Allocation Methods
David Torgerson
Director, York Trials Unit
djt6@york.ac.uk
www.rcts.org
Randomised Trials
• The ONLY distinguishing feature of a RCT
is that 2 or more groups are formed by
random allocation.
• All other things, blinding, theoretical
justification for intervention, baseline tests
may be important but are not sufficient for
a study to be a RCT.
Rejected paper
It purports to be a randomized controlled trial, but it
demonstrates none of the attributes of one. As a result, I
recommend that this article be rejected for publication.
Educational research should begin with a theory, a causal
argument, based on a careful examination of the literature. We
need to understand in an experiment why such an approach
would be examined, the historical linkages of past research to
present investigations. What conditions would lead one to
believe that this technology could make a difference in
spelling? Is it something in the software, on the computer
screen, on children's interaction with the particular curriculum.
This is often the most important part of a study, the question,
and the rationale for why the investigation is critically important.
What Randomisation is NOT
• Randomisation is often confused with
random SAMPLING.
• Random sampling is used to obtain a
sample of people so we can INFER the
results to the wider population. It is used
to maximise external or ecological validity.
Random Sampling
• If we wish to know the ‘average’ height and
weight of the population we can measure the
whole population.
• Wasteful and very costly.
• Measure a random SAMPLE of the population.
If the sample is RANDOM we can infer its
results to the whole population. If the sample
is NOT random we risk having biased
estimates of the population average.
Why do we randomise?
•
•
•
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(1) Avoid selection bias
(2) Controls for temporal effects
(3) Controls for regression to the mean
(4) Basis for statistical inference
Random Allocation
• Random allocation is completely different.
It has no effect on the external validity of a
study or its generalisability.
• It is about INTERNAL validity the study
results are correct for the sample chosen
for the trial.
Comparable Groups
• It has been known for centuries to to
properly evaluate something we need to
compare groups that are similar and then
expose one group to a treatment.
• In this way we can compare treatment
effects.
• Without similar groups we cannot be sure
any effects we see are treatment related.
Why do we need comparable
groups?
• We need two or more groups that are
BALANCED in all the important variables
that can affect outcome.
• Groups need similar proportions of men &
women; young and old; similar weights,
heights etc.
• Importantly, anything that can affect outcome
we do NOT know about needs to be evenly
distributed.
Non-random methods:
Alternation
• Alternation is where trial participants are
alternated between treatments.
• EXCELLENT at forming similar groups if
alternation is strictly adhered to.
• Problems because allocation can be
predicted and lead to people withholding
certain participants leading to bias.
Non-Random Methods
Quasi-Alternation
• Dreadful method of forming groups.
• This is where participants are allocated to
groups by month of birth or first letter of
surname or some other approach.
• Can lead to bias in own right as well as
potentially being subverted.
Randomisation
• Randomisation is superior to non-random
methods because:
» it is unpredictable and is difficult for it to be
subverted;
» on AVERAGE groups are balanced with all
known and UNKNOWN variables or covariates.
Methods of Randomisation
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Simple randomisation
Stratified randomisation
Paired randomisation
Pairwise randomisation
Minimisation
Simple Randomisation
• This can be achieved through the use of
random number tables, tossing a coin or
other simple method.
• Advantage is that it is difficult to go wrong.
Simple Randomisation:
Problems
• Simple randomisation can suffer from
‘chance bias’.
• Chance bias is when randomisation, by
chance, results in groups which are not
balanced in important co-variates.
• Less importantly can result in groups that
are not evenly balanced.
Other reasons?
• Clinicians don’t like to see unbalanced
groups, which is cosmetically unattractive
(even though ANCOVA will deal with
covariate imbalance)
• Historical – Fisher had to analyse trials by
hand, multiple regression was difficult so
pre-stratifying was easier than poststratification.
Stratification
• In simple randomisation we can end up
with groups unbalanced in an important
co-variate.
• For example, in a 200 patient trial we
could end up with all 20 diabetics in one
trial arm.
• We can avoid this if we use some form of
stratification.
Blocking and stratification
• To stratify we must use some form of
restricted allocation – usually blocking.
• One CANNOT stratify unless the
randomisation is restricted.
Blocking
• A simple method is to generate random
blocks of allocation.
• For example, ABAB, AABB, BABA, BBAA.
• Separate blocks for patients with diabetes
and those without. Will guarantee balance
on diabetes.
