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When Success Is Not Enough: The Symptom Base-Rate Can Influence Judgments of Effectiveness of a Successful Treatment

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Patients' beliefs about the effectiveness of their treatments are key to the success of any intervention. However, since these beliefs are usually formed by sequentially accumulating evidence in the form of the covariation between the treatment use and the symptoms, it is not always easy to detect when a treatment is actually working. In Experiments 1 and 2, we presented participants with a contingency learning task in which a fictitious treatment was actually effective to reduce the symptoms of fictitious patients. However, the base-rate of the symptoms was manipulated so that, for half of participants, the symptoms were very frequent before the treatment, whereas for the rest of participants, the symptoms were less frequently observed. Although the treatment was equally effective in all cases according to the objective contingency between the treatment and healings, the participants' beliefs on the effectiveness of the treatment were influenced by the base-rate of the symptoms, so that those who observed frequent symptoms before the treatment tended to produce lower judgments of effectiveness. Experiment 3 showed that participants were probably basing their judgments on an estimate of effectiveness relative to the symptom base-rate, rather than on contingency in absolute terms. Data and materials are publicly available at the Open Science Framework: https://osf.io/emzbj/
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ORIGINAL RESEARCH
published: 23 October 2020
doi: 10.3389/fpsyg.2020.560273
Edited by:
Ulrich Hoffrage,
University of Lausanne, Switzerland
Reviewed by:
Barbara Penolazzi,
University of Trieste, Italy
Elisabet Tubau,
University of Barcelona, Spain
*Correspondence:
Fernando Blanco
fernandoblanco@ugr.es
Specialty section:
This article was submitted to
Cognition,
a section of the journal
Frontiers in Psychology
Received: 08 May 2020
Accepted: 26 August 2020
Published: 23 October 2020
Citation:
Blanco F, Moreno-Fernández MM
and Matute H (2020) When Success
Is Not Enough: The Symptom
Base-Rate Can Influence Judgments
of Effectiveness of a Successful
Treatment.
Front. Psychol. 11:560273.
doi: 10.3389/fpsyg.2020.560273
When Success Is Not Enough: The
Symptom Base-Rate Can Influence
Judgments of Effectiveness of a
Successful Treatment
Fernando Blanco1*, María Manuela Moreno-Fernández1and Helena Matute2
1Faculty of Psychology, University of Granada, Granada, Spain, 2Faculty of Psychology and Education, University of Deusto,
Bilbao, Spain
Patients’ beliefs about the effectiveness of their treatments are key to the success
of any intervention. However, since these beliefs are usually formed by sequentially
accumulating evidence in the form of the covariation between the treatment use and
the symptoms, it is not always easy to detect when a treatment is actually working.
In Experiments 1 and 2, we presented participants with a contingency learning task in
which a fictitious treatment was actually effective to reduce the symptoms of fictitious
patients. However, the base-rate of the symptoms was manipulated so that, for half of
participants, the symptoms were very frequent before the treatment, whereas for the rest
of participants, the symptoms were less frequently observed. Although the treatment
was equally effective in all cases according to the objective contingency between the
treatment and healings, the participants’ beliefs on the effectiveness of the treatment
were influenced by the base-rate of the symptoms, so that those who observed frequent
symptoms before the treatment tended to produce lower judgments of effectiveness.
Experiment 3 showed that participants were probably basing their judgments on an
estimate of effectiveness relative to the symptom base-rate, rather than on contingency
in absolute terms. Data, materials, and R scripts to reproduce the figures are publicly
available at the Open Science Framework: https://osf.io/emzbj/.
Keywords: causal learning, cognitive bias, patients’ beliefs, base-rates, causal judgment
INTRODUCTION
A great deal of health-related decisions, such as deciding whether or not to quit a treatment,
or whether to replace it by an alternative option, depend on the patients’ beliefs about their
symptoms and diseases, and particularly about the effectiveness of their treatments. For instance,
one of the main reasons for treatment drop-out is the belief that the treatment is producing
little or no observable benefit (Leventhal et al., 1992;Dilla et al., 2009). Thus, understanding
how patient’s beliefs form and evolve is critical to developing strategies aimed at improving
the trust and adherence to the prescribed treatments, and therefore fostering well-being among
patients and users.
Previous research on experimental psychology suggests that many of these health-related
decisions such as treatment adherence, or therapeutic choices, can be better understood as a
result of causal learning (Rottman et al., 2017). That is, the users’ beliefs about the effectiveness
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of the treatment are causal in nature, i.e., “the treatment causes
the symptom remission,” or “the treatment prevents me from
falling ill.” Thus, it is possible to study the patients’ beliefs of
treatment effectiveness through causal learning experiments (see
reviews in Matute et al., 2015;Matute et al., 2019). This possibility
offers a number of advantages. To begin with, we can study
the formation of beliefs under highly controlled settings, by
using fictitious scenarios and computerized tasks. This would be
impossible in real life, in which researchers cannot manipulate
parameters such as the frequency with which a treatment is
used, its actual effectiveness, or the severity of symptoms. Thus,
ecological studies would be limited because it is often impossible
to run an experiment that unveils causal relationships between
different factors and health beliefs, and most research would
be limited to uncontrolled, observational studies. The second
advantage of using causal learning experiments is that we can
study health beliefs in a safe context, without putting the
participant’s health at risk. As this research normally involves
using treatments with no actual benefit, or even inducing
false beliefs of effectiveness, it would be unethical to conduct
such studies with real health outcomes. Additionally, it is
sometimes possible to use samples of real patients who deal
with fictitious or imagined health outcomes in the context of a
causal learning experiment (Meulders et al., 2018), which helps
to alleviate the limitations of ecological validity while using highly
controlled procedures.
This line of research that uses causal learning experiments to
study health beliefs has shown some promising advances. For
example, it is possible to predict which conditions will make
patients and users more vulnerable to pseudomedicine and bogus
health claims (Blanco et al., 2014;Blanco and Matute, 2020), to
discover situations in which previously acquired beliefs interfere
with actual effectiveness (Yarritu et al., 2015), to investigate
how health beliefs are affected by biases in Internet search
(Moreno-Fernández and Matute, 2020), to explain why certain
patients are hypersensitive to pain symptoms (Meulders et al.,
2018), and to improve the effect of placebos (Yeung et al.,
2014). This knowledge has the potential to offer a valuable
foundation for designing interventions aimed at debiasing
dysfunctional beliefs in real life settings (Lewandowsky et al.,
2012;Macfarlane et al., 2020).
Exploring Health Beliefs in the
Laboratory
Most causal learning experiments exploit a basic principle of
causality: causes and effects (outcomes) correlate with each other,
unless a third factor masks this relationship. Since causality
cannot be directly observed (Hume, 1748), people use this
simple principle and rely on a proxy measure, the contingency
between the cause and the outcome, to estimate causality (Allan,
1980;Wasserman et al., 1996;Vadillo et al., 2005;Blanco et al.,
2010). In a simple situation with only one binary cause and
one binary outcome, the contingency can be computed by
means of the 1p index (Allan, 1980). This is simply the result
of subtracting the probability of the outcome occurring given
that the cause occurred, P(O| C), minus the probability of the
outcome occurring given that the cause did not occur, P(O| C).
Large values of 1p correspond to situations in which the cause
increases or decreases the probability of the outcome beyond the
base-rate, P(O| C). The larger this difference is, the stronger the
association between cause and outcome, and therefore the higher
the chances that there is a causal link. According to previous
research, this is how probabilities could produce causal beliefs in
many situations (Perales et al., 2016).
