Are perceived prevalences of infection also biased and how? Lessons
from large epidemics of mosquito-borne diseases in tropical regions
Authors and affiliations:
Jocelyn Raude1,2,3*
Jean-Baptiste Combes1,4
Patrick Peretti-Watel5,6
Jeremy Ward5,6
Claude Flamand7
Pierre Verger5,6,8
1) EHESP Rennes, Université Sorbonne Paris Cité, France;
2) Aix Marseille University, IRD French Institute of Research for Development, EHESP
French School of Public Health, UMR_D 190 “Emergence des Pathologies Virales”,
Marseille, France;
3) UMR PIMIT, INSERM 1187, CNRS 9192, IRD 249. Plateforme Technologique CYROI,
Université de La Réunion, Réunion, France
4) CNRS, UMR 6051 Arènes-CRAPE Centre de Recherches sur l'Action Politique en Europe,
France
5) INSERM, UMR912 "Economics and Social Sciences Applied to Health & Analysis of
Medical Information" (SESSTIM), 13006, Marseille, France;
6) Aix Marseille University, UMR_S912, IRD, 13006, Marseille, France;
7) Institut Pasteur de Guyane, Unité d’Epidémiologie, Cayenne, France;
8) ORS PACA, Southeastern Health Regional Observatory, 13006, Marseille, France.
1
*Corresponding author:
Jocelyn Raude, PhD, Department of Social and Behavioral Sciences, EHESP French School of
Public Health, 15 Avenue du Professeur Leon-Bernard, CS 74312, 35043 Rennes Cedex, France.
Tel.: +33 029 902 2615
Email: [email protected]
Financial support: Financial support for this study was provided in part by grants from the
Health Regional Agencies of Martinique and Guyane, and the French Institute of Microbiology
and Infectious Diseases (IMMI). The funding agreement ensured the authors’ independence in
designing the study, interpreting the data, writing, and publishing the report.
2
ABSTRACT
Objectives: Although people have been repeatedly found to underestimate the frequency of risks to
health from common diseases, we still do not know much about reasons for this systematic bias,
which is also referred to as “primary bias” in the literature. In this study, we take advantage of a
series of large epidemics of mosquito-borne diseases to examine the accuracy of judgments of risk
frequencies. In this aim, we assessed the perceived versus the observed prevalence of infection by
zika, chikungunya or dengue fever during these outbreaks, as well as their variations among different
subpopulations and epidemiological settings.
Design: We used data drawn from 4 telephone surveys, conducted between 2006 and 2016, among
representative samples of the adult population in tropical regions (Reunion, Martinique, and French
Guiana). The participants were asked to estimate the prevalence of these infections by using a natural
frequency scale.
Results: The surveys showed that (1) most people greatly overestimated the prevalence of infection
by arbovirus, (2) these risk overestimations fell considerably as the actual prevalence of these
diseases increased, (3) the better-educated and male participants consistently yielded less inaccurate
risk estimates across epidemics, and (4) that these biases in the perception of prevalence of these
infectious diseases are relatively well predicted by probability weighting function.
Conclusions: These findings suggest that the cognitive biases that affect perception of prevalence of
acute infectious diseases are not fundamentally different from those that characterize other types of
probabilistic judgments observed in the field of behavioral decision-making. They also indicate that
numeracy may play a considerable role in people’s ability to transform epidemiological observations
from their social environment to more accurate risk estimates.
3
INTRODUCTION
The ability for human beings to adequately detect and estimate a variety of risks in their
social and natural environments can be undoubtedly considered as an essential cognitive function
(1). Indeed, inferences about what occurs in the world are critical to decision making, enabling
us to adopt adaptive behaviors in order to avoid harm and preserve health and life. Over the last
decades, an extensive body of research has been devoted to the study of risk perception among
humans (2). Several competing conceptualizations and measures of perceived risk have been
proposed in this the literature–which are undoubtedly due to the intrinsic polysemy of the
concept of risk within and across disciplines (3-4). Nevertheless, a trend can be identified within
health psychology towards the employment of a somewhat narrower definition, which
encompasses perceived likelihood, vulnerability, or susceptibility to harm, such as acquiring a
specific disease (5-6). Using this definition, perceived risk refers mainly to the judgments that
people make about their personal risk of experiencing harm. Such judgments have consistently
been found to motivate people to undertake health protective measures against a vast array of
diseases, such as cancer screening or influenza vaccinations (7-9).
However, given the difficulty of translating population-based estimates of health threats
drawn from large epidemiological or clinical studies into precise and reliable assessments of
personal risk or probability of developing a disease, it remains highly problematic to determine
whether such risk judgments are actually accurate or even unrealistic. As noted by Leventhal
concerning cancer risk (10:81): “Neither the epidemiological nor the biological data alone or in
combination are sufficient to answer the clinician’s or patient’s question: Precisely what is the
probability that (this specific patient/I) will contract a particular type of cancer at a given point in
4
time.” Moreover, many statisticians and philosophers assume that probabilistic rules do not apply
to single events (11). In response to these legitimate criticisms, several authors adopted from the
late 70ies a frequentist perspective to approach and assess health-related risk perception (12-13).
Basically, the frequentist approach consists of asking people to estimate the probability or
frequency of harmful events in specific populations within a given time frame. From this
perspective, risk judgments will be considered accurate (or unbiased) if mean perceived
frequencies correspond to the actual or estimated objective frequencies of harmful events.
In this article, we took advantage of a series of naturally occurring risk events – major
outbreaks of mosquito-borne epidemics in tropical regions – to examine the conditions under
which perceived prevalence of some acute illnesses is more or less biased. Since the early stages
of research on risk perception, it has been shown that people seem to display a range of recurrent
and substantial biases when asked to think about the probability or frequency of adverse events.
It should be noted however that there remains a strong argument as to whether such biases in
judgment of risk frequencies should be attributed to methodological/experimental artefacts or
poor cognitive abilities, including limited memory and computational capacities (14). The main
research questions we want to address here, through the examination of the data collected within
large samples of tropical population in a variety of epidemic settings are the following: Firstly,
do cognitive biases that have been observed in a series of laboratory experiments on judgments
about the relative frequency of a class of events also exist in a more ecologically realistic
situation, in which people are asked to estimate the prevalence of highly visible and widespread
illnesses? Secondly, are cognitive biases in judgments about the frequency of some events,
which have been documented in the experimental psychology literature, specific to WEIRD
(Western, Educated, Industrialized, Rich and Democratic) people or are they potentially
5
universal across sociocultural groups? Given the extensive body of literature that exists on the
socioeconomic and sociocultural variations in non-numerical judgments about a range of health
risks (15-17), it appears reasonable to assume that there may be significant differences among
individuals and groups regarding the nature and magnitude of cognitive biases that affect
numerical judgments about health risks, such as people’s estimates of the prevalence of some
common conditions in a population. Finally, how reliable is the probability weighting model
developed in the field of psychology of judgment and decision-making in predicting the
perceived prevalence of these infectious diseases?