Blocking and equal allocation
• Blocking will also ensure virtually identical
numbers in each group. This is NOT the
most important reason to block as simple
allocation is unlikely to yield wildly different
group sizes unless the sample size is tiny.
Blocking - Disadvantages
• Can lead to prediction of group allocation if
block size is guessed.
• This can be avoided by using randomly
sized blocks.
• Mistakes in computer programming have
led to disasters by allocating all patients
with on characteristics to one group.
Pairing
• A method of generating equivalent groups
is through pairing.
• Participants may be matched into pairs or
triplets on age or other co-variates.
• A member of each pair is randomly
allocated to the intervention.
Pairing - Disadvantages
• Because the total number must be divided
by the number of groups some potential
participants can be lost.
• Need to know sample in advance, which
can be difficult if recruiting sequentially.
• Loses some statistically flexibility in final
analysis.
Pairwise randomisation
• Sometimes we want to balance allocation
or make it predictable by centre to ensure
resources are fully utilitised (e.g., surgical
slots). Stratified randomisation by centre
increases predictablility.
• An alternative is to recruit at least 2
participants at a time and then randomise
1 to the intervention – note this not the
same as matched or paired randomisation.
Non-Random Methods
Minimisation
• Minimisation is where groups are formed
using an algorithm that makes sure the
groups are balanced.
• Sometimes a random element is included
to avoid subversion.
• Can be superior to randomisation for the
formation of equivalent groups.
Minimisation Disadvantages
• Usually need a complex computer
programme, can be expensive.
• Is prone to errors as is blocking.
• In theory could be subverted.
Example of minimisation
• We are undertook a cluster RCT of adult
literacy classes using a financial incentive.
There were 29 clusters we want to be sure
that these are balanced according to
important co-variates: size; type of higher
education; rural or urban; previous
financial incentives.
How does it work?
• The first few classes are randomly
allocated.
• After this we calculate a simple score
based on our covariates to achieve
balance.
Which covariates?
• We wanted to ensure the trial was
balanced on the following:
» Type of institution (FE or other);
» Location (rural or urban);
» Size of class (<8 or 8+)
» Previous use of incentives (yes or no).
28 randomised
Covariate
FE
Other
Rural
Urban
8+
<8
Incentive
No
Intervention
6
8
5
9
5
9
2
12
Control
8
6
6
8
6
8
1
13
th
29
class
• This class has the following
characteristics:
» Not FE;
» Urban
» Large (8+)
» No previous incentive.
Covariate
FE
Other
Rural
Urban
8+
<8
Incentive
No
Total
Intervention
Control
6
8
5
9
5
9
2
12
34
8
6
6
8
6
8
1
13
33
th
29
Class
• Because the control group has the lowest
number 33 the 29th class is allocated to
this and not the intervention.
• This will balance the groups across all the
covariates.
• If the totals are the same then
randomisation is used.
Outcomes of Trial
• Our main aim was to see if incentives
would increase the number of sessions
attended.
• The results was that on average 1.53
FEWER sessions were attended in the
intervention group than the control (95%
CIs 0.28, 2.79; p = 0.019).
Allocation – current practice
• In 2002 Hewitt et al, identified 232 RCTs in
the: BMJ; JAMA; Lancet; New Engl J Med.
• Only 19 (8%) used simple unrestricted
randomisation.
Types of Allocation in 4 general medical journals
Minimisation
17 (7.3%)
Block size small and fixed
50 (21.6%)
Block size large and fixed
18 (7.8%)
Block size mixed
15 (6.5%)
Block size random
5 (2.2%)
Block size unclear
27 (11.6%)
Simple
21 (9.1%)
Unclear
79 (34.1 %)
Total
232
Confused trialists?
• “randomisation was done centrally by the coordinating
centre. Randomisation followed computer generated
random sequences of digits that were different for each
centre and for each sex, to achieve centre and sex
stratification. Blocking was not used”. (Durelli et al)
• “randomisation was stratified according to the hospital
and tumour site (esophagus or cardia). No blocking was
used within each of the four strata”. (Hulsher et al).
Durelli et al, Lancet 2002;359:1453-1460
Hulsher et al, NEJM 2002; 2002;347:1662-1669
Conclusions
• Random allocation is USUALLY the best method
for producing comparable groups.
• Simple randomisation is usually best for large
samples sizes (e.g., 100+ allocation units)
• Alternation even if scientifically justified will
rarely convince the narrow minded evidence
based fascist that they are justified.
• Some health service researchers as well as
clinicians are still resistant to the idea of random
allocation.