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BMJ小小統計問題(18)

前言：

已經連續六周的存活分析周，針對存活分析相關概念進行介紹與說明。本周則介紹最常用來比較不同組別存活時間是否有差異的log rank test。裡面所提到的概念，相信這幾周看下來後，會發現都很熟悉了。過幾天會彙整這幾周存活分析概念的測驗題，有興趣的朋友到時可以試試。

題目：

前面的統計問題描述了存活(time to event)資料[1,2]。所使用的例子是一項隨機對照試驗，該試驗評估了與常規照護相比，整合照護方案在促進慢性下腰痛病人重返工作崗位的有效性[3]。整合照護方案是一個直接結合病人和工作場所之介入計畫。

試驗參與者為年齡在18到65歲之間的成年人，他們腰痛超過12周，並在有支薪的工作有缺席。主要結果是休假時間，即從隨機分配後到完全持續返回工作的期間。

參與者被追蹤12個月。兩組病人的存活(time to event)資料採用log rank test進行統計比較(P=0.003)。整合照護組和常規照護組在完全持續恢復工作前的天數被繪製為Kaplan-Meier存活曲線，如下圖。

圖說明

圖

Kaplan-Meier存活曲線顯示整合照護計畫病人和接受常規照護病人到完全持續恢復工作的時間。設限觀察資料使用曲線上的叉表示

下列敘述何者正確？ (複選)

a) The log rank test有助於檢驗虛無假設——在這種情況下，整合照護方案和常規照護之間的母群體群存活時間沒有差異

b) 設限觀察值在介入組進統計比較前，已被剔除

c) 在5%顯著水準上，介入組別間的存活時間存在統計學上的顯著差異

d) The log rank test提供不同介入方案組間存活時間差異的估計值

答案：

a、c正確，b、d錯誤

詳細說明：

The log rank test是一種用來比較兩組別存活時間的統計檢定法。”存活時間”為個體到達終點所需要的時間。在上述研究中，終點是在因慢性下背痛缺勤後到完全返回工作的期間。與傳統假設檢定一樣，the log rank test是從虛無假設開始，在所獲得樣本的母群體中，參加整合照護方案者和接受常規照護者在存活時間上沒有差異 (a正確)。對立假設是雙尾的，為組別間有差異存在的陳述——在所獲得樣本的母群體中，接受兩種介入者的存活時間不相等。

The log rank test評估為期12個月的研究期間，兩種介入在任何時間點是否有差異。所有的存活時間均包含在分析中，包括精確的和設限的時間(b錯誤)。設限存活時間提供了設限時間點的有用訊息，因此，被包括在存活曲線的計算以及不同治療組別的統計比較中。

統計假設檢驗的傳統顯著水準為0.05(即5%)，稱為臨界顯著水準[5]。The log rank test的結果P值為0.003。考慮到該值小於0.05，結果在5%顯著水準下具有統計意義(c正確)。因此，我們拒絕虛無假設，接受對立假設，並得出結論，兩種介入的存活時間不相等。由此數字可看出，整合照護組整體的存活時間比常規照護組短。

The log rank test 純粹是對顯著性的檢驗。它無法估計不同介入組別間存活時間差異的大小(d錯誤)。風險比值(hazard ratio)可能是提供兩介入組間存活時間差異幅度估計值的最常用方法。

原文：

The previous two statistical questions described survival (time to event) data.[1, 2] The example used was a randomised controlled trial that evaluated the effectiveness of an integrated care programme compared with usual care in facilitating the return to work of patients with chronic low back pain.[3] The integrated care programme was a combined patient and workplace directed intervention.

Trial participants were adults aged between 18 and 65 years who had experienced low back pain for more than 12 weeks, were in paid work, and were absent or partially absent from work. The primary outcome was duration of time off work—that is, from randomisation until a fully sustained return to work.

Participants were followed for 12 months. The survival (time to event) data for the two treatment groups were compared statistically using the log rank test (P=0.003). Days until a fully sustainable return to work for the group on the integrated care programme and the usual care group were plotted as Kaplan-Meier survival curves.

Figure 1

Kaplan-Meier survival curves showing the time until a fully sustained return to work for patients in the integrated care programme and those receiving usual care. Censored observations are displayed by crosses on the curves

Which of the following statements, if any, are true?

a) The log rank test facilitates testing of the null hypothesis—in this case, that there are no differences in survival times in the population between the integrated care programme and usual care

b) Censored observations were excluded before the interventions were compared statistically

c) A statistically significant difference in survival times existed between interventions at the 5% level of significance

d) The log rank test provides an estimate of the magnitude of the difference in survival times between interventions

Answers

Answers a and c are true; b and d are false.

Reference:

[1] Sedgwick P. Survival (time to event) data I. BMJ2010;341:c3537.

[2] Sedgwick P. Survival (time to event) data II. BMJ2010;341:c3665.

[3] Lambeek LC, van Mechelen W, Knol DL, Loisel P, Anema JR. Randomised controlled trial of integrated care to reduce disability from chronic low back pain in working and private life. BMJ2010;340:c1035.

[4] Sedgwick P. Statistical hypothesis testing. BMJ2010;340:c2059.

[5] Sedgwick P. P values. BMJ2010;340:c2203.