Statistical Consideration in the Design of Clinical Trials

Transcription

1 Statistical onsideration in the Design of linical Trials Hsiao-Hui Tsou 鄒小蕙 INSTITUTE OF POPULATION HEALTH SIENES, NATIONAL HEALTH RESEARH INSTITUTES, TAIWAN 國家衛生研究院 群體健康科學研究所

2 Outlines Introduce NHRI & my works in NHRI linical Trials & Statistical onsiderations Bridging study Three-arm non-inferiority clinical trial Biosimilar clinical trials

3 國家衛生研究院 ( 竹南院區 )

4 宗旨 增進國人健康福祉 提昇醫藥衛生研究水準 發展生物醫藥科技 推動衛生政策研究 培育醫學專業人才

5 群體健康科學研究所生物統計與生物資訊研究組 宗旨 : 使用統計知識及資訊技術以提昇台灣人民的健康與福祉 linical Trials ( 臨床試驗 藥物研發之研究 ) Genetic Epidemiology and Genetic Statistics ( 遺傳流行病學及遺傳統計 ) Bioinformatics and Systems Biology ( 生物資訊學及系統生物學 ) Public Health Research ( 公共衛生研究 ) Statistical Methodology Research

6 Taiwan ooperative Oncology Group (TOG, 台灣癌症臨床研究合作組織 ) -- 台灣第一個院際臨床試驗的成功合作模式 首次以多家醫院進行同一癌症治療方法的研究 有效運用病人之資源及確保臨床研究計畫之安全性及倫理性 針對癌症療法及學術研究, 建立嚴謹審核制度 整合對癌症之檢查及診斷 技術 治療方法及療後追蹤 6

7 TOG covers 24 affiliated hospitals serves more than 75% of Taiwan s cancer patients 7

8 linical Research & ollaborative Research T408- 過去曾經 B 型肝炎感染的惡性淋巴癌患者,, B 型肝炎復發的機率 T408 related research T309- 口腔癌 T20- 膽道癌 T232- 鼻咽癌計畫 M006- 抗鬱劑之人體反應與基因體藥理學之相關性研究 M008- 美沙冬維持療法療效研究 ( 何英剛院士 黃介良主任 ) 台灣老年人虛弱症 骨質疏鬆 憂鬱症之整合型計畫 分子基因所, 癌研所, 免疫與醫學中心

9 linical Research & ollaborative Research T408- 過去曾經 B 型肝炎感染的惡性淋巴癌患者,, B 型肝炎復發的機率

10 Primary Research - linical Trials Weighted Evidence Approach of Bridging Study Hsiao-Hui Tsou*, Yi Tsong, Jung-Tzu Liu, Xiaoyu Dong, Yute Wu. (202). Weighted evidence approach of bridging study. J. Biopharmaceutical Statistics. 22(5):

11 BRIDGING STUDY A bridging study is defined as a supplemental study which is performed in the new region after the medicine is approved in the original region Bridging Region Original Region: US, EU, Japan,

12 BRIDGING STUDY Different ethnicity and clinical practice between regions has been observed and discussed. Ethnic differences may affect safety, efficacy, dosage, and dose regimen Necessity of repeating all/any phase clinical trials with the same scale in the new region has been discussed and debated. 2

13 INTRODUTION Bridging Study The literature is rich with many of the proposals on design and evaluation of bridging studies. onsistency approach (Shih, 200) Sensitivity and similarity approach (how et al, 2002) Non-inferiority approach (Liu and how, 2002) Bayesian approach (Liu et al, 2002, 2004) Group sequential approach (Hsiao et al, 2003, 2005) Mixed Bayesian prior approach (Hsiao et al, 2007) 3

14 INTRODUTION Weighted Z test (Lan et al, 2005) Lan et al proposed an approach to test for the weighted combination of test statistic in the original region and in the local bridging region. The weighted Z-test is expressed as Z ω = ωz Origin + ωz Bridging where Z Bridging is the test statistic for the bridging study, which is N(0,) under null hypothesis H 0 : = 0 4

15 Weighted Evidence Approach We consider the overall treatment effect by combining the weighted effects attained in the original and bridging regions. (Non-inferiority trial in the original region) We define that the test drug is effective at the bridging region if a weighted combination of treatment effects is greater than -δ γ ( µ T, B µ, B ) + ( γ )( µ T, O µ, O ) > δ where δ > 0 is a NI margin and γ is the weight for the bridging region. Our approach is an extension of weighted Z-test, but differs from Lan s method in that we use weighted combination of two unbiased estimates of the treatment difference instead of Lan s weighted combination of two Z-test statistics.