In the context of judging a treatment’s effectiveness, this
reasoning amounts to computing how often the symptomatic
episodes appear during the treatment, P(O| C), compared to
how frequent they are without the treatment, P(O| C). This
comparison renders fairly in randomized controlled trials, in
which two comparable groups of patients are recruited (i.e.,
experimental vs. control, or treatment vs. placebo). That is,
clinicians often form their judgments on the effectiveness of a
treatment after carefully comparing the two groups, and ensuring
that occurrences of symptom remission are more frequent in the
treatment group than they are in the control group. However,
although this reasoning applies well to clinicians and researchers,
patients often lack the resources to base their decisions on such
complete information. Rather, they must form their beliefs of
effectiveness on the basis of a more limited comparison: how
often symptoms were observed before the treatment started vs.
how often they occur during the treatment, on the same patient
(usually, themselves). Most causal learning experiments do not
take into account this limitation, and instead provide participants
with information about a series of different patients (Blanco
et al., 2014;Matute et al., 2019). This is useful to investigate the
formation of causal knowledge in general, but it is not realistic
when applied to the case of patients’ beliefs of effectiveness, as the
procedure clearly departs from the actual experience of patients
with their own treatments. In the current research, we propose
a more natural setting to investigate the formation of beliefs
of effectiveness, by presenting information of a single patient
previous to, and during, a treatment (see a related approach
in Blanco and Matute, 2020).
Previous experiments that used causal learning paradigms
suggest that people can often be accurate in their judgments of
causality (Shanks and Dickinson, 1987;Wasserman, 1990;Blanco
et al., 2010), being generally sensitive to the actual contingency
presented in the experiments. However, researchers have also
reported systematic deviations, or biases. In particular, when the
probability of the desired outcome is high, judgments tend to be
higher even in null contingency conditions (Alloy and Abramson,
1979;Buehner et al., 2003;Blanco et al., 2014, 2020;Chow et al.,
2019), contributing to what has been called a “causal illusion.”
This is a bias consisting of the belief in a causal link that is actually
inexistent (Matute et al., 2015;Matute et al., 2019). The causal
illusion bias share some features with other phenomena like
the classical illusory correlation effect (Chapman and Chapman,
1967, 1969), and pseudocontingencies (Kutzner et al., 2011;
Fiedler et al., 2009).1Despite their different explanations and
1In the typical illusory correlation paradigm, which is often framed in a social
context, two groups of people (a minority group and a majority group) possess
either of two traits (a common trait and an uncommon trait). Although the two
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assumptions, all these phenomena coincide in the importance of
event probabilities, such as the probability of the cause and the
probability of the outcome, when judging causal relationships.
Thus, the causal illusion (as well as the other related
biases) has been suggested to underlie many beliefs related
to treatment effectiveness, and in particular those concerning
pseudomedicines. These are treatments claiming to be effective,
despite the lack of scientific evidence supporting levels of
effectiveness higher than those of placebo (Lilienfeld et al., 2014;
Macfarlane et al., 2020). The rationale is that, when diseases have
a high chance of spontaneous remission, people systematically
overestimate the effectiveness of treatments, even of those
treatments that are completely unable to produce an effect.
This could have serious consequences in real-life, as patients
may grant undeserved trust and reliability to treatments that
produce no actual benefit, thus losing the therapeutic opportunity
(Freckelton, 2012).
By contrast, little research has paid attention to another
possibility: that patients may also underestimate the effectiveness
of actually valid treatments. As we will show, we have reasons to
expect that causal learning can also produce this underestimation
effect under some circumstances (see an example in Yarritu
et al., 2015). For instance, by virtue of the biasing effect of
the probability of the remissions that we described above, a
treatment might appear as not effective when used on a disease
with frequent symptomatic episodes, compared to a mild disease
with less frequent symptoms.
Overview of the Experiments
In the current research, we use a causal learning procedure to
experimentally study how people form beliefs of effectiveness for
a fictitious treatment. Specifically, we present a medicine that is
able to produce a moderate improvement in symptoms (i.e., a
medicine with moderate contingency with symptom remission),
and compare the perceived effectiveness in two situations: a
disease with a high probability of symptomatic episodes, and a
disease with a low probability of symptomatic episodes. Since the
medicine equally works to reduce the frequency of episodes in
both scenarios, one would expect similar ratings of effectiveness.
However, the probability of the outcome (in this case, the
observation of symptom remissions) could bias the judgments,
producing the impression that the medicine is working better in
the group in which symptoms had lower base-rates. In contrast
with most previous studies on causal learning, we provide the
information of the treatment effectiveness on a more natural
fashion, which implies: (a) describing first how likely symptoms
are before the treatment, and then how they respond to the
introduction of the treatment, and (b) that the information given
groups have identical trait distributions, it is often concluded that the majority
group possesses the common trait to a greater extent than does the minority
group (Hamilton and Gifford, 1976). Another paradigm proposed to understand
biases in causal learning and illusory correlations is pseudocontingencies (Fiedler
et al., 2009;Kutzner et al., 2011), in which people incorrectly use the marginal
probabilities of events (e.g., the probability of the cause and the probability of
the outcome) as a hint to infer the individual-level contingency, falling prey to an
equivalent to the ecological fallacy. In practice, this means that scenarios in which
the probability of the cause and the probability of the outcome are skewed in the
same direction would produce stronger causal judgments.
through a series of trials concerns only one patient, observed
through time. This presentation format aims to mirror the
chronology and generalization ability of the observations made
by patients in real life.
ETHICS STATEMENT
The procedure was revised and approved by the Ethical Review
Board of the University of Deusto. The participants were
informed before the experiment that they could quit the study
at any moment by closing the browser window. No personal
information (i.e., name, IP address, e-mail) was collected. We did
not use cookies or other software to covertly obtain information
from the participants. All measures, groups and conditions are
disclosed. Data, materials, and R scripts for the three experiments
are publicly available at the Open Science Framework: https://osf.
io/emzbj/.
EXPERIMENT 1
Experiment 1 uses a causal learning task to investigate the
question of whether the effectiveness of a medicine can be
underestimated if the disease has a high base-rate of symptomatic
episodes. We expect that diseases that produce frequent
observations of symptoms would create the impression that the
treatment is not working as effectively as a treatment used for a
disease with less frequent symptomatic episodes.
Method
Participants
We initially planned a sample of 100 participants, which
would allow for the detection of effects of d0.57 in
the difference between two groups at 80% power. However,
data from one subject were not recorded due to technical
errors. Thus, 99 Internet users (45 male, with age M= 31.38,
SD = 9.88) participated anonymously through the Prolific
Academic platform (Palan and Schitter, 2018), in exchange
for money (0.80£ for about 10 min). The program randomly
assigned 52 participants to the Infrequent group, and 47 to
the Frequent group.
Procedure and Design
We adapted the standard trial-by-trial contingency learning
task (Wasserman et al., 1990) that is extensively used to study
human learning. The experiment was programmed in JavaScript
to run online using a web browser. The instructions (available
at the Open Science Framework, https://osf.io/emzbj/) asked
participants to imagine that they were suffering from a fictitious
disease called Hamkaoman Syndrome, which produces severe
headaches. However, this symptom appears from time to time.
Participants were told that the fictional drug Batatrim was a
potential treatment for this disease if taken on a daily basis, but it
may not work equally well for all people (i.e., “Perhaps it works in
your case, but we don’t know until we try”). The goal of the task
was to use the information to find out whether Batatrim works to
stop the headaches.
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Then, the training started by presenting a series of 40 records
sequentially. Each record corresponded to one day, and displayed
information about (a) whether the patient took Batatrim that
day and, after a delay of 1 s, (b) whether the patient reported a
headache (see Figures 1A,B). This information remained on the
screen until the button “Next” was clicked, which proceeded to
the next trial (after an inter-trial-interval of 500 ms).
