生物統計教育訓練 - 課程 Introduction to equivalence, superior, inferior studies in RCT 謝宗成副教授慈濟大學醫學科學研究所 tchsieh@mail.tcu.edu.tw TEL: 03-8565301 ext 2015 1
Randomized controlled trial Two arms trial Test treatment group vs. control group Comparison of the effects between two groups The purpose for comparison decides the type of comparison 2
Type of comparison Test for Difference ( 差異性 or 不等性 ) Test for Superiority ( 較優性 or 優越性 ) Test for Non-inferiority ( 不劣性 or 非劣性 ) Test for Equivalence ( 相等性 or 等效性 ) 3
Test for difference ( 差異性 or 不等性 ) 檢定兩者有無不等 ( 有差異 ) 4
Test for difference ( 差異性 or 不等性 ) 最常用的統計假設 最簡單, 一般統計軟體提供之分析功能 判斷原則 If p-value < α (0.05 or 0.01), 且 X t > X C (i.e., X t X C > 0) µ t > µ c If p-value < α (0.05 or 0.01), 且 X t < X C (i.e., X t X C < 0) µ t < µ c 5
Test for difference ( 差異性 or 不等性 ) 樣本數大時, X t X C 即使只比 0 大一點,p-value 仍可能小於 α µ t > µ c, 就代表 test treatment 比 control treatment 來得好?? 6
Test for superiority ( 較優性 or 優越性 ) 檢定 test treatment 是否優於 control treatment test treatment 必須比 control 至少好超過 δ 7
Test for superiority ( 較優性 or 優越性 ) δ : clinical meaningful difference Focus on efficacy 一般統計軟體不直接 support δ 如何決定? Investigator s professional judgment Based on literature Based on your maximum resource 8
Test for superiority ( 較優性 or 優越性 ) δ : clinical meaningful difference 9
Test for non-inferiority ( 不劣性 or 非劣性 ) 檢定 test treatment 是否不劣於 control treatment test treatment 不能比 control 差超過 δ 10
Test for non-inferiority ( 不劣性 or 非劣性 ) δ : clinical meaningful difference Focus on safety or convenience 一般統計軟體不直接 support δ 如何決定? Investigator s professional judgment Based on literature Based on your maximum resource 11
Test for non-inferiority ( 不劣性 or 非劣性 ) Sample size formula Total eligible S 2 = (st2 +s c 2 ) n t +nc 2 12
Test for equivalence ( 相等性 or 等效性 ) 檢定 test treatment 是否和 control treatment 差不多 test treatment 與 control 的差異在 (-δ, δ) 內 13
Test for equivalence ( 相等性 or 等效性 ) δ : clinical meaningful difference Consider both efficacy and safety; or other specific consideration E.g., Bioavailability/ bioequivalence study for generic product 14
Test for equivalence ( 相等性 or 等效性 ) 一般統計軟體不 support δ 如何決定? Investigator s professional judgment Based on literature Based on your maximum resource 15
Test for equivalence ( 相等性 or 等效性 ) Sample size calculation https://www.sealedenvelope.com/power/conti nuous-equivalence/ 16
Difference/superiority/noninferiority testing in SPSS Comparison change of blood pressure Group 1:test ; 2:control δ = 5 17
Difference/superiority/noninferiority testing in SPSS 18
Difference/superiority/noninferiority testing in SPSS 19
Equivalence testing in SPSS 20
Equivalence testing Based on two one-sided tests (TOSTs) approach If t L > t (1-α,n1 +n 2-2) and t U < - t (1-α,n1 +n 2-2) =>Equivalence is concluded 21
Equivalence testing Based on two one-sided tests approach σ = (33 1) 11.334) 2 +(45 1)(12.343 2 t L = 7.27 0.09 ( 5) 11.93 1 33 + 1 45 33+45 1 =11.93 =4.49 > t (0.95,76) =1.665 PASSED t U = 7.27 0.09 (5) =0.83 < -t (0.95,76) = -1.665 FAILED 11.93 1 33 + 1 45 Equivalence is NOT concluded 22
Key Summary Type of Comparison depends on your study purpose. Choice of δ is a key issue Balance between clinical meaningful difference and owned resource Do it in standard software by design your data 23
課後測驗 檢定 test treatment 是否和 control treatment 差不多應該用哪種 study: (1) equivalence study (2) non-inferiority study (3) superiority study 檢定 test treatment 是否效果比 control treatment 好應該用哪種 study: (1) equivalence study (2) non-inferiority study (3) superiority study δ 的選擇不應取決於 (1) clinical meaningful difference (2) owned resource (3) personal feeling Equivalence study 採用何種方法比較 (1) TOSTs approach (2) ANOVA (3) Chi-square test 以下何者不能在 SPSS 中執行 (1) Equivalence test (2)superiority test (3) non-inferiority test 24