貝氏統計模型應用於評估及預測肝癌發生率、致死率與死亡率

Abstract

背景 台灣在過去的四十年中藉由數個肝癌防治計畫的推行，使肝癌的發生率與死亡率由1990年代晚期到2000年代早期開始有逐步下降的趨勢。然而，此趨勢由於暴露於不同時續發展之肝癌防治計劃對於不同的年齡層以及在不同的地理區域是否具有一致性在過去並沒有深入地探討。釐清各肝癌防治計畫(包括新生兒全面注射B型肝炎疫苗、健保制度的實施與抗病毒藥物的使用)執行時點對於肝癌出生率以及死亡率的變化趨勢之影響與關係在預測未來肝癌造成的疾病負擔扮演重要的角色，亦有助於肝癌防治政策的訂立。 研究目標 本論文主要的研究目標包括以下三點 (1)運用統計模型結合台灣肝癌實證資料評估不同年齡層的肝癌死亡率隨時間變化的趨勢並釐清其來自於肝癌發生率與疾病死亡率的各別影響; (2)評估肝癌發生率、疾病致死率與死亡率隨時間變化的趨勢線受基礎疾病負擔 (截距項)、時間變化趨勢(斜率)以及三個轉折點(change point)對於疾病負擔隨時間演進的效果; (3)預測至2025年之肝癌發生率、致死率與死亡率隨時間變化的趨勢。 資料來源 用來估計統計模型參數值的實證資料來源為台灣的癌症登記檔與死因統計檔。收集由西元1979年到2016年肝癌每一年的發生個案數(發生率)與死亡個案數(死亡率)，總追蹤期間橫跨台灣施行的三個主要肝炎防治計畫之期間，包括西元1984年開始實施的新生兒B型肝炎疫苗的注射、1995年開始執行的全民健保計劃以及2004年開始推行的抗病毒藥物治療計劃。 研究方法 本研究根據不同年齡層與縣市別依序將肝癌死亡率之時間變化趨勢分解成為由出生率與死亡率之影響。研究中發展了一套以貝氏架構為基礎之卜瓦松迴歸模型來評估肝癌發生率與疾病致死率的變化對於死亡時間趨勢在三個肝癌防治計劃開始施行的轉折點的影響程度。研究中亦發展貝氏階層趨勢線轉折點分析統計模型並運用於評估由基礎疾病負擔、時間變化趨勢，與轉折點之一連串因果特性下對於不同年齡層與20個縣市區域在肝癌出生率、疾病致死率與死亡率的影響。 結果 在分解不同年齡層的肝癌死亡率後，研究結果顯示雖然在全年齡層中肝癌疾病致死率皆一致性的下降，但對於肝癌發生率中，<30歲、30-49歲以及50-69歲這三個年齡層的發生率皆持續下降，但是≥70歲這個年齡層的發生率則未有下降趨勢。以卜瓦松迴歸模型為基礎架構，本研究發展出一個統計模型以將肝癌死亡率隨時間變化的趨勢分解為來自於發生率與致死率的影響。我們擷取1979年到2013年30歲到84歲的肝癌死亡率與發生率評估肝癌死亡率歸因比例，並以三個肝癌防治計畫開始施行的時間點作為趨勢線的轉折點，將整個追蹤時期(1979-2013年)分作1979-1983年(時期1)、1984-1994年(時期2)、1995-2003年(時期3)和2004-2013年(時期4)。在30-49歲年齡層中，時期4的整體死亡率相較於時期1減少42.3%(95%信賴區間: 38.3-46.0%)；此死亡率之變化可歸因於發生率(增加51.3% (95%信賴區間: 47.2-55.4%))和致死率(減少71.9%(95%信賴區間: 68.8-74.8%))。以50-69歲年齡層來看，時期4的整體死亡率相較於時期3減少22.8%(95%信賴區間: 21.5-24.1%)；死亡率的變化歸因於發生率的變化為減少10.7%(95%信賴區間: 9.3-12.1%)，此效應源於抗病毒藥物的使用對於降低肝癌發生之成效。以≥70歲年齡層來看，時期4的整體死亡率相較於時期2增加41.0%(95%信賴區間: 39.0-43.0%)；即使疾病致死率之歸因比為減少47.7%(95%信賴區間: 45.3-50.0%)，但發生率增加達69.2%(95%信賴區間: 68.2-70.1%)，以致於老年族群的死亡率持續上升。 本研究進而運用貝氏階層合併轉折點分析之統計模型，評估三個肝癌防治計畫對於肝癌死亡率、發生率與致死率的個別效果以及作用於各縣市的效果，接著預測到西元2025年時，不同年齡層與不同縣市的變化。根據預測的結果，在西元2025年時，<30歲、30-49歲、50-69歲以及≥70歲這四個年齡層的發生率分別為:男性為每十萬人0.41(95%信賴區間: 0.29-0.54)、17.9(95%信賴區間: 16.1-20.0)、110.0 (95%信賴區間: 99.8-120.8)和314.9 (95%信賴區間:285.9-346.8)；女性為每十萬人0.26 (95%信賴區間: 0.16-0.39)、2.85 (95%信賴區間: 2.36-3.40)、30.1 (95%信賴區間: 26.7-34.0)和183.7 (95%信賴區間: 163.8-205.1)。而<30歲、30-49歲、50-69歲以及≥70歲這四個年齡層的死亡率分別如下:男性為每十萬人0.08 (95%信賴區間: 0.05-0.11)、9.9 (95%信賴區間: 9.1-10.8)、69.1 (95%信賴區間: 65.0-73.4)和274.1 (95%信賴區間: 257.1-291.8)；女性為每十萬人0.09 (95%信賴區間: 0.05-0.17)、1.5 (95%信賴區間: 1.2-1.8)、17.9 (95%信賴區間: 16.4-19.5)和 165.4 (95%信賴區間: 153.2-178.2)。在2025年，整體致死率的預測值為0.60 (95%信賴區間: 0.42-0.82)。 結論 本研究藉由貝氏卜瓦松的統計模型之架構發展用於評估三個肝癌防治計劃對於發生率和致死率影響之效果。而貝氏階層趨勢轉折點分析之統計模型則運用於預測到西元2025年的肝癌疾病負擔。本研究結果對於不同的年齡層與縣市別在未來制訂個別的肝癌防治計畫可提供新的實證視角，並據以來針對年齡與區域之特性發展肝癌防治策略，以期達成肝癌防治之目的。

