Transcript www.rhoworld.com

When Is Stratification Detrimental
to a Clinical Trial Design?
Part I
Gretchen Marcucci, M.S.
Biostatistician, Rho, Inc.
and
Katherine L. Monti, Ph.D.
Rho, Inc. and University of North Carolina
Outline
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Introduction
Motivation for the literature search
Why stratify? Advantages
Why not stratify? Disadvantages
If you want to stratify …
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Outline
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How many strata?
Alternatives
Limitations of the literature
Conclusions
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Introduction
•
This paper presents the results of a literature
search on the use of stratified randomization,
with particular interest in clinical trials.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Introduction
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Stratification in clinical trials is different from classical
stratification in survey sampling, or from blocking in
experimental design.
In stratified sampling, “the population is divided into
subgroups, or strata, each of which is sampled
randomly with a known sample size.”
In experimental design, treatments are assigned
within blocks, which are defined by factors that are
largely determinable and controllable (e.g., temp,
water level in a greenhouse setting). Again, the
sample size in each block is part of the design.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Introduction
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In clinical trials, stratification refers to the
assignment of treatment to homogeneous
groups defined by patient-related
characteristics that may affect outcome.
– These factors are generally not controllable (e.g.,
stage of disease, age within the allowable range).
– Until the end of the study, the sample size of each
factor level is generally unknown.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Introduction
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Sometimes stratification is beneficial.
Some trialists maintain that it is never
harmful.
– Is that the case?
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Motivation
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A drug company’s design:
– 120 subjects
–
4 treatments (placebo, three drug doses)
– 30 sites
–
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1 prognostic factor with 2 levels (hi and low levels,
continuous covariate)
Randomization:
– At each site, NOT centralized
– In blocks of 4 within factor level within site
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Motivation
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Those designing the study thought that
randomizing within factor level
– would increase balance in the design,
– “couldn’t hurt”.
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Others argued that randomizing within factor
level would increase the imbalance in the
design.
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Motivation
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120 subjects / (30 sites) =
4 subjects per site
Perfect balance with 4 treatments.
120 subjects / (30 sites x 2 levels) =
2 subjects per site for each level
Balance not assured with 4 treatments.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Motivation
• Although 2 subjects/level/site is not a
realistic enrollment pattern, it is unlikely
that stratification would help balance the
design.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Motivation
• What does the literature have to say
about stratification in clinical trials?
– When is stratification beneficial?
– When is stratification harmful?
– Is it true that it “couldn’t hurt”?
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Why stratify? Advantages
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To keep variability of subjects within strata as
small as possible and between-strata
variability as large as possible in order to
have the most precision of the treatment
effect. (Chow and Liu, 1998)
Avoid imbalance in the distribution of
treatment groups within strata.
Increase efficiency.
Protect against Type I and Type II errors.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Why stratify? Advantages
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Avoid confounding.
Satisfy prevailing investigator assumptions.
Provide credibility to choice of analysis
covariates.
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Why not stratify? Disadvantages
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More costly and complicated trial.
More opportunity to introduce error.
Power loss from unstratified randomization
may be very small in many cases.
Gain in precision of estimates is small once
(number of subjects) / (treatment) > 50.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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If you want to stratify …
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Consider
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If the covariates are imprecisely assessed, then may
introduce error.
If there are too many covariates,
– then there is a higher chance of imbalance, or
– the effect is the same as simple randomization.
If covariates are not related to outcome, then the gain
in efficiency will be small or negative.
If there are too many strata with small number of
subjects / stratum, the analysis model may be
overparameterized.
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Consider
How many strata depends on:
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Total number of subjects in the trial.
Expected number to be in each stratum.
Importance of prognostic factors.
Type of allocation scheme (permuted blocks
vs. dynamic allocation).