Theoretical background
In a series of famous laboratory experiments aiming to test the basic assumptions of the
standard theory of decision making under risk, cognitive psychologists and behavioral
economists have shown that probabilistic judgments are subject to numerous biases (e.g.,
unrealistic optimism or base rate neglect). These are attributable to a range of cognitive
heuristics we are likely to use to estimate the number or probability of occurrences, such as the
availability, representativeness or affect heuristics (18). In particular, it has been repeatedly
found that people are likely to underestimate more frequent events and conversely, to
overestimate less frequent events. As applied to epidemiological events, this phenomenon of
miscalibration has been called “primary bias” in the psychological literature (14, 19). During the
late eighties, a more fine-grained analysis of this cognitive bias has shown that human perception
of probability or relative frequency is generally characterized by a series of remarkable
properties (20). Primarily, probabilistic judgments are found to be regressive, i.e., there exists an
6
inflexion point above which the perceived frequencies are generally lower than the actual
frequencies of adverse events (and the reverse, in which perceived frequencies are generally
higher than actual frequencies). Secondly, probabilistic judgments are consistently found to be
asymmetrical, i.e., there exists a fixed point at which the perceived frequencies equal the actual
frequencies of adverse events. Thirdly, the probabilistic judgments tend to be s-shaped, i.e., the
perceived risk frequencies are concave until the above-mentioned inflexion point, after which it
is then convex. These empirical findings have led to a model for the perception of risk
probability in behavioral economic literature using non-linear functions of transformation of
objective probabilities, which show that the smaller frequencies are overweighted and the larger
frequencies are underweighted by individuals. According to Prelec (21: 497), these
subproportional probability weighting functions are generally “regressive, s-shaped and with a
fixed point and invariant inflection point at 1/e = .37.”
These research results have nevertheless raised a number of criticisms among
psychologists and behavioral scientists. Most of the underlying data has been collected from
small, convenient, and non-representative samples of undergraduate students from WEIRD
populations so that we can hardly generalize these results to the population as a whole. In a
recent meta-analysis, Heinrich et al. (22) have notably shown that about 80% of study
participants in the top psychology journals were recruited among undergraduate students, and
that about 96% of all psychology samples came from countries that account for only 12% of the
world’s population. Furthermore, most of the cognitive biases have been found to disappear in
more ecologically realistic conditions by using relative frequencies rather than statistical
probability in laboratory experiments (11, 23). Finally, early extensions of research into risk
perception to the area of health and illness has led to the collection of contradictory evidence
7
(24-25). In a famous experimental study conducted in the late seventies, Lichtenstein et al (12)
found that people tend to misjudge the absolute frequencies of deaths from various biomedical
causes. Their subjects were likely to overestimate the small frequencies and underestimate large
ones, such as those related to cancer or cardiovascular diseases. It should be noted that this study
was successfully replicated by Hakes and Viscusi (13) among a non-representative sample of
U.S. citizens, then by Hertwig et al. (26) among a convenience sample of German students.
However, when other researchers came to examine the perceived risks related to leading causes
of morbidity and mortality by asking questions about their relative frequencies among larger
samples of WEIRD individuals, it turned out that subjects were likely to substantially
overestimate some of the more relatively common health-related risks, such as those associated
with cigarette smoking (27-28), diabetes or hypertension (29). In other words, introducing
questions about the relative frequencies of harmful events, rather than their absolute frequencies,
seems to lead to inconsistent or even contradictory results in risk perception research.
To the best of our knowledge, the capacity of probability weighting models, such as those
developed from experimental works conducted by Tversky and Kahneman in the field of
behavioral decision-making, to represent and predict adequately such cognitive biases in more
ecologically realistic conditions has not to date been seriously investigated (31-32). Furthermore,
we still do not know whether the cognitive biases observed in the judgments of probability or
frequency are either potentially universal, or specific to WEIRD people. However, risk
perception research has shown consistent differences between white/richer/better educated men
and non-white/less-rich/less well-educated women in their numerical and non-numerical
judgments on a variety of health-related risks (13, 16, 33, 34). Nevertheless, one of the main
practical difficulties we have identified in achieving this objective in the health domain is that
8
both communicable and chronic diseases overtly affecting large segments of population (>30%)
are rather rare. For instance, cancers and cardiovascular diseases are estimated to affect about 5%
and 28% of the French adult population, respectively (35).
Setting
To further examine whether and how the perceived prevalence of common diseases may
be biased, we took advantage of four major epidemics of mosquito-borne diseases which recently
occurred in three tropical areas. The first is a large-scaled outbreak of chikungunya fever that
occurred on Reunion Island in 2005/06. Reunion Island is a French-speaking tropical territory
located in the Indian Ocean, where about 800,000 people of various regional origins live. From
March 2005 to February 2006, thousands of cases of chikungunya infection were reported by
public health authorities from countries located in the Southwest Indian Ocean. At the end of the
epidemic, it was estimated, based upon a large sero-prevalence survey conducted in Reunion
Island, that the disease would have infected between 35.9% and 40.5% of the population, with a
sudden peak in the number of cases in the winter of 2005/06 (36). The second epidemic was a
major outbreak of dengue fever that mostly occurred in 2010 on La Martinique Island, which is a
French-speaking territories located in the West Indies. According to the last census, about
380,000 inhabitants permanently reside on La Martinique Island. In October 2010, the clinical
incidence of disease that occurred during this epidemic was estimated at about 8.6%–10.4%
(with a 95% CI) on the basis of a population-based telephone survey that we performed among
1,006 households. It should be noted that this estimate was largely congruent with the 10%
attack rate calculated from the epidemiological data collected by the regional surveillance system
(37). The third and fourth epidemics were major outbreaks of chikungunya, then zika disease that
9
hit the population of French Guiana (about 250,000 inhabitants), as well as those of the other
Latin American and Caribbean countries in 2014 and 2015/16, respectively. At the time of our
surveys, there was no official estimation of the chikungunya and zika attack rate in the region.
