以多階段馬可夫模式探討肝癌術後病人治癒-復發或無復發-死亡過程之世代研究

The Multistate Markov Model for Cure-Recurrence (with/without)-Death Process in Patients Diagnosed as Hepatocellular Carcinoma after Curative Hepatectomy

郭明正(Ming-Jeng Kuo)

指導教授 ： 陳秀熙

共同指導教授 ： 陳祈玲(Chi-Ling Chen)

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/NTU201601268

摘要

研究背景
儘管肝癌術後的長期存活在近年來已有長足的改善，但術後的高復發率對肝癌預後而言仍然是很大的挑戰。因此更深入的了解肝癌術後從治療後的復發或無復發到死亡的臨床病程有其相當的必要性。雖然過去也有許多關於術後肝癌的預後的研究。然而，大多數的研究在方法學上仍有待改進之處，包含未將復發和死亡視為連續動態的過程、未個别考慮狀態間轉移的決定因子、復發及死亡風險模式的建立及未考量復發停留時間對疾病進程的影響。上述問題有待進一步的統計模型來驗証也正是本篇論文想要解決的問題。

研究目的
本論文利用臺灣肝癌網登記的肝癌患者術後長期追蹤資料進行研究，以達成以下研究目的，包含:
一、以三階段馬可夫模式來模擬接受肝臟切除術術後患者的臨床疾病進程，包括無復發、復發及死亡，並估計不同臨床狀態間的轉移機率及經由動力學曲線表現不同追蹤時間點無復發、復發及死亡的機率。
二、在考量臨床肝癌術後患者早期及晚期復發的前提下，進一步將三階段馬可夫模型延伸至四階段馬可夫模式，並估計不同臨床狀態間的轉移機率並經由動態曲線表現不同追蹤時間點無復發、早期復發、晚期復發及死亡的機率。
三、分別以三及四階段馬可夫模式探討不同狀態間轉移包含治癒至復發、復發至死亡、無復發至死亡的決定因子(包含宿主因子、腫瘤因子、術後病理學發現及病毒因子等)，並根據前述因子來訂定風險分數，並將不同階段間的轉移做風險分層。
四、在考量臨床因子的風險分數在無復發到復發以及復發到死亡間轉移狀態的相互影響下，將各階段風險組合成9個危險分層,並依此危險分層分別探討其對肝癌患者術後復發及死亡的動力學曲線之影響。
五、在調整不同階段風險分數條件下，形成單一危險分數，並據以將復發或死亡風險定位為低、中高三類，並依此三類危險分層探討其對肝癌患者術後累積復發率及死亡率的影響。
六、藉由三階段馬可夫分段模式找出肝癌術後復發分類的最佳時間切點，並在重新定義復發型態後，找出復發及死亡的非固定風險與轉移機率。
七、發展三階段半馬可夫模式，在考量不同轉移狀態停留時間及相關因子的影響下，重新評估肝癌患者術後的臨床疾病進程。

材料與方法
本論文針對臺灣肝癌網(Taiwan Liver Cancer Network, TLCN)中於2005年至2011年之間的2976名接受根治性肝臟切除術(Curative hepatectomy)的病患其術前血清檢查結果及術後病理資料進行分析。首先以Polytomous羅吉斯迴歸模式評估影響早期及晚期復發的危險因子，以時間相關Cox比例風險回歸方法分析腫瘤復發對患者存活的影響。接著利用一系列的隨機過程模式建構肝癌由治癒—復發(有/無)—死亡的過程與其相關的危險因子，上述隨機過程包含三階段及四階段馬可夫模式用以建構肝癌病人在無復發、復發及肝癌死亡間的轉移機率、三階段馬可夫分段模式及三階段半馬可夫模式考量轉移速率隨著時間變動或復發至死亡的危險性可能因停留在復發階段而有異等狀況。以此多階段隨機過程模式為基礎，發展不同轉移所對應的危險分數，並且利用指數迴歸模型求得預測因子對於不同階段間轉移的相對風險。根據前述因子來訂定風險分數，並利用動力學曲線預測不同風險分層肝癌患者術後復發及死亡的機率。三階段馬可夫分段模式及三階段半馬可夫模式則用以找出區分早期及晚期復發個案的最佳時間切點，並在考量危險因子對復發階段的停留期間之影響探討各預測因子於不同階段間轉移的相對風險。