Background After a series of prevention programs of hepatocellular carcinoma (HCC) over four decades, the overall incidence and mortality of HCC have started to decline between the late 1990s and the early 2000s in Taiwan. However, whether such declining trends of incidence and mortality have the same pattern by age groups and geographic areas is still elusive. Elucidating the time trends of both incidence and mortality in relation to these prevention programs play an important role in predicting the disease burden of HCC for decision-makers. Aims This thesis aimed to (1) report and assess the respective contributions of both time trends in incidence and case-fatality rate to the time trend of mortality by different age groups with empirical data and the modelling approach; (2) assess the effects of baseline (intercept), gradient (slope), and three change-point on time trends of incidence, case-fatality rate, and mortality; (3) predict three time trends of incidence, case-fatality rate, and mortality rate until 2025. Data Sources Empirical data used for estimating the parameters of the underlying model were derived from national vital statistics on incident cases of and deaths from HCC between 1979 and 2016 spanning three main interventions, mass vaccination, national health insurance, and antiviral therapy commencing from 1984, 1995, and 2004 (three change-points), respectively. Methods The empirical time trends of mortality were decomposed into both of incidence and case-fatality by age groups and geographic areas. We then developed a Bayesian mortality decomposition Poisson regression model to estimate the attributable proportion of incidence and case-fatality contributing to mortality due to three change-points of intervention programs. Bayesian hierarchical change-point models were proposed to model a cascade of the impacts from baseline values, gradients, and change-point on incidence, case-fatality, and mortality with respect to four age groups and 20 geographic areas. Results Based on Poisson regression underpinning, a statistical method was developed to decompose the trend change in mortality into the proportions attributable to incidence and case-fatality. The HCC mortality and incidence of individuals aged 30 to 84 years between 1979 to 2013 was extracted to evaluate the attributable proportion. Based on the time trends of HCC mortality and incidence incorporated with the time points for the implementation of interventions, the changing points were set in 1984, 1995 and 2004. 