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Statistics 542 Introduction to Clinical Trials Issues in Analysis of Randomized Clinical Trials

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  1. Statistics 542Introduction to Clinical TrialsIssues in Analysis of Randomized Clinical Trials

  2. Issues in Analysis of Randomized Clinical Trials • Reference: May, DeMets et al (1981) Circulation 64:669-673 Peto et al (1976) British Journal of Cancer

  3. Sources of Bias 1. Patient selection 2. Treatment assignment 3. Patient Evaluation 4. Data Analysis Methods to Minimize Bias 1. Randomized Controls 2. Double blind (masked) 3. Analyze what is randomized

  4. What Data Should Be Analyzed? • Basic Intention-to-Treat Principle • Analyze what is randomized! • All subjects randomized, all events during follow-up • Randomized control trial is the “gold” standard” • Definitions Exclusions • Screened but not randomized • Affects generalizability but validity OK Withdrawals from Analysis • Randomized, but not included in data analysis • Possible to introduce bias!

  5. Patient Closeout • ICH E9 Glossary • “Intention-to-treat principle - …It has the consequence that subjects allocated to a treatment group should be followed up, assessed, and analyzed as members of that group irrespective of their compliance with the planned course of treatment.”

  6. Intention To Treat (ITT) Principle • Analyze all subjects randomized & all events • Beware of “look alikes” • Modified ITT: Analyze subjects who get some intervention • Per Protocol: Analyze subjects who comply according to the protocol

  7. Patient Withdrawn in Analysis (1) • Common Practice - 1980s • Over 3 years, 37/109 trials in New England Journal of Medicine published papers with some patient data not included • Typical Reasons Given a. Patient ineligible (in retrospect) b. Noncompliance c. Competing events d. Missing data

  8. Patient Withdrawn in Analysis (2) A. Patient INELIGIBLE • After randomization, discover some patients did not in fact meet entry criteria • Concern ineligible patients may dilute treatment effect • Temptation to withdraw ineligibles • Withdrawl of ineligible patients, post hoc, may introduce bias

  9. Betablocker Heart Attack Trial(JAMA, 1982) • 3837 post MI patients randomized • 341 patients found by Central Review to be ineligible • Results % Mortality PropranololPlacebo Eligible7.39.6 Ineligible6.7 11.3Best Total7.2 9.8  In the ineligible patients, treatment works best

  10. Anturane Reinfarction Trial (1980) NEJM • Randomized, double blind, placebo controlled AnturanePlaceboTotal Randomized813816 1629 Ineligible3833 71 • Reasons for ineligible 1/3 - time since MI: < 25 days or > 35 days 1/3 - enzymes not elevated 1/3 - other: age, enlarged heart, prolonged hospitalization, .… • Number ineligible about the same in each treatment group BUT

  11. Anturane Reinfarction Trial (1980) • 1629 patients randomized • 1631 entered, but two patients randomized twice • Need to delete 03013, 17008 • Use first randomization! • Declared post hoc 71 “ineligible” patients

  12. Anturane Reinfarction Trial (1980) Placebo Anturane Total All 817 812 1629 Ineligible 33 38 71 Eligible 784 774 1558 < 7 day rule 15 15 30 Analyzable subjects 769 759 1528 (Table 3) Analyzable Deaths - Within 7 days of being off drug

  13. 1980 Anturane Mortality Results Anturane Placebo P-Value Randomized 74/813 (9.1%) 89/816 (10.9%) 0.20 “Eligible” 64/775 (8.3%) 85/783 (10.9%) 0.07 “Ineligible” 10/38 (26.3%) 4/33 (12.1%) 0.12 P-Values for 0.0001 0.92 eligible vs ineligible Reference: Temple & Pledger (1980) NEJM, p. 1488

  14. 1980 Anturane Mortality Results • AnturanePlacebo • Withdrawn10 4 • “Early” discontinuation43 • “Late” discontinuation6 1

  15. Total MortalityAnturane Reinfarction Trial (1980) I. All Pts - 1629 All DeathsRandomDeaths* NEJM accounts for only Anturane 81274 106 Placebo 81789 43 Total1629 *163 149 P = 0.20 (Table 3+6) II. 1558 Subjects - Exclude 71 Non-eligibles All DeathsRandomDeaths“71" Anturane 774 64(10) Placebo 784 85 (4) Total1558 149P = 0.07

  16. Total MortalityAnturane Reinfarction Trial (1980) • III. 1528 Subjects - Exclude 71 Non-eligibles + 30<7 days • All DeathsRandomDeaths • Anturane 759 60 • Placebo 769 80 • Total1528 140 • IV. 1528 Subjects • Analyzable DeathsRandomDeaths • Anturane759 44 • Placebo769 62 • Total1528 106 • P = 0.076

  17. Total MortalityAnturane Reinfarction Trial (1980) Consider Patients Excluded I. < 7 day rule - 30 pts AliveDeadTotal Placebo10515 Anturane11415 Total21930

  18. Total MortalityAnturane Reinfarction Trial (1980) II. 71 "ineligibles" AliveDeadTotal Placebo29433 Anturane281038 Total571471