結果
利用三階段馬可夫模式所估計出的年復發率為0.22 (95% CI: 0.21-0.24)，復發至死亡及未復發至肝癌死亡的年風險率分別為0.20 (95% CI: 0.18-0.22)及0.0025 (95% CI: 0.0014-0.0037)。在運用此三階段馬可夫模式評估各分險因子對於個疾病階段造成之影響結果顯示，門脈高血壓分別在復發(RR=1.32 , 95% CI: 1.09-1.62)、復發至死亡(RR=1.38, 95% CI: 1.00-1.91)、無復發至死亡(RR=5.46, 95% CI: 1.34-22.11)之進程具有顯著影響。AST>80也分別對三階段疾病進程具顯著性影響，其風險在復發為1.26 (95% CI: 1.05-1.51)、復發至死亡為1.54 (95% CI: 1.15-2.02)、無復發至死亡為7.24 (95% CI: 1.71-29.93)。多數關於病人特性的因子皆作用於復發階段，但低身體質量指數對於復發(RR=1.12, 95% CI: 0.99-1.26)及復發至死亡(RR=1.32, 95% CI: 1.08-1.6)兩階段皆有影響。多數與腫瘤特性相關因子則對於復發及復發至死亡兩階段有顯著影響；B、C型肝炎病毒量及肝炎基因型僅作用於復發階段而腫瘤分化不良只作用於復發到死亡階段。
由三階段馬可夫分段模式的分析結果中，我們發現將時間切點定在2個月(極早期復發)、8個月(早期復發)及2.5年(晚期復發)的4種復發類型相較於區分為兩段與三段之模式下為最佳模式。儘管術後2個月內就復發的機率並不高 (每追蹤100人年只有7.63人發生)，但就這些患者而言，其死亡率卻為最高(73%，95% CI: 42%-100%)。術後兩個月之後，復發率漸增至2到8個月的44.52%(早期復發)，再漸減至2.5年及之後的10.44%(晚期復發)。死亡率則隨時間漸減(由早期復發的 33%降至晚期復發的 8%)。
由三階段半馬可夫模式的分析結果我們得到從無復發到復發以及復發到死亡的轉移風險呈∩型態的變化。其中復發風險在術後4.2個月達到頂點；而死亡風險在4.5個月達到頂點。藉由半馬可夫模型評估影響階段轉移的決定因子在調整其對於疾病復發時間的影響後則與三階段馬可夫模式分析之結果大致相同。

結論
本篇論文發展了治癒-復發或無復發-肝癌死亡之多階段過程，並實際以多種多階段模型運用於全國性肝癌病患追蹤資料，探究肝癌病患接受治癒性手術療法之後續病程發展，以提供下列重要臨床問題之答案：
1. 運用三階段馬可夫模型，肝癌病患在術後之年復發率為 22%；復發後之死亡率為20%。病患有極小之可能不經由復發路徑而發生死亡。運用此結果建構之疾病動態曲線顯示在七年的追蹤後，有21%的術後病患處於治癒狀態、35%的病患發生復發，有44%的病患死亡；利用四階段馬可夫模型之估計結果顯示，在七年的追蹤後，20%的病患處於治癒狀態、13%發生早期復發、23%發生晚期復發，44%死亡。此一估計結果提供了關於肝癌病患術後之基本疾病進展至復發以及肝癌死亡過程，並可運用並做為評估新療法之比較基礎。
2. 利用三階段馬可夫迴歸模型，本研究釐清各疾病階段之預後因子對於疾病進展之影響，包含治癒到肝癌復發、肝癌復發到肝癌死亡，以及治癒到不經由復發之死亡。其中以門脈高壓以及麩氨酸-草醋酸轉氨基酶(AST)大於80最為重要並且作用於疾病進展之所有三個階段(包含治癒到肝癌復發、肝癌復發到肝癌死亡，以及治癒到不經由肝癌復發之死亡)。對於治癒到肝癌復發以及肝癌復發到肝癌死亡兩段疾病進程皆有影響者包含顯微血管侵犯(microvascular invasion)、腫瘤大於5公分、甲型胎兒蛋白(AFP)高於20ng/ml、身體質量指數(BMI)小於25、以及肝硬化。作用於治癒到復發階段之因子包含年齡大於65歲、抽菸、多發性腫瘤、腫瘤清除手術邊緣(surgical free margin)小於1公分、高病毒量之B型肝炎感染、C型肝炎感染，以及C型肝炎基因型第一型；而僅作用於肝癌治癒到死亡階段者為Edmonson 組織分級第III與第IV級。
3. 本研究運用上述2.發展了疾病進展危險分數並用以將肝癌術後病患分為高、中、低三個危險層級，並以復發與死亡之危險層級區分病患為九類風險族群，預測此九類病患之死亡風險。
4. 運用四階段分段式馬可夫模型，本研究將肝癌之復發區分為極早期復發(2個月內復發)、早期復發(2到8個月)、晚期復發(9個月到2.5年)，以及極晚期復發(超過2.5年)。此一分類乃基於肝癌術後病患之復發風險在術後2個月內急遽上升，並且維持至8個月，繼而漸趨下降。肝癌復發至死亡之風險則隨時間漸減，由兩個月的73%(22/28)降至2.5年的8%。
5. 運用半馬可夫模型，本研究顯示肝癌之復發風險以及死亡風險隨時間之變化呈∩型。復發風險之極高值出現於術後第四個月；而肝癌復發到死亡之風險極高值出現於術後第五個月。影響各階段疾病進展之因素在運用半馬可夫模型分析結果在調整對於復發狀態時間之影響後，與三階段馬可夫迴歸模型之結果相似。

