Endgames Statistical question

Allocation bias

BMJ 2009; 338 doi: https://doi.org/10.1136/bmj.b2162 (Published 03 June 2009) Cite this as: BMJ 2009;338:b2162
  1. John Fletcher, clinical epidemiologist
  1. 1BMJ, London WC1H 9JR
  1. jfletcher{at}bmj.com

    Which, if any, of the following methods is unlikely to introduce bias in the allocation of people to treatments in a trial?

    • a) People are matched according to age and sex, and for each person allocated to one treatment, a matching person is allocated to the other

    • b) The clinician treating the person tosses a coin to decide which treatment to give

    • c) People whose initial letter of their last name is in the first half of the alphabet receive one treatment; those in the second half of the alphabet receive the other

    • d) People with an even date of birth receive one treatment, those with an odd date of birth receive the other


    None—Matching for age and sex may reduce bias for these two characteristics but will not eliminate bias due to other characteristics. The more characteristics that are used for matching, the harder it is to find comparable people. Even so, there may be important prognostic factors unknown at the time of the study that can still be unevenly balanced between groups. Randomisation ensures that any imbalance is slight and owing only to chance.

    In order to avoid bias, not only must the allocation mechanism be free from bias but the allocation must also be concealed at the time people enter into the study.

    Tossing a coin is unlikely to be biased, but it is almost too tempting for clinician and patient to toss the coin again if their preferred treatment does not come up heads!

    Allocating by initial letter may introduce ethnic or cultural biases; for example, a lot of Chinese people have last names beginning with X or Y. Date of birth would seem to be an unbiased way of sorting people into two groups. It’s hard to see how even v odd birth date could be associated with personal characteristics.

    Any method that reveals the likely allocation before people are entered into a trial can result in one group or the other being less likely to participate. If, for example, it was known that people with an even birth date would receive placebo, then either the clinician or the patient might decide not to take part if they were particularly troubled by their condition, because they would want to receive an active treatment. This approach could introduce bias by allocating sicker patients to the active treatment arm.


    Cite this as: BMJ 2009;338:b2162

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