Unequal Randomisation

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Unequal Randomisation
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Background

• Most RCTs randomised participants into equally
  sized groups.
• Equal randomisation 11 ratio is statistically
  the most EFFICIENT method.
• For any given TOTAL sample size the most power to
  detect a difference occurs with equal group
  sizes.
• Statisticians usually recommend 11 as this
  satisfies their desire for POWER.

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Allocation Ratios and Power

• Although a ratio of 11 does produce the most
  power ratios of 21 or 32 do not substantially
  reduce power. 21 for example moves a studys
  power from 80 to 75.
• Therefore, quite LARGE imbalances in sample sizes
  have little effect on power.

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Why unequal allocation?

• Sometimes it is better to put more participants
  into one group than another.
• Reasons are as follows
• Practical
• Learning curve
• Cost
• Statistical

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Practical/Administrative

• For some treatments such as group therapy
  sessions there might be a minimum number of
  participants needed to make the group sessions
  viable.
• For example, Hundley et al allocated more women
  in a mid-wives trial to the new intervention in
  order to keep the ward full.

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Learning Curve

• A new technique, e.g. surgery, may require some
  learning. More participants allocated to the new
  treatment can allow a more precise estimate of
  any learning effects.
• For example Garry et al, (BMJ 2004,328,129) used
  unequal allocation in favour of a laparoscopic
  surgery so surgons had more people to practice on.

Interestingly, they did not look at the effects
of learning in their analysis
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Treatment experience

• As well as learning curve we might be interested
  in the side-effect profile of a new treatment.
  For standard therapy side-effects will be well
  established, but for the new treatment there are
  more unknowns. Therefore, we might have more
  people so that we have more power to pick up any
  unknown side-effects.

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Ethics

• Some people advocate unequal allocation to
  minimise exposure to either the control treatment
  or new, hazardous treatment. This suggests, to
  me, that there is a strong belief in one
  treatment, which would question the necessity of
  the trial. I would not use unbalanced allocation
  for ethical reasons.

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Cost

• An important reason, commonly overlooked, is due
  to cost.
• One treatment may be much more expensive than the
  alternative and the trial can be made much
  cheaper if more people are allocated to the
  cheaper treatment.
• Indeed this could make a trial more powerful.

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Cost and power

• ALL trials have a limited budget.
• We want to get MOST power from this money.
• The idea behind putting more people onto the
  cheaper treatment is that it the savings released
  can be used to put MORE people into the trial.

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Cost savings

• Trial cost efficiency may be improved by
  allocating more participants to the less
  expensive treatment and more to the cheaper
  treatment.
• Statistical power can be maintained by increasing
  the sample size.
• OR power can even be increased by recruiting MORE
  participants.

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Optimum Randomisation Ratio

• The most efficient allocation ratio is calculated
  by the square root of the cost ratio of two
  treatments.
• If treatment A costs 4 X as much as treatment B
  then the optimum allocation ratio is 2 or 9 x as
  much then the ratio is 3.

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Example

• MRC Taxol trial for ovarian cancer. The new
  drug, taxol, extremely expensive about 10,000
  per patient.
• In order to reduce costs the trialists allocated
  twice as many women to the control group (21)
  than in the treatment arm.

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Cost Savings of Unequal allocation
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Cost Savings

• By using an unequal allocation ratio the trial
  saved about 1 million.
• Many studies do not have as dramatic cost
  difference but important savings can still be
  made.

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Hip Protector Trial

• In the hip protector trial a key additional cost
  was the cost of the hip protectors (about 80 per
  person for 3 pairs including postage).
• The cost of controls, after recruitment costs,
  was mailing out follow-up qnaires.

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Estimating the ratio

• Initially we thought we would recruit 10 of
  women we approached. The cost of the mailout was
  about 1 a person. To recruit 100 women would
  cost 1,000 (10 per person). To follow-up the
  women would be another 5 in postage after
  randomisation (15 in total). The intervention
  group would cost an additiona 80 (95 in total)
  95/15 6.3, square root 2.51.

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Ratio

• We, therefore adopted an allocation ratio of 21.
• BUT recruitment costs went up to 20 per woman
  therefore the ratio of costs were 4.2, square
  root is about 2. Therefore, our optimum ratio
  still remained about 2.

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Cost savings

• We estimated to have saved 10 of our research
  budget by using unequal allocation, which allowed
  us to mail out to more participants (to
  compensate for the unexpected shortfall in
  recruitment) and follow up participants for
  longer.

20
Recruitment with fixed budget

• Increase allocation to control using saved money
  to increase mail out.
• Disadvantages will increase workload for local
  trial co-ordinators in terms of data entry and
  data management.

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Allocation Ratio - lessons

• A fixed allocation ratio is unlikely to be
  correct through the lifetime of a trial.
• Should plan for an adaptive allocation and change
  ratio during recruitment if cost ratio changes.
• Budget planning should probably start with an
  inefficiently high allocation (e.g. 32 or 11)
  ratio and adapt downwards (e.g. 21) as trial
  proceeds if necessary.

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Allocation ratios a review

• What is done in actual practice? To find out we
  are undertaking a review of trials using unequal
  allocation ratios to see why.
• We searched electronic databases using unequal
  allocation, unbalanced randomisation etc, plus
  personal knowledge. We couldnt find many
  trials. This confirms that it is not used widely
  (unfortunately).

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Reasons for unequal allocation
Dumville et al, 2005.
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Other reasons

• Expected variability differs in trial arms. Can
  increase power if more patients are allocated to
  group with larger SD as central limit theorum
  helps improve normality.
• Comparison of two treatment arms vs a control
  treatment (larger numbers in treatment arms to
  increase power of treatment vs treatment
  comparison).

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Comparison of treatments

• We might have 3 arms control dose 1 dose 2.
  To compared dose 1 and 2 we would expect a muted
  treatment response, and therefore, we would need
  larger sample sizes to observe a treatment effect.

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A Digression

• Unequal allocation, if undertaken randomly, STILL
  results in equivalent groups in terms of equal
  distribution of confounders.
• It does NOT lead to BIASED allocation.

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Analysis of unequal allocation

• This is exactly the same as a trial that uses
  equal allocation EXCEPT if the allocation ratio
  changes part of the way through the study. If
  the allocation does change this needs to be taken
  into account in the analysis.

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Summary

• Most trials have unequal costs and probably could
  benefit from unequal randomisation.
• Most trials use even allocation.
• WARNING - many grant referees do NOT understand
  unequal allocation and some see it as
  UNSCIENTIFIC.