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Commentary on ‘Measurement in clinical trials: A neglected issue for statisticians?’

Julious and Senn have hit a raw nerve: why is that we statisticians, we self-defined stewards of data, are so cavalier about measurement? The authors offer some examples of our failure as a profession to consider measurement seriously. I cannot resist adding some of my personal pet peeves to their list. Many protocols present sample sizes to the nearest whole digit. A typical sample size calculation uses standard ingredients: a comfortable alpha and beta, a median time to failure (calculated from unreliable historical data) measured in months, a projected rate of loss to follow-up plucked from some arbitrary guess, and a effect size that satisfies some mixture of prior data and hope. But the sample size for a two-group study will be so precise, something like 431. Another example comes from reporting p-values calculated to four (or five or six) significant figures. In chemistry or physics laboratories, high-school students are graded down for false precision; why do so many statisticians think that imprecise inputs and asymptotic approximations lead to finely honed probabilities? My examples are irritants much less important than the issues Julious and Senn raise, but they provide a window into the same phenomenon—statisticians’ frequent failure to think seriously about the meaning of numbers. The authors’ catalogue of ways by which statisticians ignore fundamental principles of measurement is sobering. I am often amused—and frustrated—when statisticians capitulate to a clinician’s plaint that ‘you statisticians might like such-and-such, but so-and-so is more clinically interpretable.’ The authors address several of these plug-in-the-blanks: if such-and-such is ‘change’, so-and-so might be ‘percentage change’; if such-and-such is ‘analysis of covariance’, so-and-so might be ‘change-score’. How can some measure be more clinically interpretable if it is less statistically valid or less efficient than another one? The examples the authors present of failure to recognize when a measurement incorporates a post-treatment parameter provide important warnings to statisticians and clinicians alike. These ‘outcome–outcome’ analyses, which are conditional on some post-treatment effect, are all too common in medical studies and journals. We should all heed the authors’ warning about degradation of continuous variables into ordered categories, analyses of ordered categories ignoring the order, and arbitrary definitions of ‘responders’ that can lead to absurdities. I disagree, however, with the authors if they are making a blanket recommendation against dichotomizing continuous variables. As the authors remind us, if the data