  19. Anturane Sudden Death (SD) I. All Patients (N = 1629) RandomizedNDA-SDsNEJM-SDs Placebo81641498 Anturane 81327303 Total1629 68 79 P-value0.08 0.03 11 additional SD's were defined from submission of NDs to publications II. Exclude 71 Protocol Violators (N = 1558) RandomizedNDA-SDsNEJM-SDs Placebo 78340 46 Anturane 7752628 Total1558 6664 P-value0.080.03 Difference of 8 SD's

  20. Anturane Sudden Death (SD)for Total Follow-up • III. Exclude 71 Protocol Violators & 30 7 Day Rule Violators • (N = 1528) • RandomizedNDA-SDsNEJM-SDs • Placebo7683737 • Anturane 7602422 • Total1528 6159 • P-value0.09 0.04 • * Information not necessarily given in NEJM articlebut used to prepare tables presented

  21. Anturane Analysis Table D - 1978 Article Comparison of the Mortality Experience for the 4 Patient Groups Percent Mortality Patient GroupAnturanePlaceboP-value 1620 5.6 (45/806)+7.5 (61/814)0.10 15675.2 (41/781)7.4 (58/786)0.07 15474.6 (35/768)7.4 (58/779)0.01 14754.4 (32/733)7.1 (53/742)0.02 Article '783.4 (25/733)5.9 (44/742)0.016 +Number of deaths/number at risk

  22. ART (NEJM, 1978)Comparisons of the Mortality Experience for the 73 Patients with "Objective" and "Subjective" Baseline Exclusions Groups Compared% Mortality Placebo vs. Anturane in the 73**8.6 (3/35)*26.3 (10/38) 73 vs. 1547*** 17.8 (13/73) 6.0 (93/1547) (Both Treatment Groups) 73 vs. 1547 (Anturane Group) 26.3 (10/38) 4.6 (35/768) 73 vs. 1547 (Placebo Group) 8.6 (3/35)7.5 (58/779) * Number of deaths/number at risk ** 73 refers to the group of 73 patients with "objective" or "subjective" reasons at baseline for exclusion *** 1547 refers to the total group of randomized patients with the 73 patients with objective and subjective baseline exclusions removed

  23. ART (NEJM, 1978)P-Values Using Two Techniques for Survival Curve Comparisons of the Groups P-Values Groups ComparedMantel-Haenszel Gehan Method Method Placebo vs. Anturane in the 730.0450.052 73 vs. 1547 (Both Treatment Groups)0.00090.0003 73 vs. 1547 (Anturane Only)< 0.0001 < 0.0001 73 vs. 1547 (Placebo Only)0.91 0.98

  24. Acceptable PoliciesFor Ineligible Subjects 1. Delay randomization, confirm eligibility and allow no withdrawals (e.g. AMIS) (Chronic Studies) 2. Accept ineligibles, allow no withdrawals (e.g. BHAT, MILIS) (Acute Studies) 3. Allow withdrawals if: a. Procedures defined in advance b. Decision made early (before event) c. Decision independent and blinded d. Use baseline covariates only (two subgroups) e. Analysis done with and without

  25. B. WITHDRAWL FOR NON-COMPLIANCE • References: Sackett & Gent (1979) NEJM, p. 1410 • Coronary Drug Project (1980) NEJM, p. 1038 • Two Types of Trials • 1. Management • - "Intent to Treat" Principle • - Compare all subjects, regardless of compliance • 2. Explanatory • - Estimate optimum effect, understand mechanism • - Analyze subjects who fully comply • WITHDRAWALS FOR NON-COMPLIANCE • MAY LEAD TO BIAS!

  26. Breast Cancer Adjuvant TherapyProbability of Disease Free Survival for Years Post Mastectomy (Method I) Redmond et al (1983) Cancer Treatment Report

  27. Breast Cancer Adjuvant TherapyProbability of Disease Free Survival for Years Post Mastectomy (Method II) Redmond et al (1983) Cancer Treatment Report

  28. Breast Cancer Adjuvant Trial • Results using stratification by compliance analysis can be re-ordered according to definition • Both previous graphs are for the placebo arm • Lesson: Compliance is an outcome & analysis of one outcome, stratified by another, is highly vulnerable to bias

  29. Cancer Trial (5-FU & Radiation)Gastric Carcinoma • Reference: Moertel et al. (Journal of Clinical Oncology, 1984) • 62 patients randomized • No surgical adjuvant therapy vs. • 5-FU and radiation • 5 year survival results RandomizedPercent (%) Treatment23%P < 0.05 No Treatment4%

  30. Cancer Trial (5-FU & Radiation)Gastric Carcinoma • According to treatment received 5 year survival • Received % SurvivalTreatment20% • Refused Treatment30%NSControl4%

  31. Example: Coronary Drug Project5-Year Mortality Clofibrate Placebo N % Deaths N % Deaths Total (as reported) 1103 20.0 2782 20.9 By Compliance 1065 18.2 2695 19.4 < 80% 357 24.6 882 28.2 > 80% 708 15.0 1813 15.1 • Adjusting for 40 covariates had little impact • Compliance is an outcome • Compliers do better, regardless of treatment

