授課老師 : 劉仁沛教授 國立台灣大學 與 國家衛生研究院 臨床試驗 Inference on Treatment Effects for Targeted Clinical Trials under Enrichment Design 1 【本著作除另有註明外，採取創用 CC 「姓名標示 －非商業性－相同方式分享」台灣 3.0 版授權釋出】創用 CC 「姓名標示 －非商業性－相同方式分享」台灣 3.0 版

2 Outline Introduction. Molecular Markers and Designs Enrichment Design for Targeted Clinical Trials. Inference for Treatment Effects. Simulation Studies. Numerical Example. Discussion.

3 Targeted Clinical Trials After completion of a Human Genome Project, the disease targets at certain molecular level can be identified Personalized medicine Targeted treatments and drugs Precision Medicine Initiatives

4 Targeted Clinical Trials The traditional clinical trials, inclusion and exclusion criteria are usually based on some clinical endpoints, signs or symptoms They are not sufficiently correlated with the clinical benefits of the treatments Ignore the genetic or genomic variability of the trial participants

5 Introduction Current Treatment. Shut-gun approach. No benefit for most of patients. Targeted Therapy. Guided-missile approach. Knowledge of the molecular targets. Device for detection of the molecular targets. Treatment for the molecular targets.

Introduction 6

7

Type MTA Intended Target Indication Small Molecule Imatinib Bcr-abl tyrosine kinase Chronic myelogenous Leukemia Gastrointestinal stromal Tumors Dasatinib Bcr-abl tyrosine kinase Chronic myelogenous Leukemia Sunitinib Multi-receptor Advanced renal cell cancer tyrosine kinase Sorafenib Multi-receptor Advanced renal cell caner tyrosine kinase Advanced hepatocellular carcinoma Gefitinib Epidermal growth factor Advanced non-small cell lung cancer receptor Erlotinib Epidermal growth factor Advanced non-small cell lung cancer receptor Lapatinib Human epidermal growth metastatic breast cancer factor receptor 8

Introduction Monoclonal Trastuzumab Human epidermal growth metastatic breast cancer Antibody factor receptor Bevacizumab Vascular endothelial growth metastatic colorectal cancer factor Advanced non-small cell lung cancer Therapeutic Sipuleucel-T antigen-presenting cells metastatic hormone Vaccine refractory prostate cancer Ipilimumab cytotoxin T-lymphocyte advanced melanoma Antigen 4 (CTLA 4) 9

10 Introduction Development of targeted drugs involves translation from the accuracy of diagnostic devices for the molecular targets. Evaluation of targeted drugs is much more complicated than that of the traditional drugs. Drug-diagnostic Co-development (FDA, 2005). In Vitro Diagnostic Multivariate Index Assay (FDA,2007).

Designs for Targeted Clinical Trials The FDA Draft Drug-Diagnostic Co-Development Concept Paper (2005) proposed three different designs to meet different objectives of targeted clinical trials  Unselected Design All SubjectsAll testedRandomizationTreatmentControl 11

Examples of Unselected Design  The epidermal growth factor receptor (EGFR) inhibitor for the non-small cell lung cancer.  Iressa (gefitnib) target at the EGFR pathway – EGFR tyrosine kinase inhibitor  Efficacy is correlated to race 、 number of gene copies 、 protein expression or EGFR mutation 13 12

Designs for Targeted Clinical Trials Stratified Design All Subjects All testedBiomarker+RandomizationTreatmentControlBiomarker-RandomizationTreatmentControl 13

Examples of Stratified Design  MARVEL (Marker Validation for Erlotinib in Lung Cancer)  Objective: To evaluate whether EGFR status can be used to guide the treatment of these patients FISH +: erlotinib better than pemetrexed (superiority) FISH - : pemetrexed no worse (or better) than erlotinib(non-inferiority ) 2 nd line NSCLC with specimen Initial Registration FISH Testing EGFR FISH + (~ 30%) EGFR FISH − (~ 70%) Erlotinib Pemetrexed Erlotinib Pemetrexed StrataRandomize 957 patients 1196 patients 15 14