However, the number of symptomatic cases reported by participants within their households
allows us to estimate the clinical prevalence of the diseases at about 12.2%–14.6% of the
population, with a 95% CI for chikungunya, and at about 7.1%–8.9% of the population for zika
infection.
Like zika, chikungunya, and dengue fever are infectious diseases transmitted by bites of
infected Aedes mosquitoes – also known as Asian tiger mosquitoes because of their distinctive
black and white stripes on their body – and are a prominent species of mosquito in tropical
zones. Typical symptoms of these mosquito-borne diseases are similar, since they include sudden
fever, headache, fatigue, muscle and joint pains, and skin rash. There are, however, some
considerable clinical differences between the diseases, as most people infected by the
chikungunya virus have been shown to develop symptoms, whereas dengue fever and zika
infections are generally asymptomatic (38-41). Given the substantial proportion of the
populations that was affected by these mosquito-borne disease outbreaks, it is expected that most
people in our surveys would have experienced the disease, either directly through the observation
and discussion of symptomatic cases of these illnesses which occurred in their social circles, or
indirectly through the intensive media coverage by regional newspapers, and television. Thus,
these three massive epidemics of tropical mosquito-borne diseases may be used as a series of
natural field experiments that enable us to examine further how accurately people judge the
frequency of harmful events.
10
MATERIAL AND METHODS
Participants and Procedure
Participants in these studies were adult individuals who were recruited by telephone during
major outbreaks of mosquito-borne diseases in the above-mentioned tropical French-speaking
regions between 2006 and 2016. A random digit dialling procedure was used to contact the
potential informants. Next, a proportional quota sampling method based on gender, age, and
occupation was implemented to ensure that the samples were representative of the general
population. The interviews were conducted in French or Creole by professional interviewers of a
regional survey company (IPSOS). The methodological details of these four studies are
displayed in Table 1, including research designs, sample sizes, and maximum margins of error
(with a confidence level of 95%) for the participants’ frequency estimates. The surveys were
carried out in accordance with the recommendations of the National Data Protection Authority
(CNIL), which is responsible for the ethical issue and protection of individual data collected in
France. All subjects gave oral informed consent in accordance with the Declaration of Helsinki.
[Insert Table 1 here]
Measures
Sociodemographic and illness-related variables
Sociodemographic and
illness-related
characteristics of the respondents
were
systematically collected. These included gender, sex, age, education, occupation, household
income, location, housing conditions, personal history of mosquito-borne diseases (dates, type of
mosquito-borne diseases), and details about the diagnosis and treatment. The participants were
11
also asked about the number of cases of chikungunya (or dengue fever) which occurred within
their household during the previous epidemic.
Perceived risk of contracting zika, dengue or chikungunya
To date, there is still no agreement among scientists on how perceived health risk should
be measured in empirical research (8). As noted by Viscusi (27: 1256): “Obtaining meaningful
survey responses regarding individuals' risk perceptions is not a straightforward task”. This
methodological problem can also be attributed to the fact that elicitation methods are more or
less natural and often require considerable cognitive efforts from individuals. As mentioned
above, there also exist substantial variations in the definition and measurement of health risks
(4). For epidemiologists, a common method to appraise health risk is to assess the incidence
(frequency estimate of harmful events within a given time frame) or prevalence (cumulative
frequency estimate at a certain time point) of an illness or disability in a given population.
Epidemiological information about the relative frequency of an illness can be interchangeably
expressed in terms of fractions, odds or percentages. Nevertheless, people’s understanding of
these numerical expressions has been found to pose a variety of difficulties in research on risk
perception (42-44). To address this issue, participants can be asked to estimate the prevalence of
mosquito-borne diseases by using a natural frequency scale based on a reference sample of 100
individuals, which allows easy transformation of their judgements to a percentage scale. Even
though subjects in laboratory experiments were shown to have some difficulties using and
understanding numerical information, there is sound evidence that the utilisation of relative
frequencies to elicit probabilistic judgments is a better method than directly dealing with
probabilities or fractions (11). Furthermore, ordinal or discrete rating scales (e.g., 1-5 or 0-10
scales), which are widely used in the risk perception literature, were found to be inappropriate
12
for measuring probabilities or frequencies (45). In our surveys, the format and phrasing of the
questions were adapted from the item developed by Viscusi (27): “Among 100 people living in
(Region), how many do you think have been infected with (Disease) since the beginning of the
epidemic? Please give a value between 0 and 100”. Thus, the percentage obtained through this
method provides a yardstick to evaluate the accuracy of judgments that people express about the
relative frequency of particular illnesses (the perceived risk) by comparing them with the
estimates of “objective” risk based on epidemiological or survey data (the observed risk).
Statistical Analysis
Arithmetic means and 95% confidence intervals of the estimates of relative frequencies of
chikungunya or dengue fever were calculated for each sociodemographic and illness-related
variable. To compare statistical differences in mean risk estimations among various categories of
respondents, t-tests or analyses of variance were calculated across epidemiological contexts.
Generalized linear models (GLM) were then used to determine the multivariate associations
between sociodemographic characteristics, health status and risk estimation in the four studies.
The sociodemographic and illness-related variables were dichotomized, when appropriate, to
reduce the potential instability of these models. All the data collected in the surveys were treated
and analyzed using IBM SPSS 19.0 (Statistical Package for the Social Sciences) and R 3.3.1
(with R Studio 0.99).
To examine the relationship between the perceived (subjective) and observed (objective)
prevalence of the diseases, we used one of the most popular probability weighting models
developed in the field of behavioural decision-making (21), when compared with more
conventional predictive models. As noted in the introduction, behavioral studies of judgment and
13
decision-making under risk have demonstrated through a series of laboratory experiments that
the relationship between subjective and objective probabilities of events can be adequately
described by a nonlinear transformation of the relative frequencies function:
w(p) = exp(–β(–ln p)α, where (0, 0) ≤ (α, β) ≤ (1, 1) )
This subproportional, regressive and s-shaped function implies that there exists an inflection
point under which the deviation between the perceived and observed prevalence of the mosquitoborne diseases gets smaller as actual prevalence increases (and vice versa). The parameters of the
equation for the judgements of relative frequency of infection across epidemiological settings
can be estimated with double log coordinate using simple ordinary least squares (21).