  32. Example: Coronary Drug Project2-Year Mortality Compliance Assessed Estrogen Placebo N % Deaths N % Deaths Total 903 6.2 2361 5.7 < 80% 488 6.1 436 9.9 > 80% 415 6.3 1925 4.8 • Comments • Higher % of estrogens patients did not comply • Beneficial to be randomized to estrogen & not take it • (6.1% vs. 9.9%) • Best to be randomized to placebo & comply (4.8%)

  33. Example: Wilcox et al (1980) Trial, BMJ6-Week Mortality PropranololAtenololPlacebo N % DeathsN% DeathsN% Deaths Total1327.61278.712911.6 Compliers883.4762.68911.2 Non-compliers4415.95117.64012.5 • Comments • Compliers did better than placebo • Treatment non-compliers did worse than placebo • Placebo non-compliers only slightly worse than compliers • Analysis by compliers overestimates benefit

  34. Aspirin Myocardial Infarction Study (AMIS) % Mortality Compliance Aspirin Placebo Good 6.1 5.1 Poor 21.9 22.0 Total 10.9 9.7

  35. Summary of Compliance • No consistent pattern Example Non-compliance Did Worse CDP Clofibrate, AMISBoth Treatment & Control CDP EstrogenControl Only Beta-blocker, Wilcox Two Treatments, Not Control • Compliance an outcome, not always independent of treatment • Withdrawal of non-compliers can lead to bias • Non-compliers dilute treatment • Try hard not to randomize non-compliers

  36. II. Competing Events • Subject may be censored from primary event by some other event (e.g. cancer vs. heart disease) • Must assume independence • If cause specific mortality used, should also look at total death • If non-fatal event is primary, should also look at total death and non-fatal event • Problem for some response measures

  37. III. Problem of Definitions • Cause specific definitions hard to apply • Example: Anturane Reinfarction Trail (ART) • (NEJM, 1980) Sudden Death ClassificationAnturane PlaceboP-value ART30/81248/8170.03 Another Committee 28/812 39/817 0.17

  38. Anturane Reinfarction TrialSudden Death CategorySourcePlaceboAnturaneP-value All patients & all NEJM48/81730/8120.03 sudden deathsAC39/81728/8120.17 "Eligible" patients & NEJM46/78528/7750.03 all sudden deathsAC37/78225/7730.12 • Problem of cause specific definitions • AC = Another review committee

  39. IV. "Wrong", Inconsistent, Outlying Data • "Wrong" or "outlying" data may in fact be real • Decisions must be made blind of group assignment • All modifications or withdrawals must be documented

  40. V. Missing Outcome Data • Design with zero • missingness may be associated with treatment • for analysis, data are not missing at random • even if same number missing, missing may be for different reason in each treatment group • Implement with minimum possible • Analyze exploring different approaches • if all, or most, agree, then more persuasive

  41. “Best” and “Worst” Case Analyses Treatment Control Total Events 170 220 Lost to Follow-up 30 10 "Best" Case 170 230 "Worst" Case 200 220

  42. VI. Poor Quality Data

  43. Poor Quality Data (1) • Lost to Follow-up (enforced withdrawals)  NO DATA: PROBLEMS: • Not necessarily independent of treatment • Raises questions about study conduct

  44. Poor Quality Data (2) SOLUTIONS: • Keep to a minimum • Easiest if vital status is the outcome • Hardest if the response variables are time-related measures requiring a hospital or clinic visit • Censor at the time lost • Can be done in survival analysis • Assumes independence of treatment

  45. Poor Quality Data (3) SOLUTIONS: 3.Estimate missing data using previous data or averages 4. “Best” case and “worst” case analyses

  46. VII. Poor Clinic Performance in a Multicenter Study • If randomization was stratified by clinic, then withdrawal of a clinic is theoretically valid • Withdrawal must be done independent of the outcome at that clinic

  47. Mortality in Aspirin Myocardial Infarction Study (AMIS) • AspirinPlaceboP-value • All 30 Centers246/2267219/2257 0.99 • 7 “Selected” Centers3966 < 0.01 • In “selected” centers, aspirin showed superiority

  48. Mortality in Beta-Blocker Heart Attack Trial (BHAT) • PropranololPlaceboP-value • All 32 Centers138/1916188/1921< 0.01 • Cox adjusted Z = 3.05 • 6 “Selected” Centers4326< 0.05 • In “selected” centers, propranolol worse

  49. VIII. Special Counting Rules • Events beyond a specified number of days after treatment stopped not counted "non-analyzable" • Examples 1. "7 Day Rule" Anturane (1978) NEJM 2. "28 Day Rule" Timolol (1981) NEJM • If used, must • Specify in advance • Be a long period to insure termination not related to outcome • Analyze results both ways

  50. IX. Fishing orDichotomizing Outcomes • Common practice to define a response (S,F) from a non-dichotomous variable • By changing our definition, we can alter results • Thus, definitions stated in advance • Definitions should be based on external data