Designs for Targeted Clinical Trials Enrichment Design All Subjects All testedBiomarker+Randomization Treatment Control Biomarker- 15

Examples of Enrichment Design  Herceptin (trastuzumab): an antibody to inhibit human epidermal growth factor receptor (HER2)  Patients: metastatic breast cancer that over- expresses HER2 by the IHC assay with weak to more than moderate staining (2+ or 3+)  Randomization: 1 to 1 ratio to herceptin + chemotherapy versus chemotherapy alone 17 16

17 In practice, no diagnostic test is perfect with 100% positive predicted value (PPV) For example, Herceptin  (trastuzumab) is targeted at the patients with metastatic breast cancer with an over-expression of HER2 (human epidermal growth factor receptor) protein Observed either by IHC (immunohistochemical) assay or FISH (Fluorescence in situ hybridization) Targeted Clinical Trials 17

18 Targeted Clinical Trials Treatment effects as a function of HER2 over-expression or amplification. Source : Study 3 in the U.S. FDA Draft Package Insert of Herceptin  (2006). 18

19 The patients with a clinical trial assay (CTA) score of 3+, Herceptin  plus chemotherapy provides a superior clinical benefit of survival over mere chemotherapy alone On the other hand, for the patients with a CTA score of 2+, the results imply that Herceptin  plus chemotherapy may not provide additional survival benefit for the patients Targeted Clinical Trials 19

20 The FDA Draft Drug-Diagnostic Co-Development Concept Paper (2005) proposed three different designs One of the designs is the enrichment design Under the enrichment design, the targeted clinical trials consist of two phases Enrichment phase Each patient is screened by a diagnostic device for detection of the pre-defined molecular targets Randomized phase Patients with a positive result by the diagnostic device are randomized to receive either the targeted treatment or the untargeted concurrent control Targeted Clinical Trials

21 Enrichment Design for Targeted Clinical Trials Enrichment design for targeted clinical trials. The diagnostic device for the molecular targets is not a perfect device. Patients with a positive diagnosis may not have the molecular targets. The true status of molecular targets for each patient is not available.

22 Simon and Maitournam proposed the methods of evaluating the efficiency and computing sample size for targeted clinical trials Targeted clinical trials can be much more efficient than traditional untargeted designs Targeted Clinical Trials

23 Inference for Treatment Effects Diagnostic is positive Truth condition status Total R=(+)R=(-) Experimental treatment Treatment (T) Control (C) Total To find the

24 Inference for Treatment Effects Population Means by Treatment and Diagnosis. γ is the PPV. Accuracy of diagnosis γ 1-γ Test Group Control Group Difference Truth target condition

25 Inference for Treatment Effects The hypothesis for detection of treatment difference in the patient population truly with the molecular target: Let and be the sample means of test and control treatments, respectively. It follows that the expected value of mean difference:

26 Inference for Treatment Effects The difference in sample means actually under- estimates the true treatment effects of the molecular targeted drug in the patient population truly with the molecular target. The bias of the difference in sample means decreases as the PPV increases. On the other hand, the PPV of a diagnostic test increases as the prevalence of the disease increases.

27 Inference for Treatment Effects Under the assumption of homogeneity of variance. y ij are independently distributed as a mixture of two normal distributions with mean  i+ and  i- respectively, and a common varianceσ 2 : where denotes the density of a normal variable.

28 Inference for Treatment Effects For each patient, we have a pair of variables (Y ij, X ij ), where Y ij is the observed primary efficacy endpoint of patient j in treatment i and X ij is the latent variable indicting the true status of the molecular target of patient j in treatment i; j=1,…,n i, i=T,C. In addition, X ij are assumed i.i.d. Bernoulli random variables with probability  for the molecular target. Let containing all unknown parameters, and are the observed primary efficacy endpoints.