The training comprised two consecutive phases. During Phase
1, as the instructions indicated, participants observed the records
corresponding to the time before the treatment had started
(“In the first round of records, you will observe the diary entries
corresponding to the time before you had any treatment, when you
were just waiting for the doctor to give you Batatrim.”). That is,
Phase 1 contained 20 medicine-absent trials, in which either the
patient reported a headache or not, and did not take any drug,
therefore it conveyed the information to compute P(O| C).
Then, in Phase 2, participants started observing the 20 records
that corresponded to the time after the treatment had started
(“You have already learned about the symptoms produced by the
Hamkaoman Syndrome when no treatment is given. Now, your
pills have arrived, and you will start taking Batatrim on a daily
basis.”). This means that only medicine-present trials were shown
FIGURE 1 | Screenshots showing the contingency learning task. (A) At the beginning of the trial, the information about the medicine (top part of the screen) is shown
for 1 s. (B) Then, the information about the presence or absence of the symptoms is shown in the center of the screen (in this example, the patient did not report
symptoms). Pressing the “Next entry” button leads to next trial after a delay (ITI) of 500 ms in which the screen is cleared. (C) After the training session, we collect an
effectiveness judgment on a –100 to +100 scale.
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Blanco et al. Symptom Base-Rate
in Phase 2, which serves to compute P(O| C). The order of the
trials within each phase (outcome-present or outcome-absent)
was randomly determined for each participant.
Table 1 summarizes the experimental design. In the Frequent
group, the symptoms were initially very frequent: 14/20 trials
in Phase 1 (before treatment), and 8/20 in Phase 2 (during
treatment). By contrast, in the Infrequent group, the symptoms
were reported less often: 8/20 trials in Phase 1, and 2/20 in
Phase 2. However, the objective contingency between treatment
and symptom occurrence was the same in both groups. In the
Frequent group, the contingency is computed as P(O| C) – P(O|
C) = 0.4–0.7 = 0.3; and in the Infrequent group it yields the
same number, P(O| C) – P(O| C) = 0.1–0.4 = 0.3. That is,
according to the contingency rule for determining effectiveness
(1p), the two groups were depicting a medicine that was equally
effective (a difference of 30% in the symptoms occurrence, in
absolute terms), although they differed in the symptom base-rate.
After the sequence of 40 trials (20 in each phase), participants
were asked several questions. First, we collected an effectiveness
judgment (i.e., “How effective is Batatrim?”), which was our main
dependent variable. The judgment was collected on a scale from
100 (“Batatrim clearly worsens your symptoms”) to 0 (“Batatrim
does not have an effect on your symptoms”), to +100 (“Batatrim
clearly improves your symptoms”). To help interpret the response
scale, we included five evenly separated small pictures of faces
ranging from 100 (sick face) to +100 (happy face). When
participants hovered the mouse pointer over these pictures, a
small box appeared with a verbal label as shown in Figure 1C.
No time constraints were imposed to answer these questions.
Second, we asked two conditional probability questions (in
random order for each participant): P(O| C) judgment (“Imagine
a different person who suffers from the same syndrome. This person
takes Batatrim on 100 consecutive days. Out of these 100 days
in which the person takes Batatrim, on how many of them will
the person report having headaches?”), and P(O| C) judgment
(“Imagine a different person who suffers from the same syndrome.
This person does not take Batatrim on 100 consecutive days. Out
of these 100 days in which the person does not take Batatrim, on
how many of them will the person report having headaches?”).
These two pieces of information, combined, serve to compute
the contingency between treatment and symptoms, and hence
are necessary to correctly assess effectiveness. By examining these
two questions, we will be able to detect whether participants
correctly encode the two probabilities.
Finally, we requested a judgment about the tendency to opt for
an alternative treatment different from Batatrim (“If you had the
chance, would you stick to your current treatment with Batatrim,
or would you try a different treatment?”). This was answered on a
scale with five options (“I’m sure I would stick to Batatrim”/“I
would probably stick to Batatrim” / “I don’t know” / “I would
probably try a different treatment” / “I’m sure I would try a
different treatment”). We expected that participants who felt that
the medicine was not working well would be more likely to stop
taking it and try a different treatment.
Results and Discussion
The main results are those obtained from the effectiveness
judgments, depicted in Figure 2. Although the medicine
was identically effective in both groups according to the
contingency information, the effectiveness judgments were
significantly higher in the Infrequent group (which featured
a lower symptom rate before the medicine was taken) than
in the Frequent group, t(97) = 4.96, p<0.001, d= 0.998.
This suggests that those diseases that course with frequent
symptomatic episodes will produce an underestimation of the
actual effectiveness of the treatment relative to those with less
frequent symptoms.
Next, we examine the judgments measuring the tendency
to switch to alternative treatments, whose descriptive statistics
appear in Table 2. The judgments could range between 1 (“I’m
sure I would stick to Batatrim”) and 5 (“I’m sure I would try a
different treatment”). These judgments were significantly higher
in the Frequent group than in the Infrequent group, t(97) = 4.22,
p<0.001, d= 0.850. That is, those participants who observed a
disease with frequent symptomatic episodes were not only more
likely to produce lower estimates for the effectiveness of the
medicine, but they were additionally less willing to adhere to the
treatment with Batatrim, despite the medicine being identically
effective in the two groups.
Finally, we analyzed the conditional probability judgments to
gain insight into how participants learned these two pieces of
information, the probability of symptoms when the medicine
was taken, P(O| C) and the probability of symptoms when no
medicine was taken, P(O| C). These judgments are depicted in
Figure 3. We conducted a mixed 2 (Group) ×2 (Probability),
revealing a main effect of Group, F(1,97) = 117.0, p<0.001,
η2
p=0.55. Overall, probability judgments were greater in the
Frequent group than in the Infrequent group, which is consistent
with the actual symptom probabilities in each group. We also
found a main effect of Probability, F(1,97) = 327.91, p<0.001,
η2
p=0.77, which just reflects the fact that the symptoms reduced
their frequency from Phase 1 to Phase 2 (i.e., the medicine was
effective). Importantly, there was no interaction, F<1. To better
interpret these results (and those of subsequent experiments,
with additional groups), we computed a “perceived contingency
score” by subtracting the two conditional probability judgments
TABLE 1 | Design of Experiment 1.
Group Phase 1 Phase 2 P(O| C) P(O| C) Contingency (1p)
Frequent Symptoms reported: 14/20 trials Symptoms reported: 8/20 trials 0.70 0.40 0.30
Infrequent Symptoms reported: 8/20 trials Symptoms reported: 2/20 trials 0.40 0.10 0.30
The two groups differ in the base-rate with which the symptoms appeared. The medicine was equally effective in both groups according to the contingency rule 1p,
because the difference in the symptom probability before and after treatment was the same in both groups, in absolute terms.
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FIGURE 2 | Mean effectiveness judgments in Experiment 1. Higher positive
values indicate a strong belief that the medicine works to reduce the
symptoms. Jittered data points are superimposed to the plot (to avoid
overplotting, the placement of data points of a given condition along the
x-axes is random). Error bars depict 95% confidence intervals for the mean.
TABLE 2 | Descriptive statistics for the alternative treatment judgments in the
three experiments.