16 Hypothesis testing & sample size determination To test the hypothesis, the test statistics can be defined as T(γ*) = [ γ *( ˆ µ ˆ ) ( *)( ˆ ˆ T, B µ, B + γ µ T, O µ, O ) + δ ] (3.3) 2[ γ * 2 s 2 B / n B + ( γ *) Null hypothesis is rejected if T(γ*) > K α, where K α is the ( α/2) critical value of the t-distribution under the corresponding H 0 To support the planning of the bridging study, approximate sample size formulas were derived. We can find the sample size ratio fulfilling ( = n / n O B to achieve at least β power ) ς P T ( γ *) 2 s 2 O / n ( > t ) β α / 2, υ O ]

17 ς ( = n O / nb ) Table.. Approximate is shown when n O = 00, s O = 5, δ =.0, α = 0.05, α* = 0.005, β = 0.2. ( ˆ µ ˆ µ ) γ *: weight for bridging region, s = 2 2 B As O B γ* A , T B = ( ˆ µ, B T, O ˆ µ, B, O, ) 7

18 An example (an antidepressant study) We use an example in patients with major depressive disorder (MDD; documented 2-item HAM-D total score > 7) to illustrate the proposed method. Goal: to evaluate if the treatment effects of an innovative antidepressant (Test) is non-inferior to an Escitalopram (A) Primary endpoint: mean change of HAMD total score from baseline to week 8 8

19 An example (cont.) The foreign clinical data contained in the omplete linical Data Package (DP) Table 4.. Actual sample size and HAM-D. Anti-depressant drug Sample size Mean change of HAM-D total score Sample standard deviation Innovative Antidepressant (Test) Escitalopram (A)

20 An example (cont.) We assumed that Region is the region of interest to examine whether the result from U.S.A. (original region) can be applied to Region (bridging region) For simplicity, we assumed that there were 20 patients within each group with equal standard deviation of 7 in original trial. the non-inferior margin δ=.5 To give an 80% power for detecting a non-inferiority result between the Escitalopram (0mg/day) and innovative antidepressant (0mg/day) in the new region for a one-sided statistical significant test (a α-level of 0.025) 94 (47 2) patients were enrolled in this bridging trial, divided equally between the two treatment groups correspond to γ*=

21 Table 4.2. Summary statistics in bridging region. γ* n n 2 ˆµ ˆµ ŝ 2 ŝ2 ŝb Test statistic T(γ*) = 2.85 We claim that the efficacy of innovative anti-depressant (Test) is non-inferior to Escitalopram (A) in bridging trial because T(γ*) > K α =.96 2

22 Summary With this weighted evidence approach, the total sample size required might be reduced (we got in the example). The simulation study shows that the proposed method reasonably keeps type I errors under the targeted nominal level. the proposed procedure gives power at the desired nominal level Therefore, our approach is very robust to design parameters and is appropriate to be used in practice. 22

23 Primary Research - linical Trials Non-inferiority trials -- --Three arm trial (gold standard design) Jung-Tzu Liu, hyng-shyan Tzeng, Hsiao-Hui Tsou*. Establishing Noninferiority of a New Treatment in a Three-Arm Trial: Apply a Step-Down Hierarchical Model in a Papulopustular Acne Study and an Oral Prophylactic Antibiotics Study. International Journal of Statistics in Medical Research. 204, 3, -20. (* orresponding author) 23

24 Issues in Active ontrol NI trials Most of the difficulties and challenges discussed are because of the absence of a placebo arm. The importance of placebo is clearly unquestionable. When the placebo arm is present in the noninferiority trial design (this is often referred to as Gold Standard design), the effect of the active control will be estimated concurrently and hence these issues will not be present. (Hung et al, 2009, Biometrical Journal ) 24

25 Sample size allocation in a 3 arm trial E: Test drug R: Reference drug (A) P: Placebo E:R:P=3:2: E:R:P=2:2: E:R:P=:: How can we optimize the sample size allocation? 25

26 Hierarchical testing procedure H 0 : T P (required by HMP, 2005) H 02 : P H 03 : T δ Family-wise type I error rate is controlled. 26

27 Statistical test procedure Thus, the test statistics is given by Non-inferiority can be claimed if where denotes the 00(- α)-percentile of the standard normal distribution with mean 0 and variance. 27 ( ) ( ) ( ) ( ) ( ) P P P T T T P T n X X n X X n X X T + + = = ˆ ˆ ˆ ˆ 2 2 θ θ θ θ σ ψ > α z T z α