29 Inference for Treatment Effects It follows that the complete-data log-likelihood function for is given by:

30 Inference for Treatment Effects Using the EM algorithm (Dempster et al., 1977; McLachlan and Krishnan, 1997), and the bootstrap technique (Efron and Tibshirani, 1993). To incorporate the uncertainty on the accuracy of the diagnostic device in detection of the molecular targets for the inference of the treatment effects. The EM algorithm is the method for obtaining the maximum likelihood estimators (MLE) of the parameters for an underlying distribution from a given data set when the data is incomplete or has missing values. To apply the parametric bootstrap method to estimate the standard error of 30

31 Inference for Treatment Effects It follows that the null hypothesis is rejected and the efficacy of the molecular targeted test drug is different from that of the control in the patient population truly with the molecular target at the  level if The corresponding (1-  )100% asymptotic confidence interval for can be constructed as (Basford et al., 1997) : where z  /2 is the upper 100(  /2) percentile of a standard normal distribution. 31

32 Simulation: Relative bias and the coverage probability

33 Simulation: The Empirical Powers

34 Simulations: Summary of Results The EM algorithm for estimation of the treatment effects is not only unbiased but also provide sufficient coverage probability. The proposed testing procedure can adequately control the type I error rate at the nominal level. The results clearly demonstrate that the proposed testing procedure for the treatment effects based on the EM algorithm is uniformly more powerful than the traditional method.

35 The required sample size with incorporation of inaccuracy and uncertainty of diagnostic accuracy is given as Discussion

36 Discussion Extension Binary endpoints (published) Censored endpoints (exponential distribution: published; Cox’s proportional hazard model: in preparation) Traditional parallel design with diagnosis of molecular markers Treatment-by-target interaction Further investigation on performance of the Bayesian approach in the targeted clinical trials is also suggested.

37 Diagnostic is positive. Diagnosis is + Test Group Control Group R= (+) R= (-) R= (+) R= (-) R Inference for Treatment Effects 37

38 Inference for Treatment Effects At the (k+1)st iteration, the E-step requires the calculation of the conditional expectation of the complete-data log- likelihood, given the observed data, using currently fitting for The E-step is calculated by replacing X ij, by its conditional expectation given y ij. 38

39 Inference for Treatment Effects The M-step requires the computation of i = T,C, by maximizing. It follows that on the M-step of the (k+1)st iteration, the current fit for the positive predicted value of test drug group and control group is given by: Under the assumption of n T =n C, it follows that the overall positive predicted value is estimated by: 39

40 Inference for Treatment Effects The means of the molecularly target test drug and control can then be estimated respectively as: 40

41 Inference for Treatment Effects Using the EM algorithm (Dempster et al., 1977; McLachlan and Krishnan, 1997), and the bootstrap technique (Efron and Tibshirani, 1993). To incorporate the uncertainty on the accuracy of the diagnostic device in detection of the molecular targets for the inference of the treatment effects. The EM algorithm is the method for obtaining the maximum likelihood estimators (MLE) of the parameters for an underlying distribution from a given data set when the data is incomplete or has missing values. To apply the parametric bootstrap method to estimate the standard error of 41

42 Inference for Treatment Effects It follows that the null hypothesis is rejected and the efficacy of the molecular targeted test drug is different from that of the control in the patient population truly with the molecular target at the  level if The corresponding (1-  )100% asymptotic confidence interval for can be constructed as (Basford et al., 1997) : where z  /2 is the upper 100(  /2) percentile of a standard normal distribution. 42

授課老師 : 劉仁沛教授 國立台灣大學 與 國家衛生研究院 臨床試驗 Design and Analysis of In Vitro Diagnostic Devices 43 【本著作除另有註明外，採取創用 CC 「姓名標示 －非商業性－相同方式分享」台灣 3.0 版授權釋出】創用 CC 「姓名標示 －非商業性－相同方式分享」台灣 3.0 版