關鍵字

肝癌 ； 肝臟切除術 ； 馬可夫模式 ； 復發 ； 死亡

並列摘要

Background
Although long-term survival of hepatocellular carcinoma (HCC) patients after surgical resection has been substantially improved, high intrahepatic recurrence rate after these treatments is still a major challenge for clinical management of HCC patients. A better understanding of clinical course from curative hepatectomy, through recurrence, and finally to death is therefore indispensable and has been extensively studied. However, the previous studies addressing such clinical course are fraught with a series of flaws in methodology including the failure of treating recurrence and death as a continuous dynamic process, considering the separation of the transition from cure to death without occurrence from overall death, identifying state-specific predictors for two processes, developing state-dependent risk scores, and taking into account the influence of the duration of recurrence. These pitfalls render many clinical questions still unresolved and require a series of delicate statistical models that become the main subject of my thesis.

Aims
By using a nationwide cohort of HCC patients undergoing surgical resection with a long-term follow-up, the purposes of this thesis to achieve statistical attempts were
(1)to develop a three-state Markov process for depicting clinical course of HCC patients after curative hepatectomy covering three transitions (i.e. cure to recurrence, recurrence to HCC death, and cure to HCC death without recurrence) and to estimate three corresponding transition rates for deriving the kinetic curves for the description of evolution from cure, recurrence, until HCC death;
(2)to extend the three-state model in the aim (1) to the four-state Markov process to cover five transitions pertaining to early and late recurrence and to estimate five corresponding transition rates for deriving kinetic curves of the evolution from cure answering clinical question (1);
(3)to ascertain state-specific factors (host-related factors, tumor characteristics, histopathological findings, and viral factors) responsible for each transition of the underlying two multi-state Markov models to build up three risk scores corresponding to three transitions, cure to recurrence, recurrence to death, and cure to death without recurrence;
(4)to classify nine risk groups for elucidating the kinetic curves of the time from cure to recurrence and the time from cure to HCC death with the joint distribution of the two risk scores;
(5)to classify three risk groups for cumulative risk of recurrence and HCC death with the distribution of one-step risk score with adjustment for the other risk score;
(6)to develop three-state piecewise Markov model to identify a series of cutoffs distinguishing early and late recurrence and even more refined classification of recurrence to allow for non-constant hazards of transitions for recurrence and HCC death; and
(7)to develop three-state semi-Markov model to assess how the duration of recurrence with and without covariates as indicated in the aim affects the subsequent progression from recurrence to death from HCC.

Materials and Methods
A cohort of 2976 patients who underwent partial hepatectomy with pre-operative serum and post-operative pathology-verified HCC samples in the Taiwan Liver Cancer Network (TLCN) program between Jan 2005 and Aug 2011 were used for the elucidation of disease progression after curative hepatectomy. The study subject was categorized into no recurrence, early recurrence and late recurrence and using a polytomous regression to assess the effect of relevant factors. Considering the rate of fatality, Nelson-Aalen estimate was used followed by using a time-dependent Cox regression model to consider the state of recurrence varying with time. A cure-recurrence(with/without)-death Markov process was proposed for further elucidation of the mechanism of disease progression and the derivation of state-specific factors. With the application of a series of multi-state models including three- and four-state homogenous Markov model, three-state piecewise Markov model and three-state semi-Markov model, the clinical course of HCC recurrence and death was elucidated with the consideration of non-constant rate of disease progression and also the recurrence of duration- dependent transition rate. Based on the cure-recurrence(with/without)-death process, the three state-specific risk scores for the identification of subjects with different risk groups were derived. The further use of semi-Markov model and the piecewise model identified the optimal duration of early and late recurrence together with the effect of death-specific factors on the risk for HCC death with adjustment for the effect of covariates on the duration of recurrence.

