despite current biological testing. The survey technique

presented here will allow future investigators to generate

continued reference estimates of the prevalence of doping.

Key Points

Although elite athletes routinely receive biological

tests to detect prohibited doping, these tests likely

fail to detect many cutting-edge doping techniques,

and thus the true prevalence of doping remains

unknown.

We utilized a ‘‘randomized response technique’’—a

method that guarantees anonymity for individuals

when answering a sensitive question—to estimate

the prevalence of past-year doping at two major

international athletic events: the 13th International

Association of Athletics Federations World

Championships in Athletics (WCA) in Daegu, South

Korea and the 12th Quadrennial Pan-Arab Games

(PAG) in Doha, Qatar, both held in 2011.

After performing numerous sensitivity analyses,

assessing the robustness of our estimates under

various hypothetical scenarios of intentional or

unintentional noncompliance by respondents, we

found that the prevalence of past-year doping was at

least 30% at WCA and 45% at PAG.

These ﬁndings suggest that biological testing greatly

underestimat es the true prevalence of doping in elite

athletics, and indicate the need for future studies of

the prevalence of doping in athletics using

randomized response techniques.

1 Introduction

Recent decades have seen increasingly sophisticated bio-

logical testing programs to deter doping among athletes,

especially at elite international competitions [1–3]. Among

Olympic-level athletes tested between 1987 and 2013, the

percentage of positive test results has ranged from 0.96% to

2.45% [1]. However, with sophi sticated modern dopin g

schemes [4–8], many athletes may beat the tests. Given the

numerous recent highly publicized doping scandals in

major sports [9–11], one might guess that the proportion of

such undetected cheats is high. Nevertheless, the true rates

of both false-negative and false-positive cases among tes-

ted athletes remain unknown, while subject to much con-

tinuing speculation and debate [12–15]. Several recent

commentaries have suggested technical, human, political,

and ﬁnancial factors that may have contributed to ﬂawed

results from current biological testing techniques

[

4, 16, 17]. Unfortunately, however, one cannot estimate

the rates of such false test results without an estimate of the

true underlying prevalence of doping [12, 18].

To pursue this issue, we assessed the prevalence of doping

at two major international athletic competitions using a novel

method, the so-called ‘‘randomized response technique

(RRT).’’ This technique allows investigators to pose sensi-

tive questions to respondents in a manner that visibl y guar-

antees the respondent’s anonymity—thus encouraging

truthful responses. The basic idea of the technique and its

variants is to include a random element that masks each

individual’s answer to the sensitive question, thereby

encouraging honest reports (for reviews see [19, 20]). An

extensive meta-analysis of RRT research [21] has shown that

these survey techniques indeed resu lt in more valid data than

conventional question-and-answer methods.

The RRT was originally developed by Warner in 1965

[22] to estimate the propor tion p

of ‘‘yes’’ answers to

sensitive questions on issues where a respondent might be

reluctant to disclose the true answer for fear of loss of

conﬁdentiality or other reasons. In Warner’s model, the

respondent receives one of two questions about a sensitive

issue. For example, Question A might be, ‘‘have you ever

used illicit drugs?’’ while Question B would be the reverse

question, ‘‘have you never used illicit drugs?’’ There is a

known probability p that the respondent will receive

Question A, and the complementary probability 1—p that

the respondent will receive Question B. A random element

(e.g., the throw of a die seen only by the respondent)

determines which of the two questions the respo ndent

receives. Thus, when the investigators obtain a ‘‘yes’’ or

‘‘no’’ answer from a given respondent, they cannot know

the status of that speciﬁc respondent on the sensitive item,

since they cannot know which of the two questio ns that

particular individual has received and answered. However,

given a large survey population, and knowing the value of

p and the total number of ‘‘yes’’ answers, the investigators

can estimate the prevalence of the sensitive item in the

overall population. However, one limitation of Warner’s

original techniq ue is that both questions involve the sen-

sitive topic. Thus, some respondents may believe that there

is a trick that enables the investigators to ﬁgure out their

real status on the sensitive item. To address this problem

and make Warner’s procedure psychologically more

acceptable, Greenberg, Abul-Ela, Simmons, and Horvitz in

1969 [

23] proposed the unrelated question model (UQM;

see Fig. 1). Although the basic proce dure of the UQM is

analogous to Warner’s technique, Question B is replaced

by a neutral question, such as ‘‘think of someone close to

you whose birth date you know, and answer ‘yes’ if that

person was born during the ﬁrst half of the year.’’ In this

212 R. Ulrich et al.

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