Experiment Group Mean SD
Experiment 1 Frequent 2.85 1.23
Infrequent 1.90 1.00
Experiment 2 Frequent-Experimental 2.66 1.18
Infrequent-Experimental 1.73 0.83
Frequent-Control 3.96 0.99
Infrequent-Control 3.87 0.95
Experiment 3 High Continency-Large Change 1.98 0.91
Low Continency-Large Change 1.91 0.85
Low Continency-Small Change 3.03 1.07
The judgment was collected on a scale from 1 to 5 (1: “I’m sure I would stick to
Batatrim”; 2: “I would probably stick to Batatrim”; 3: “I don’t know”; 4: “I would
probably try a different treatment”; 5: “I’m sure I would try a different treatment”).
following the 1p rule, i.e., P(O| C)-P(O| C). These scores
can then be interpreted as the amount of contingency that
a participant perceived, based on the conditional probability
ratings. The resulting values showed no differences between
groups, t(97) = 0.65, p= 0.51, d= 0.13, indicating that the
perceived contingency was the same in both base-rate groups,
as the conditional probability estimations only differed between
groups in their absolute values. Taken together, the results
suggest that participants were able to capture accurately the
probabilities involved in the computation of contingency, as the
mean estimations were close to the actual values presented in
the task. Therefore, the underestimation of effectiveness that we
reported above cannot be explained as a failure to learn the
conditional probabilities.
FIGURE 3 | Mean conditional probability judgments in Experiment 1. Jittered
data points are superimposed to the plot (to avoid overplotting, the placement
of data points of a given condition along the x-axes is random). Error bars
depict 95% confidence intervals for the mean.
EXPERIMENT 2
Experiment 1 successfully showed that the base-rate of the
symptomatic episodes can bias the judgments of treatment
effectiveness: diseases with a higher probability of symptoms
produced lower perceived effectiveness, even if the actual
contingency was identical. This aligns with the evidence obtained
in different situations (e.g., null contingencies), and also with
results from experiments conducted in related paradigms (e.g.,
pseudocontingencies, Kutzner et al., 2011).
Still, our results could be interpreted as if our participants
were simply ignoring the contingency information, guiding their
judgments by the probability of symptoms only. That is, it could
be possible that if a medicine drives the probability of symptoms
close to zero, it would be judged as effective even if the initial
base-rate without treatment was also small, as people could just
ignore the initial base-rate. In fact, as we mentioned above,
there is ample empirical evidence indicating that judgments of
causality can be strongly biased by the probability of the outcome,
at least in null contingency situations (Alloy and Abramson,
1979;Buehner et al., 2003;Blanco et al., 2014;Chow et al., 2019;
Blanco and Matute, 2020).
Experiment 2 aims to replicate the findings of Experiment 1,
while introducing two control groups in which the actual
contingency between the treatment and symptom remissions is
zero: In these two control groups, the probability of the symptoms
is the same before and after the treatment (i.e., the medicine does
not work at all). These two probabilities match those of the two
experimental groups when taking the medicine, P(O| C), which
are identical to those used in Experiment 1. That is, for half of the
participants, symptoms will be frequent, and for the other half
they will be infrequent. Orthogonally, for half of the participants,
the medicine will work (by reducing the symptom probability in
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30%, in absolute terms), whereas for the other half it will not work
at all. Thus, if participants judge the effectiveness of the treatment
only by attending to the frequency of the symptoms and ignoring
the contingency, then the control groups would not differ from
the experimental groups, revealing that participants are only
biased by the base-rate of the effect. Conversely, if participants
do take into account contingency, they should note that control
medicines are not effective.
Method
Participants
The planned sample size was N= 200, which allows detecting
effects of d0.57 at 80% power. Data from three participants
were not recorded due to technical errors. The final sample
consisted of 197 anonymous Internet users (105 male, 91 female,
1 non-binary, with age M= 30.8, SD = 11.3), who participated
through Prolific Academic (Palan and Schitter, 2018) in exchange
for money (0.80textsterling for about 10 min). The program
randomly assigned 52 to the Frequent-Control group, 47 to
the Frequent-Experimental group, 47 to the Infrequent-Control
group, and 51 to the Infrequent-Experimental group.
Procedure and Design
The procedure was identical to that in Experiment 1. The only
change was the inclusion of two new groups that work as control
conditions (see the design in Table 3). In these groups, the actual
contingency between medicine and recovery from the symptoms
was null, which means that the medicine was completely
ineffective. That is, in addition to the two groups already present
in Experiment 1, we had the Infrequent-Control group, which
showed a base-rate of symptomatic episodes of 0.10 (i.e., 2/20
trials), both in Phase 1 and in Phase 2; and the Frequent-Control
group, which showed a base-rate of symptomatic episodes of 0.40
(i.e., 8/20 trials), both in Phase 1 and in Phase 2. In sum, now
we have included null-contingency controls for the two base-
rate conditions that were previously tested. This will allow us to
compare the two factors: will judgments depend on the symptoms
base-rate, or on contingency (or both)?
Results and Discussion
The mean effectiveness judgments are displayed in Figure 4. They
were submitted to a 2 (Base-rate) ×2 (Contingency) factorial
ANOVA. The main effect of Contingency was significant,
F(1,193) = 392.4, p<0.001, η2
p=0.67, indicating that
participants were sensitive to contingency, producing higher
judgments when the medicine was effective (Experimental
groups) than when it was not effective (Control groups). The
main effect of base-rate was also significant, F(1,193) = 12.3,
p<0.001, η2
p=0.06, meaning that the infrequent groups
produced stronger beliefs of effectiveness. Finally, the interaction,
F(1,193) = 10.0, p= 0.002, η2
p=0.05, indicated that, while the
two experimental groups were sensitive to base-rate, meaning
that we successfully replicated the effect reported in Experiment
1, t(96) = 5.67, p<0.001, d= 1.15, the two control groups
did not differ from each other, p= 0.827. That is, base-rate
information only affected the effectiveness judgments in the two
contingent groups.
The judgments about the likelihood to switch to an
alternative treatment (Table 2) aligned with the previous
conclusions. They showed, again, the main effect of Contingency,
F(1,193) = 148.55, p<0.001, η2
p=0.43, the main effect of
base-rate, F(1,193) = 13.08, p<0.001, η2
p=0.06, and the
interaction, F(1,193) = 8.92, p= 0.003, η2
p=0.04. The two
experimental groups differed from each other as in Experiment
1, t(96) = 4.56, p<0.001, d= 0.92, thus replicating the previous
result, while the two controls did not differ, p= 0.648. In
sum, the results concerning the alternative treatment judgments
were consistent with those of the effectiveness judgments:
participants in the control groups were more likely to try a
different therapeutic option, while in the experimental group
the symptom base-rate mattered, so that the higher the
symptom base-rate, the more unlikely they were to adhere
to the treatment.
Finally, we analyzed the conditional probability judgments
(Figure 5). The two Experimental groups replicated the results
from Experiment 1: P(O| C) was estimated higher than P(O|
C) in both base-rate levels, t(46) = 11.0, p<0.001, d= 1.60
(Frequent), and t(50) = 10.6, p<0.001, d= 1.49 (Infrequent),
while overall both probabilities were close to the actual values.
In the control groups, there were no differences between the
two conditional probabilities, which is consistent with the low
effectiveness judgments, p= 0.41 (Frequent), and p= 0.29
(Infrequent). Like in Experiment 1, to make the interpretation
of these results easier, we decided to compute a “perceived
contingency” score by subtracting the judgments to the P(O| C)
and to the P(O| C) questions, thus following the contingency
equation 1p. A 2 (Base-rate) ×2 (Contingency) ANOVA on
these perceived contingency values revealed a main effect of
Contingency, F(1,193) = 156.89, p<0.001, η2
p=0.45, with
no other significant effects or interaction (both Fs<0.2). The
effect of contingency means that the two experimental groups
(who were exposed to a positive contingency) perceived higher
TABLE 3 | Design of Experiment 2.