We estimate the following Equation 1:
w(p) = exp(β(log(p)α)
(Equation 1)
We change the variable log(p) = x and get the Equation 2
w(p) = exp(βxᾱ)
(Equation 2)
of which we take the ln and multiply by minus 1, log(w(p)) = βxᾱ, and change the variable
log(w(p)) = y, we take the log again and get Equation 3:
log(y) = log(β) + αlog(x)
(Equation 3)
Equation 3 can easily be estimated by Ordinary Least Square (OLS). The estimation is simple
enough, as long as values are strictly positive before taking the logarithm.
We first estimate Equation 3 by using standard GLM function in R. Then we perform an
estimation of equation 1 using a Nelder and Mead (46) optimization which is available through
the optim function in R. Results differ, and based on Mean Squared Prediction Error (MSPE), we
prefer the Nelder-Mead estimation compared with OLS. MSPE compares the true values for
14
w(p), with the estimated values for the latter based on the estimation of α and β . MSPE gives a
standard statistic to assess the capability of the model to provide correct estimations (47).
Comparing the MSPE with the OLS and the Nelder-Mead estimation enables a comparison of
models. These models also allow determining whether different subgroups of a population
follow the same perceptive curve.
RESULTS
Are there differences in perceived prevalence among subpopulations?
All the populations were found to have greatly overestimated the prevalence of diseases
regardless of the epidemiological setting. Indeed, the magnitude of the epidemics was significantly
overestimated by an average of 16 percentage points in La Reunion (t = - 22.1; p < 0.001), 26
percentage points in La Martinique (t = - 32.1; p < 0.001), 26 percentage points (chikungunya
epidemic) (t = - 24.4; p < 0.001), and 23 percentage points (zika epidemic) (t = - 31.9; p < 0.001) in
French Guiana. However, as shown in table 2, there were considerable statistical differences in the
average overestimations, depending on the sociodemographic and illness-related characteristics of the
respondents. With the notable exception of age in study 1, all the sociodemographic variables under
investigation – such as household income, level of education, gender, age, and history of infection –
were found to influence significantly the way in which individuals estimated the proportion of people
who have been infected at the time of the survey (p < 0.01) across regions. These results suggest that
social and cultural conditions may play an important role in the magnitude of the biases that have
been repeatedly observed when people are asked to estimate the prevalence of a health disorder.
[Insert Table 2 here]
15
As the sociodemographic and health-related variables are known to be strongly intercorrelated, a multivariate analysis using generalized linear models was performed in order to assess
the robustness of the influence of each of these personal factors on the perceived prevalence,
independent of other factors. As shown in table 3, the results of the multivariate analyses were
relatively consistent with those from earlier bivariate analyses. However, it should be noted that only
gender and the level of education of the participants were found to affect directly judgments about the
relative frequency of the diseases across regions and epidemiological contexts (p < 0.001). Therefore,
after adjusting for potential confounding variables, female participants were found to overestimate
the prevalence of the diseases by an average of 6 to 11 percentage points more than their male
counterparts, while the most educated participants tended to overestimate them on average by 7 to 15
percentage points less than the other participants.
[Insert Table 3 here]
What is the relationship between perceived and observed prevalence of the diseases?
The mean percentage deviation – which measures biases in perceived prevalence relative to
the actual prevalence of the disease – was statistically significant for each of the 4 studies (p < 0.001).
However, the average overestimations calculated for each group show large differences, depending
on the magnitude of the epidemic. As shown in figure 1, the prevalence estimations provided by the
participants are closer to the line of identity, which represents the correct prevalence estimation, as
the magnitude of the epidemic increases. Thus, the overestimation bias among participants was
significantly higher for the “smaller” epidemics (from +284% to +182% in studies 2 and 4,
respectively) than for the largest epidemic (+43% in study 1). In other words, the perceived
prevalence tended to increase more slowly than the observed prevalence.
[Insert Figure 1 here]
16
To examine the relationship between estimated and actual prevalence, we used the probability
weighting function developed by Prelec (1998). The best fitting model (using Error! Reference
source not found.) is w(p) = exp(–0.641(–ln(p))0.616. These parameters enable to estimate the
inflexion point, i.e., the point at which perceived and actual prevalences are equal, at 73.0%. That
means that below a prevalence threshold of 73%, individuals tend to overestimate the actual
prevalence (and vice-versa). For the male participants, the best fitting model is w(p) = exp(–0.732(–
ln(p))0.619, with an inflexion point at 64.4%, whereas that of female participants is w(p) = exp(–
0.562(–ln(p))0.664, with an inflexion point at 83.5%. For the best educated participants, the best fitting
model is w(p) = exp(–0.837(–ln(p))0.468, with an inflexion point at 48.9%, whereas that of less
educated participants is w(p) = exp(–0.586(–ln(p))0.642, with an inflexion point at 79.9%.
Graphically, this relationship is shown in Figure 1 by the asymmetric s-shaped curves representing
the perceived prevalence predicted by the probability weighting model. The results are displayed
separately for the male and female participants, and for the most educated and the less educated
participants in Figure 1. After the prevalence estimations were averaged across different subgroups of
the population, arithmetic means for each epidemiological setting fell fairly close to the predicted
curves.
To test further the hypothesis that perceived prevalences can be adequately represented by a
subproportional, regressive, and s-shaped function of observed prevalence, we compared the fit of the
probability weighting model with the fit of a linear model (w(p) = a + n × p) and a power model
(ln(w(p)) = ln(a’) + n’ × ln(p)). For the sake of comparison, all models were estimated by using
ordinary least squares (OLS). The probability weighting model was found to fit the data drawn from
the surveys better than the other models (R² = 13.0%, t = 19.4, P < 0.001, versus R² = 12.6%, t =
22.0, P < 0.001 for the linear model and R² = 11.8%, t = 22.2, P < 0.001 for the power model).
17
DISCUSSION
During the last decade, we took advantage of a series of large epidemics of mosquitoborne diseases as a natural experiment to test empirically the hypothesis that there exists a
primary bias in the way people perceive the risk of infection. Indeed, since the pioneering studies
of Lichtenstein et al. (12), the accuracy of people’s estimates of health-related risk frequencies
has been the subject of intense and stimulating discussions among psychological and behavioural
scientists (14). Today, there is sound evidence, based on a series of laboratory experiments, that
people from WEIRD societies tend to overestimate the absolute frequency of rare
epidemiological events such as deaths caused by botulism or measles. In contrast, they are likely
to underestimate the incidence of frequent epidemiological events such as mortality attributable
to lung cancer or cardiovascular diseases. This evidence is convergent with the well-established
psychophysical law according to which individuals have the tendency to underestimate large
magnitudes in volume, height, weight or even calories (48). Nevertheless, subsequent studies
involving the general population have shown that a number of common health risks (e.g. those
related to cigarette or alcohol consumption) were substantially overassessed by the public when
they were asked about their relative frequency (27-28, 49).
