以貝氏馬可夫模式探討乳房攝影表徵之乳癌自然病史及預後

Mammography-featured Natural History and Prognosis of Breast Cancer with Bayesian Markov Model

莊書琳(Shu-Lin Chuang)

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(2014年)

https://doi.org/10.6342/NTU.2014.01306

摘要

背景
　　隨著利用乳房攝影作為乳癌篩檢工具之盛行，不同乳房攝影表徵下之乳癌自然病史以及相關預後因子亦可用來評估篩檢偵測與臨床偵測乳癌個案之存活差異。由於傳統腫瘤特質亦會影響不同乳房攝影表徵下之乳癌個案預後情形，因此在比較不同乳房攝影表徵間，篩檢偵測與臨床偵測乳癌個案之存活差異前，我們對於考量傳統腫瘤特質後，分析不同乳房攝影表徵之平均滯留期以及敏感度感到相當有興趣。

研究目的
本論文研究目的如下：
(一) 考量篩檢工具敏感度，建構以Tabar乳房攝影表徵分類之乳癌自然病史。
(二) 評估篩檢偵測以及臨床偵測乳癌個案之存活差異，與傳統腫瘤特質、治療方法、乳房攝影表徵、腫瘤表徵及病理型態等變項之間的關係，並將之量化。
(三) 評估以Tabar乳房攝影表徵分類下，並考量隨著時間改變之預後因子，篩檢偵測與臨床偵測乳癌個案之存活差異，並利用篩檢工具敏感度進行前導期偏差 (Lead-time bias)校正。

研究方法
　　我們以貝氏馬可夫模式(包括三階段模式以及考量腫瘤大小或淋巴侵襲情形之五階段模式)中Gibbs隨機抽樣方法，估計不同乳房攝影表徵從篩檢偵測至臨床階段的平均滯留期，來模擬在不同的篩檢時間間隔以及偵測早期乳癌個案能力下，隨機分派試驗可能出現的結果，進一步提升篩檢過程品質。本研究為一回溯性世代研究，始自1977年瑞典Kopparberg與Östergötland兩區以乳房攝影篩檢作為乳癌篩檢工具之隨機分派試驗(1977年至1985年)至今，由於預後因子之影響會隨著時間改變，我們以貝氏方法進行偉伯存活時間分析，以1996年至1998年時期所得到之乳癌診斷資料包括傳統腫瘤特質資料、腫瘤表徵(乳癌基底細胞表現等)以及病理型態(單發、多發或瀰漫性)等訊息作為概似函數(Likelihood)，再加上1977年至1995年時期所得到之事前分佈(Prior)來估計事後分佈(Posterior)之參數，最後利用從篩檢偵測至臨床階段的平均滯留期，來校正前導期偏差，比較不同篩檢偵測模式下之存活差異。

