1. To Prevent Selection Bias
Minimal Balance is Sufficient
Wenle Zhao, PhD
Medical University of South Carolina, Charleston, SC, 29425, USA
Society for Clinical Trials 36th Annual Meeting
Arlington, VA, USA - May 17-20, 2015

2. Contents Where does Selection Bias Come From?
How to prevent selection bias?
How to avoid random serious imbalance?

3. A Completed Trial with Suspicious Selection Bias.
The Worst Thing in the World of Clinical Trials
Funding?
Recruitment?
A Completed Trial with Suspicious Selection Bias.

4. Defense Measurements against Selection Bias
Treatment Allocation
Real-time Subject Randomization
Subject Enrollment
Outcome Assessment
Random
Allocation
Allocation Concealment
Treatment Masking
The only reliable protection left against selection bias.

5. Allocation Randomness
Target allocation ratio
Random variable ~U(0,1)
To balance treatment distribution
Permuted Block Randomization
Biased Coin, Urn Design
To balance baseline covariate
Stratified Randomization
Minimization
Allocation Randomness
Complete Randomization
Permuted Block
Randomization
Minimization

6. Predictability Defeats Concealment & Masking
Deterministic Assignment
100%
~ 87%
Proportion of DA
50%
33%
25%
20%
B = 2
B = 4
B = 6
B = 8
Minimization
Permuted Block Randomization

7. Evidence of Selection Bias in Randomized Trials
1. Heparin for myocardial infarction E
2. University Group Diabetes Program P
3. Talc and mustine for pleural effusions P
4. Tonsillectomy for recurrent throat infection in children P
5. Oxytocin and amniotomy for induction of labor P
6. Western Washington Intracoronary Streptokinese Trial E
7. RSV immune globulin in infants and young children E
8. A trial to assess episiotomy E
Selection bias evidence identified P
9. Canadian National Breast Cancer Screening Study P
10. Surgical Trial P
11. Lifestyle Heart Trial E
12. Coronary Artery Surgery Trial P
13. Etanercept for children with juvenile rheumatoid arthritis E
14. Edinburgh Randomized Trial of Breast Cancer Screening P
15. Captopril Prevention Project P
16. Göteborg (Swedish) Mammography Trial E
17. HIP Mammography Trial E
18. Hypertension Detection and Follow-up Program P
19. Randomized Trial to prevent vertical transmission of HIV-1 P
20. Effectiveness trial of diagnostic test E
21. S African trial of high-dose chemotherapy for metastatic breast cancer P
22. Randomized study of a culturally sensitive AIDS education program P
23. Runaway Youth Study
Suspicious election bias due to
p-value < 0.05 P
24. Cluster randomized trial of palliative care P P
25. Randomized trial of methadone with or without heroin P
26. Randomized NINDS trial of tissue plasminogen activator for acute ischemic stroke P
27. Norwegian Timolol Trial P
28. Laparoscopic versus open appendectomy P
29. The Losartan Intervention for Endpoint reduction in Hypertension Study P
30. The Heart Outcomes Prevention Evaluation Study

8. P > 0.3 Protect Trials Against Selection Bias P < 0.05 ?
Selection bias will result small p-values
Complete randomization may (5% chance) see a p-value < 0.05
P < 0.05 ?
P > 0.3
P > 0.2

9. The Logic Real-time complete randomization
Eliminates selection bias due to allocation predictability
Eliminates selection bias due to allocation concealment failure
Totally eliminates selection bias
Without selection bias, complete randomization may still have
Imbalance in treatment distribution
 Power loss is trivial
Imbalance is baseline covariate distribution
 Adjustment, not balancing, is the solution
Serious baseline covariate imbalance with p-value < 0.05
 5% chance for any covariate
 60% chance for at least one in 10 covariates
 Suspicion of selection bias
 Trouble in trial result interpretation

10. Options We Have Stratified Restricted Randomization
Permuted Block Randomization
Biased Coin Design - Efron
Urn Design - Wei
Big Stick Design – Soares & Wu
Maximal Procedure – Berger et al.
Block Urn Design – Zhao & Weng
Unnecessarily tighten control imbalances.
Disabled when number of strata getting large.
Minimization
Most assignments are deterministic.
Dynamic Hierarchy Balancing
Hierarchy order is hard to justify.