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Consider
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The number of strata should be less than (total
sample size) / (block size). (Hallstrom and Davis, 1988)
In our case, N=120, B=4,
– Recommendation: < 30 strata
– Design: 60 strata
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Stratification begins to fail (in terms of balance) if the
total number of strata is greater than approximately
N/2 (for 2 treatments). (Therneau, 1993)
– or N/k, k= number of treatments
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Number of strata: notes
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“One can inadvertently counteract the
balancing effects of blocking by having too
many strata.”
“…, most blocks should be
filled because unfilled blocks permit
imbalances.” (Piantadosi,1997)
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Number of strata: notes
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“If ‘institution effect’ were to be introduced as
a further prognostic factor, …, the total
number of strata may then be in the hundreds
and one would have achieved little more than
purely random treatment assignment.” (Pocock
and Simon, 1975)
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Alternatives
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Dynamic allocation / adaptive stratification
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Minimization by Taves.
Pocock and Simon’s method.
Zelen’s method.
Begg and Iglewics.
Others.
Post-stratification (ANCOVA).
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Minimization
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Keeps track of the current imbalance and
assigns the treatment that reduces the
imbalance.
Advantages:
- Produces less imbalance than conventional
stratification.
- Can accommodate more factors.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Minimization
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Disadvantages:
- Need to keep track of current imbalance.
- None of the assignments are completely random.
- Since it only aims to balance marginal totals,
precision is only increased if the interaction
between prognostic factors is not pronounced. (Tu
et. al., 2000)
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Post-stratification
If stratification is not done at randomization,
covariate analysis can be performed.
- Easier and less costly to implement.
- Often nearly as efficient.
- May be less convincing, in particular if covariate
was not mentioned in the protocol.
- Cannot correct for cases of extreme imbalance.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Limitations of the literature
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Literature refers mostly to trials of two
treatments.
Little attention is paid to operational
disadvantages of more complex designs.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Conclusions
Consider stratifying only if:
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Prognostic factors are known to be related to the
outcome and are easy to collect prior to
randomization.
Operational costs justify any gain.
Sample size is small ( N < 100), but the stratified
design does not induce imbalance.
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The number of strata should be less than (total sample
size) / (block size). (Hallstrom and Davis, 1988)
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Conclusions
Authors are still (1999) concluding that
“Stratification is … harmless always,
useful frequently, and important rarely”.
(Kernan et. al., 1999)
The preconception that stratification
would improve the balance and could
not hurt should be reconsidered.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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Contact Information
[email protected]
Slides: www.rhoworld.com
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References
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Begg CB, Iglewicz B. A treatment allocation procedure for sequential
clinical trials. Biometrics 36: 81-90, 1980
Chow SC, Liu JP. Design and Analysis of Clinical Trials. John Wiley
and Sons; 1998.
Hallstrom A, Davis K. Imbalance in treatment assignments in stratified
block randomization. Control Clin Trials 1988; 9:375-382.
Kernan WN, Viscoli CM, Makuch RW, et al. Stratified randomization for
clinical trials. J Clin Epidemiolol 1999; 52: 19-26.
Piantadosi, S. Clinical Trials. A methodologic perspective. John Wiley
and Sons; 1997.
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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References
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Pocock SJ, Simon R. Sequential tretment assignment with balancing
for prognostic factors in the controlled clinical trial. Biometrics 1975;
31:103-115.
Taves DR. Minimization: A new method in assigning patient to
treatment and control group. Clinical Pharmacology and Therapeutics
15: 443-453, 1974.
Therneau TM. How many stratification factors is "too many" to use in a
randomization plan? Control Clinical Trial 14: 98-108, 1993.
Tu D, Shalay K, Pater J Adjustment of treatment effect for covariates in
clinical trials: Statistical and Regulatory Issues Drug Info Journal
34:511-523, 2000.
Zelen M. The randomization and stratification of patients to clinical
trials. Journal of Chronic Dis, 27:365-375, 1974 .
2003 Gretchen Marcucci. All rights reserved. No part of this document may be copied without express written consent.
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