Sample Size Determination for Effectiveness of Mass Screening for Breast Cancer

背景 利用主要終點做癌症篩檢的評估通常需要長期的追蹤以及龐大的成本，尤其針對年輕婦女或規劃不同篩檢間隔計畫時，此問題特別嚴重。使用替代終點藉由降低變異數進而減少所需樣本數是一個可行的方法。過去很少有研究針對使用主要終點與替代終點間的樣本數估計進行比較。 目的 本論文的研究目的主要針對替代終點之統計操作型定義評估，驗證因替代終點導致變異數之減少進而降低樣本數需求，及如何應用此替代終點提升評估篩檢間隔頻率之統計檢定力。 1. 利用Prentice替代終點之定義探討替代終點之統計操作型定義，應用此定義評估乳房攝影篩檢降低死亡效益之替代終點，如腫瘤大小(Tumour size)、淋巴結侵襲(Lymph node involvement)及組織分化程度(Histological grade)。 2. 利用上述所得替代終點之變項比較替代終點及主要終點變異數，進而估計替代終點與主要終點所需樣本數之比較。 3. 接續上述替代終點，建立以此替代終點為主之多階段馬可夫模式，並利用電腦模擬評估不同篩檢間隔下比較替代終點及主要終點的所需樣本數。 資料來源 我們利用瑞典兩郡的乳癌篩檢資料應用於本論文的統計方法，進而計算出使用替代終點及主要終點所需的樣本數。 結果 1. 本研究以Prentice對於替代終點選擇之科學邏輯方式推衍應用於乳癌篩檢替代終點之論述與衍生。利用Cox比例風險迴歸模式映證其論述，結果發現在瑞典乳癌篩檢試驗研究中，若僅考慮篩檢組相對於對照組所得到的迴歸係數為-0.451，若在篩檢組別變項之外再加上腫瘤變項，則篩檢組別所對應到的迴歸係數變為接近虛無假說，變成-0.228，組別效應被腫瘤大小解釋了49.4%。在考慮組別及淋巴結轉移兩變項情況下，組別效應會被淋巴結轉移解釋45.2%，若同時考量腫瘤大小與淋巴結轉移，則其解釋力可達到62%。 2. 本研究利用瑞典乳癌隨機臨床試驗為例，推估利用替代終點預估欲驗證篩檢可以有效降低乳癌死亡所需之樣本數 (1) 利用單一替代終點以腫瘤大小分為DCIS、<20 mm及≧20 mm三類所進行計算的估計樣本數，在給定α為0.05，統計檢定力(1-β)為90%之下需38,914人，若以淋巴結轉移情形所得樣本數則是75,764人。以腫瘤大小分類做為替代終點所需的樣本數少於利用淋巴結轉移狀態所需的樣本數。 (2) 結合腫瘤大小及淋巴結轉移情形所計算出的所需樣本數為33,657人，僅為利用主要終點所推估樣本數(82,261人)的40.9%，且少於僅利用單一腫瘤大小(38,914人)或僅使用淋巴結轉移(75,764)所得到的預估樣本數。 3. 本研究以多階段馬可夫鏈模式評估不同篩檢策略之間，例如改變篩檢間隔，是否能得到較佳效益所需之樣本數。以40-49歲利用腫瘤大小做為替代終點為例，若欲証明一年篩檢相對於二年篩檢的差異，需要261,292人的樣本數，若欲比較一年與三年的差異，需要120,916人，若欲比較二年與三年的篩檢效益差異，則需要超過100萬以上婦女。若使用主要終點進行評估時，則所需的樣本數將大幅增加至利用替代終點時的四倍。相同現象可見於以淋巴結轉移做為單一替代終點，或在50-59歲及60-69歲婦女族群。 結論 本論文利用替代終點計算樣本數的統計方法應用於癌症篩檢時，相較於利用主要終點所得到的樣本數估計，可獲得顯著的減少。此方法對於規劃大規模篩檢，尤其是針對年輕婦女或規劃不同篩檢間隔計畫時將非常有幫助。Background Evaluation of mass screening for cancer based on primary endpoint often encounters long-term follow-up and enormous costs, especially when rare diseases are investigated. These problems are also particularly serious for young women screening with mammography and also the determination of optimal inter-screening interval by using randomized controlled trials. The expedient strategy is to use surrogate endpoint which can reduce variance which in turn reduce sample size. The application of surrogate endpoint to evaluation of cancer screening for the comparison of required sample sizes between surrogate endpoint and primary endpoint have been barely addressed. Objective The objectives of this thesis were (1) to expand the statistical operational definition for surrogate endpoints defined by Prentice. We also aim to assess whether tumor size, lymph node involvement, histological grade, and combined use of these tumor attributes can be used as surrogate endpoints for replacing breast cancer mortality reduction as a result of mammography screening. (2) to demonstrate how the variance can be reduced by comparing a simple binary outcome and informative surrogate endpoints, and to compare the required sample sizes with primary endpoint and surrogate endpoint. (3) to apply computer simulation in the light of multi-state Markov model for breast cancer natural history using tumor size or lymph node involvement to compare the required sample sizes with primary endpoint and surrogate endpoint with different inter-screening intervals. Data source We used the Swedish Two-county breast screening trial data to illustrate the application of our statistical method to calculate sample size based on primary and surrogate endpoint, respectively. Results 1. Based on the statistical operational definition for surrogate endpoints from Prentice, we found that tumour size can explain partial effect of screening group by 49.4% by using Cox proportional hazards regression model. The magnitude of partial effect were 45.2% and 62% for use of lymph node involvement and for combined use of lymph node involvement and tumour size for surrogate endpoints. 2. By using tumour size (DCIS、