 2.02 (1.63 to 2.52) to 2.75 (2.01 to 3.77) for CPI

並列關鍵字

Measurement error ； Risk Factors ； Calibration ； Multi-state Markov Chain Model ； Periodontal Disease Screening ； Colorectal Cancer Screening

參考文獻

References

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