44 Outline Introduction Clinical Performance Evaluation Study Design Measures of Diagnostic Accuracy Reporting Results Discussion and summary

45 Clinical Performance Evaluation Characteristics Evaluation of accuracy of the device to correctly detect a pre-specified disease status at a particular time point Cross-section in nature Different persons administer the device and evaluate the device

46 Clinical Performance Evaluation Characteristics Specimen Samples obtained by diagnostic procedures – mammogram, CT scan, MRI, PET, etc. Samples obtained by diagnostic tests – blood samples, sputum samples, or tissue blocks, etc. Two phases Specimen collection phase Retrospective or prospective Specimen evaluation phase Prospective

47 Clinical Performance Evaluation Designs for specimen collection phase One-group sequence design (Design C1) Traditional two-group parallel design (Design C2) Standard 2x2 crossover design (Design C3) Randomized specimen design (Design C4) For the first three designs, a stratified randomization is applied to the normal and disease subjects

48 Clinical Performance Evaluation

49 Clinical Performance Evaluation

50 Clinical Performance Evaluation

51 Clinical Performance Evaluation Designs for specimen evaluation phase Assignment of specimens to readers or evaluators Procedures for evaluation of specimens Independent image evaluation Consensus image evaluation Separate image evaluation Combined image evaluation Analytical procedures for blood samples Variation due to day, operator and run

52 Clinical Performance Evaluation Independent image evaluation Readers are not aware and influenced by the findings of other readers Only independent image evaluation can be served as the primary image evaluation Consensus image evaluation Different readers evaluate the same sets of images together Not assess images independently and can not be served as the primary image evaluation

53 Clinical Performance Evaluation Separate (unpaired) image evaluation Readers evaluate an image of a subject independently of other test images of the same subject Images from different conditions and times of all subjects are mixed and then randomized Combined (paired) image evaluation Different images of the same subject from different conditions and times are evaluated simultaneously. More likely to introduce bias

54 Clinical Performance Evaluation Designs for assignment of specimens to readers or evaluators

55 Clinical Performance Evaluation Designs for assignment of specimens to readers or evaluators

56 Clinical Performance Evaluation Designs for assignment of specimens to readers or evaluators

57 Clinical Performance Evaluation Designs for assignment of specimens to readers or evaluators

58 Clinical Performance Evaluation Combination of designs for specimen collection and evaluation C2 + E2 Unpaired subject and unpaired reader design C3 + E2 Paired subject and unpaired reader design

59 Clinical Performance Evaluation Measures of Diagnostic Accuracy Sensitivity (Se) Specificity (Sp) False positive rate (FPR) False negative rate (FNR) Area under the receiver operating characteristic curve Percent agreement

60 Clinical Performance Evaluation T: the result of a diagnostic device which is a continuous random variable with higher values more indicative of the disease D: indicate variable of true status of disease. 1 = diseased; 0 = non-diseased c: a pre-specified threshold to classify subjects into diseased or non-diseased subjects

61 Clinical Performance Evaluation Y = {T|D=1}, the result of a diagnostic test of a subject with the disease of interest X = {T|D=0}, the result of a diagnostic test of a subject without the disease of interest

62 Clinical Performance Evaluation Sensitivity, specificity, FPR, and FNR at c:

63 Clinical Performance Evaluation

64 Clinical Performance Evaluation

65 Clinical Performance Evaluation

66 Clinical Performance Evaluation Estimates pf Se(c) and Sp(c) Estimates of FPR(c) and FNR (c) Se(c)=100(n 11 /n. 1 )%, and Sp(c)=100(n 22 /n. 2 )% FPR(c)=100(n 12 /n. 2 )%, and FNR(c)=100(n 21 /n. 1 )%

