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In a controversial show about cholesterol drugs, the Australian (ostensible) science show, Catalyst, reported an interview with Professor Rita Redberg:

Professor Rita Redberg: There are a lot of ways that one can manipulate data in a trial. Trials do what they call a washout period, and what that means is before they choose the people that are going to be in the trial, they give everybody the drug, and the people that have side effects get excluded from the trial. And they say that so people aren't uncomfortable when they are in the trial. But of course it takes out all the people that have side effects, and that's very commonly done in drug trials.

Dr Maryanne Demasi: So the side effects would be grossly underestimated.

Professor Rita Redberg: Yes, it would definitely grossly underestimate the number of people that have side effects. They're not as safe as they're made out to be, no.

However, Wikipedia's definition of washout period suggests it is a period without treatment.

Do clinical trials that measure drug side-effects use washout periods to screen out people with side-effects from the study, and thus bias their figures?

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Summary

Wash-out periods are periods without treatment between cross-over trials to minimize carry-over between the trials.

What the quoted discussion is talking about is a run-in period, where participants either given placebo or active treatment prior to the study with the intention of excluding non-compliant participants or participants with intolerable side effects.

Definitions

From http://www.cochrane.org/glossary:

Run-in period: A period before randomisation when participants are monitored but receive no treatment (or they sometimes all receive one of the study treatments, possibly in a blind fashion). The data from this stage of a trial are only occasionally of value but can serve a valuable role in screening out ineligible or non-compliant participants, in ensuring that participants are in a stable condition, and in providing baseline observations. A run-in period is sometimes called a washout period if treatments that participants were using before entering the trial are discontinued.

From http://www.cochrane-net.org/openlearning/html/modA2-3.htm:

In the acupuncture trial, a three-week 'washout' period was built into the trial between the two treatment periods. This is a common method to minimize 'carry-over' effects and ensure the participant is in the same state at the beginning of each period, though it is not always sufficient.

From http://handbook.cochrane.org/chapter_16/16_4_2_assessing_suitability_of_cross_over_trials.htm:

Many cross-over trials include a period between interventions known as a washout period as a means of reducing carry-over.

Effect on external validity

From http://apps.who.int/rhl/Lancet_365-9453.pdf:

Pre-randomisation run-in periods are also often used to select or exclude patients. In a placebo run-in, all eligible patients receive placebo and those who are poorly compliant are excluded. There can be good reasons for doing this, but high rates of exclusion will reduce external validity. For example, one trial of the effect of salts on blood pressure excluded 93% of patients in a placebo run-in period. Active treatment run-in periods in which patients are excluded if they have adverse events or show signs that treatment may be ineffective are excluded are more likely to undermine external validity. For example, two RCTs of carvedilol, a vasodilatory blocker, in chronic heart failure excluded 6% and 9% of eligible patients in treatment run–in periods because of worsening heart failure and other adverse events, some of which were fatal. In both trials, the complication rates in the subsequent randomised phase were much lower than in the run-in phase.

So, yes, run-in periods that exclude a high number of participants have lower external validity.

How to account for this when reading or doing research

See (Berger and Durkalski) and (Brittain and Wittes).

The effect of run-in periods on research simply changes how we should expect the results of these studies to transfer to practical treatment. In the case of compliance-based exclusion, a follow-up pragmatic study (Roland and Torgerson) would reveal the discrepancy. In the case of exclusion based on adverse effects, sometimes that test-dosing is reported. While the external validity of the eventual study may be lessened, good studies will make this limitation clear, describe the demographics of the selected participants, and provide details about the pre-trial exclusion. Be alert for large numbers of unexplained pre-trial exclusions.

References

Berger, Vance W., and Valerie L. Durkalski. "Run‐In Period." Wiley Encyclopedia of Clinical Trials.

Brittain, Erica, and Janet Wittes. "The run-in period in clinical trials: the effect of misclassification on efficiency." Controlled Clinical Trials 11, no. 5 (1990): 327-338.

Roland, Martin, and David J. Torgerson. "Understanding controlled trials: What are pragmatic trials?." Bmj 316, no. 7127 (1998): 285.

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