Consistent with these previous empirical analyses, we found in our surveys that (1) people from
a variety of French tropical regions substantially overestimated the prevalence of infection by
arbovirus, and (2) these risk overestimations fell considerably as the actual prevalence of these
diseases increased. The strong convergence of the results of our studies with a range of
investigation conducted in the domain of chronic diseases indicates that this deviation may be
robust, regardless of the type of health threat and/or population. Furthermore, we found that
18
probability weighting functions better predicted the magnitude of biases observed in perceptions of
prevalence of these infectious diseases than did more ordinary predictive models, such as a linear
regression model. This is a striking result since this cognitive bias in probabilistic judgments was
experimentally elicited through indirect methods, using gambles and lotteries as a model to
investigate judgments or decisions made under uncertainty. Overall, this empirical evidence as well
as that from the previous afore-mentioned studies, demonstrates that there is no systematic
underestimation in the perception of prevalence of the most common health threats in both
WEIRD and non-WEIRD population samples, since neither arboviral infection nor lung cancer
could be considered to be an infrequent epidemiological event. Therefore, these inconsistent
findings regarding risk magnitude judgments should lead us to question whether the primary bias
is an artefact triggered by particular experimental conditions, as its existence seems to depend to
a large extent on the method used to elicit and measure it.
To date, many researchers in the field of risk perception have ignored some of the
methodological and conceptual distinctions – for instance, absolute frequency versus relative
frequency – which are essential in determining the accuracy of risk beliefs, as well as in
characterizing the magnitude and pattern of the cognitive bias observed in their studies.
However, there is now a crucial need for discussion and clarification of the effects induced by
the concepts and methods employed to investigate risk frequency judgements. As discussed by
Gigerenzer (11:83), by using certain frequency formats rather than others to elicit probabilistic
judgments, “we can make apparently stable errors disappear, reappear, or even invert”. Where
risk perception is concerned, it seems highly plausible that people underestimate relatively
common health risks when they are questioned about their absolute frequencies, while they
overestimate them when they are asked about their relative frequencies, based on a reference
sample of 100 or 1,000 individuals.
19
Furthermore, little is known about the possible social and cultural variations in estimating
the frequency or prevalence of diseases, especially in the context of an outbreak (13). Our
surveys show that all the groups of participants have a tendency to overestimate the prevalence
of infection by arbovirus. Nevertheless, and consistent with previous studies dedicated to risk
magnitude judgments, we found systematic differences among subgroups of the population in the
way people perceive these health risks. In particular, when other sociodemographic factors were
held constant, better-educated and male subjects consistently exhibited far fewer inaccurate risk
frequency judgments across epidemics than did their less-educated and female counterparts.
There is considerable evidence that male and better-educated individuals are less subject to
measurement errors when they have to estimate risk frequency (13). However, we do not know
much about what drives these systematically larger disproportionate biases in health risk
perception among females and less-educated individuals. In our opinion, formal education and
gender could be a proxy for group differences in numeracy skills, which refers to person’s
capacity to correctly understand, process and use numeric information to form judgments and
make decisions (44). Indeed, it has been consistently shown that highly-numerate individuals are
generally less subject to a range of errors when asked to translate some basic mathematic or
probabilistic expressions, such as proportions or percentages, into meaningful information about
risks (50). Therefore, it might be reasonable to assume that the ability to transform
epidemiological information (e.g., observations of cases of chikungunya, zika or dengue fever)
arising from the social environment into accurate judgments about their relative frequencies
relies to a large extent on the numeracy skills that an individual might have developed over his or
her life course.
CONCLUSION
20
To conclude, it should be noted that the pattern of perceived prevalence found across our
surveys is relatively compatible with the probability weighting models developed in the field of
psychology of judgment and decision-making (20), which assumes a nonlinear transformation of
the probability scale among decision-makers (with an overweighting of probabilities lower than
about 40% and conversely). This is particularly true if one considers that the potential inflexion
point between overestimation and underestimation of the perceived prevalence decreases as the
level of formal education of the participants increases. Nevertheless, given that a vast majority of
western, educated, and rich individuals were enrolled in laboratory experiments devoted to
heuristics and cognitive bias (22), these empirical findings provide the opportunity to refine the
models of cognitive processes that are proposed in the research literature to explain and predict
the emergence of these biases. Last but by no means least, even though scientists have proposed
a range of possible explanations for gender and education gaps in health-related risk perceptions,
the cause of these sociodemographic and cultural variations in the magnitude of this bias remains
unclear and, therefore, there is still a need for a better understanding of why some subgroups of
the population make less inaccurate risk frequency estimates than others.
21
REFERENCES
1. Sharot T. The optimism bias. Current Biology. 2011; 21(23): 941-45. R941-R945. doi:
10.1111/j.1539-6924.1993.tb00741.x
2. Bodemer N, Gaissmaier W. Risk perception. In: Cho H, Reimer TO, McComas KA, eds. The
SAGE handbook of risk communication. Thousand Oaks, CA: Sage; 2015. p 10-23.
3. Slovic P. Are trivial risks the greatest risks of all? Journal of Risk Research. 1999; 2(4): 28188. Available from: URL: http://dx.doi.org/10.1080/136698799376727 . Accessed 10 March
2017.
4. Althaus CE. A disciplinary perspective on the epistemological status of risk. Risk Analysis.
2005;25(3):567-88. doi:10.1111/j.1539-6924.2005.00625.x
5. Weinstein ND. Perceived probability, perceived severity, and health-protective behavior.
Health Psychology. 2000;19(1):65. doi: 10.1037/0278-6133.19.1.65
6. Brewer NT, Weinstein ND, Cuite CL, Herrington JE. Risk perceptions and their relation to
risk behaviour. Annals of Behavioral Medicine. 2004;27(2):125-30.
