Random and Quasi-random Allocation Presentation

Surprisingly many researchers do not understand the concept of random allocation.
For example, a Professor of Psychiatry criticising the WHI study’s findings that HRT increased all cause dementia, was critical because the researchers failed to measure the genetic susceptibility of the women to Alzheimer’s Disease.

1. Random and Quasi-random
Allocation

2. Background

Surprisingly many researchers do not
understand the concept of random
allocation.

For example, a Professor of Psychiatry
criticising the WHI study’s findings that
HRT increased all cause dementia, was
critical because the researchers failed to
measure the genetic susceptibility of the
women to Alzheimer’s Disease.

3. As one researcher put it

“Whilst it is possible for all or the
majority of the 16,000 women with a
genetic susceptibility to dementia to
be allocated into the HRT arm it is
about as likely as Elvis Presley landing
a UFO on top of the Loch Ness
monster”.

BUT – I believe Elvis Presley lives!

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.

6. 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.

7. The Quest for 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.

8. 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.

9. The unknown unknowns
Those things we know about we can
measure (e.g., age);
Those things we know are unknown
(health status) we can often control for
(e.g, proxy for health status SF36?);
Those things that affect outcome that
we do not know or cannot know is why
we randomise.

10. 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.

11. Born in August and British?

BAD Luck.

August born children get a raw deal from the
UK educational system as they are young for
their year and consequently comparisons
between August children and September
children show August children do better.

Consequently quasi-alternation by month of
birth will be biased towards the September
group.

12. Non-random methods:
“True “ Alternation
Alternation is where trial participants are alternated
between treatments.
EXCELLENT at forming similar groups if alternation is
strictly adhered to.
Austin Bradford-Hill one of the key developers of
RCTs initially advocated alternation because:

It is easy to understand by clinicians;

Leads to balanced groups if done properly.
BUT Problems because allocation can be predicted
and lead to people withholding certain participants
leading to bias.

13. 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.

14. Methods of Randomisation

Simple randomisation

Stratified randomisation

Paired randomisation

Minimisation

15. 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.

16. 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.

17. Why is chance bias a
problem?

Unless you are able to ‘adjust’ for co-
variates in the analysis imbalance can
result in bias.

For small samples it is possible for a
numerical imbalance to occur with a
consequent loss of power.

18. 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 post-stratification.

19. 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 or most of the
20 diabetics in one trial arm.
We can avoid this if we use some
form of stratification.

20. 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.

21. 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.

22. 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.

23. Too many variables.

Many clinicians want to stratify by
lots of variables. This will result in
cells with tiny sample sizes and can
become impracticable to undertake.

24. Centre Stratification

Many, if not most, trials that stratify
stratify by centre. This can lead to
the predictability of allocation so that
subversion can occur.

25. Stratification Disadvantage

In trial steering meetings often large
amounts of time are WASTED
discussing what variables to stratify by.

Many amateur trialists think it is very
important to stratify (perhaps it gives
them a raison d’etre for being there as
they know various obscure clinical
characteristics on which to stratify).

26. 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.

27. 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.
Can reduce the statatistical power of the
study.

28. Summary allocation
methods

If your trial is large (which it should
be if you are doing proper research),
then I would generally use simple
randomisation as this has strong
advantages over the other
approaches (exception being cluster
trials).

29. The ‘Average Trial’
ON AVERAGE trials are balanced across all
variables. But some trials will be
unbalanced across some variables.
What will happen?

Large imbalance in trivial variables (we have
more women called Mavis who were born on a
Monday in the intervention group);

Small imbalance in important variables (e.g.,
age);

Even small imbalances can lead to a biased
estimate.

30. What can we do?

“If it exists, we can measure it, if we can
measure it, we can put it into a regression
equation” (Health Economist).

IMPORTANT measurable variables (e.g., age,
baseline health status) SHOULD be adjusted
for in ANCOVA (regression analysis). This
‘post-stratification’ deals with any chance
imbalance, and even if there is no
imbalance increases the power of the study.

31. What about my small cluster
trial?
Cluster trials are an exception – small
units of allocation can easily lead to
imbalance at the cluster level. Also,
whilst it is possible to adjust using
sophisticated statistical methods of
cluster level imbalances if we were
sure of balance we can use simple
cluster means t-test (albeit with some
loss of power).

32. Randomising clusters

Two ways to do this:

We can use stratified random allocation
but with small effective sample sizes we
can easily have empty cells.

OR we can use minimisation.

33. 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.

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

35. Cluster trials and balance
In cluster trials (where we randomise
groups of participants, e.g., patients
of GPs) there are usually very few
clusters (e.g., 20-30 or fewer).
Chance imbalance can easily occur.
Some form of restricted allocation is
usually necessary. Because units of
allocation are known in advance this
avoids subversion.

36. Example of minimisation

We are undertaking a cluster RCT of
adult literacy classes using a financial
incentive. There are 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.

37. Example of minimisation
I C Next
FE
Other
6
8
8
6
Other
Rural
Urban
5
9
6
8
Urban
8+
<8
5
9
6
8
8+
Incent
No
2
12
1
13
None

38. Example of minimisation
I C Next I = 34
FE
Other
6
8
8
6
OtherC = 33
Rural
Urban
5
9
6
8
UrbanNext
goes to C
8+
<8
5
9
6
8
8+
Incent
No
2
12
1
13
None

39. What is wrong with?

“In this randomised study, we took a
random sample of doctors from the
Southern area where guideline A was
being implemented and compared
their outcomes with a random
sample of doctors from the Northern
area where there was no guideline”

40. Is this OK?

“We randomised doctors into two
groups using a telephone
randomisation service. We then took
a random sample of patients from
each group and compared the effect
of guidelines on their health status”.

41. Study A

From a database of 2000 heroin addicts
we will take a random sample of 1,000
and randomise these into two groups of
500 each. The intervention group will
be offered pharmaceutical heroin. The
control group will not be contacted.

At 6 months both groups will be invited
attend a clinic to measure outcomes.

42. Study B

From a database of 2000 heroin addicts we
will take a random sample of 500 this
group will be offered pharmaceutical
heroin.

At 6 months we will invite these addicts to
attend a clinic to measure outcomes. At
the SAME time we will take another
random sample of 500 addicts and
measure their outcomes.

43. Which is the RCT?

Study A or Study B?

44. Conclusions

Random allocation is USUALLY the
best method for producing
comparable groups.

Alternation even if scientifically
justified will rarely convince the
narrow minded evidence based fascist
that they are justified.

Best to use random allocation.