結果
(一) 乳房攝影表徵的平均滯留時間
　　 對於1977年至1985年之小於1.5公分的腫瘤而言，在未調整敏感度的情況下，星狀乳房攝影表徵具有最長的平均滯留期5.61年(95%信賴區間：4.40年, 7.22年)，粉狀與碎石狀乳房攝影表徵之平均滯留期為5.28年(95%信賴區間：3.02年, 9.35年)，而環形狀乳房攝影表徵的平均滯留期為3.60年(95%信賴區間：2.59年, 5.15年)。在1977年至1985年間，粉狀與碎石狀乳房攝影表徵有最高的敏感度(95.79%，95%信賴區間：82.00%, 99.29%)，其次為環形狀乳房攝影表徵(95.24%，95%信賴區間：80.53%, 99.29%)，最差的為星狀乳房攝影表徵(83.42%，95%信賴區間：66.42%, 95.70%)。
　　考量不同乳房攝影表徵具有不同的敏感度下，由於生物特質因素影響，不同乳房攝影表徵之平均滯留期皆變長，星狀乳房攝影表徵有最長的平均滯留期(6.01年，95%信賴區間：4.23年, 9.19年)，隨後是粉狀與碎石狀乳房攝影表徵(4.30年，95%信賴區間：2.42年, 8.53年)和環形狀乳房攝影表徵(3.03年，95%信賴區間：2.28年, 5.19年)。
　　值得注意的是在1996年至2010年間診斷小於1.5公分的腫瘤之平均滯留期也具有相同的趨勢，但平均滯留期相較於1977年至1985年期間較短，並且敏感度改善到95%以上。
　　在不考量腫瘤大小情形下，亦有相似的現象存在。在1977年至1985年間，乳房攝影表徵為粉狀與碎石狀的敏感度最高(91.60%，95%信賴區間：65.60%, 99.27%)，隨後為星狀(84.86%，95%信賴區間：71.37%, 96.25%)，環形狀最低(76.23%，95%信賴區間：63.00%, 86.04%)，且在1996年至2010年的平均滯留期皆短於1977年至1985年所診斷的乳癌個案，而敏感度已趨近100%。
　　腫瘤小於1.5公分且乳房攝影表徵為環形狀的乳癌個案，與大於1.5公分腫瘤的乳癌個案類似，其臨床前期轉移至臨床期之速率較快，而在不考量腫瘤大小情形下，乳房攝影表徵為環形狀的乳癌個案，自臨床前期轉移至臨床期的轉移速率也是最快的，並且篩檢間隔間個案發生率比上期望發生率(I/E ratio)也最高，因而相較於其他乳房攝影表徵分類，需要更密集的進行篩檢以及高敏感度之篩檢工具，來減少篩檢間隔個案的產生。對於降低1.5公分以上的腫瘤與淋巴侵襲的癌症上，相較於星狀與粉狀與碎石狀乳癌攝影表徵，環形狀效益最差。當篩檢間隔拉長到每(二) 評估可能解釋早期篩檢偵測與臨床偵測個案之差異
　　在1977年至1995年間的乳癌篩檢，篩檢偵測個案相較於臨床偵測個案死於乳癌的風險比值為0.22 (95%信賴區間: 0.17, 0.29)，在調整傳統腫瘤特質後該風險比值為0.53 (95% 信賴區間：0.34, 0.76)。在服務性乳癌篩檢計畫進入較為成熟時期(1996年至1998年)後，未調整腫瘤表徵、乳房攝影表徵、組織病理分佈與傳統腫瘤特質前，死於乳癌的風險比值為0.23 (95%信賴區間：0.08, 0.44)，而調整後該風險比值為0.71 (95%信賴區間：0.26, 1.47)。
(三) 不同乳房攝影表徵下之替代效益估計
　　乳房攝影表徵為星狀之乳癌個案，考量事前經驗下，1996年至1998年間之篩檢偵測個案相對於臨床偵測個案死於乳癌風險比值之事後估計值為0.31 (95%信賴區間：0.20, 0.48)，在考慮其他影響因子後升至0.57倍 (95%信賴區間：0.36, 0.89)。
　　同樣地，乳房攝影表徵為環形狀之乳癌個案，篩檢偵測個案相對於臨床偵測個案死於乳癌風險比值之事後估計值為0.34 (95%信賴區間：0.20, 0.58)，在考慮其他影響因子後升至0.51倍(95%信賴區間：0.29, 0.89)。就粉狀與碎石狀乳房攝影表徵個案而言，篩檢偵測個案相對於臨床偵測個案死於乳癌風險比值之事後估計值為0.27倍(95%信賴區間：0.15, 0.48)，在考慮其他影響因子後升至0.39倍 (95%信賴區間：0.22, 0.69)。

結論
　　本論文藉由貝氏馬可夫模式估計在不同乳房攝影表徵下，從篩檢可偵測至臨床階段的平均滯留期以及篩檢工具敏感度。結果發現不同乳房攝影表徵其平均滯留期及敏感度各具異質性。儘管存有偽陰性的可能，星狀乳房攝影表徵的乳癌個案之平均滯留期較長，而環形狀乳房攝影表徵的乳癌個案不但有較高的偽陰性機率，且其平均滯留期較短。粉狀或碎石狀乳房攝影表徵的乳癌個案的偽陰性機率較低，其平均滯留期也較長。篩檢工具敏感度在服務性篩檢較為成熟的階段均可達95%以上。透過估計不同階段轉移速度及敏感度，經模擬發現在不同篩檢時間間隔結合不同敏感度之組合下，可進一步了解在篩檢計畫中對於各種型態之乳房攝影表徵，其可能降低篩檢間隔個案、大於1.5公分腫瘤或淋巴侵襲個案等之影響。研究發現環形狀乳房攝影表徵個案，其篩檢效益較其他型態之乳房攝影表徵分類差，由於平均滯留期較短，因此有必要進行更密集之篩檢，或提高篩檢工具之敏感度，降低篩檢間隔個案發生率與期望發生率之比例(I/E)。
　　本論文利用貝氏臨床推理來看以乳房攝影術作為乳癌篩檢之長期追蹤資料，考慮隨時間改變之傳統腫瘤特質以及腫瘤表徵與病理型態，評估不同乳房攝影表徵下篩檢偵測個案與臨床偵測個案之存活差異並考量前導期(lead-time)偏差之影響。

