Random and Quasi-random Allocation

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Random and Quasi-random Allocation
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Background

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

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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!

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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.

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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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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.

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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.

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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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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.

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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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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.

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Non-random methodsTrue 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.

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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
• 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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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.

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

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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.

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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.

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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.

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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.

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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.

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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
  detre for being there as they know various
  obscure clinical characteristics on which to
  stratify).

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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.
• Can reduce the statatistical power of the study.

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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).

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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.

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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.

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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).

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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.

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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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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.

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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.

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Example of minimisation
I C Next
FE Other 6 8 8 6 Other
Rural Urban 5 9 6 8 Urban
8 lt8 5 9 6 8 8
Incent No 2 12 1 13 None
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Example of minimisation
I C Next I 34
FE Other 6 8 8 6 Other C 33
Rural Urban 5 9 6 8 Urban Next goes to C
8 lt8 5 9 6 8 8
Incent No 2 12 1 13 None
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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

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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.

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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.

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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.

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Which is the RCT?

• Study A or Study B?

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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.