Group Phase 1 Phase 2 P(O| C) P(O| C) Contingency (1p)
Frequent-Experimental Symptoms reported: 14/20 trials Symptoms reported: 8/20 trials 0.70 0.40 0.30
Infrequent-Experimental Symptoms reported: 8/20 trials Symptoms reported: 2/20 trials 0.40 0.10 0.30
Frequent-Control Symptoms reported: 8/20 trials Symptoms reported: 8/20 trials 0.40 0.40 0.00
Infrequent-Control Symptoms reported: 2/20 trials Symptoms reported: 2/20 trials 0.10 0.10 0.00
In addition to the two experimental groups, identical to those in Experiment 1, this experiment included two control groups in which the probability of the symptoms during
the treatment were the same as in the experimental groups, but the contingency was null (the medicine did not work at all).
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FIGURE 4 | Mean effectiveness judgments in Experiment 2. Higher positive
values indicate a strong belief that the medicine works to reduce the
symptoms. Jittered data points are superimposed to the plot (to avoid
overplotting, the placement of data points of a given condition along the
x-axes is random). Error bars depict 95% confidence intervals for the mean.
FIGURE 5 | Mean conditional probability judgments in Experiment 2. Jittered
data points are superimposed to the plot (to avoid overplotting, the placement
of data points of a given condition along the x-axes is random). Error bars
depict 95% confidence intervals for the mean.
contingency levels than did the two control groups (who were
exposed to a null contingency), irrespective of the differences in
base-rate. Thus, the experimental groups replicated the results
of Experiment 1, by not finding an effect of base-rate on the
perceived contingency: it seems that the perceived contingency
was the same regardless of the frequency of presentation
of the symptoms.
EXPERIMENT 3
The results of Experiment 2 suggested that the effectiveness
judgments produced by participants were affected by the
symptom base-rate. However, participants were not completely
ignoring the contingency information, as they, at least, were able
to discriminate between a low/moderate contingency level (0.30)
and a null contingency (0). The question is: how do participants
use base-rate information to form their judgment?
Contingency, as described in section “Introduction,” is an
objective rule used to assess treatment effectiveness, which in
principle allows the comparison of treatments for different
cases, with different levels of symptom frequency. The two
previous experiments suggested that participants, however,
produce effectiveness judgments that are not only determined by
contingency, but also biased by the frequency of the symptoms.
It is possible to further investigate the way in which people
use symptom base-rates when judging effectiveness. In fact, in
our previous experiments, we fixed the contingency level to a
given value of 0.30 (or zero in the control groups in Experiment
2), which means that the treatment always produced the same
amount of change in the symptom probability in absolute terms.
However, the groups differed in the amount of change in the
symptom probability relative to the base-rate level. That is, when
the treatment reduces the symptom occurrence from 0.70 to 0.40
(i.e., group Frequent), the absolute difference, or contingency,
is 0.30, but the amount of reduction relative to the base-rate
is 43%, i.e., (0.40–0.70)/0.70 = 0.43. By contrast, when the
treatment reduces the symptom occurrence from 0.40 to 0.10
(i.e., group Infrequent), the absolute change remains 0.30 but
the relative change is larger, 75%, i.e., (0.10–0.40)/0.40 = 0.75.
Thus, it is possible that participants in our previous experiments
were judging effectiveness by using the change in the symptoms
proportional to the base-rate, rather than by using the absolute
difference (contingency). This would be a different strategy to
deal with effectiveness information that takes into account base-
rates, and that could explain our results so far (note that using
this strategy can also explain the results from the two groups with
a null contingency).
Therefore, we designed Experiment 3 to test for this
possibility. In Experiment 3, the groups differed either in the
contingency level (high vs. low) or in the amount of change
proportional to the base-rate (small vs. large). The parameter
constellations were chosen such that the two possible drivers
for participants’ judgments (absolute differences vs. relative
differences) could be pit against each other.
Method
Participants
We planned a sample size of N= 150 for this design
of three groups (50 participants per group), which allows
detecting effects for the difference between pairs of groups
of d0.57 at 80% power. Data from one participant were
lost due to technical errors/connection issues. The final sample
consisted of 149 participants (70 women, 79 men, with age
M= 27.3, SD = 8.66), recruited in the same way as in
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the previous experiments. The program randomly assigned
55 to the High Contingency-Large Change group, 57 to the
Low Contingency-Large Change group, and 37 to the Low
Contingency-Small Change group.
Procedure and Design
The procedure was identical to the previously reported
experiments, except for the probability of observing symptoms
during the training, which was manipulated across the three
groups to obtain two different levels of contingency and
two different levels of the change proportional to the base-
rate (Table 4). That is, in the High Contingency-Large
Change group, the contingency between the treatment and
the symptom occurrence was high (0.60) in absolute terms,
and the change proportional to the symptom base-rate was
large (a reduction of 75% from the initial symptom base-
rate); in the Low Contingency-Large Change group, the
contingency was low (0.30), but when considered as a
proportion of the initial symptom base-rate, the change was
still large (a reduction of 75% of the initial symptoms);
finally, in the Low Contingency-Small Change group, the
contingency was low (0.30), and the change proportional
to the base-rate was small (a reduction of 37.5% of the
initial symptoms). By comparing these groups pairwise, as
they share one of the parameters (either contingency or
proportional change) but not the other, we can eventually find
out which of the two parameters more clearly affects judgments
of effectiveness.
Results and Discussion
Figure 6 contains the mean effectiveness judgments in the
three groups of Experiment 3. We were only interested in the
comparisons between the groups that shared one parameter
value (either contingency or proportional change) and differed
on the other. The Low Contingency-Large Change and the
Low Contingency-Small Change groups, despite having
identical contingency, differed significantly, t(92) = 5.87,
p<0.001, d= 1.24, suggesting that contingency was not
a key aspect for effectiveness judgments, and rendering
plausible that the proportional change played a role in
this effectiveness assessment. This possibility was further
reinforced by the finding that the Low Contingency-Large
Change and High Contingency-Large Change groups,
which shared the same proportional change but show
different contingency, did not significantly differ from each
other, p= 0.81.
The judgments about the likelihood to switch to an alternative
treatment (Table 2) showed the same pattern as the effectiveness
judgments: In the Low Contingency-Large Change group,
participants were significantly more likely to stick to the
treatment than they were in the Low Contingency-Small Change
group, t(92) = 5.61, p>0.001, d= 1.18. As it happened
with effectiveness judgments, no differences were found in the
likelihood to adhere to the actual treatment when comparing
groups with similar proportional change, i.e., Low Contingency-
Small Change vs. High-Small, p= 0.92.
Finally, Figure 7 depicts the conditional probability
judgments for Experiment 3. Once again, the judgments
were close to the actual values presented in the training. In all
three groups, the difference between P(O| C) and P(O| C)
was significant (all ps<0.001), consistent with the perception
of at least some degree of effectiveness. Additionally, we used
these conditional probability judgments to reconstruct the
perceived contingency (by subtracting the two conditional
probabilities) and the perceived proportional change between
phases (by computing the contingency and dividing it by the
symptom base-rate before the treatment). We found that groups
with different contingency levels showed different perceived
contingency scores: the High Contingency-Large Change
group produced a larger difference between the conditional
probabilities than did the other two groups, both ps<0.007.
On the other hand, groups with an identical contingency level
did not differ in this measure: Low Contingency-Large Change
vs. Low Contingency-Small Change, p= 0.95. Concerning
the perceived proportional change, this score was higher for
the groups with larger changes, even if they implied the same
contingency: Low Contingency-Small Change differed both from
High Contingency-Large Change and from Low Contingency-
Large Change (both ps<0.030). By contrast, groups with
similar proportional change did not differ in this measure:
Low Contingency-Large Change vs. High Contingency-Large
Change, p= 0.998.
In a nutshell, it seems that effectiveness judgments
were sensitive to proportional change in the conditional
probabilities, but not to their absolute differences. This effect
was also found in the desire to replace the treatment by an
alternative. However, conditional probabilities seemed to be
accurately captured.
