Poor dental hygiene is a risk factor for dental diseases.1,2 In a survey of dental hygiene in China, 31% of 20–29 year olds admitted to brushing their teeth less than twice a day.3 The validity of these estimates may be questioned, however, because self-reported hygiene practices are likely to be distorted owing to socially desirable responses.4–6 Validation studies comparing self-report data against gold standard measures have repeatedly shown over-reporting of desirable behaviors such as physical activity7 and under-reporting of undesirable behaviors such as drug use,8,9 energy intake,10,11 and sexual risk behavior.12 Thus, there is reason to suspect that these reported prevalence estimates of dental hygiene habits may have been inflated by social desirability bias.
The randomized-response technique13 was developed to overcome this response bias by increasing the confidentiality of responses. The basic idea is to add random noise to the responses such that there is no direct link between a participant's response and his or her true status.14 In the forced-response variant15 of this technique, a randomization device (with known probability distribution) is used to determine whether participants are asked to respond truthfully or whether they are prompted to provide a prespecified response regardless of their true status. This procedure guarantees that affirmative responses are no longer unequivocally linked to a socially undesirable attribute and therefore no longer stigmatizing for the participants. Consequently, the randomized-response technique encourages more honest responses and, in turn, may provide more valid prevalence estimates of sensitive issues, such as drug use16–18 and sexual behavior.19,20
Despite its successful applications,21,22 the randomized-response technique has been criticized as being susceptible to respondents who are not answering as directed by the randomization device.23 The randomized-response technique underestimates the prevalence of sensitive behaviors to the extent that participants fail to comply with the instructions by denying a sensitive attribute even when prompted to admit to it by the randomization device.
Addressing this issue, Clark and Desharnais24 proposed a cheating-detection modification of the randomized-response technique to explicitly assume that some respondents might fail to comply with the instructions. The modification (Fig.) divides the population into 3 distinct and disjoint groups. The first group (π) consists of compliant respondents who honestly admit being carriers of the sensitive attribute. The second group (β) consists of compliant respondents who truthfully deny the sensitive attribute. The third group (γ = 1 − π − β) consists of noncompliant cheaters who do not conform to the instructions by denying the sensitive attribute irrespective of the randomization process. By symmetry, there may also be respondents who are not carriers of the sensitive attribute but claim it. However, we expect that such a self-incriminating behavior is rare, and we, therefore, ignore it in the model.24
It is important to note that nothing is assumed regarding the true status of noncompliant respondents. It is conceivable that these respondents deny a sensitive behavior in which they have been engaged, but it is also possible that innocent respondents want to rule out even the slightest suspicion and therefore deny that they committed an undesirable act despite being told otherwise by the randomization procedure. The estimated proportion of cheaters can be used to compute an upper bound in a worst-case scenario, which assumes that all noncompliant respondents are, in fact, carriers of the sensitive attribute.25,26
To explore the magnitude of response bias in self-reported hygiene habits, the cheating-detection modification was employed to investigate teeth-brushing behavior among Chinese college students. In addition, the modification was compared with an anonymous self-report measure to estimate how much response bias can be reduced by this method.
A total of 2254 (55% women; aged 18–24 years) undergraduates from the University of Beijing, China, volunteered to participate in this study. Students completed the questionnaire during their regular classes.
Measures and Procedures
The participants completed an anonymous questionnaire comprising demographic information, several questions not pertinent to this study, and the sensitive question: “Do you brush your teeth at least twice a day?” The participants were randomly assigned to 1 of 3 conditions. Two conditions with different probabilities of being prompted to reply “no” (P1 and P2) are required to make the cheating-detection modification identifiable.24 The participants' month of birth was used as the randomization device to keep the randomization procedure simple and transparent. In the low probability condition (P1: n = 900; 56% women), participants born in January or February were instructed to reply “no” independently of their true behavior, whereas participants born in another month were prompted to reply truthfully. In the high probability condition (P2: n = 891; 54% women), participants born in January or February were asked to respond truthfully, whereas the remaining participants were prompted to reply “no.” According to birth statistics provided by the National Bureau of Statistics of China, the randomization probabilities P1 and P2 approximated 0.17 and 0.83, respectively. In the direct questioning condition (n = 463, 54% women), participants were simply asked to respond truthfully.
Closed-form solutions24 for parameter estimation in the cheating-detection modification do not allow a statistical comparison of subgroups. We, therefore, conducted our analysis within the more general framework of multinomial models.27–29 By converting the nonbinary tree model into a statistically equivalent binary tree representation (for details, see Ostapczuk et al25), established statistical procedures of multinomial modeling can be used to estimate the parameters and to test restrictions on them. Parameter estimates were obtained by minimizing the asymptotically χ2-distributed log-likelihood ratio statistic G2 using the EM-algorithm.27,30
There were sizeable differences in the proportion of men (35%; SE = 3.3) and women (10%; SE = 1.9) admitting insufficient teeth brushing behavior with direct questioning. The cheating-detection modification was therefore estimated separately by sex (Table).
Using the cheating-detection modification, πm = 51% (SE = 3.2) of men and πf = 20% (SE = 2.7) of women reported insufficient dental hygiene. The estimates were considerably higher than the estimates with direct questioning for both men and women, indicating substantial under-reporting with direct questioning. Moreover, a substantial proportion of noncompliance with the instructions was observed for both men (γm = 10.1%; SE = 2.4) and women (γf = 13.0%; SE = 2.5).
Depending on whether noncompliant respondents were considered to have engaged in insufficient teeth brushing, the lower-bound estimate for the proportion admitting to insufficient teeth brushing was πm = 51% for men and πf = 20% for women; the respective upper-bound estimate was πm + γ = 62% for men and πf + γ = 32% for women.
Survey data may reflect what respondents want to tell the investigator, rather than their actual behavior. We used a cheating detection modification of the randomized-response-technique to improve the validity of response data on dental hygiene habits in a sample of Chinese college students. Consistent with previous studies, only 35% of men and 10% of women reported insufficient dental hygiene habits when questioned directly. When the cheating-detection modification was employed, however, the proportions increased considerably for men, and almost doubled for women. Assuming that all noncompliant respondents in fact brushed their teeth less than twice a day, the upper-bound prevalence estimate of insufficient dental hygiene habits in the present sample was 62% for men and 32% for women. Prevalence estimates of dental hygiene habits may also be positively biased in other populations. More generally, direct questioning may provide strongly distorted prevalence estimates in surveys of socially undesirable behavior. The same is also true, however, for traditional variants of the randomized-response technique not capable of detecting cheating, because the prevalence of a sensitive attribute is underestimated to the extent there is noncompliance with instructions.
Several limitations should be considered. First, randomized-response models introduce random error and induce greater sampling variance. The randomized-response technique, therefore, requires considerably larger samples than a direct question. This loss of efficiency is outweighed by a gain in precision only when the attribute under investigation is sufficiently sensitive. Second, the randomized-response technique is more complicated to administer because the respondents have to understand how the randomized-response technique protects their privacy.31 Although the randomized-response technique has been successfully used with older and less educated respondents, noncompliance rates tend to increase in such populations.14,26,32,33 Finally, as the true status of any individual remains unknown, it is difficult to compute measures of association between an randomized-response-technique-variable and other variables of interest.34–36 Such limitations notwithstanding, the cheating-detection modification provides a means to improve prevalence estimates of sensitive behaviors, and may be useful in epidemiologic surveys of sensitive behaviors.
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