28 Sample sizes calculation Assume, then asymptotically. 28 P P T : : n n n : : = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + +, N ~ ˆ var ˆ ˆ ˆ ˆ 2 2 P P P T T P T T P P T n θ θ θ ψ θ

29 Sample sizes calculation The sample size needed for achieving a desired power of -β can be obtained by solving 29 ( ) ( ) ( ) ( ) ( ) α β θ θ θ + = z z n P P P T T P TP T

30 Optimal allocation which yields Let The optimal values for and P are given as partial derivatives of (25) at zero. This leads to 30 ( ) ( ) ( ) ( ) = P P P T T P TP T z z n θ θ θ α β ( ) ( ) ( ) T T P P P = θ ( ) ( ) T T = θ (25) P T n n n N + + = 0 for < < θ

31 Sample sizes allocation Optimal allocation n T 3

32 Example: Papulopustular acne study Ernesta et al.(ontraception, 2009) 32 32

33 Real Example: Papulopustular acne study---method Goal To prove that the mg EE/2 mg DNG (test) is superior to placebo and noninferior to mg EE/2 mg PA (control) Total 338 female patients (6-45 years old) have mild to moderate papulopustular acne and without contraindications to O use 33

34 Before Randomization Total N = 338 EE/DNG N T = 530 EE/PA N = 54 Placebo N P =

35 After (optimal allocation) Randomization Total N = 338 EE/DNG N T = 6 EE/PA N = 538 Placebo N P = Additionally 78 patients can be treated by therapy instead of placebo 35

36 Optimal sample size allocation Placebo 4% EE/DNG 46% EE/PA 40% 36

37 Economical & Ethical Before Total sample size 338 After Total sample size 23 37

38 Biosimilar linical Trials 38

39 Introduction Biologics ( 生物藥品 ) have become an increasingly important part of therapies to treat many diseases. usually produced by living cells or organisms the manufacturing processes are highly complex. noted as some of the most expensive medicines (Pharma Times-Vol.44-No.05-May 202) In 200, Sales of biologics reached US$00 billion worldwide with the top 2 biologics generating US$30 billion. By 205, biologics responsible for $20 billion in annual sales will go off patent. 39

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41 表 年全球前十大暢銷藥中有五個是單抗藥物 排名商品名單抗特性適應症行銷公司 Lipitor 降膽固醇 Pfizer 輝瑞 / Astellas 2 Plavix 動脈硬化 BMS 必治妥 / Sanfi-Aventis 2009 年營業額 ( 億美金 ) 3 Advair 氣喘 GSK 葛萊素 78 4 抗 -TNF 類風濕性關節炎 J&J 嬌生 7 Remicade 5 抗 -TNF 類風濕性關節炎 Pfizer/ 66 Enbrel Amgen 6 Diovan 高血壓 Novartis 諾華 60 7 Avastin 抗血管增 大腸直腸癌 Roche 羅氏 / 57 生 Genetech 8 Rituxan 抗 -D20 非何杰金氏淋巴瘤 Roche/ 56 Genetech 9 Humira 抗 -TNF 類風濕性關節炎 Abbot 亞培 Seroquel 精神分裂 AstraZeneca 阿斯特 4 5

42 表 2-5- 即將專利過期的生技暢銷藥 全球暢銷藥排名 商品名 專利到期年 適應症 原藥廠 2009 年營業額 ( 億美金 ) 4 Remicade 202 類風濕性關節炎 J&J 嬌生 Enbrel 202 類風濕性關節炎 Pfizer 輝瑞 / Amgen Avastin 209 大腸直腸癌 Roche 羅氏 / Genetech 8 Rituxan 203 非何杰金氏淋巴瘤 Roche 羅氏 / Genetech Humira 206 類風濕性關節炎 Abbot 亞培

43 Introduction Biosimilar (Follow-on biologic, 生物相似藥 ) is a copy of the innovator biological product. More and more innovator biologics are losing their patent protection. The development of follow-on biologics has received much attention from both sponsors and regulatory authorities However, biosimilars are fundamentally different from generic chemical drugs due to the size and complexity of the active ingredients and the nature of the manufacturing processes. 43