TABLE 4 | Design of Experiment 3.
Group Phase 1 Phase 2 P(O| C) P(O| C) Contingency (1p) Change (%)
High Contingency-Large Change Symptoms reported: 16/20 trials Symptoms reported: 4/20 trials 0.80 0.20 0.60 75
Low Contingency-Large Change Symptoms reported: 8/20 trials Symptoms reported: 2/20 trials 0.40 0.10 0.30 75
Low Contingency-Small Change Symptoms reported: 16/20 trials Symptoms reported: 10/20 trials 0.80 0.50 0.30 37.5
In this experiment, the probability of observing a symptom was manipulated between groups so that two of them showed the same low level of contingency (groups Low
Contingency-Large Change and Low Contingency-Small Change), contrasting with a high contingency group (High Contingency-Large Change). Additionally, the amount
of change between phases proportional to the symptom base-rate was identical (large) in two groups (High Contingency-Large Change and Low Contingency-Large
Change), despite they diverged in their contingency level, and different from the Low Contingency-Small Change group.
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FIGURE 6 | Mean effectiveness judgments in Experiment 3. Higher positive
values indicate a strong belief that the medicine works to reduce the
symptoms. Jittered data points are superimposed to the plot (to avoid
overplotting, the placement of data points of a given condition along the
x-axes is random). Error bars depict 95% confidence intervals for the mean.
FIGURE 7 | Mean conditional probability judgments in Experiment 3. Jittered
data points are superimposed to the plot (to avoid overplotting, the placement
of data points of a given condition along the x-axes is random). Error bars
depict 95% confidence intervals for the mean.
GENERAL DISCUSSION
Which Is the Rule for Estimating
Effectiveness?
Beliefs of treatment effectiveness can be understood as the
result of causal learning (Rottman et al., 2017), under the
assumption that an effective treatment produces a change in
the likelihood of symptom improvement compared to a control
condition (e.g., taking no treatment). This allows us to investigate
effectiveness beliefs by means of causal learning experiments,
and to advance predictions based on the results described in
this literature. Previous studies have focused on how completely
ineffective medicines (e.g., pseudomedicines) can appear to be
effective under some circumstances (Blanco et al., 2014;Matute
et al., 2019). However, fewer experiments have been conducted
to explore the possibility that actually effective treatments are
seen as less effective due to the biases described in the causal
learning literature.
Here, we have reported how beliefs of effectiveness are
sensitive to the base-rate of the symptomatic episodes in a way
that does not conform to the rule for computing contingency,
1p. That is, in Experiments 1 and 2, a fictitious medicine
with a low/moderated contingency with health improvement
(reduction of 0.30 in the probability of symptoms, in absolute
terms) was tested in two different scenarios: a disease with
high base-rate of symptoms and a disease with low base-rate
of symptoms. Our results indicated that base-rates affected the
judgments of effectiveness, so that a valid medicine was judged
as less effective when the symptoms were very frequent before
the treatment. This would modulate the perceived effectiveness
of a treatment as a function of the symptom frequency, which
could lead to mistaken conclusions when patients examine their
treatments’ effectiveness, or when they compare between diseases
or patients with diverging symptom base-rates. In fact, according
to our results, it is those patients who show symptoms with
greater probability who will be more likely to underestimate the
effectiveness of a moderately valid treatment. The implication of
this is that these patients who suffer from frequent symptomatic
episodes should be carefully supervised, as we know that
treatment effectiveness beliefs are core to treatment adherence
(Leventhal et al., 1992;Dilla et al., 2009). Additionally, those
patients who underestimate the effectiveness of their treatment
will be probably at risk of replacing their scientifically valid
treatment by a different, probably less effective one, or even by
a pseudomedicine, as our experiments also reveal through the
alternative treatment question. Not surprisingly, lack of trust in
scientific medicine is one of the predictors of pseudomedicine
usage (Macfarlane et al., 2020).
The underestimation of the effectiveness when the symptom
base-rate is high (Experiment 1) could be due to participants
judging effectiveness on the basis of how infrequent the
symptoms are when the treatment is taken. That is, any medicine
that drives the probability of symptoms close to zero (i.e.,
complete healing) would be judged as effective, while the initial
base-rate without treatment could be ignored. This possibility
was examined in Experiment 2, which included control groups
with null contingency: that is, the symptom-base-rate was kept
identical before and during the treatment. Since participants
in Experiment 2 were able to discriminate between the two
contingency levels while still replicating the bias reported in
Experiment 1, it seems that people’s judgments are not entirely
driven by the symptom level obtained at the end of the treatment.
Finally, Experiment 3 tested a potential way in which people
could be using the symptom base-rate information when making
their judgment, which is different from contingency. As we have
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described it, contingency is simply the difference between the
symptom probability before and during the treatment, in absolute
terms. Thus, it is an objective measure that is independent of the
initial base-rate level. That is, a reduction of symptom probability
from 0.70 to 0.40 is the same as one from 0.40 to 0.10. In this
type of scenario, a contingency index, 1p (Allan, 1980), has been
used as the traditional benchmark to assess causality and, hence,
treatment effectiveness. However, people could be focusing on
the reduction in symptom probability relative to the initial base-
rate value, instead of in absolute terms. That is, when symptoms
decrease from 0.40 to 0.10, they are reducing in 75% of the initial
value. Experiment 3 presented three groups varying in either
their contingency or their change proportional to the base-rate.
Judgments were systematically guided by the change proportional
to base-rate, rather than by contingency, suggesting that this is
the way people use base-rate information to estimate effectiveness
in this type of experiments. The explanation is compatible with all
the results that we report in this article.
Is it reasonable to use proportional change, rather than
absolute change (contingency) when assessing treatment
effectiveness? In fact, researchers commonly use proportional
change as a success index when testing the effectiveness of an
intervention (especially in repeated-measures designs). For
example, a treatment for depression could be regarded as useful
if it reduces depressive symptoms by 10% from the baseline
(see an example of the use of percent change from baseline, Lin
et al., 2013). This is the logic underlying likelihood ratios (e.g.,
probability of the outcome given the treatment, relative to a
control condition with no or other treatment) and odd ratios,
which are common to estimate treatment effectiveness, test
sensitivity, and risk in scientific studies (the same rationale is
also present in the widely used Bayes Factors, Kass and Raftery
(1995), which represent the support for one hypothesis relative
to the null by means of an all-purpose likelihood ratio, although
their computation is completely different). However, when
used directly to assess the effectiveness of a treatment from the
observation of the conditional probabilities, this approach can be
problematic, and methodologists recommend to avoid it in most
cases (Vickers, 2001;Tu, 2016). First, proportional change makes
sense only with variables measured in ratio scales, in which zero
is a meaningful value (fortunately, this condition holds in our
case, as we are comparing probabilities). Additionally, note that,
while contingency is an effectiveness measure that is insensitive
to the symptom base-rate, the proportional change will strongly
depend on this piece of information, so that those patients or
conditions in which symptoms appear very often (i.e., high base-
rate) will produce systematically smaller proportional changes
than those in which symptoms are less frequent. Indeed, research
works using this proportional change as outcome variable
usually report strong correlations between the effectiveness of
the manipulation and the baseline level (Tu and Gilthorpe, 2007;
Tu, 2016), so that higher baseline levels apparently “reduce” the
effectiveness. Moreover, despite it appearing to be an intuitive
concept, presenting the information as proportional change
can be confusing for patients. For example, when laypeople are
presented with the results of a study on risk factors in terms of
proportional change from baseline, they tend to erroneously
interpret it as change in absolute terms (e.g., a reduction of 10%
is interpreted as if a baseline score of 50 were reduced to 40,
rather than 45) (Bodemer et al., 2014). Admittedly, there are
situations in which proportional change could be a more useful
measure of effectiveness than is direct difference (e.g., causes
that produce a multiplicative effect), but most of times changes
expressed as proportions are hard to generalize, as they depend
on baseline levels that can vary between conditions or individuals
(e.g., a change of 0.3 points in absolute terms can be small when
the baseline is 0.9, but large when the baseline is 0.35). Thus, a
direct difference measure such as the 1p index could be more
versatile than likelihood ratios and related measures based on
proportional change. In sum, proportional change from baseline
is neither an accurate index for assessing treatment effectiveness,
nor a good way to communicate it, at least in most situations.
