How Many Subjects?: Statistical Power Analysis in Research by Helena Chmura Kraemer & Christine Blasey

Author:Helena Chmura Kraemer & Christine Blasey
Language: eng
Format: epub
ISBN: 9781483319551
Publisher: SAGE Publications, Inc.
Published: 2016-07-14T16:00:00+00:00

A baseline variable defines the horizontal axis. The outcome measures the vertical axis. The mean response for participants with each baseline value in the T1 and T2 groups are represented as two straight lines.

Now the expected mean difference between treatment group responses (coded as we have) in the two-group design is β1, and in the matched pairs test is β1, but for a subpopulation matched on a specific M, it is β1 + β3M, which equals β1 only when B is not a moderator of treatment response. If B is a moderator of treatment response, there is no one answer to the question “How good is this treatment for me compared to others like me (in B)? The answer differs depending on what B is. It doesn’t matter which approach is taken—the answer one obtains is that for the typical participant(M = 0), not for any participant.

Then (making normality and equal variance assumptions), if a two-sample test were used,

δ = β1/(β22 + .25β32 + σ2E)1/2

Δ = δ/(δ2 + 4)1/2 (balanced design),

ν = n – 2 (n the number of participants).

If a matched-pairs test were used,

δ = β1/(β32 + 2σ2E)1/2,

Δ = δ/(δ2 + 1)1/2

ν = n – 1 (n the number of pairs).

Which of these two tests is more powerful to test the null hypothesis they both test depends on the reliability of the measure used (σ2E) and then on the relative magnitudes of the effect of B on O and the interactive effect of treatment by B (β2 and β3). The bottom line is that one needs to have a great deal of information on which baseline measures (B) affect treatment outcome in the two groups and exactly how they do so, to make the right decision as to how best to design the study. Moreover, one can interpret what results in either case as the treatment effect on all participants regardless of the B value, only if it is known that B is NOT a moderator of treatment response. Otherwise, the treatment effect should only be interpreted as the treatment effect on the typical participant with B = 0.

There are two messages here: One should not consider “controlling for” any baseline variable that has not already been shown in previous studies to be related to outcome in one or another of the treatment groups, and how one might “control” may be different. The earliest studies comparing two treatments should be simple two-sample designs, “controlling for” no baseline variables. However, when that study is completed, exploratory analyses should be done, using the data from that study, to determine which baseline variables are likely to be irrelevant to treatment outcome and which variables are either nonspecific predictors or moderators of treatment response. These exploratory studies then set up the rationale and justification for future studies that would take baseline characteristics into account, but do so appropriately.

Currently, many researchers argue that all sorts of baseline variables should be “controlled for”: age, sex, education level, race, ethnicity, and so forth. This is done just in case any of these are associated with outcome.

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