半母數存活外插法：利用RERF世代來驗證模型正確性

Abstract

背景 若要評估愛滋病的醫療介入措施的成本效益，知道愛滋病病人能夠活多久是很重要的問題，因此我們需要一個可靠的存活統計方法來預測病人的存活。半母數存活外插法是根據病人與一般人的存活比W來估計病人未來存活情形的一個方法。若一特定疾病或暴露的額外風險為常數，存活比經過邏輯斯轉換之後對時間作圖的曲線就會隨時間延長而趨近一條直線，可以使用線性外插來估計病人的預期存活。短期外插的正確性已被驗證，但是長期外插的正確性仍然不清楚。 方法與主要發現 LSS世代來自長崎廣島原子彈爆炸的倖存者，是世界上追蹤最久的資料之一。我們使用LSS世代的部分資料來驗證此方法長期外插的正確性，同時發展出一些數理準則使此方法能夠更好的應用在樣本數較小的資料。我們首先證明當病人/受暴露者的存活比年齡/性別配對的一般人還要差時，logit W曲線的斜率就會是負值，並且發展出一個斜率-時間診斷圖。使用放射線暴露量>1000 mGy的人作為指標族群，發現：(1)logit W在48年的時間以後仍然持續向零收斂，故使用logit W曲線的右端區段來做外插會比使用中間區段更好；(2)如果使用較短的區段來做回歸估計斜率，例如6個月，估計出的斜率可能會有較大的隨機變異。診斷圖可以讓方法的使用者選出可產生穩定斜率估計的最短區間；(3)以同一個世代沒有放射線暴露的人，利用1950-1960的放射線暴露追蹤資料，並用上述的方法所選出來的時間點與時間區間做38年後的外插可得到相當精確的估計；如果使用1960年的生命命表作為對照，外插的結果就會因橫斷面預期壽命與世代預期壽命算法之間的落差而低估。 結論 長期半母數外插法能夠得到正確並且精確的結果。使用此方法的建議步驟如下： 1.利用追蹤資料製作logit W(t) 圖 2.利用不同的時間長度(例如：6, 12, 24, 36, 48個月)來製作斜率-時間的診斷圖。選擇能夠得到穩定斜率估計的最短時間長度 3.在前面選出的診斷圖中，排除那些斜率為正者，並盡可能地找出最靠近追蹤時間末端的區間來做外插，已得到最好的結果

Background How long can a human immunodeficiency virus (HIV)-infected patient live is a crucial question, especially for the evaluation of the cost-effectiveness of medical interventions. A semi-parametric survival extrapolation method has been developed based on a logit survival ratio W between a patient cohort and a reference population. If the excess hazard of a specific disease/exposure remains constant, then the logit survival ratio curve will converge to a straight line over time, which allows linear extrapolation to estimate survival beyond the follow-up time. The accuracy of short-term projection has been validated, while the validity and accuracy of life-long projection remains unclear. Method and Principal Findings We used a subset of the Life Span Study (LSS) cohort, which comprised atomic bomb survivors from Hiroshima and Nagasaki and is one of the longest follow-up data cohorts in the world. With this dataset, we tested the validity and accuracy of life-long semi-parametric extrapolation as well as developed mathematical criteria for applying this method to data of limited sample size. We first proved the biological premise that disease/exposure is associated with premature mortality when compared with age- and gender-matched general populations, which is mathematically equivalent to a negative slope in the logit W plot at all times. In addition, we developed a slope-time diagnostic plot. Using those cohort members with >1000 mGy radiation exposure as the index group, we found that (1) the logit W curve continued to converge toward zero at the end of a 48-year follow-up, which indicated that extrapolation based on the right end of the curve should provide a more accurate estimate than that based on the central part of the curve; (2) the slope of the logit W curve can have large random variation if the length of time used for regression is short, such as 6 months, and the diagnostic plot allows users to select the shortest time length that provides a stable slope estimation; (3) a 38-year extrapolation from the end of the 10 year (1950–1960) follow-up data, using the above-stated criteria to select the length of time and the time period for regression, yielded an accurate projection in comparison with the actual 38-year follow-up (1960–1998) data if the cohort members without radiation exposure were used as the source of reference. If the 1960 life table is used as the source of reference, then the projection will underestimate the true long-term survival due to the discrepancy between the time period and the cohort life expectancy. Conclusion Long-term semi-parametric survival extrapolation can be valid and accurate. The recommended steps in applying this methodology are as follows: 1.Create a logit W(t) plot from the follow-up data. 2.Create Slope-Time diagnostic plots using different lengths of time (for example: 6, 12, 24, 36, and 48 months) for regression. Select the shortest length of time that provides stable slope estimation without significant random variations. 3.For the selected diagnostic plot, exclude the time periods with positive slopes and find the time period as close to the end of the follow-up time as possible to obtain the best slope estimate for extrapolation.