關鍵字

乳癌 ； 乳房攝影表徵 ； 存活分析 ； 貝氏分析 ； 多階段馬可夫模式 ； 篩檢可偵測至臨床階段的平均滯留時間 ； 敏感度 ； 前導期偏差

並列摘要

Abstract
Background
In parallel with the evolution of breast cancer screening with mammography, temporal natural history of breast cancer and prognostic factors affecting the comparison of the difference of breast cancer survival between the screen-detected and the clinically-detected mode (two detection modes) are related to mammographic appearances. As conventional tumor attributes responsible for the prognosis of breast cancer are related to mammography-featured temporal natural history of breast cancer. It is therefore interesting to estimate the mean sojourn time and sensitivity by each type of mammographic appearance before explaining the difference of survival between the two detection modes for each type of mammography by considering the dynamics of these prognostic factors.

Objectives
The purposes of my thesis are (1) to develop Tabar-mammography-featured natural history of breast cancers taking sensitivity into account;(2) to assess how the difference between screen-detected and clinically detected cancer can be explained by conventional tumor attributes and treatment as well as mammographic appearance and the recently proposed tumor phenotypes and histological extent of tumor distribution; and (3) to throw light on the difference of breast cancer survival in the two detection modes, screen-detected and clinically-detected mode by Tabar classification of mammographic appearance of invasive breast cancer considering dynamics of these prognostic factors and the lead-time derived from the mean sojourn time allowing for sensitivity.
Methods
To model the simulation of the randomized controlled trial by inter-screening intervals and also the ability to detect early breast cancer (sensitivity) to improve the performance of screening to enhance the quality of screening procedure, we developed Bayesian directed acyclic graphic multistate Markov models (including three-state model and five-state model considering tumour size and node status) to estimate the mean sojourn time and sensitivity by different mammographic appearances by using Bayesian Gibbs sampling. These models were applied to data derived from a retrospective cohort from the original one of counties in the Swedish Two-county randomized controlled trial since 1977. Regarding the prognosis part, the prior estimates from 1977 and 1985 was further updated by the likelihood between 1996 and 1998 with data on new markers such as basal phenotype and histological tumor distribution, in addition to conventional tumor attributes, to spawn the updated posterior estimates with parametric Weibull survival model with Bayesian approach. The lead-time distribution derived from the sojourn time distribution was applied to make the comparison of the survival between the two detection modes.