44 Molecule omparison 單株抗體 降血鈣素 ( 胺基酸 )

45 Introduction From Genentech s illustration 45

46 Introduction Generic drug: pill or capsule Biosimilars: infusion or injection 46

47 Introduction European Medicines Agency (EMA) published general guidelines on biosimilars in 2005 and approved its first biosimilar in Based on the foundational principles of EMEA guideline, biosimilars are expected to be similar, but not identical, to the innovator biologics they seek to copy. 47

48 On February 9, 202, FDA issued three draft guidance documents on biosimilar product. Section 35(i) of the PHS Act defines biosimilarity to mean that the biological product is highly similar to the reference product notwithstanding and that there are no clinically meaningful differences between the biological product and the reference product in terms of the safety, purity, and potency of the product. The FDA draft guidance discusses important approaches for assessing biosimilarity, including the following: (i) a stepwise approach to demonstrating biosimilarity and (ii) the totality of the evidence approach to be used for the regulatory review and approval of biosimilar applications. 48

49 In the current draft guidance, however, no specific statistical methods for assessment of biosimilarity were mentioned. The standard statistical methods for the assessment of ABE may not be appropriate for the assessment of biosimilarity of follow-on biologics due to fundamental differences between small-molecule drug products and biological (large-molecule) drug products (how & Liu, 200; Hsieh et al., 200). how et al (200b): current regulation for assessment of bioequivalence may be too loose to be applied for assessment of biosimilarity. 49

50 Tsou et al (203) 50

51 A onsistency Approach for Evaluation of Biosimilar Products Tsou et al (203) proposed a consistency approach to evaluate the consistency between a biosimilar product and the innovator biologic (using the predictive probability density function). The innovator product: already approved (due to its proven efficacy against placebo control) Assume K historical reference studies exist For evaluating the similarity of a biosimilar product to the innovator product: a clinical trial was conducted to compare the difference in efficacy and safety between the biosimilar and the innovator product. 5

52 A onsistency Approach for Evaluation of Biosimilar Products Goal: to assess whether B y B can reasonably be thought of as consistent with the K previous results. We use the predictive probability density function (Aitchison and Dunsmore, 975): p( v w) = = 2 where p ( ν, w) is a p.d.f. of N(, σ B ) and p( w) is a posterior probability density function We can also construct w i p( v, p( v ν = x w) d, w) p( w i 2 = xi yi ~ N(, σ i ) w) d p( w), where for i=,, K. 52

53 onsistency criterion ν = x We say that the result B y B (sample mean diff) is consistent with the reference result w = ( w,..., w K ) if and only if p( v w) ρ min{ p( wi w), i =,..., K}, (Higher score indicates stronger therapeutic effect) for some pre-specified predictive probability density function for ν ρ 0.9 or ρ = predictive probability density function for w The proposed approach could be applied to responses not only for therapeutic efficacy but also for adverse effects. 53

54 A onsistency Approach for Evaluation of Biosimilar Products We also show that the consistency criterion p( v w) ρ min{ p( wi w),for i =,..., K} holds if and only if where and p i 2 2 ( v w) 2τ B ln( ρ τ B p0) = 2 exp{ τ i ( w w) 2 i 2τ p0 = min{ pi, i =,..., K} i }. 54

55 A onsistency Approach for Evaluation of Biosimilar Products (Tsou et al, 203) Sample size determination Assume that both efficacy responses for the test product and placebo control for the new clinical trial are normally distributed with known variance σ 2. n represent the numbers of patients studied per treatment group in the new trial. 2 2 Let R = { v : ( v ω) 2τ B ln( ρ τ B p0)} be the expanse of all consistent trials. The sample size per treatment group, n, is determined to ensure that the cover probability of consistency expanse be at least γ, say for example 80%. p ( B 0 R) = 2Φ( 2ln( ρ τ p )) γ 55

56 Sample size formula (Tsou et al, 203) Then the sample size n can be determined by finding the smallest n such that n ( ρ p 0 ) 2 2σ exp{ Z } Σ Note that the denominator may be negative. 2 Our experience shows that the possibility of getting negative denominator can be reduced when K 2. 2 γ

57 A onsistency Approach for Evaluation of Biosimilar Products (Tsou et al, 203) use an example in patients with human growth hormone (hgh, 人類生長激素 ) deficiency to illustrate the proposed method. With this consistency approach, the total sample size required for evaluation of biosimilarity only based on the consistency criterion might be reduced (under equal variance assumption). The magnitude of similarity should be taken into account when determining the magnitude of consistency trend, ρ. We suggest that be 0.9 or greater to ensure the sufficient similarity of the biological product. 57

58 58