The study found that at least 30 per cent of athletes in the 2011 International Association of Athletics Federations (IAAF) World Championships and 45 per cent of athletes at the Pan-Arab Games in 2011 claimed to have taken doping drugs or used other doping methods.
Only a fraction of these cases were detected by biological tests. At the World Championships, 0.5 per cent of biological tests showed positive for doping agents. The figure rose to 3.6 per cent for the Pan-Arab games.
The method ensures the anonymity of the respondents to allow them to answer honestly without fearing negative consequences.
"The randomised response method is used for sensitive topics. In a direct face-to face interview, respondents would be strongly motivated to provide socially desirable responses, even if these responses were not true. Anonymity gives protection, allowing the respondents to answer honestly," said Rolf Ulrich from the University of Tubingen in Germany.
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Therefore, if an athlete answered "yes," the researchers could not tell whether the athlete was answering "yes" to the unobtrusive question or "yes" to the sensitive question - thus guaranteeing the athlete's anonymity.
Researchers used statistical methods to closely estimate the percentage of athletes in the overall study group who had answered yes to the doping question.
"As we note in the paper, this is probably due to the fact that athletes have found various ways to beat the tests," said Pope, who is also a professor at the Harvard Medical School.
Tests immediately before and during a competition find evidence of doping on average of only 1-3 per cent.
However, doping agents are often no longer biologically detectable at this time if they have been taken long before.
Somewhat better results are achieved with the "biological passport," which tracks the athlete's medical data and offers a higher detection rate of about 14 per cent.