67 Clinical Performance Evaluation The score confidence interval

68 Clinical Performance Evaluation Sensitivity, specificity, FPR, and FNR are the measures of diagnostic accuracy at a particular threshold c They change as c changes They can not provide a summary of the overall accuracy of the diagnostic device

69 Clinical Performance Evaluation A measure for the summary of pairs of sensitivity and false positive rate over all possible thresholds A receiver operating characteristic (ROC) curve is a summary measure of diagnostic accuracy which is a plot of sensitivity on the y-axis versus false positive rate on the x-axis on a unit square

70 Clinical Performance Evaluation

71 Clinical Performance Evaluation Define a = (  Y -  X )/  Y and b =  X /  Y. Under the normal assumption for both X and Y, Then the ROC curve can be expressed as

72 Clinical Performance Evaluation Area under the ROC curve (AROC) is given as

73 MLE of AROC Clinical Performance Evaluation

74 Clinical Performance Evaluation Confidence for θ(MLE)

75 Clinical Performance Evaluation Nonparametric estimator Partial AROC [(b 2 – a 2 )/2 to (b-a)]

76 Clinical Performance Evaluation

77 Clinical Performance Evaluation When no gold standard is available Report format the 2x2 table of results comparing the new device with the non-reference standard a description of the non-reference standard measures of agreement and corresponding confidence intervals

78 Clinical Performance Evaluation

79 Clinical Performance Evaluation Measures Overall percent agreement = 100%×(a+d)/(a+b+c+d) Positive percent agreement = 100%×a/(a+c) Negative percent agreement = 100%× d(b+d)

80 Clinical Performance Evaluation

81 Clinical Performance Evaluation Overall percent agreement = 100%×(43+99)/168 = 84.5% Positive percent agreement = 100%×43/(43+26) = 62% Negative percent agreement = 100%×99/(0+99) = 100%. The 95% score confidence for the overall percent agreement is (78%, 89%).

82 Clinical Performance Evaluation

83 Clinical Performance Evaluation

84 Clinical Performance Evaluation

85 Clinical Performance Evaluation OverallPositive Negative Table %90.90%96.69% Table %96.67%95.44% Table %67.44%99.65%

86 Clinical Performance Evaluation

87 Clinical Performance Evaluation

88 Clinical Performance Evaluation

89 Clinical Performance Evaluation Discussion and Summary Frequent changes during the pre-market development and during the life-cycle after approval because of advance technology No control and unable for blinding and randomization for most device trials Bayesian approaches to bring the information from historical control and to update the current state-of-art information

90 Clinical Performance Evaluation FDA issued an guidance on Bayesian approaches to device trials in 2010 For in-vitro diagnostic test Non-clinical performance Limit of detection, precision, linearity Clinical performance Design, accuracy measures, reporting results

91 Clinical Performance Evaluation References U.S. FDA (2007) Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests. U.S. FDA (2010) Guidance for the Use of Bayesian Statistics in Medical device Clinical Trials Clinical Laboratory Standard Institute (2004) EP5-A2 Evaluation of Precision Performance of Quantitative Measurement Methods; Approved Guideline, Second Edition. Wayne, PA. Clinical Laboratory Standard Institute (2003) EP6-A. Evaluation of the Linearity of Quantitative Measurement Procedures: A Statistical Approach; Approved Guideline, Wayne, PA, U.S.A. Clinical Laboratory Standard Institute (2004) EP17-A. Protocols for Determination of Limits of Detection and Limits of Quantitation. Approved Guideline, Wayne, PA, U.S.A. Li, C.R., Liao, C.T., and Liu, J.P.* (2008) On the exact interval estimation for the difference in the paired areas under ROC curves, Statistics in Medicine. Vol. 27, Li, C.R., Liao, C.T., and Liu, J.P.* (2008) A non-inferiority test for diagnostic accuracy based on the paired partial areas under ROC curves, Statistics in Medicine. Vol. 27, Hsieh, E., and Liu, J.P.* (2008) On statistical evaluation of linearity in assay validation, Journal of Biopharmaceutical Statistics. Vol. 18, Liu, J.P.*, Lu, L.T., and Liao, C.T. (2009) Statistical inference for the within-device precision of quantitative measurements in assay validation, Journal of Biopharmaceutical Statistics, Vol. 19(5), Liu, J.P.*, Chow, S.C. and Hsieh, E. (2009) Deviations from linearity in statistical evaluation of linearity in assay validation, Journal of Chemometrics, Vol. 23(3),