7. Peters E, McCaul KD, Stefanek M, Nelson W. A heuristics approach to understanding cancer
risk perception: Contributions from judgment and decision-making research. Annals of Behavioral Medicine. 2006;31(1):45-52. doi: 10.1207/s15324796abm3101_8
8. Weinstein ND, Kwitel A, McCaul KD, Magnan RE, Gerrard M, Gibbons FX. Risk perceptions: Assessment and relationship to influenza vaccination. Health Psychology. 2007;26(2):146.
doi: 10.1037/0278-6133.26.2.146
22
9. Sheeran P, Harris PR, Epton T. Does heightening risk appraisals change people’s intentions
and behavior? A meta-analysis of experimental studies. Psychological Bulletin. 2014;140(2):511.
doi: 10.1037/a0033065
10. Leventhal H, Kelly K, Leventhal EA. Population risk, actual risk, perceived risk, and cancer
control: A discussion. Journal of the National Cancer Institute. Monographs. 1999;25:81-5.
11. Gigerenzer G. How to make cognitive illusions disappear: Beyond “heuristics and biases”.
European Review of Social Psychology. 1991;2(1):83-115. Available from: URL:
http://dx.doi.org/10.1080/14792779143000033 Accessed 10 March 2017.
12. Lichtenstein S, Slovic P, Fischhoff B, Layman M, Combs B. Judged frequency of lethal
events. Journal of Experimental Psychology: Human Learning and Memory. 1978;4:551–78.
Available from: URL: http://dx.doi.org/10.1037/0278-7393.4.6.551 Accessed 10 March 2017.
13. Hakes JK, Viscusi WK. Dead reckoning: Demographic determinants of the accuracy of
mortality risk perceptions. Risk Analysis. 2004;24(3):651-64. doi: 10.1111/j.02724332.2004.00465.x
14. Gigerenzer G, Fiedler K, Olsson H. Rethinking cognitive biases as environmental
consequences. In: Todd PM, Gigerenzer G, eds. Ecological rationality: Intelligence in the world.
Oxford, England: Oxford University Press; 2012. p 80-110.
15. Savage I. Demographic influences on risk perceptions. Risk analysis. 1993;13(4):413-20.
16. Finucane ML, Slovic P, Mertz CK, Flynn J, Satterfield TA. Gender, race, and perceived risk:
The 'white male' effect. Health, Risk & Society. 2000;2(2):159-72. Available from: URL:
http://dx.doi.org/10.1080/713670162 Accessed 10 March 2017.
17. Kpanake L, Chauvin B, Mullet E. Societal risk perception among African villagers without
access to the media. Risk Analysis. 2008;28(1):193-202. doi: 10.1111/j.1539-6924.2008.01008.x
23
18. Gilovich, T, Griffin D, Kahneman D. Heuristics and biases: The psychology of intuitive
judgment. Cambridge, England: Cambridge University Press; 2002.
19. Johnson EJ, Tversky A. Affect, generalization, and the perception of risk. Journal of
Personality and Social Psychology. 1983;45(1):20. doi: 10.1037/0022-3514.45.1.20
20. Tversky A, Kahneman D. Advances in prospect theory: Cumulative representation of
uncertainty. Journal of Risk and Uncertainty. 1992;5(4):297-323. doi: 10.1007/BF00122574
21. Prelec D. The Probability Weighting Function. Econometrica. 1998;66(3):497-527. doi:
10.2307/2998573
22. Henrich J, Heine SJ, Norenzayan A. The weirdest people in the world? Behavioral and Brain
Sciences. 2010;33(2-3):61-83. doi: 10.1017/S0140525X0999152X
23. Cosmides L, Tooby J. Are humans good intuitive statisticians after all? Rethinking some
conclusions from the literature on judgment under uncertainty. Cognition. 1996;58(1): 1-73.
Available from: URL: http://dx.doi.org/10.1016/0010-0277(95)00664-8 Accessed 10 March
2017.
24. Weinstein ND. Accuracy of smokers' risk perceptions. Annals of Behavioral Medicine.
1998;20(2):135-40.
25. Sutton SR. How accurate are smokers’ perceptions of risk? Health, Risk & Society.
1999;1(2):223-30. doi: 10.1080/13698579908407020
26. Hertwig R, Pachur T, Kurzenhäuser S. Judgments of risk frequencies: Tests of possible cognitive mechanisms. Journal of Experimental Psychology: Learning, Memory, and Cognition.
2005;31(4):621. doi:10.1037/0278-7393.31.4.621
27. Viscusi WK. Do smokers underestimate risks? Journal of Political Economy.
1990;98(6):1253-69. doi: 10.1086/261733
24
28. Lundborg P, Lindgren B. Do they know what they are doing? Risk perceptions and smoking
behaviour among Swedish teenagers. Journal of Risk and Uncertainty. 2004;28(3):261-86. doi:
10.1023/b:risk.0000026098.84109.62
29. Frijling BD, Lobo CM, Keus IM, Jenks KM, Akkermans RP, Hulscher ME, Grol RP.
Perceptions of cardiovascular risk among patients with hypertension or diabetes. Patient
Education and Counseling. 2004;52(1):47-53. Available from: URL:
http://dx.doi.org/10.1016/S0738-3991(02)00248-3 Accessed 10 March 2017.
30. Weinstein ND. Exploring the Links Between Risk Perceptions and Preventive Health
Behavior. In: Suls J. ed. Social Psychological Foundations of Health and Illness. Oxford, UK:
Blackwell; 2003. p 22-53.
31. Pashler H, Harris CR. Is the replicability crisis overblown? Three arguments examined. Perspectives on Psychological Science. 2012;7:531–36. doi: 10.1177/1745691612463401
32. Ioannidis J, Doucouliagos C. What's to know about the credibility of empirical economics?
Journal of Economic Surveys. 2013;27(5):997-1004. doi: 10.1111/joes.12032
33. Raude J, Fischler C, Setbon M, Flahault A. Scientist and public responses to BSE‐related
risk: A comparative study. Journal of Risk Research. 2005;8(7-8):663-78. Available from: URL:
http://dx.doi.org/10.1080/13669870500194825 Accessed 10 March 2017.
34. Peters E. Numeracy and the Perception and Communication of Risk. Annals of the New York
Academy of Sciences. 2008;1128: 1–7. doi:10.1196/annals.1399.001
35. [DREES] Direction de la recherche, des études, de l'évaluation et des statistiques. L’état de
santé de la population en France. Rapport 2015. 2015. Available from: URL : drees.socialsante.gouv.fr/IMG/pdf/rappeds_v11_16032015.pdf. Accessed 10 March 2017.
