Individual response to treatment: is it a valid assumption?
BMJ 2004; 329 doi: https://doi.org/10.1136/bmj.329.7472.966 (Published 21 October 2004) Cite this as: BMJ 2004;329:966
- Stephen Senn (stephen@stats.gla.ac.uk), professor of statistics1
- 1 Department of Statistics, University of Glasgow, Glasgow G12 8QQ
- Accepted 11 August 2004
Introduction
Imagine a trial with 1000 representative patients, chosen from a population of patients with erectile dysfunction, until now resistant to treatment. Each is given the opportunity of trying a new treatment once. Seven hundred succeed in gaining an erection; the other three hundred fail. How should we interpret these results?
One common interpretation is that the treatment works for 70% of patients 100% of the time and for 30% of the patients 0% of the time. However, nothing in the data forbids a radically different interpretation—namely, that the treatment works in 100% of the patients 70% of the time. In the first case, ability to succeed on treatment is a permanent feature of the patient. In the second case, individual response cannot be predicted: the patients are indistinguishable from each other regarding response to treatment. They sometimes respond and they sometimes do not. Intermediate cases between these two extremes are, of course, also possible.
Examples of confusion
Most clinical trials do not permit us to distinguish between these two extreme cases or indeed any intermediate case. Yet many trialists plump for the first explanation—that of individual response to treatment—rather than pure random variability. In fact, you do not have to search far in the pages of the BMJ to find examples of the unstated assumption of individual response to treatment dictating the interpretation of clinical trials. I shall consider two from the BMJ and a third example from elsewhere.
My first concerns a statement of Allen Roses, which was reported by Richard Smith, the former editor of the BMJ, as follows: …
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