1979 to 1983, 1984 to 1994, 1995 to 2003 and 2004 to 2013 were defined as Period 1, 2, 3 and 4. The overall mortality reduction for Period 4 compared with Period 1 was -42.3% (95% CI: -46.0 to -38.3%) in the middle-aged group (30-49 years). When the mortality change was separated into the impact of incidence and survival, the results showed an increase in +51.3% (95% CI: 47.2 to 55.4%) attributable to incidence which was overwhelmed by a reduction in case-fatality rate (-71.9%, 95% CI: -74.8 to -68.8%). The overall mortality reduction for Period 4 compared with Period 3 was -22.8% (95% CI: -24.1 to -21.5%) in the middle-age group (50-69 years). This was separated into the proportion attributable to incidence and survival, which showed a reduction by -10.7% (95%CI: -12.1 to -9.3%) in HCC incidence during the period of national viral hepatitis therapy program. The change in HCC mortality for Period 4 compared with Period 2 was +41.0% (95% CI: 39.0 to 43.0%) in the old-age group. When further decomposing the mortality change for the elders into the proportion attributable to incidence and case-fatality, the results showed a reduction by -47.7% (95% CI: -50.0 to -45.3%) in HCC deaths due to improved survival after universal health care implementation. However, the efficacy was compromised by the increase in incidence rate (+69.2%, 95% CI: 68.2 to 70.1%) in the old age group. Using significant impacts of three intervention programs at individual and county level estimated by using Bayesian hierarchical change-point model, time trends of incidence until 2025 were predicted as 0.41 (95%CI: 0.29-0.54), 17.9 (95%CI: 16.1-20.0), 110.0 (95%CI: 99.8-120.8), and 314.9 (95%CI: 285.9, 346.8) per hundred thousand for < 30, 30-49,50-69, and ≥ 70 years for male and as 0.26 (95%CI: 0.16-0.39), 2.85 (95%CI: 2.36-3.40), 30.1 (95%CI: 26.7-34.0), and 183.7 (95%CI: 163.8-205.1) per hundred thousand for < 30, 30-49,50-69, and ≥ 70 years for female, respectively. For mortality, time trends until 2025 were predicted as 0.08 (95%CI: 0.05-0.11), 9.9 (95%CI: 9.1-10.8), 69.1 (95%CI: 65.0-73.4), and 274.1 (95%CI: 257.1-291.8) per hundred thousand for < 30, 30-49,50-69, and ≥ 70 years for male and as 0.09 (95%CI: 0.05-0.17), 1.5 (95%CI: 1.2-1.8), 17.9 (95%CI: 16.4-19.5), and 165.4 (95%CI: 153.2-178.2) per hundred thousand for < 30, 30-49,50-69, and ≥ 70 years for female, respectively. For overall fatality, time trends until 2025 were predicted as 0.60 (95%CI: 0.42-0.82). Conclusions Bayesian Poisson were developed here to assess the respective contributions of three main prevention program to incidence and case-fatality and Bayesian hierarchical change-point models were used to predict the disease burden of HCC until 2025. These findings have significant implication for providing a new insight into health care planning for prevention of HCC by different age groups and different counties.