Hence, using proportional change could be considered a strategy
that measures effectiveness, but in a suboptimal way that could
lead to erroneous conclusions in some circumstances.
However, the finding that people spontaneously tend to
use proportional change as an effectiveness index (as the
results of Experiment 3 indicate) is interesting for theoretical
reasons. Research on human causal and contingency learning
has traditionally focused on objective measures such as 1p
or similar rules (Perales and Shanks, 2007), not considering
the possibility that participants use proportional change as a
direct cue to causality assessment. Nonetheless, certain Bayesian
theories of causal induction such as Causal Support (Griffiths
and Tenenbaum, 2005) formalize causal inference in a way that
involves likelihood ratios, that is, the probability of observing
the data given one hypothesis (and model) relative to the
probability of observing the data given an alternative one, which
is structurally similar to a Bayes Factor (Kass and Raftery,
1995). For example, Causal Support computes a ratio of the
likelihood of observing the current data under the model that
assumes a causal link between cause and outcome, relative
to the model that assumes no causal link, P(data| hypothesis,
model1)/P(data| hypothesis, model0). The computation of Causal
Support is more complex than merely comparing the two
conditional probabilities, and it involves additional assumptions
about causality. However, we mention it here because there could
be some structural resemblance between the way the model
computes causal strength (and the way Bayes Factors express
support for a hypothesis) and the strategy apparently exhibited
by our participants. Our experiments were not designed to
investigate these questions, but the findings of Experiment 3
could inspire further studies to better understand how people
incorporate base-rates to assess effectiveness and causality.
In fact, there is evidence that people use proportional change
as a cue in completely different paradigms. For example, when
they compare two numbers, people’s responses are affected
by the ratio between the two quantities (i.e., “numerical size
effect”; Moyer and Landauer, 1967). Additionally, studies on
Bayesian reasoning also show that participants can use the
information expressed as likelihood ratios to elaborate their
judgments [although these judgments are often incorrect,
especially when the information is given in terms of probabilities
rather than natural frequencies (Gigerenzer and Hoffrage, 1995;
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Hoffrage et al., 2015)]. Nevertheless, this paradigm is quite
different from ours: Bayesian reasoning tasks first provide the
conditional probabilities and base-rates, and then ask about
the probability that an individual observation corresponds to a
given category (which requires using the base-rate information),
whereas our contingency learning task provides a sample of
observations already classified, and then requests a generalized
rule (i.e., whether there is a causal link or not) that in principle
should hold regardless of the particular base-rate observed.
Further studies should examine the potential similarities and
connections between these numerical cognition effects and
contingency learning phenomena.
It is also worth discussing the results concerning the
conditional probability judgments. Across the three experiments,
we found that the departure from contingency was detected in
effectiveness judgments, formulated as a causal question, but not
in the conditional probability judgments. This is in line with
recent studies on the causal illusion (Chow et al., 2019) and
coincides with previous claims that, generally, causal estimations
are more prone to bias than are other types of judgments, such
as predictions (Vadillo et al., 2005). This also has theoretical
implications: some authors have proposed that biases in causal
learning are the result of processes that appear in the moment
of emitting the judgment, rather than in the encoding phase
(Allan et al., 2008). Indeed, in our experiments, the basic pieces
of information needed to compute the contingency index 1p,
P(O| C) and P(O| C), seem to have been correctly acquired.
Therefore, the effects we have described in this article might be
explained by the strategies or rules that people use to combine the
information and form their judgment (e.g., using proportional
change instead of contingency), rather than by learning or
encoding phenomena. However, we must remain cautious when
interpreting the conditional probability judgments, as they were
always requested after the effectiveness judgment, and therefore
they could be contaminated.
Methodological Aspects
Additionally, these experiments included several procedural and
methodological innovations that depart from most previous
literature, and that deserve discussion. First, most experiments
using causal learning tasks in medical scenarios present the four
types of trial (i.e., medicine-healing, medicine-no healing, no
medicine-healing, and no medicine-no healing) in intermixed,
often random, orders. Additionally, the information given
on each trial concerns usually a different patient. Thus, the
traditional task resembles a clinical study in which a sample of
patients is examined, in no particular order. This causal learning
task has advantages. For example, it prevents participants
from assuming that trials are autocorrelated (i.e., that there is
dependency between trials, so that the outcome of one trial
can be affected by previous trials) and avoids order effects by
randomizing the trial order. However, this procedure does not
capture well the experience of patients who judge their own
treatments, which is a highly common situation in real life.
Patients cannot normally access a sample of participants to test
the treatment. Rather, they can only test the effectiveness on
themselves, and the information is, most of the time, examined
in a particular order: first, they know how often the symptoms
appear before the treatment, i.e., they observe P(O| C). Then,
they start the treatment and may check if this base-rate is
affected, i.e., they observe P(O| C). In our two experiments,
we tried to present a situation that mirrors this natural setting,
by observing instances of symptom occurrences on a single
individual (additionally, the task was described in second person,
to help the participants imagine that they were the patients), and
by arranging the information in two phases, one before and one
during the treatment.
This choice to split the training session into two phases, P(O|
C) and P(O| C), seems to have yielded interesting results. In
most similar studies with the traditional task (with the trials
arranged in random order), a common finding is that null
contingencies are overestimated when the probability of the
outcome is high (see reviews in Matute et al., 2015, 2019).
Here, Experiment 2 presented a null contingency condition
with high chances of remission: in fact, the training in the
Infrequent-Control group in which the symptoms were absent
in 90% of the trials is almost identical to previous studies that
showed strong overestimations of effectiveness, or causal illusions
(Blanco et al., 2014;Blanco and Matute, 2019), except for the
fact that the trials were separated into two phases, one for
P(O| C), and one for P(O| C). This difference seems to have
abolished the causal illusion, as Experiment 2 shows clearly that
most participants correctly identified the null contingency. We
can only speculate as to why this procedural change makes
such a big effect on judgments. One possibility is that, by
arranging the trials in separate phases, the working memory
demands are lower than in the usual experiment, thus making
the task easier to solve. A previous study by Willett (2017)
tested a related argument. In her experiment, the contingency
information was presented in a summarized, pictorial format
(depicting faces that represent the cases), rather than trial
by trial. The design featured two levels of P(O), high and
low, in a null contingency situation. Critically, the pictorial
information could be presented in either an “organized” way
(which groups together the pictures of faces corresponding to
the outcome, on the one hand, and the pictures that represent
the no-outcome, on the other hand), or in a “scrambled”
way (which intermixed the pictures in a random fashion). We
can see a similarity between the scrambled condition and the
usual contingency training with intermixed trials, and between
the organized condition and our two-phases procedure. This
experiment showed that the overestimation of contingency
was stronger in the scrambled condition than it was in the
organized condition, although the results were only marginally
significant. However, one must be cautious when interpreting
this evidence, as the information was presented in table format
in Willett’s experiment, whereas our experiments used the trial-
by-trial format. Future experiments should further investigate the
potential sensitivity of causal illusions to cognitive demands on
standard trial-by-trial procedures. A second option to interpret
the reduced illusion that we found in our Experiment 2 is that,
by separating the phases, we are highlighting that outcomes can
occur in two different contexts (i.e., in the presence and in the
absence of the treatment), hence, implicitly inviting participants
to compare them, as in the 1p rule (Allan, 1980). This possibility
could be explored in future studies.
