1 臨床試驗 Statistical analysis (I) 統計分析 ( 一 ) 指標種類與選擇 簡國龍老師 【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 Roles and applications of statistics in clinical trial Hypothesis testing and estimation Continuous data Categorical data Censored data Repeated measures Interim analysis Sample size determination Problems not resolved by statistics

3 The role of statistic in clinical trials Sample size estimation Randomized assignment of treatment Analyze results (hypothesis testing and effect estimation) Control for confounding

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5 Use of statistics Power calculation and efficiency considerations Sample size calculation, Group sequential methods, Cross-over design, Factorial design,.. Random assignment of treatment groups Fixed allocation, adaptive allocation Estimation of clinical effects / difference and Hypothesis testing Chi-square, t-test, ANOVA, log-rank test, GEE Control for confounding and identification of prognostic factors  Stratified analysis and Multivariate analysis

6 Methods of Randomization Fixed randomization Allocation ratio (i.e. simple randomization) Allocation strata (i.e. stratified randomization) Block size (randomized block design, Moses-Oakford algorithm) block size can be fixed or variable Adaptive randomization Number adaptive (e.g. Efron’s biased coin method) Baseline (prognostic factor) adaptive (e.g. Pocock & Simon, Begg & Iglewicz) Outcome adaptive (e.g. Zelen’s play-the-winner design)

7 Efficiency considerations Optimal allocation of resources: Information/subject, Information/visit, Information/ ＄ Cross-over design Factorial design  Evaluation of the combination of two or more drugs  Evaluation of two drugs if their mechanism are independent

8 Hypothesis testing Assumptions about of data distribution Formulate H O and H A F(data) = S P = (S ∣ H O and distribution)  P reject  P > α = = = > cannot reject H O

9 Effect estimation Point estimate : How large is the clinical effect? Confidence interval (CI) : What is the possible range of the clinical effects? 95% CI corresponds to α = 0.05

10 Objectives of a clinical trial : estimate the therapeutic difference ( △ ) Therapeutic difference :95% CI of △ exclude 0 Therapeutic equivalence : 95% CI of △ is within a pre- specified range

11 Different types of data Continuous data : Blood pressure, Cholesterol, Urinary flow,… Categorical data Dichotomous : death, relapse Ordinal : Complete response, Partial response, Stable disease, Progression Time-to-event data / Failure time data : Treatment-to- relapse,… Correlated data : Repeated measures, Correlated end-points

12 Continuous data Estimation  Mean, SD, Test statistics  H0 vs. Ha  Student’s t test, paired t test, two-sample test  ANOVA: one-way, two-way  ANCOVA Stratified randomization Nonparametric methods  Wilcoxon signed rank test, rank sum test, Kruskal-Wallis test

13 Categorical data One sample  Pre-post comparison: change from baseline analysis Independent samples  Chi-square test Ordered categorical data Combining categorical data  Stratification, Mantel-Haenszel test Model-based methods  Logistic regression

14 Different follow-up methods in clinical trials Fixed follow-up period Variable follow-up period Longitudinal study Interim analyses

15 Figure censoring pattern in calendar time. o ： event; × ： censored.

16 Figure censoring pattern in duration of treatment. o ： event; × ： censored.

17 Censored data Survival function Comparison between survival functions  Logrank test Cox’s proportional hazard model Calendar time and information time  Recruit N in the time interval (0, Tc)  The contribution by each subject to the total information depends on the numbers of measures of primary endpoints, proportional to the length of duration staying in a trial

18 Survival analysis / Analysis of failure-time data (e.g. time-to relapse, time-to-death) Censoring in follow-up of patients Right censoring and Left censoring Informative vs. uninformative censoring Estimation of survival probability S(t) from censored data e.g. S(5th year) = five-year survival, S(median survival) = 50% Kaplan-Meier curve and Greenwood formula for CI: a non- parametric approach Life-table method : an approximate approach Survival function Hazard function,…

19 Survival analysis / Analysis of failure-time data (e.g. time-to relapse, time-to-death) Comparison of two survival curves Log rank test : equal weight for all t Generalized Wilcoxon test : more weight for early t Multivariate analysis  Dependent variable : hazard at time t  Independent variables : Min effect : Treatment assignment  Covariates : Age, Sex, Staging, Center,…

20 Analysis of correlated data e.g. Blood pressure measured every week for six weeks pain score, Walking distance, Joint score at sixth week Problem : multiple comparison! Solution 1. Adjusted P-values at each comparison (may be too conservative) e.g. Bonferroni adjustment Scheffe and Duncan procedure in ANOVA 2. Multivariate analysis of variance Requires asymptotic assumptions (sufficient sample size and normal distribution) 3. Generalized Estimating Equation method (GEE) Robust and flexible 4. Composite end-points

21 Repeated measures Assessment of overall average effect across time Detection of time effect Treatment-by-time interaction GEE methods Continuous response vs. categorical response

22 Interim analyses / Group sequential methods Multiple “peeks” during the course of the trial  Continuous sequential design (paired subjects)  Open sequential plan and Closed sequential plan  Group sequential design (Repeated significant testing) Adjust p-value at each “peek” to maintain nominal significance levels. Expected number of enrolled subjects or expected total follow-up person-time Stopping rules and Data Monitoring Committee should be pre-specified in the protocol.

