Dear Laszlo,
The principle of recruiting a greater number to one group than to the
other is well established in epidemiology (e.g. in a case-control study,
recruiting multiple controls per case owing to limited availability of the
latter; pretty much the situation you describe). You may therefore find
support for this approach in the epidemiology literature (though probably
with reference to logistic models rather than the t test).
I don't have it to hand, but I seem to recall that Stuart Pocock's book
'Clinical Trials' discusses unequal allocation, mainly in relation to
power, so there may also be something there that you can cite in your
support.
Also, John Matthews says 'Unequal allocation can be very useful and is
probably underused in practice: it can provide investigators with greater
experience of a new treatment and may even encourage recruitment in
certain trials' ('Introduction to Randomized Controlled Clinical Trials',
2nd ed, p54). A slightly different motivation for the practice than in
your study, admittedly, but an endorsement nonetheless.
Unequal allocation makes the t test less robust to any violations of its
assumptions, especially homogeneity of variance, so maybe you could
reassure the reviewer on this, in case that is what is worrying him/her.
Best wishes,
Julius
> dear list members,
>
> i would be grateful for opinion from the statistical community on an
> issue i first thought trivial, but later... here it goes:
>
> we recruited n1 = 200 patients of a disease and n2 = 380 healthy
> controls to compare them in terms of some outcome using t tests.
>
> as part of a publication process in a reputable journal which shall
> remain unnamed, a reviewer complained that this setting is unbalanced;
> n1 should be equal to n2.
>
> assuming that the reviewer wants to see the principle "50-50% split
> gives greatest power" upheld, we explained in a rebuttal that n1 was
> limited by factors beyond our control, while n2 was not, so the choice
> was either to limit n2 (and the test's power) artificially to ensure
> balance or to put allocated study resources to good use and recruit more
> controls and, with them, extra power and precision for our analysis.
>
> they still, however, insist that balance is all crucial. clearly, we
> cannot now (and could not have at design time) set n1 = n2 = 290. the
> only way we could satisfy them would be by throwing away a random 180
> extra controls and re-analyzing with n1 = n2 = 200.
>
> my key question: could the reviewer be right on this? are there any
> circumstances under which the trade-off bottom line between a
> full-balance, lower power and a broken-balance, higher power approach
> favors the former, if these are the only two options? if not, are there
> any literature sources (or word from high-up stats experts) explicitly
> clarifying this issue, something we can refer to rather than expect them
> to take our word for it?
>
>
> on a more general note, what is the current common wisdom on how to
> handle disagreements with peer reviewers on strictly statistical issues?
> i hear "the reviewer is always right" from time to time, but then find
> myself feeling uncomfortable when this happens to go directly counter
> even to the very basics of my med stats education.
>
> best regards,
>
> laszlo
>
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