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頁碼作品版權圖示來源 / 作者 11 台灣大學劉仁沛教授。 以創用 CC 「姓名標示－非商業性－相同方式分享」臺灣 3.0 版授權釋出。 12 Helfrich BA, Raben D, Varella-Garcia M et al., Antitumor activity of the epidermal growth factor receptor (EGFR) tyrosine kinase inhibitor gefitinib (ZD1839, Iressa) in non-small cell lung cancer cell lines correlates with gene copy number and EGFR mutations but not EGFR protein levels. Clin Cancer Res Dec 1;12(23): 本作品依據著作權法第 46 、 52 、 65 條合理使用。 台灣大學劉仁沛教授。 以創用 CC 「姓名標示－非商業性－相同方式分享」臺灣 3.0 版授權釋出。 16 Patients: metastatic breast cancer that over- expresses … 《 Handbook of Adaptive Designs in Pharmaceutical and Clinical Development 》， 作者 :Annpey Pong, Shein-Chung Chow ，出版社 : CRC press ， p.22-4 。本作品依據著作權法第 46 、 52 、 65 條合理使用。 17 For example, Herceptin  (trastuz umab) is targeted at the patients S Damodaran et al. Targeting the Human Epidermal Growth Factor Receptor 2 Pathway in Breast Cancer. Hosp Pract Oct; 40(4): 7–15. 本作品依據著作權法第 46 、 52 、 65 條合理使用。 93 版權聲明

頁碼作品版權圖示來源 / 作者 《 Study 3 in the U.S. FDA Draft Package Insert of Herceptin(2006) 》 U.S. Food and Drug Administration Protecting and Promoting Your Health pdfhttp:// pdf 本作品依據著作權法第 46 、 52 、 65 條合理使用。 Enrichment phase Each patient is screened by a diagnostic… 《 Translational Medicine: Strategies and Statistical Methods 》， 作者 :Dennis Cosmatos ， Shein-Chung Chow ，出版社 : CRC press ， p.107 。本作品依據著作 權法第 46 、 52 、 65 條合理使用。 23 台灣大學劉仁沛教授。 以創用 CC 「姓名標示－非商業性－相同方式分享」臺灣 3.0 版授權釋出。 Liu JP, Lin JR, Chow SC Inference on treatment effects for targeted clinical trials under enrichment design. Pharmaceutical Statistics 2009, 8: 本作品依據著作權法第 46 、 52 、 65 條合理使用。 94 版權聲明 Diagnostic is positive Truth condition status Total R=(+)R=(-) Experimental treatment Treatment (T) Control (C) Total

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頁碼作品版權圖示來源 / 作者 59 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.656 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.656 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.656 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.657 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.657 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 版權聲明

頁碼作品版權圖示來源 / 作者 65 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.656 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.658 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 , 71 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.659 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.659 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.660 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 版權聲明

頁碼作品版權圖示來源 / 作者 75 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.661 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.662 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.667 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.667 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.668 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 版權聲明

頁碼作品版權圖示來源 / 作者 84 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.669 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.668 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.671 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.670 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 88 《 Design and analysis of clinical trials: concepts and methodologies 》， 作者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition) ， p.671 。本作品依據著作權法第 46 、 52 、 65 條合 理使用。 版權聲明