23 Protocol deviations Before randomization : Enroll subjects who are likely to comply with the protocol Doctor-patient relationship, Run-in phase, Financial reward,.. After randomization : Once randomized, always analyze  Intent-to-treat analysis / Intention-to-treat analysis vs. per- protocol analysis

24 Protocol deviations Common reasons for protocol deviations  incorrect diagnosis,  incorrect selection criteria,  departure from treatment schedule,  loss of follow-up,  administrative error, … Conditions for protocol deviations, if not specified in the protocol, are usually determined by the Data monitoring Board.

25 Intention-to-treat analysis vs. per- protocol analysis Compare the treatments that are intended to be given to the patients, not what the patients actually received. Preservation of the comparability of populations is of utmost importance. Other methods, such as the per-protocol method (i.e. exclude non-compliant patients) are not statistically valid.

26 Confounding Comparability-based criteria  The factor is unevenly distributed in the treatment groups.  The factors is an independent risk factor for the disease.  The factor is not an intermediate variable in the therapeutic mechanism. Collapsibility-based criteria.  Adjusted effect does not equal to apparent effect.  The factor is not an intermediate variable in the therapeutic mechanism.

27 Effect modification (interaction) Effect in group A ≠ Effect in group B A confounder is an independent risk / prognostic factor.It is something that we want to control / avoid. An effect modifier modifies the treatment effect, it may or may not be an independent prognostic factor. Effect modification is a biological phenomenon that we want to explore.

28 Figure Adjustment for covariate in estimation of treatment effect. Case I: Common slope.

29 Figure Adjustment for covariate in estimation of treatment effect. Case I: Different slope, same direction but different magnitude.

30 Figure Adjustment for covariate in estimation of treatment effect. Case III: Different slopes, different direction with different magnitude.

31 Figure Difference in treatment means and 95% confidence intervals. Mean test drug change from the baseline minus the mean placebo change from the baseline. (Source: U.S. FDA Guideline for the Format and Content of the Clinical and statistical Sections of an Application, 1988).

32 Multiple linear regression analyses The primary goal is to estimate the difference between the two (or more) treatment groups or to test the null hypothesis of no difference. Given good study design, sufficient sample size, and randomization, multivariate analyses is usually not necessary. If, unfortunately, confounding exists, multivariate analysis can help. Results for treatment effect if valid but results for confounders can only be used to generate further hypothesis. Results of post-hoc stratification (post-stratification analysis) can only serve to generate further hypothesis.

33 Identification of prognostic factors in clinical trials 1. Effect on primary end-point is positive, and the effect is more pronounced in certain subgroups = = > prognostic factor is identified 2. Effect on primary end-point is negative, but the effects is statistically significant in one subgroup = = = > requires further investigations

頁碼作品版權圖示來源 / 作者 1-35 本作品轉載自 Microsoft Office 2010 PowerPoint 設計主題範本 -Pixel ，依據 Microsoft 服務合約及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 4 《 Responsibilities of the statistical unit in a clinical trial group 》 中研院統計科學研究所，陳珍信。本作品依據著作權法第 46 、 52 、 65 條合理使用。 15 《 Design and analysis of clinical trials: concepts and methodologies 》， 作 者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition ) ， p.391 。本作品依據著作權 法第 46 、 52 、 65 條合理使用。 16 《 Design and analysis of clinical trials: concepts and methodologies 》， 作 者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition ) ， p.392 。本作品依據著作權 法第 46 、 52 、 65 條合理使用。 21 Assessment of overall average effect across time… 《 Design and analysis of clinical trials: concepts and methodologies 》， 作 者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition ) ， p.332 。本作品依據著作權 法第 46 、 52 、 65 條合理使用。 版權聲明 34

頁碼作品版權圖示來源 / 作者 22 Group sequential methods…Multiple “peeks” … 《 Design and analysis of clinical trials: concepts and methodologies 》， 作 者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition ) ， p.391 。本作品依據著作權 法第 46 、 52 、 65 條合理使用。 28 《 Design and analysis of clinical trials: concepts and methodologies 》， 作 者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition ) ， p.538 。本作品依據著作權 法第 46 、 52 、 65 條合理使用。 29 《 Design and analysis of clinical trials: concepts and methodologies 》， 作 者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition ) ， p.539 。本作品依據著作權 法第 46 、 52 、 65 條合理使用。 30 《 Design and analysis of clinical trials: concepts and methodologies 》， 作 者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition ) ， p.539 。本作品依據著作權 法第 46 、 52 、 65 條合理使用。 31 《 Design and analysis of clinical trials: concepts and methodologies 》， 作 者 :Chow, SC, Liu, JP ，出版社 : Wiley(third edition ) ， p.548 。本作品依據著作權 法第 46 、 52 、 65 條合理使用。 版權聲明 35