Results
The crude rate of transition from cure to recurrence, from recurrence to death, and from cure to death without recurrence were estimated as 0.22 (95% CI: 0.21-0.24), 0.20 (95% CI: 0.18-0.22), and 0.0025 (95% CI: 0.0014-0.0037), respectively. Considering the state-specific effect of risk factors, portal hypertension (RR=1.32 (95% CI: 1.09-1.62), 1.38 (95% CI: 1.00-1.91), and 5.46 (95% CI: 1.34-22.11) for cure to recurrence, recurrence to death, and cure to death without recurrence, respectively) and elevated AST (with corresponding RRs of 1.26 (95% CI: 1.05-1.51), 1.54 (95% CI: 1.15-2.02, and 7.24 (95% CI: 1.71-29.93)) had significant role in all of the three transitions. While body mass index (BMI) has a significant role on both the transition from cure to recurrence (RR=1.12, 95% CI: 0.99-1.26) and from recurrence to death (RR=1.32, 95% CI: 1.08-1.63). Most of factors associated with patient characteristics play role on the transition from cure to recurrence. In contrast, except for the viral load and the genotype of HBV and HCV which play role on recurrence rate and Edmonson grade which has effect of the transition rate from recurrence to death, most of the tumor associated profiles had significant role on both the recurrence rate and the transition from recurrence to death.
The three-state piecewise Markov model suggests four-phase model, dividing recurrence at cutoffs of 2 months (very early), 8 months (early), and 2.5 years (late), was superior to 2- and 3-phase model. Although annual recurrence rate within two months (very early recurrence) was low (7.63%), annual death rate was highest for this population (73% 95% CI: 42%-100%). After two months, the recurrence rate increased with time up to 44.52% for early recurrence between 2 and 8 months and then declined to 10.44% from 2.5 years (late recurrence) or longer. Annual death rates waned with time (from 33% for early recurrence to 8% for late recurrence).
The results of the three-state semi-Markov model shows that the hazard functions of transitions from cure to recurrence and from recurrence to death were ∩-shaped with the maximum hazard rates for these two transitions, being 4.2 months and 4.5 months, respectively. The significant state-specific factors for transitions between states were similar to those in the three-state Markov model, albeit still slightly differently, after adjustment for the effect of relevant factors on the duration of recurrence.

Conclusion
This thesis developed cure-recurrence (with/without)-death process for HCC patients after curative surgical resection by modelling this clinical course with various multi-state Markov models to fit a nationwide HCC patients after surgical resection to answer important clinical questions
(1)The use of three-state Markov model gave a 22% annual recurrence and 20% HCC death and very small chance of being susceptible to HCC death without recurrence, which yielded the kinetic curve showing 21% cured patients, 35% patients potential of staying in recurrent state and 44% death from HCC after seven-year follow-up. The corresponding proportions using four-state Markov model gave 20% cured patients, 13% early recurrence, 23% late recurrence, and 44% % death from HCC. These figures provide baseline information on the evolution of recurrent state and death from HCC for evaluation of the proposed new treatment and therapy.
(2)The use of three-state Markov regression model identified state-dependent predictors including two predictors, portal hypertension and AST greater than 80, making significant contribution to all the three transitions (cure-recurrence, recurrence-death, cure-death without recurrence), factors accounting for both recurrence of and death from HCC (including microvascular invasion, tumour size larger than 5 cm and AFP greater 20 ng/ml, body mass index less than 25, and cirrhosis), and factors accounting for the time from cure to recurrence (including age, smoking, number of nodule greater than 1, free surgical margin less than 1 cm, HBV(+) with high viral load , HCV (+) or HCV(+) genotype 1, and factors accounting for the time from recurrence to HCC death (only Edmonson grade III&IV).
(3)The development of three state-dependent risk scores based on the findings in 2 classified three risk groups adjusting for one of two risk scores and nine risk groups considering two joint risk scores simultaneously for predicting the risk of HCC death.
(4)The use of four-phase peiecewise Markov model classified recurrent HCC into very early recurrence (< 2 months), early recurrence (2-8 months), late recurrence (9 months -2.5 years), and very late recurrence (> 2.5 years) with the corresponding findings that recurrence rate increased from 2 months until the peak of 8 months and then waned with the longer duration of recurrence but the hazard from recurrence to death waned with time from 73% (22/28) at two months to 8% after 2.5 years.
(5)The use of semi-Markov model identified the inverse U-shape recurrence rate and death rate with the highest risk at fourth month for cure to recurrence and 5 months for recurrence to HCC death, respectively. The effects of death-specific predictor for HCC death were assessed with the findings that were similar to those with three-state Markov regression model after adjusting for the effect of each predictor on the duration of recurrence.

並列關鍵字

Hepatocellular carcinoma ； Hepatectomy ； Markov model ； Recurrence ； Death

參考文獻

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