Allocation Methods

1
Allocation Methods

• David Torgerson
• Director, York Trials Unit
• djt6_at_york.ac.uk
• www.rcts.org

2
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.

3
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.
4
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.

5
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.

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Why do we randomise?

• (1) Avoid selection bias
• (2) Controls for temporal effects
• (3) Controls for regression to the mean
• (4) Basis for statistical inference

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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.

8
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.

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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.

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Non-random methodsAlternation

• 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.

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Non-Random MethodsQuasi-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.

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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 co-variates.

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Methods of Randomisation

• Simple randomisation
• Stratified randomisation
• Paired randomisation
• Pairwise randomisation
• Minimisation

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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.

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Simple RandomisationProblems

• 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.

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Other reasons?

• Clinicians dont 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
  post-stratification.

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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.

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Blocking and stratification

• To stratify we must use some form of restricted
  allocation usually blocking.
• One CANNOT stratify unless the randomisation is
  restricted.

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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.

20
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.

21
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.

22
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.

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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.

24
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.

25
Non-Random MethodsMinimisation

• 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.

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Minimisation Disadvantages

• Usually need a complex computer programme, can be
  expensive.
• Is prone to errors as is blocking.
• In theory could be subverted.

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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.

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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.

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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 (lt8 or 8)
• Previous use of incentives (yes or no).

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28 randomised
Covariate Intervention Control
FE 6 8
Other 8 6
Rural 5 6
Urban 9 8
8 5 6
lt8 9 8
Incentive 2 1
No 12 13
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29th class

• This class has the following characteristics
• Not FE
• Urban
• Large (8)
• No previous incentive.

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Covariate Intervention Control
FE 6 8
Other 8 6
Rural 5 6
Urban 9 8
8 5 6
lt8 9 8
Incentive 2 1
No 12 13
Total 34 33
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29th 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.

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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).

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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.

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Types of Allocation in 4 general medical journals
 
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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 20023591453-1460 Hulsher
et al, NEJM 2002 20023471662-1669
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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.