Results
(1) The MST by mammographic appearance
The length of sojourn time is the longest for the stellate type (MST=5.61yrs)　(95%CI: 4.40, 7.22), followed by powdery and crushed-stone-like type (MST=5.28 yrs) (95%CI: 3.02, 9.35), and the circular type (MST=3.60 yrs) (95%CI: 2.59, 5.15) without adjusting for sensitivity among small tumour less than 1.5 cm in the period of 1977-1985. The results found the highest sensitivity was noted in the powdery and crushed stone type (95.79% (95%CI: 82.00%, 99.29%)), followed by the circular type (95.24% (95%CI: 80.53, 99.29%)) and the least for the stellate type (83.42%, 95% CI: 66.42%, 95.70)) in the period of 1977-1985.
While the sensitivity was taken into account, the MST due to biological property for each type would turn to be longer. While the estimate of sensitivity by each type of mammographic appearance was considered the slowest progression was noted for the stellate type (MST=6.01 years) (95%CI: 4.23, 9.19), followed by the powdery and crushed stone type (MST=4.30) (95%CI: 2.42, 8.53) and the circular type (MST=3.03 years) (95%CI: 2.28, 5.19).
It is very interesting to note that the similar trend for the MST was observed for breast tumour smaller than 1.5 cm in the period of 1996-2010 but the MST was shorter in the period of 1996-2010 than that in the period of 1977-1985 and the sensitivity was improved to 95% or above.
The similar phenomenon was also observed for breast cancer with all size. The sensitivity was the highest in the powdery and crushed stone type (91.60%, 95%CI: 65.60%, 99.27%), followed by the stellate type (84.86%, 95%CI: 71.37%, 96.25%), and the lowest in the circular type (76.23%, 95%CI: 63.00%, 86.04%) in the period of 1977-1985. The MST was shorter in the period of 1996-2009 than that in the period of 1977-1985 and the sensitivity was improved to almost 100%.
For small breast tumour, the circular type is the highest and almost identical to the breast tumour larger than 1.5 cm for the transition from the PCDP to the CP. For all size breast tumour, the circular type was still the most rapid progression from the PCDP to the CP. The circular type was the highest I/E ratio. It requires an intensive screening and high sensitivity so as to reduce interval cancer compared with other types of mammographic appearance. The circular type was the poorest benefit of reducing breast tumour larger than 1.5 cm and node positive compared with the stellate type and the powdery and crushed stone type. When the inter-screening interval is lengthened to three years only 21% (95%CI: 2%, 0.35%) reduction for breast tumour larger than 1.5cm and 29% (6%, 46%) reduction for breast tumour with node positive.
(2) Assessing the possible factors in explanation of the difference between early-detected and clinical-detected breast cancers
In the early period of mammographic screening (1977-1995), the crude hazard ratio (HR) of breast cancer death for screen-detected cases compared with symptomatic ones was 0.22 (95% CI: 0.17, 0.29) compared with 0.53 (95% CI: 0.34, 0.76) when adjusted for conventional tumor attributes only. Using the data from the mature service screening period, 1996-98, the HR was 0.23 (95% CI: 0.08, 0.44) unadjusted and 0.71 (95% CI: 0.26, 1.47) after adjustment for tumor phenotype, mammographic appearance, histological tumor distribution, and conventional tumor attributes.
(3) Estimates for surrogates by mammographic appearance
Regarding the stellate type, the estimated HR for the two detection modes based on informative prior and the data on the period between 1996 and 1998 was 0.31 (95%CI: 0.20, 0.48) and was inflated to 0.57 (95%CI: 0.36, 0.89), making allowance for all other prognostic factors.
Similarly, the estimated HR for the circular type was 0.34 (95%CI: 0.20, 0.58) and was inflated to 0.51 (95%CI: 0.29, 0.89) after making allowance for conventional tumour attributes, treatment, tumour phenotype, and histological tumour distribution. As far as the casting type and architecture distortion are concerned, the estimated HR was 0.27 (95%CI: 0.15, 0.48) and was inflated to 0.39 (95%CI: 0.22, 0.69).

Conclusions
By using a novel Bayesian Markov models, the interplay between sensitivity and the mean sojourn time related to the progression from the PCDP to the CP for each type of mammographic appearance has been well elucidated. The results are heterogeneous. The average time for early detection of breast cancer within detectable window is longer for the stellate type whereas the detectable window for the circular type is short. The powdery and crush-stone-like is easily detected and the window of sojourn time for detection is also longer. The sensitivity for each type of mammographic appearance was improved up to at least 95% from the trial period to the service screening period. These transition parameters together with sensitivity are further applied to simulate the effect of inter-screening interval in combination with sensitivity on reducing interval cancer and also reducing tumour larger than 1.5 cm and node positive.
As the circular type has the shorter sojourn time intensive screening interval or high sensitivity is therefore required. Otherwise, the I/E ratio was higher and the benefit of screening was modest compared with other types of mammographic appearance.
Bayesian clinical reasoning approach was further adopted to make the comparison of survival of breast cancer between screen-detected breast cancer and clinically-detected ones while using information on conventional tumour attributes and also lead time distribution derived from the mean sojourn time.

並列關鍵字

Breast cancer ； Mammographic appearance ； Survival analysis ； Multi-state Markov model ； Preclinical detectable phase (PCDP) ； Sensitivity ； Lead-time bias

參考文獻

嚴明芳、陳秀熙、郭旭崧、賴美淑、張金堅 (民88)。利用馬可夫鏈模式評估臺灣地區多中心乳癌高危險群篩檢計畫。中華衛誌，18(2)，95-104。

Sotiriou C, Pusztai L. Gene-expression signatures in breast cancer. N Engl J Med. 2009; 360(8):790-800.

Tabar L, Gad A. Screening for breast cancer: the Swedish trial. Radiology, 1981; 138:219-22.

Tabar L, Fagerberg G, Chen HH, Duffy SW, Gad A. Tumour development, histology and grade of breast cancers: prognosis and progression. Int J Cancer. 1996 ;66(4):413-9.

Tabar L, Chen HH, Duffy SW, Yen MF, Chiang CF, Dean PB, Smith RA. A novelmethod for prediction of long-term outcome of women with T1a, T1b, and 10-14 mm invasive breast cancers: a prospective study. Lancet. 2000 ; 355(9202):429-33.