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The second methodological change from most previously
published experiments is the use of a bidirectional scale. As
the association between two variables can be either positive or
negative, contingency (usually assessed with the 1p index) can
take on either positive or negative values, which translates to
causally generative scenarios and causally preventive scenarios
(Perales et al., 2016). Consequently, the response scale in our
experiments was bidirectional, from 100 (the medicine worsens
the symptoms) to +100 (the medicine improves the symptoms).
Note that most research carried out on contingency learning
biases have used the unidirectional scale, from 0 (no effect)
to +100 (perfect effectiveness), see, e.g., Matute et al. (2019).
The bidirectional scale that we used here has the advantage of
correctly capturing the potential range of the contingency and
causality values. However, it is also more difficult to understand
for some participants. Previous research has suggested that,
in general, both types of scale are valid to capture common
contingency learning phenomena (see, e.g., Blanco and Matute,
2020, who report the same effects with unidirectional and
bidirectional scales).
Finally, in addition to effectiveness judgments and conditional
probability estimations, we also collected judgments about the
likelihood of using an alternative treatment, aimed at measuring
the desire to quit the treatment and look for alternatives. Since
the results were the same as those found in the effectiveness
ratings, we could conclude that beliefs of effectiveness generalized
to this question: participants who saw the disease with high
symptom base-rate underestimated the effectiveness of the
medicine, and were less willing to adhere to it. Our alternative
treatment question contributes, thus, to fill the gap between
causal estimations that are typically collected in contingency
learning experiments and actual decisions made by patients
when dealing with real diseases. The practical implication of our
finding is that those patients who underestimate their treatment’s
effectiveness are less satisfied, and perhaps are more vulnerable
to the offer of alternative options such as pseudomedicines and
fraudulent health products (Macfarlane et al., 2020).
Practical Implications
More generally, we can outline a few implications of our
research to clinical practice, although they involve some degree
of speculation. Since our procedure is more ecological than
the traditional causal learning experiment in certain aspects
(order of the information that is presented, observation of only
one patient instead of samples. . .), these experiments are well
endowed to inform decisions and insights for real patients
using real medicines. The first one is that people use, at best,
inefficient methods for assessing effectiveness. Either they are
biased by the symptom base-rate directly (as Experiments 1
and 2 initially suggested), or they use proportional change
from the symptom base-rate (as Experiment 3 indicated),
which is better but still biases the effectiveness assessment,
producing lower estimations of effectiveness with larger symptom
base-rates. Thus, it is necessary that practitioners watch their
patients closely to prevent them from underestimating their
treatments’ success, and consequently abandoning the treatment
or resorting to pseudomedicine. As mentioned, the patients
who are most vulnerable to the effectiveness underestimation
are those who initially experience frequent symptoms. Perhaps
the misestimation of effectiveness could be reduced if clinicians
try to make patients aware that changes in symptom rate
proportional to the baseline can be in fact misleading, and
provide them with more objective statistics such as absolute
differences, when they are available. Previous research suggests
that giving this information in frequency format (Bodemer
et al., 2014) or pictorial format (Tubau et al., 2019) can
greatly improve patients’ comprehension and the chances of
communication success. On the other hand, as Experiment
2 shows, the chronological order in which patients usually
know the contingency information in natural settings (i.e., first
they get to know the symptom base-rate without treatment,
then they experience the symptom occurrence rate during
the treatment) seems to alleviate other effectiveness estimation
problems such as the causal illusion (Matute et al., 2015, 2019)
that is more easily observed when the trials are presented
in random order. Thus, in this case the natural presentation
order works in our favor to prevent the overestimation
of effectiveness.
DATA AVAILABILITY STATEMENT
The experiment materials, the datasets analyzed for this study,
and the R scripts to reproduce the tables and figures can be found
in the Open Science Framework: https://osf.io/emzbj/.
ETHICS STATEMENT
The studies involving human participants were reviewed and
approved by the Ethical Review Board of the University of
Deusto (CEUD). The patients/participants provided their written
informed consent to participate in this study.
AUTHOR CONTRIBUTIONS
FB, MM-F, and HM contributed to the conception and design
of the study. MM-F programmed the experiment. FB performed
the statistical analysis. FB wrote the first draft of the manuscript.
All authors contributed to the manuscript revision, read, and
approved the submitted version.
FUNDING
Support for this research was provided by Grants PSI2017-83196-
R, RTI2018-096700-J-I00, and PSI2016-78818-R from Agencia
Estatal de Investigación of the Spanish Government (AEI)
awarded to FB, MM-F and HM, respectively, as well as Grant
IT955-16 from the Basque Government awarded to HM.
ACKNOWLEDGMENTS
We thank the editor and the two reviewers who read an early
version of this research for pointing us to this limitation of
Experiments 1 and 2, and thus for inspiring Experiment 3.
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Blanco et al. Symptom Base-Rate
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Conflict of Interest: The authors declare that the research was conducted in the
absence of any commercial or financial relationships that could be construed as a
potential conflict of interest.
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... Thus, the higher the probability of the cause, the higher the contingency reported between cause and effect, even in the case in which the actual contingency is null [52][53][54] . A similar effect has been described when the effect is presented with high frequency 53,[55][56][57][58] . ...
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Many experiments have shown that humans and other animals can detect contingency between events accurately. This learning is used to make predictions and to infer causal relationships, both of which are critical for survival. Under certain conditions, however, people tend to overestimate a null contingency. We argue that a successful theory of contingency learning should explain both results. The main purpose of the present review is to assess whether cue-outcome associations might provide the common underlying mechanism that would allow us to explain both accurate and biased contingency learning. In addition, we discuss whether associations can also account for causal learning. After providing a brief description on both accurate and biased contingency judgments, we elaborate on the main predictions of associative models and describe some supporting evidence. Then, we discuss a number of findings in the literature that, although conducted with a different purpose and in different areas of research, can also be regarded as supportive of the associative framework. Finally, we discuss some problems with the associative view and discuss some alternative proposals as well as some of the areas of current debate. (PsycINFO Database Record (c) 2019 APA, all rights reserved).
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Impaired selective fear learning has been advanced as a core mechanism involved in excessive spreading of protective responses such as pain-related fear and avoidance leading to disability in chronic pain conditions. Using the litmus test for selective learning effects, the blocking procedure, we tested the hypothesis that fibromyalgia patients show less selective threat learning than healthy controls. We introduce a novel selective learning task based around a clinical diary scenario. On a trial-by-trial basis, participants rated whether they expected certain situations (A, B, Z, X) in the diary of a fictive fibromyalgia patient would trigger pain in that patient. The procedure did not involve any experimental pain induction, since the verbal outcomes "pain" or "no pain" were used. During the elemental acquisition phase, one situation was followed by "pain" (A+, e.g. "Kim slept badly, and reports pain"), whereas another situation was followed by "no pain" (Z-, e.g. "Kim was stressed, and reports no pain"). During the compound acquisition phase, another situation (X), referred to as the blocked stimulus, was presented in compound with a previously pain-eliciting situation and also paired with "pain" (AX+, e.g., Kim slept badly" and "Kim has vacuumed", and reports pain). Simultaneously, a novel situation was introduced and also followed by "pain" (B+). Within-group comparisons showed blocking (i.e., significant difference between B and X) in the healthy controls, but not in the fibromyalgia patients. This study is the first in directly assessing differences in selective learning between fibromyalgia patients and healthy controls using a blocking procedure.