25
36. Gérardin P, Guernier V, Perrau J, Fianu A, LeRoux K, Grivard P, Michault A, de
Lamballerie X, Flahault A, Favier F. Estimating Chikungunya prevalence in La Reunion Island
outbreak by serosurveys: Two methods for two critical times of the epidemic. BMC Infectious
Diseases. 2008;8(1):99. doi: 10.1186/1471-2334-8-99
37. Rosine J, Adélaïde Y, Anglio J, Blateau A, Bousser V, Davidas M, Ledrans M, Romagne
MJ, Suivant C, Quénel P. Bilan de l'épidémie de dengue en Martinique, 2010. Bulletin de veille
sanitaire. 2011;9/10:2-5.
38. Burke DS, Nisalak A, Johnson DE, Scott RM. A prospective study of dengue infections in
Bangkok. The American journal of tropical medicine and hygiene. 1988;38(1):172-80.
39. Gallian P, Cabié A, Richard P, Paturel L, Charrel RN, Pastorino B, DeLamballerie X. Zika
virus in asymptomatic blood donors in Martinique. Blood. 2017;129(2):263-66. Available from:
URL: https://doi.org/10.1182/blood-2016-09-737981 . Accessed 10 March 2017.
40. Burt FJ, Rolph MS, Rulli NE, Mahalingam S, Heise MT. Chikungunya: a re-emerging virus.
The Lancet. 2012;379(9816):662-71. Available from: URL: http://dx.doi.org/10.1016/S01406736(11)60281-X . Accessed 10 March 2017.
41. Sissoko D, Moendandze A, Malvy D, Giry C, Ezzedine K, Solet JL, Pierre V. Seroprevalence and risk factors of chikungunya virus infection in Mayotte, Indian Ocean, 2005-2006: A
population-based survey. PLoS ONE. 2008;3(8):3066. doi:10.1371/journal.pone.0003066
42. Diefenbach M, Weinstein ND, O’Reilly J. Scales for assessing perceptions of personal risk
susceptibility. Health Education Research. 1993;8:181–92. Available from: URL:
https://doi.org/10.1093/her/8.2.181 . Accessed 10 March 2017.
26
43. Rothman AJ, Kiviniemi MT. Treating people with information: An analysis and review of
approaches to communicating health risk information. Journal of the National Cancer Institute.
Monographs. 1999;25:44-51. doi: 10.1093/oxfordjournals.jncimonographs.a024207
44. Peters E. Numeracy and the perception and communication of risk. Annals of the New York
Academy of Sciences. 2008;1128(1):1-7. doi: 10.1196/annals.1399.001
45. Viscusi WK, Hakes J. Risk ratings that do not measure probabilities. Journal of Risk
Research. 2003;6(1):23-43. Available from: URL:
http://dx.doi.org/10.1080/1366987032000047789 . Accessed 10 March 2017.
46. Nelder JA, Mead R. A simplex method for function minimization. The computer journal.
1965;7(4):308-13.
47. Abadie A, Diamond A, Hainmueller J. Synthetic control methods for comparative case
studies: Estimating the effect of California’s tobacco control program. Journal of the American
statistical Association, 2010;105(490):493-505.
48. Chandon P, Wansink B. Is obesity caused by calorie underestimation? A psychophysical
model of meal size estimation. Journal of Marketing Research. 2007;44(1):84-99. Available
from: URL: http://dx.doi.org/10.1509/jmkr.44.1.84 . Accessed 10 March 2017.
49. Lundborg P, Lindgren B. Risk perceptions and alcohol consumption among young people.
Journal of Risk and Uncertainty. 2002;25:165–83. doi: 10.1023/A:1020695730192
50. Reyna VF, Nelson WL, Han PK, Dieckmann NF. How numeracy influences risk comprehension and medical decision making. Psychological Bulletin. 2009;135(6):943. doi:
10.1037/a0017327
27
Table 1. Characteristics of the studies
Geographical area
Date
Type of disease
Actual prevalence (95% CI)
Research design
Maximum margin of error
Observations (n)
Population (N)
Study 1
La Reunion Island
April 2006
Chikungunya
37.2% (33.9%-40.5%)
Cross-sectional study
3.0%
1,035
794,000
Study 2
Study 3
La Martinique Island
French Guiana
September 2010
April 2015
Dengue fever
Chikungunya
9.5% (8.6%-10.4%) 13.9% (12.2%-14.6%)
Cross-sectional study Cross-sectional study
3.1%
4.2%
1,006
553
380,000
250,000
28
Study 4
French Guiana
June 2016
Zika
8.0% (7.1%-8.9%)
Cross-sectional study
2.9%
1,129
250,000
Table 2. Differences between the perceived and observed prevalence of chikungunya, zika or
dengue fever by sociodemographic and health characteristics in studies: arithmetic means (95%
CI).
Total
Gender
Male
Female
Education
Some high school and lower
High School graduate
Some college
College graduate and higher
Household income
Lowest
Lower-middle
Upper-middle
Highest
Age group
18 to 29
30 to 44
45 to 59
60 or older
Occupation
Employed or self-employed
Unemployed (looking for work)
Unemployed (not looking for work)
Student
Retired
Personal history of infection
Present
None
Number of cases in the household
0
1
2
>2
Study 1 (n=1,035)
16.0 (14.6; 17.4)
***
11.3 (9.4; 13.3)
20.2 (18.2; 22.2)
***
26.3 (23.0; 29.5)
19.2 (16.7; 21.6)
11.2 (8.4; 14.0)
6.9 (4.5; 9.3)
***
22.4 (16.8; 27.9)
21.3 (18.9; 23.6)
11.7 (9.7; 13.9)
10.1 (6.5; 13.7)
NS
17.1 (14.7; 19.4)
16.1 (13.7; 18.5)
14.0 (10.6; 17.4)
16.2 (11.9; 20.5)
***
11.0 (8.8; 13.2)
20.3 (17.1; 23.5)
24.9 (21.2; 28.6)
16.9 (13.8; 19.9)
8.6 (4.0; 13.3)
***
20.7 (18.4; 22.9)
12.7 (10.8; 14.5)
***
11.7 (9.4; 14.0)
15.4 (11.3; 19.5)
16.4 (13.1; 19.7)
21.6 (19.9; 25.3)
Study 2 (n=1,006)
26.2 (24.6; 27.8)
***
22.5 (20.2; 24.9)
29.2 (27.0; 31.4)
*
28.8 (24.9; 32.7)
28.2 (25.0; 31.4)
26.9 (23.7; 30.1)
22.4 (19.8; 25.1)
**
29.0 (23.6; 34.4)
27.6 (24.5; 30.6)
26.4 (23.7; 29.2)
20.1 (16.8; 23.4)
**
31.2 (28.2; 34.1)
25.1 (22.3; 27.9)
26.4 (23.1; 29.7)
20.9 (17.0; 24.9)
**
25.4 (22.8; 28.1)
28.3 (24.9; 31.7)
27.2 (22.4; 32.0)
32.1 (27.6; 36.7)
21.2 (17.4; 25.0)
**
32.8 (27.8; 37.9)
25.4 (23.8; 27.1)
***
24.9 (23.0; 26.9)
31.9 (25.7; 38.2)
33.4 (27.9; 38.9)
35.7 (28.3; 43.2)
*significant at 5% level, **significant at 1% level, ***significant at 1‰ level.
29
Study 3 (n=553)
25.3 (22.8; 27.8)
***
19.6 (16.3; 22.8)
31.1 (27.4; 34.8)
***
30.3 (23.7; 36.8)
31.0 (26.3; 35.9)
30.5 (25.6; 35.3)
13.5 (9.6; 17.3)
***
35.9 (31.8; 40.0)
23.9 (19.9; 27.9)
17.2 (11.2; 23.2)
9.0 (3.5; 14.6)
**
32.2 (28.0; 36.3)
25.5 (20.9; 30.0)
19.6 (14.6; 24.6)
19.6 (11.9; 27.3)
***
18.9 (15.5; 22.2)
34.6 (28.5; 40.7)
36.7 (28.9; 44.5)
31.7 (25.8; 37.7)
17.7 (9.0; 26.5)
**
39.4 (30.2; 48.6)
24.0 (21.4; 26.6)
***
22.4 (19.8; 25.0)
37.2 (28.1; 46.4)
34.1 (22.4; 45.9)
58.4 (48.0; 68.7)
Study 4 (n=1,127)
22,7 (21.3; 24.1)
***
16,4 (14.2; 18.6)
26,1 (24.4; 27.9)
***
23,9 (18.6; 29.0)
26,6 (23.8; 29.4)
23,4 (20.6; 26.1)
19,2 (17.1; 21.3)
***
27.7 (24.9; 30.4)
23.7 (21.4; 25.9)
17.6 (14.9; 20.3)
17.9 (13.7; 22.0)
***
19.9 (18.1; 21.6)
29.8 (26.0; 33.6)
25,5 (21.0; 30.0)
26,9 (22.6; 31.3)
19,6 (14.5; 24.7)
***
32,4 (28.0; 36.8)
21,6 (20.1; 23.0)
***
21.5 (20.0; 23.0)
27.3 (23.6; 31.1)
32.1 (-92.0; 108)
44,4 (33.9; 55.0)
Table 3. Association between the sociodemographic characteristics, health status and estimated
prevalence of chikungunya, zika or dengue fever across epidemics: adjusted coefficients (95%
confidence intervals) calculated from generalized linear models.
Intercept
Gender
Male
Female
Education
Some college and lower
College graduate and higher
Household income
Lower-middle and lower
Upper-middle and higher
Age group
15 to 29
30 to 44
45 to 59
60 or older
Occupation
Employed or self-employed
Unemployed (looking for work)
Unemployed (not looking for work)
Student
Retired
Personal history of infection
None
Present
Number of cases in the household
None
One or more
MLE
Study 1 (n=1,035)
48.9 (44.2; 53.7)***
Study 2 (n=1,006)
35.7 (25.2; 46.3)***
Study 3 (n=553)
31.9 (26.7; 37.2)***
Study 4 (n=1,127)
22.4 (17.7; 27.1)***
Reference
6.3 (3.6; 9.1)***
Reference
8.9 (5.7; 12.2)***
Reference
10.9 (7.4; 14.4)***
Reference
8.9 (6.1; 11.8)***
Reference
-8.7 (-12.1; -5.4)***
Reference
-6.9 (-10.6; -3.3)***
Reference
-9.6 (-14.3; -4.9)***
Reference
-7.0 (-9.9; -4.0)***
Reference
-4.5 (-8.4; -0.6)*
Reference
-6.0 (-10.2; -1.8)**
Reference
-4.7 (-9.5; 4.0)
Reference
-2.2 (-6.5; 1.9)
-4.8 (-9.6; 0.1)
-0.6 (-7.1; 5.9)
Reference
-6.9 (-11.9; -1.8)**
-8.2 (-13.4; -2.9)**
-11.7 (-22.3-1.2)*
Reference
-4.8 (-9.7; 0.2)
-6.0 (-11.4; -0.6)*
-3.8 (-14.4; 6.7)
Reference
-4.5 (-8.4; -0.6)*
-10.2 (-14.5; -5.9)***
-12.0 (-19.5; -4.5)***
Reference
4.4 (0.5-8.4)*
7.1 (2.7; 11.5)**
1.3 (-3.8; 6.3)
-5.6 (-12.1; 0.8)
Reference
4.0 (-7.2; 15.3)
2.2 (-7.9; 12.2)
3.4 (-6.5; 13.3)
4.9 (-4.9; 14.7)
Reference
10.3 (4.9; 15.6)***
5.8 (-0.0; 11.6)
6.1 (-0.8; 12.9)
-4.4 (-16.7; 7.8)
Reference
4.5 (-0.7; 13.3)*
1.6 (-3.2; 6.3)
1.5 (-4.1; 7.1)
3.2 (-5.2; 11.7)
Reference
5.2 (1.7-8.6)**
Reference
4.1 (-1.5; 9.8)
Reference
15.4 (9.3; 21.5)***
Reference
10.4 (3.0; 17.8)**
Reference
2.4 (-1.2; 5.9)
448.5
Reference
3.1 (-0.5; 6.7)
502.1
Reference
3.5 (-2.4; 9.4)
514.7
Reference
1.0 (-5.4; 7.4)
448.4
*significant at 5% level, **significant at 1% level, ***significant at 1‰ level.
30
Figure 1. Predicted estimation curves, mean perceived prevalence and 95% confidence intervals by
gender (top) and level of formal education (bottom).
31