11. Minimal Sufficient Balance Procedure
Subject ready for randomization
T-test for continuous var.
χ2 test for categorical var. N
Any serious imbalance?
Any p-value < 0.2? Y
Current assignment can effectively reduce imbalances? Y N
Complete randomization
Biased coin assignment
The proportion depends on p-value threshold and biased coin probability
Next subject

12. Example : NINDS rt-PA Stroke Study
p-value
Site
NIHSS
Age
OTT
Glucose
Stroke Subtype
Sex
Fibrinogen
Weight
Systolic BP
Diastolic BP
Observed in the Original Study
0.9987
0.1398
0.0289
0.8662
0.7804
0.0733
0.6265
0.1808
0.0111
0.5968
0.2810
Serious imbalances found
in 2 of the 11 baseline covariates.

13. Example : NINDS rt-PA Stroke Study
NINDS rt-PA Stroke study data.
Simulations = 5000
Baseline covariates:
Severity (NIHSS)
Age
Onset to treat
Glucose
Center

14. Example : NINDS rt-PA Stroke Study
Balance 11 baseline covariates
Distribution of p-Values for baseline covariate imbalance tests with 11 covariates controlled*
NINDS rt-PA data, Imbalance control limit p-Value ≥ 0.3. ξ= 0.65, simulation = 1000/scenario.
p-value
Site
NIHSS
Age
OTT
Glucose
Stroke Subtype
Sex
Fibrinogen
Weight
Systolic BP
Diastolic BP
Low 2.5% boundary
0.226
0.259
0.237
0.262
0.244
0.214
0.245
0.239
0.252
0.246
Low 5% boundary
0.276
0.295
0.279
0.288
0.280
0.292
0.277
0.278
0.281
0.287
Low 10% boundary
0.309
0.341
0.316
0.323
0.315
0.326
0.322
0.319
0.330
Median
0.605
0.631
0.626
0.624
0.638
0.609
0.634
0.610
Observed in the Original Study
0.9987
0.1398
0.0289
0.8662
0.7804
0.0733
0.6265
0.1808
0.0111
0.5968
0.2810

15. Summary
Complete randomization eliminates selection bias due to allocation predictability.
Real-time randomization eliminates selection bias due to allocation concealment failures.
Minimization method has the highest proportion of deterministic assignments, and therefore is vulnerable to selection bias.
Power loss due to treatment imbalance is trivial.
Justification, not balancing, is the solution for covariate confounding effects.
Using Minimal Sufficient Balancing to prevent random serious imbalances, while maintaining a high level of allocation randomness.

16. Thank You!
Contact me at:

17. Some of my works on Randomization
Zhao W, Ciolino J, Palesch Y. Step-forward randomization in multicenter emergency treatment clinical trials. Acad Emerg Med Jun;17(6): doi: /j x. PMID: .
Zhao W, Weng Y, Wu Q, Palesch Y. Quantitative comparison of randomization designs in sequential clinical trials based on treatment balance and allocation randomness. Pharm Stat Jan-Feb;11(1): doi: /pst.493. PMID:
Zhao W, Weng Y. Block urn design - a new randomization algorithm for sequential trials with two or more treatments and balanced or unbalanced allocation. Contemp Clin Trials Nov;32(6): doi: /j.cct PMID:
Zhao W, Hill MD, Palesch Y. Minimal sufficient balance--a new strategy to balance baseline covariates and preserve randomness of treatment allocation. Stat Methods Med Res Jan 26. [Epub ahead of print] PMID:
Zhao W. Selection bias, allocation concealment and randomization design in clinical trials. Contemp Clin Trials Sep;36(1): doi: /j.cct Epub 2013 Jul 19. No abstract available. PMID:
Zhao W. A better alternative to stratified permuted block design for subject randomization in clinical trials. Stat Med Dec 30;33(30): doi: /sim PMID:
Zhao W, Durkalski V. Managing competing demands in the implementation of response-adaptive randomization in a large multicenter phase III acute stroke trial. Stat Med Oct 15;33(23): doi: /sim Epub 2014 May 22. PMID:
Zhao W, Mu Y, Tayama D, Yeatts SD. Comparison of statistical and operational properties of subject randomization procedures for large multicenter clinical trial treating medical emergencies. Contemp Clin Trials Mar;41: doi: /j.cct Epub 2015 Jan 29. PMID: