10-(4-Phenylpiperazine-1-carbonyl)acridin-9(10H)-ones and related compounds: Synthesis, antiproliferative activity and inhibition of tubulin polymerization

Article abstract of DOI:10.1016/j.bmcl.2020.127687

As part of our continuing search for potent inhibitors of tubulin polymerization, two novel series of 42 10-(4-phenylpiperazine-1-carbonyl)acridin-9(10H)-ones and N-benzoylated acridones were synthesized on the basis of a retrosynthetic approach. All newly synthesized compounds were tested for antiproliferative activity and interaction with tubulin. Several analogs potently inhibited tumor cell growth. Among the compounds tested, 10-(4-(3-methoxyphenyl)piperazine-1-carbonyl)acridin-9(10H)-one (17c) exhibited excellent growth inhibitory effects on 93 tumor cell lines, with an average GI₅₀ value of 5.4 nM. We were able to show that the strong cytotoxic effects are caused by disruption of tubulin polymerization, as supported by the EBI (N,N'-Ethylenebis(iodoacetamide)) assay and the fact that the most potent inhibitors of cancer cell growth turned out to be the most efficacious tubulin polymerization inhibitors. Potencies were nearly comparable or superior to those of the antimitotic reference compounds. Closely related to this, the most active analogs inhibited cell cycling at the G2/M phase at concentrations down to 30 nM and induced apoptosis in K562 leukemia cells. We believe that our work not only proves the excellent suitability of the acridone scaffold for the design of potent tubulin polymerization inhibitors but also enables synthetic access to further potentially interesting N-acylated acridones.

Full text of DOI:10.1016/j.bmcl.2020.127687

J. Dairy Sci. 97:3394–3408
http://dx.doi.org/10.3168/jds.2013-7087
© American Dairy Science Association®, 2014.
Open access under CC BY-NC-ND license.
Quantifying veterinarians’ beliefs on disease control and exploring
the effect of new evidence: A Bayesian approach
H. M. Higgins,*1 J. N. Huxley,† W. Wapenaar,† and M. J. Green†
*Faculty of Health and Medical Sciences, School of Veterinary Medicine, Guildford, University of Surrey, GU2 7TE, United Kingdom
†University of Nottingham, School of Veterinary Medicine and Science, Sutton Bonington Campus, Leicestershire, LE12 5RD, United Kingdom
ABSTRACT
beliefs. The wide variations observed have implications
for designing future projects. Although many factors
influence disease control, nonetheless the heterogeneity
in beliefs also raises concern over the extent to which a
broadly consistent approach is currently being achieved;
it supports the argument for more randomized clinical
trials and for national programs to control nonstatu-
tory endemic diseases.
The clinical beliefs (expectations and demands) of
veterinarians regarding herd-level strategies to control
mastitis, lameness, and Johne’s disease were quanti-
fied in a numerical format; 94 veterinarians working
in England (UK) were randomly selected and, during
interviews, a statistical technique called probabilistic
elicitation was used to capture their clinical expecta-
tions as probability distributions. The results revealed
that markedly different clinical expectations existed for
all 3 diseases, and many pairs of veterinarians had ex-
pectations with nonoverlapping 95% Bayesian credible
intervals. For example, for a 3-yr lameness intervention,
the most pessimistic veterinarian was centered at an
11% population mean reduction in lameness prevalence
(95% credible interval: 0–21%); the most enthusiastic
veterinarian was centered at a 58% reduction (95%
credible interval: 38–78%). This suggests that a major
change in beliefs would be required to achieve clinical
agreement. Veterinarians’ clinical expectations were
used as priors in Bayesian models where they were
combined with synthetic data (from randomized clini-
cal trials of different sizes) to explore the effect of new
evidence on current clinical opinion. The mathematical
models make predictions based on the assumption that
veterinarians will update their beliefs logically. For ex-
ample, for the lameness intervention, a 200-farm clinical
trial that estimated a 30% mean reduction in lameness
prevalence was predicted to be reasonably convincing
to the most pessimist veterinarian; that is, in light of
this data, they were predicted to believe there would be
a 0.92 probability of exceeding the median clinical de-
mand of this sample of veterinarians, which was a 20%
mean reduction in lameness. Currently, controversy ex-
ists over the extent to which veterinarians update their
beliefs logically, and further research on this is needed.
This study has demonstrated that probabilistic elicita-
tion and a Bayesian framework are useful for evaluat-
ing the diversity and strength of veterinarians’ clinical
Key words: evidence-based medicine, Bayesian up-
dating, clinical belief, probabilistic elicitation
INTRODUCTION
In the United Kingdom, most major endemic dis-
eases of cattle are not under statutory control and
hence the health of the national herd is critically reliant
on farmers and their advisors. The clinical beliefs held
by veterinarians working in private practice are thus
important because they underpin the advice provided
to farmers, the decisions that are made, and the way
in which new research evidence is interpreted and ap-
plied. If new research is to have any effect it must be
capable of changing veterinarians’ current beliefs, and
ultimately those of the farmers, otherwise it risks being
of limited value and will not deliver a cost beneficial re-
turn on the investment necessary to conduct the work.
If the unknown parameter of interest, say θ, is de-
fined as the effect of a specified treatment (or disease
intervention), then a veterinarian’s clinical expectations
regarding θ pertain to the possible values they believe θ
will take, based on their current clinical experiences and
knowledge (i.e., their beliefs, which includes informa-
tion and influences from all possible sources). Within
a Bayesian statistical framework, clinical expectations
can be expressed in a numerical format as a probability
distribution, using a statistical technique called proba-
bilistic elicitation (O’Hagan et al., 2006). Once expec-
tations are captured as probability distributions, it is
possible to quantitatively study the variation in clinical
expectations, and to explore, using Bayesian statisti-
cal models, the response of veterinarians with different
clinical expectations to new information (Parmar et al.,
1994). For a single continuous unknown parameter, θ,
Bayes theorem can be written as
Received May 31, 2013.
Accepted February 12, 2014.
1Corresponding author: h.higgins@surrey.ac.uk
3394

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QUANTIFYING BELIEFS AND BAYESIAN UPDATING
π(θ|x) v π(x|θ) π(θ),
[1] different initial beliefs and predicted that important dif-
ferences in opinion would exist in light of the evidence.
where, in the context of this paper, π(θ) is the vet- However, to the authors’ knowledge, no studies have ac-
erinarian’s current clinical expectation for θ, expressed tually quantified veterinarians’ clinical expectations or
as a probability distribution; π(x|θ) is the likelihood demands concerning herd-level interventions to reduce
function (based on new synthetic data, x); and π(θ|x) is the endemic diseases of cattle. This omission is striking
the posterior probability distribution that encapsulates because, in analogy with human medicine (Spiegelhal-
everything that is now known about θ, having updated ter et al., 2004), a potentially important obstacle to the
the veterinarian’s current clinical expectation with the widespread implementation of veterinary interventions
new information contained in the data. In Bayesian on farms may relate to the variability of veterinarians’
terminology, π(θ) is referred to as the prior. Equation beliefs concerning the effectiveness of disease control
[1] states that the extent of any logical change in be- measures. If veterinarians currently have very different
lief depends on both the current clinical expectation clinical expectations, then other approaches, such as
π(θ) and the strength of the new evidence π(x|θ); thus, more convincing research evidence, will be required to
Bayes theorem quantifies (probabilistically) how new alter these beliefs. Although this is not to say that it
data should, logically, influence pre-existing expecta- is only research evidence that influences what veteri-
tions about an uncertain parameter.
narians believe. Our hypothesis was that demonstrable
Clinical expectations have been probabilistically variation exists for veterinarians’ clinical expectations
elicited in human medicine and to a lesser extent in and demands regarding mastitis, lameness, and Johne’s
veterinary medicine (O’Hagan et al., 2006). In ad- disease.
dition, at the same time as eliciting doctors’ clinical
The first objective of this study was to report a
expectations, some studies have elicited doctors’ “clini- probabilistic elicitation that aimed to quantify the
cal demands,” θmin. A new treatment almost invariably current variation in veterinarians’ clinical expectations
carries economic and other costs (e.g., adverse reac- and demands with respect to herd-level interventions to
tions, toxicity, or drug resistance). As a result, doctors reduce mastitis, lameness, and Johne’s disease in dairy
usually demand that a “minimum clinically worthwhile cattle. The second objective was to explore, within
effect” (i.e., θmin) must be achieved in order for them to a Bayesian statistical framework, the implications of
consider the treatment worthwhile implementing when the heterogeneity in beliefs. This was done by using
compared against alternative approaches. Eliciting a a mathematical model to make predications regarding
clinical demand requires a doctor to weigh all the po- how new evidence will alter what veterinarians cur-
tential advantages and disadvantages of the treatment rently believe. The model makes the assumption that
and assign a single value (or range of values) to θmin veterinarians will update their beliefs logically.
(Parmar et al., 1994). To our knowledge, clinical de-
mands have not been elicited from veterinarians work-
MATERIALS AND METHODS
ing in farm animal medicine.
In a Bayesian analysis (Equation [1]), θmin can be
Recruitment of Veterinarians
juxtaposed on the posterior distribution π(θ|x), and the
null hypothesis (no treatment effect) is rejected in favor
It was of interest to compare the beliefs of veteri-
of the alternative hypothesis (θ > θmin) when the poste- narians with and without postgraduate qualifications.
rior distribution assigns a “sufficiently large” probabil- However, without some targeted selection, it was pos-
ity to θ taking values greater than θmin(Spiegelhalter sible that no veterinarians holding postgraduate quali-
et al., 2004). This probability, denoted here by λ, is a fications would be included in the sample. Therefore,
subjective choice but “sufficiently large” is often taken to be eligible for selection, veterinarians must have
to be λ ≥ 0.95. The choice for λ affects when the trial been currently providing healthcare to dairy cattle in
is stopped and the larger the value of λ, the greater England during their normal working hours and be em-
the probability that the minimum clinically worthwhile ployed by a veterinary practice that contained at least
effect will be realized.
one veterinarian possessing a postgraduate cattle quali-
In a retrospective Bayesian analysis, a recent study fication; that is, the European College of Bovine Health
used a range of theoretical clinical expectations (priors) Management Diploma, the Royal College of Veterinary
aimed at representing different opinions (from “severely Surgeons Certificate or Diploma in Cattle Health and
skeptical” to “very enthusiastic”) to model the effect of Production, or the University of Liverpool Diploma in
a clinical mastitis trial (Green et al., 2009). The study Bovine Reproduction. None of the veterinarians were
explored how the results of the trial would be inter- exclusively involved in providing emergency care or
preted by veterinarians with theoretically constructed consultancy.
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3396
HIGGINS ET AL.
A 2-stage cluster design stratified by geographic loca- make clinically observable reductions in disease levels
tion was used. First, 20 practices were selected with varies with the disease. For the task, it was assumed that
probability proportional to the number of veterinarians all dairy farms in England had been recently visited by
they contained. Subsequently, if the practice had >5 their local veterinarian to discuss the disease in ques-
eligible members, then 5 were selected using the random tion. The population under consideration was all the
number generator function in the software program R farmers who, following this consultation, subsequently
version 2.15.2 (R Core Team, 2012). In practices that decided to proceed with the disease intervention
contained ≤5 eligible participants, all veterinarians
The disease outcomes were as follows. For the masti-
were recruited. This sampling strategy meant that ev- tis intervention, it was assumed that in the year before
ery veterinarian had approximately the same chance and in the year after the intervention took place, the
of selection, independent of the size of the practice in number of clinical cases of mastitis per 100 cows was
which they worked (Kalton, 1987). The Royal College reliably measured for each farm in the population, to
of Veterinary Surgeons online database (http://www. calculate the population mean mastitis incidence before
rcvs.org.uk/) provided a list of veterinary practices. and after the intervention; subclinical mastitis was not
Face-to-face, individual interviews were conducted by considered. For lameness, it was assumed that for each
H.M.H. between June 8 and September 1, 2011. Veteri- farm in the population, the entire dairy herd was reli-
narians were provided with an inconvenience allowance ably scored for lameness at the start of the intervention
of £100/h (pro rata). A standard script was used for and then again at the end, to determine the population
consistency, and basic descriptive information concern- mean prevalence of lameness; lame was defined as ob-
ing the veterinarians was gathered.
servably lame in one or more limbs, with any severity
of limp. For Johne’s disease, it was assumed that for
each farm in the population all the adult cattle (≥24
mo old) were blood sampled before and after the inter-
vention and the percentage of blood-test-positive adults
was used as an approximation for the population mean
prevalence of Johne’s disease; it is acknowledged that
this is an estimate because of the limited sensitivity of
the test. These outcomes were chosen because veteri-
narians were likely to be familiar with them. The popu-
lation mean outcome before and after the intervention
are denoted ψd0 and ψd1, respectively. As before, subscript
d refers to the endemic disease (d = m, l, j).
Clinical Expectations
We examined 3 epistemic parameters of interest (θm,
θl, θj), each of which related to the population mean
effect of an intervention strategy aimed at reducing an
endemic disease. The subscript refers to the endemic
disease, such that θm was defined as the population mean
effect of a 1-yr mastitis intervention, θl a 3-yr lameness
intervention, and θj an 8-yr Johne’s disease intervention.
In addition, θd is used to refer more generally to the
population mean effect of a disease intervention (d = m,
l, j). For each disease, what was meant by “an interven-
tion strategy” was described to each participant in detail
(see Appendix) and can be summarized as follows. For
all 3 diseases, an initial assessment of any available farm
data was conducted, in conjunction with a farm visit,
to assess the risks and achieve a working diagnosis. For
mastitis and Johne’s disease, the initial assessment was
additionally taken to include some strategic laboratory
testing, and for lameness, some locomotion scoring. As
a result, a list of farm-specific recommendations was
made, based on current best evidence where possible,
prioritized, and discussed with the farmer. During
quarterly farm revisits, the farm data and risks were
reassessed, allowing the control measures to be modified
in a timely manner, and encouragement and support
were provided to implement the control measures. Note,
that in the UK, uncomplicated cases of mastitis and
lameness are often diagnosed and treated initially by
farm personnel, following a standard protocol agreed
with their veterinarian.
The scale used was the difference in the population
mean outcome (before and after the intervention)
divided by the population mean outcome before the
intervention, expressed as a percentage:
ψd0 − ψd1
θd =
×100, ψd0 > 0.
[2]
ψd0
Hence, θ ∈ −∞,+100 for d = m, l, j. On this scale,
[
]
d
positive percentages reflect reductions in disease and
negative percentages reflect increases in disease. Thus,
for example, θl = 20% is a 20% reduction in lameness
prevalence, averaged across all farms, with a 3-yr lame-
ness intervention. Veterinarians’ expectations for θd
were elicited using a method that enabled probability
distributions to be fitted to their answers (see next sec-
tion).
The 3 parameters (θd) were elicited conditional on
the assumption that without an intervention delivered
with the help of a veterinarian, the change in popula-
tion mean over the time period would be zero for each
Different time periods were chosen for the interven-
tions and these reflect the fact that the time taken to
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QUANTIFYING BELIEFS AND BAYESIAN UPDATING
disease. In addition, despite the fact that the popula- used on the grounds that the majority of veterinarians
tion parameters related to farmers who had volunteered would believe that the disease interventions in ques-
to participate with the intervention, it was possible tion would typically reduce disease, and therefore the
that some farmers may not actually implement any example explained how they should give their answers
of the recommendations either at all or to a sufficient but avoided biasing them toward a certain disease
standard, such that their intervention had no chance reduction. It is also worth noting that during their in-
of having any effect at all. Therefore, veterinarians terviews the veterinarians were asked for their current
were asked to provide a single estimate for the per- clinical expectations and in particular, they were not
centage of farmers who would fall into this category shown any data pertaining to any of the parameters, θd.
of zero implementation for each disease. Veterinarians
The Sheffield Elicitation Framework is a freely avail-
were told to exclude these farmers from the population able package of guidance documents, templates, and
under consideration when they made their estimates software specifically designed for carrying out proba-
for θd; however, it was also stated that even with this bilistic elicitation (SHELF; http://www.tonyohagan.
exclusion, there was likely to remain a wide diversity in co.uk/shelf/). Probability distributions were fitted to
the scale and effectiveness of farmer implementation.
the veterinarians’ 5 judgments using computer code
In summary, veterinarians’ beliefs were sought for provided with this package (SHELF version 1.01) and
the expected (future) outcome of the specified disease run in the software program R, version 2.15.2 (R Core
intervention, on average, across all farms who imple- Team, 2012). The probability distributions were fitted
mented at least some of the recommendations (θd). For during the interviews and graphically presented to each
example, for the 8-yr Johne’s program, θj documents veterinarian. Furthermore, some of the inferred, but
veterinarians’ beliefs regarding the final outcome of this not directly elicited, probabilities were cited to them;
intervention, given that it commenced today.
this enabled veterinarians to visualize their answers and
gave them the opportunity to revise their 5 judgments
appropriately until they felt the fitted distributions
were a fair reflection of their beliefs.
Probabilistic Elicitation Method
The fixed-interval method was used, such that for
each parameter (θd), 5 values were elicited to allow
a probability distribution to be fitted: the minimum
and maximum values, median, and lower and upper
Clinical Demands
For each disease, veterinarians were asked to weigh
quartiles. The minimum and maximum values for all the benefits of implementing the intervention on
the parameter together constituted a plausible range, many thousands of farms, against all the costs (see
such that the veterinarian considered it “exceedingly Appendix). The minimum population mean reduction
unlikely” that the actual answer would fall outside this they would want the intervention to deliver, to consider
range. The order in which these values are elicited is the intervention clinically worthwhile implementing on
important to avoid an anchoring and adjustment heu- a large scale, is subsequently referred to as their “’clini-
ristic; thus, the plausible range was elicited first so that cal demands” (θdmin, d = m, l, j). Veterinarians were
further judgments were made relative to this range. If, asked to either give a single value or, if they preferred,
for example, the median were elicited first, then there a range of values.
would be a tendency for this to act as an anchor, and
In addition, for each disease intervention, veterinar-
the maximum and minimum values may not be ad- ians were asked to give a value for λ: λd, d = m, l,
justed far enough away from the median (O’Hagan et j. That is, they were asked for the probability (as a
al., 2006).
percentage chance) that the actual mean reduction in
Current best practice for probabilistic elicitation was disease would be greater than what they had stated
used, whereby a face-to-face interview between the first was a minimally clinically worthwhile effect. This value
author and each veterinarian was conducted at the for λ was placed in the context of the veterinarian need-
veterinarian’s own place of work and lasted between 70 ing to be “convinced that the disease intervention is
and 100 min. The first part of the elicitation involved a clinically useful and worthwhile implementing on many
15- to 25-min training exercise, whereby the scale upon farms,” based on the evidence produced by a clinical
which veterinarians needed to give their answers was trial alone.
explained, as well as the meaning of the 5 judgments
The purpose of eliciting λ was to explore any differ-
they needed to make, using a fictitious example of a ences between veterinarians in terms of the strength of
veterinarian who was convinced that an unspecified evidence needed to be convincing to them. However,
disease intervention would certainly make the disease this is not to say that it is only evidence from clini-
problem worse (Parmar et al., 1994). This example was cal trials that influences how convinced veterinarians
Journal of Dairy Science Vol. 97 No. 6, 2014

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HIGGINS ET AL.
are regarding the outcome of a disease intervention in centered in the same enthusiastic or pessimistic place,
reality. Many factors (e.g., marketing campaigns, clini- then the most confident veterinarian was selected.
cal experience, farmer experience, colleagues) can have
Modeling the Implications of the Heterogene-
an effect. It was beyond the scope of this project to ity in Clinical Beliefs. The clinical expectations of
quantify and mathematically model the influence of the most enthusiastic and pessimistic veterinarians were
all possible factors. However, because it is hoped that used as priors in a Bayesian analysis to predict how
new evidence has some influence on veterinarians’ con- their current clinical expectations would be updated in
fidence in the usefulness of disease interventions, it is the light of new data, as follows. The prior belonging
of interest to know how veterinarians differ in terms of to each veterinarian was combined using Bayes theorem
the strength of evidence they would like to be presented (Equation [1]) with synthetic data originating from a
with; by eliciting λ, this is what our study has focused randomized clinical trial to produce a posterior distri-
on.
bution for each veterinarian. This posterior distribution
The study was approved by the Research and Ethics can be considered to represent what each veterinarian
committee, School of Veterinary Medicine and Science, would believe if they were shown the data and updated
University of Nottingham.
their current clinical expectations logically in accor-
dance with Bayes theorem.
For the Bayesian analysis, it was necessary to specify
a likelihood function (i.e., to probabilistically specify
the new information about θd arising from an experi-
Data Analysis
Due to the scale involved; that is, θ ∈ −∞,+100 , a
[
]
d
suitable choice was to fit normal (Gaussian) probability ment). For each disease, a clinical trial was assumed to
density functions to the 5 elicited values for θm, θl, and have been conducted and designed such that farms
θj, for each veterinarian. The normal family of probabil- were randomly assigned to 1 of 2 groups (control and
ity density functions is characterized by 2 parameters: intervention) with n farms in each group. The control
the mean and the variance. In keeping with Bayesian farms received no intervention. For all farms enrolled in
terminology, these are referred to as “hyperparameters” the trial, in the year before and after the intervention
to distinguish them from the elicited (population) pa- the clinical outcome was measured (as previously de-
rameters. The R code provided in SHELF was used to scribed), and from this information the sample mean
find the best fitting hyperparameters by minimizing change in disease was calculated for the control and
the sum of the squared differences between the fitted intervention farms (in analogy with Equation [2]) and
cumulative distribution and the elicited cumulative denoted yc and yd , respectively. Assuming independent
distribution; this uses numerical optimization based on random observations, then by virtue of the central
the simplex algorithm (Nelder and Mead, 1965). In ad- limit theorem,
dition for each disease, the 5 raw elicited values were
each arithmetically averaged (across the veterinarians),
and a normal distribution fitted to these 5 averaged
numbers; for each disease, this distribution will be re-
ferred to as the “clinical expectations for the average
veterinarian.” It should be noted that this is a theo-
retical concept because it is unlikely to represent the
actual belief of any individual person.
Visualizing the Diversity in Clinical Opinion
for θd. To illustrate the diversity in clinical expec-
tations among the sample of veterinarians for each
disease, 3 different individuals were identified: (a) the
most ambivalent, (b) the most pessimistic, and (c) the
most enthusiastic. Veterinarian (a) was identified based
on the widest plausible range for θd, veterinarians (b)
and (c) were identified based first on the lowest and
highest median belief for θd, respectively, and then if
tied results existed (e.g., two or more veterinarians
had the same highest median belief) the veterinarian
was selected that had the narrowest plausible range.
In other words, “enthusiasm/pessimism” was based on
center of location, and if more than one veterinarian was
σd2
σd2
⎛
⎞
⎟
⎟
⎟
⎟
⎛
⎞
⎟
⎟
⎟
⎟
⎜
⎜
⎜
⎜
yd ≈ N θd ,
and y ≈ N θc,
,
⎜
⎜
⎜
c
⎜
⎜
⎝
n ⎟
n ⎟
⎜
⎝
⎠
⎠
where θd is the population mean change in disease for
farms with an intervention in place, θc is the same pa-
rameter but for the control farms, and σd2 is the popula-
tion variance for the disease and is assumed to be the
same for both control and intervention farms. Subscript
d is used to refer generally to the diseases: d = m, l, j
for mastitis, lameness, and Johne’s disease, respectively.
The parameter of interest was the difference in the
population mean change in disease: θd – θc. A point
estimate for this difference from the trial data can be
obtained using y = yd −yc, and the normal likelihood is
given by
σd2 σd2
⎛
⎞
⎟
⎟
⎟
⎟
⎜
⎜
y ≈ N θd −θc,
+
;
⎜
⎜
n
n ⎟
⎜
⎝
⎠
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3399
QUANTIFYING BELIEFS AND BAYESIAN UPDATING
2σd2
2n is the total size of the clinical trial and was given
values of 20, 50, 100, and 200 farms. For clinical de-
mands, because θdmin was elicited from each veterinari-
an, the median value (across all veterinarians) was
used; note that because a few veterinarians elected to
give a range of values, the lower value of the range was
taken to calculate the median clinical demand. As de-
scribed, this Bayesian model explores how large a clini-
cal trial would be required to convince the most pessi-
mistic veterinarian that the median clinical demand of
this sample of veterinarians will be exceeded. It also
explores, theoretically, how large a clinical trial would
be required to bring the most pessimistic and most en-
thusiastic veterinarian into general agreement; that is,
assuming veterinarians revise their beliefs logically in
keeping with Bayes theorem. As explained, the model
makes some assumptions regarding the data produced
by a new clinical trial.
⎛
⎞
⎟
⎟
⎟
⎟
⎜
⎜
that is; y ≈ N θd ,
,
[3]
⎜
⎜
n ⎟
⎜
⎝
⎠
because, in keeping with the condition used for eliciting
the veterinarians’ beliefs, θc is assumed to be zero for
each disease. Veterinarians’ clinical expectations were
elicited for θd given θc = 0, and because normal distri-
butions were fitted to their beliefs, the priors took the
form
2
⎛
⎜
⎜
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
θ −ϕ
(
)
1
2
di
di
p θ ∝ exp −
,
(
)
⎜
⎜
⎜
di
τd2i
⎜
⎝
where i denotes the veterinarian and takes values i = 1,
…, 94 (94 veterinarians were interviewed), and ϕdi and
τdi are the fitted hyperparameters (mean and standard
deviation) for each veterinarian. With the normal likeli-
hood specified by Equation [3]; that is,
RESULTS
2
⎛
⎜
⎜
⎜
⎜
⎝
⎞
Response Rates and Description of Participants
⎟
⎟
⎟
⎟
⎟
⎟
⎠
y −θ
n
(
)
1
2
d
y |θ ∝ exp −
,
⎜
d
2σd2
⎜
Not all the veterinarians in one initially selected vet-
erinary practice agreed to participate; another practice
was selected from the same region and consented. From
the 20 consenting practices, 94 of the 96 selected vet-
erinarians were interviewed (2 were unavailable during
the data collection period). Of the 20 practices, 7 were
located in the North, 2 in the Midlands, and 11 in the
South of England.
The data set included 36 partners and 58 assistants;
sex was split 59 males to 35 females; and years qualified
ranged from 0 to 37 yr, with a median of 7 yr. Of the
94 veterinarians, 19 (20%) held a postgraduate cattle
qualification. Time spent working with dairy cows was
as follows: 6 participants spent 0 to <25% of their
time, 16 participants 25 to <50%, 27 participants 50 to
<75%, and 45 participants 75 to <100%.
the Bayesian analysis (i.e., Equation [1]) is conjugate,
and it can be shown (Spiegelhalter et al., 2004) that the
posterior distribution also takes the shape of a normal
distribution, as follows:
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
ϕdi
yn
2σd2
n
2σd2
+
+
2
τ
1
di
θ |y ∼ N
,
.
[4]
di
1
1
n
+
τdi 2σd2
2
di
2
⎟
⎟
⎜
⎝
τ
⎠
In combination with the elicited values for θdmin and
λd, Equation [4] can be used to explore the implications
of the heterogeneity in veterinarians’ clinical expecta-
tions because it provides the formula to calculate the
posterior distribution (i.e., the predicted belief) for
each veterinarian and for each disease.
Elicited Clinical Beliefs
Descriptive statistics concerning the raw elicited pa-
rameters θd are provided in Table 1. For each disease
and each veterinarian, their raw elicited plausible range
and median values for θd are presented in Figure 1,
In Equation [4], ϕ and τdi were derived from the raw
elicitation data (obdtiained during the interviews), and
the remaining variables y,n,σ2 require specification.
(
)
d
along with θdmin
.
The value chosen for y (i.e., the difference in the sample
means between the control and intervention farms in
the trial) was the median value (i.e., across the 94 par-
ticipating veterinarians) of the median clinical expecta-
In Figure 2, the fitted normal distributions are plot-
ted for the most ambivalent, enthusiastic, pessimistic,
and “average” veterinarian. For example, Figure 2B
tion for θd. For each disease, the population variance σd2 shows that the most pessimistic veterinarian concern-
is unknown and therefore sensitivity of the results to 2 ing the 3-yr lameness intervention had a normal distri-
choices were explored: σd = 10% and 25% for d = m, l, bution centered at an 11% population mean reduction
j. As n is the number of farms in each arm of the trial, in lameness prevalence with a 95% credible interval of 0
Journal of Dairy Science Vol. 97 No. 6, 2014

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HIGGINS ET AL.
Table 1. The elicited clinical expectations of 94 veterinarians for the population mean effect of a disease
intervention1
Population mean reduction (%)
Mastitis
incidence
Lameness
prevalence
Johne’s disease
prevalence
Elicited value
Minimum
Lower quartile
Median
Upper quartile
Maximum
10 (5–15)
24 (17–33)
30 (20–40)
36 (25–46)
50 (40–60)
10 (5–20)
24 (15–35)
30 (20–40)
39 (25–50)
50 (40–65)
10 (5–30)
33 (20–50)
40 (30–60)
52 (38–65)
70 (50–80)
1Values shown are median (interquartile range).
to 21%, whereas the most enthusiastic veterinarian was values: λm = λl = λj = 80%; lower quartile λm = λl =
centered at a 58% reduction with a 95% credible inter- λj = 75%; upper quartile: λm = 88%, λl = λj = 90%.
val of 38 to 78%; thus the enthusiastic veterinarian had
The distributions and summary statistics for vet-
a more uncertain belief (wider credible interval) com- erinarians’ estimates of the percentage of farmers who
pared with the most pessimistic veterinarian. Figures they believed would implement none of the disease
1 and 2 together show the considerable heterogeneity interventions to any effective extent, despite initially
in veterinarians’ clinical expectations, both in terms of agreeing to participate, are provided in Figure 4.
central location and clinical confidence. The diversity
in opinion was greater for the Johne’s disease interven-
tion compared with the other diseases, as highlighted
by the marked polarization in beliefs displayed by the
most enthusiastic and pessimistic veterinarians (Figure
2C).
Modeling the Implications
of the Heterogeneity in Beliefs
Figure 5 predicts (using Equation [4]) how the vet-
erinarian with the most pessimistic clinical expectation
Across the 94 veterinarians, the median clinical de- and the veterinarian with the most enthusiastic clinical
mand was a 20% population mean reduction in incidence expectation, regarding the lameness intervention, would
for a 1-yr mastitis intervention with an interquartile update their expectations in light of new (synthetic)
range of 10 to 25%, a 20% reduction in mean prevalence clinical trial data of different strengths. In Figure 5,
for a 3-yr lameness intervention (interquartile range the 4 plots (A to D) show the effects of clinical tri-
10–30%), and a 35% reduction in mean prevalence for als of different sizes, involving 20, 50, 100, and 200
an 8-yr Johne’s disease intervention (interquartile range farms in total. For each clinical trial, it was assumed
25–50%). Comparing these figures with Table 1, it can that the data provided a point estimate, y, equal to a
be seen that the median clinical demand was below the 30% mean reduction in lameness prevalence in favor
median clinical expectation for all 3 diseases.
of the intervention farms (over the control farms), and
Figure 3 shows how each veterinarian’s clinical de- that the population variance, σd, was 25%. Hence, the
mand compared with their median (best guess) clinical only difference between the clinical trials is that they
expectation; that is, whether each of the crosses (Fig- are increasing in size, and because the likelihood is
ure 1) was below, above, or in the same place as the encapsulating the information arising from the clinical
corresponding dot. It reveals that for both the mastitis trial, it can be seen that the evidence from the trial
and lameness interventions, most veterinarians (≥79%) becomes stronger (i.e., narrower and taller) from plot
had clinical demands that were lower than their me- (5A) through to plot (5D) as the trial increases in size,
dian expectations. In contrast, for Johne’s disease, only but remains centered at 30%.
51% of veterinarians had clinical demands that were
On each plot in Figure 5, normal distributions have
lower than their median expectation; that is, there was been fitted to the elicited values belonging to the most
more pessimism in terms of the effect that veterinarians pessimistic and enthusiastic veterinarians and reflect
clinically wanted and what they expected to happen for their current clinical expectations (priors), as they stat-
Johne’s disease compared with mastitis and lameness.
ed during their interviews; that is, the “prior enthusiast”
The summary statistics for veterinarians’ values for and “prior pessimist” curves. The plots show how the
λd; that is, the probability they would require (as a priors are updated when combined with the likelihood
percentage chance) that the mean reduction would be (i.e., the new data) using Bayes theorem. Hence the
at least their own estimate for θdmin, were similar for “updated enthusiast” and “updated pessimist” curves
each disease intervention and are as follows. Median are the posterior distributions and represent what the
Journal of Dairy Science Vol. 97 No. 6, 2014

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QUANTIFYING BELIEFS AND BAYESIAN UPDATING
Figure 1. The clinical expectations of 94 veterinarians concerning the population mean reduction in disease achievable with (A) a 1-yr masti-
tis intervention, (B) a 3-yr lameness intervention, and (C) an 8-yr Johne’s disease intervention; median beliefs (dots) and plausible range (lines).
Crosses (x) denote the minimum clinically worthwhile reduction stipulated by each veterinarian (i.e., the clinical demand). For each disease,
veterinarians were ordered along the x-axis by their median belief (dots). Color version available in the online PDF.
most pessimistic and enthusiastic veterinarian are pre- straight vertical line. Plot 5A shows that in light of a
dicted to believe if they had been shown the clinical clinical trial involving 20 farms, the most pessimistic
trial data, and updated their opinions coherently in veterinarian is predicted to believe that there will only
accordance with Bayes theorem. To emphasize, the vet- be an 0.11 probability (11% chance) that this clinical
erinarians were not shown any data during their inter- demand will be exceeded (area under the “updated pes-
views, and the posterior distributions shown in Figure 5 simist” curve to the right of the vertical 20% line, as a
are predictions arising from the Bayesian models.
proportion of the total area under the curve). As the
Across the 94 veterinarians, the median clinical de- size of the clinical trial increased, the most pessimistic
mand for the 3-yr lameness intervention was a 20% veterinarian was predicted to become more convinced
mean reduction in prevalence, shown in Figure 5 by the that this goal would be realized, such that with a trial
Journal of Dairy Science Vol. 97 No. 6, 2014

3402
HIGGINS ET AL.
Figure 3. Each veterinarian’s clinical demand, θdmin, compared
with their median (best guess) for the expected clinical outcome θd.
a “reasonable skeptic” (i.e., the most pessimistic veteri-
narian in this sample) that the intervention is clinically
worthwhile. However, for the lameness intervention, the
majority of veterinarians interviewed provided a value
for λl that was <0.90 (upper quartile λl = 90%), and
therefore on this basis, a clinical trial of 200 farms may
be expected to be sufficiently convincing to the major-
ity of veterinarians who participated in this study.
Figure 5 also shows how the most enthusiastic vet-
erinarian is predicted to have their enthusiasm damped
by the trial results. The most enthusiastic veterinarian
was expecting a mean reduction in prevalence centered
in the region of 60% (“prior enthusiast” curve), and
for example, plot 5C shows that this is predicted to
be reduced to a more confident belief that is centered
around a 35% reduction (“updated enthusiast” curve)
with a 100-farm trial.
Figure 5C also shows that in the light of the evidence
originating from a 100-farm trial, the most pessimistic
and enthusiastic veterinarians are predicted to have up-
dated beliefs that are still almost entirely in disagree-
ment (updated curves barely overlapping).
In plots A to D (Figure 5), the population stan-
dard deviation σl was assumed to be 25%. For a given
size of clinical trial, taking σl to be 10%, results in a
stronger likelihood (because there is less variation of
farms around the mean value), and therefore affects
the analysis. Plots E to H (Figure 5) show an identical
analysis to plots A to D (Figure 5), but with σl assumed
to be 10%. It shows that because the evidence from the
Figure 2. Normal probability distributions fitted to the elicited
clinical expectations (θd) belonging to the most ambivalent, enthu-
siastic, pessimistic, and “average” veterinarians: (A) a 1-yr mastitis
intervention, (B) a 3-yr lameness intervention, and (C) an 8-yr Johne’s
disease intervention.
involving 200 farms, they were predicted to believe that trial is stronger, a 50-farm trial is predicted to convince
there was a 0.92 probability that this clinical demand (with a 0.99 probability) the prior pessimist that a 20%
would be exceeded (plot 5D).
The null hypothesis is usually rejected in favor of
mean reduction in lameness prevalence will be realized.
A similar analysis to that presented in Figure 5
the alternative hypothesis when the posterior distribu- was run for the mastitis and Johne’s disease interven-
tion assigns a “sufficiently large” probability to θ taking tions; for the mastitis intervention, the median clinical
values greater than θmin; because this probability (λ) is demand was 20% (the same as for the lameness in-
often taken to be ≥0.95, then, on this basis, a 200-farm tervention) and for Johne’s disease, it was 35%. For
clinical trial is not strong enough evidence to convince the mastitis intervention, the synthetic trial data were
Journal of Dairy Science Vol. 97 No. 6, 2014

3403
QUANTIFYING BELIEFS AND BAYESIAN UPDATING
Figure 2 shows that the most pessimistic veterinar-
ian for the mastitis intervention (plot A) was more
confidently pessimistic (narrower and taller distribu-
tion) compared with the most pessimistic veterinarian
for the lameness intervention (plot B); consequently,
as Table 2 reveals, this veterinarian needs stronger
evidence, according to Bayes theorem, to be convinced
that the clinical demand will be exceeded. Thus, the
most pessimistic veterinarian concerning mastitis inter-
vention is predicted to be entirely unconvinced, even by
a trial involving 200 farms (if the population standard
deviation is indeed 25%) because they are predicted
to give only a 12% chance that a 20% reduction in
mastitis will be achieved. This is demonstrably differ-
ent from the most pessimistic veterinarian concerning
the lameness intervention, who would be substantially
convinced by a 200-farm trial (0.92 probability), with
the same population variance assumption.
DISCUSSION
The results revealed that markedly different clinical
opinions currently exist; hence, for all 3 disease inter-
ventions, a major change in clinical expectations would
be required to bring the most enthusiastic and most
pessimistic veterinarians into clinical agreement. It
may not be desirable for veterinarians to be completely
united in their clinical beliefs, but broad agreement for
the major endemic diseases is important both for the
credibility of the profession and to provide a unified
approach to disease control. The wide heterogeneity
observed raises concerns over the extent to which a
broadly consistent approach to controlling these en-
demic diseases is currently being achieved. This in
turn supports the argument for the implementation of
national disease control programs for nonstatutory en-
demic diseases. This is because national disease control
Figure 4. Veterinarians’ estimates for the percentage of dairy
farmers who, having agreed to undertake a structured disease inter-
vention and had an initial visit, subsequently fail to implement any
of the required changes to any successful extent: (A) a 1-yr mastitis programs help to provide a coordinated and consistent
intervention, (B) a 3-yr lameness intervention, and (C) an 8-yr Johne’s
disease intervention.
approach to disease control. As the variability between
veterinarians increases, the potential gain derived from
implementing a national disease control program also
increases.
set to provide a point estimate of a 30% reduction in
clinical mastitis incidence, and for Johne’s disease, a
40% reduction in prevalence (these figures were the
median expected reduction in disease elicited across the
94 veterinarians, Table 1). The analyses were run for
population standard deviations of 10% and 25% and,
for each disease, the predicted probability of exceeding
the median clinical demand in light of the clinical trial
data was calculated for the most pessimistic veterinar-
ian. The results are presented in Table 2, where the
lameness results from Figure 5 have also been included
to allow comparison.
Explanation for the observed heterogeneity in clinical
expectations is likely to be multifactorial. In this regard,
the paucity of literature quantifying the effects of these
interventions is worth noting. To our knowledge, only
1 randomized clinical trial has estimated the effect of a
clinical mastitis intervention of the type described here
(Green et al., 2007); this 1-yr intervention study found
a 22% reduction in the proportion of cows affected with
clinical mastitis on the intervention farms compared
with the control farms. There appears to be an absolute
lack of randomized clinical trials estimating the effects
of lameness and Johne’s disease interventions. More
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HIGGINS ET AL.
Figure 5. A Bayesian analysis to predict how the most pessimistic and enthusiastic veterinarians regarding the 3-yr lameness intervention,
would update their clinical opinions in light of new synthetic trial data of different sizes. For plots A to D, the population standard deviation
(SD) was assumed to be 25%; for plots E to H, SD = 10%. In each plot, the trial data (likelihood) was assumed to provide a point estimate
equal to a 30% mean reduction in lameness prevalence. “Updated enthusiast/pessimist” is the posterior distribution obtained by combining the
relevant prior belief with the likelihood using Bayes theorem. “Clinical demands” (= 20%) is the median “minimum clinically worthwhile reduc-
tion” elicited across the 94 veterinarians. The probability (P) that the “updated pessimist” assigns to this value being exceeded is given (area
under the curve to the right of the straight vertical line). Color version available in the online PDF.
Journal of Dairy Science Vol. 97 No. 6, 2014

3405
QUANTIFYING BELIEFS AND BAYESIAN UPDATING
Table 2. The predicted probability of exceeding the median clinical demand (20% mastitis, 20% lameness,
35% Johne’s disease) for the most pessimistic veterinarian, when their prior clinical expectation is combined
with synthetic trial data of different sizes using Bayes theorem; the trial data provided a point estimate of
a 30% reduction in clinical outcome for mastitis and lameness, and 40% for the Johne’s disease intervention
Size of randomized clinical trial (no. of farms)
Disease
intervention
Population
SD (%)
20
50
100
200
Mastitis
10
25
10
25
10
25
0.02
<0.001
0.73
0.43
0.001
0.99
0.97
0.01
1.00
0.12
1.00
0.92
0.94
0.003
Lameness
1.00
0.11
0.29
0.61
Johne’s disease
<0.001
<0.001
0.037
<0.001
0.41
<0.001
clinical trials to quantify the effects of intervention financial, and labor investments. Fourth, the reduc-
strategies to reduce the major endemic diseases of dairy tion the veterinarian needs to consider the intervention
cattle are required because there is a lack of knowledge clinically worthwhile solely from the perspective of
in this area. In our data set, we did not find any sta- their patient; that is, the cow. In a sense, the latter is
tistically significant differences in veterinarians’ beliefs analogous to the scenarios for which clinical demands
by the following factors: time spent working with dairy have been elicited and reported in human medicine,
cows, possession of postgraduate qualifications or not, where the doctor is faced with deciding what is best for
job status (assistant vs. partner), or sex of respondent. their patient, given the treatment will be freely avail-
However, this is not to say that these factors are not able and the patient will almost certainly take it.
associated with different opinions.
In this study, it was stipulated that clinical demands
Notably, clinical expectations were elicited condition- related to the first point only. However, it may be dif-
al on an assumption that the population mean change ficult to compartmentalize these issues. Thus, part of
in disease would be zero in the absence of a disease the variation in veterinarians’ clinical demands may
intervention; it is necessary to know what veterinar- have related to how they chose to weigh the vested
ians were basing their clinical expectations for a disease interests of all stakeholders; for example, veterinarians
intervention against. It is acknowledged that some may who estimated a very small clinical demand may have
believe this to be a larger assumption to make for the given greatest weight to the interests of the cow, or to
Johne’s intervention compared with the mastitis and the environment, whereas those who gave the highest
lameness interventions. We made this assumption for clinical demands may have given more weight to the
the purpose of simplicity and in the absence of any financial cost-effectiveness for the farmer. Another pos-
data.
sible explanation for the variation in clinical demands
The results also showed considerable variation in may concern differences between veterinarians in terms
veterinarians’ estimates for the percentage of farmers of their beliefs about the economic benefits of control-
who would not effectively implement any of the inter- ling the different diseases. This may, in turn, reflect
vention to any extent, despite initially agreeing to do differences in undergraduate teaching between universi-
so. The median estimates were nontrivial percentages: ties.
20, 24, and 30% for the mastitis, lameness, and Johne’s
It is important to note that the Bayesian analysis
disease interventions, respectively. This may, in part, presented here has modeled the effect of new clinical
reflect veterinarians’ practical experiences with main- trial data on veterinarians’ current opinions, assuming
taining farmer engagement with a disease intervention. they would update their beliefs logically in accordance
Understanding ways to facilitate and support farmers with Bayes theorem. This means that as the size of the
to make the changes needed to implement a disease trial increases, the mathematical model predicts that
intervention is important.
veterinarians will become more convinced because the
“Clinical demands” in a herd health context could be evidence from larger trials is stronger. However, contro-
interpreted in 4 different ways. First, the reduction the versy currently exists in the literature over the extent
veterinarian would want to consider the intervention to which people are actually able to logically value, in-
clinically worthwhile. Second, what the veterinarian terpret, and revise their opinions when presented with
thinks the farmer would want to hear to be convinced new information (Tversky and Kahneman, 1974; Kynn,
enough to implement the intervention. Third, what 2008; Westover et al., 2011). Recent findings suggest
the farmer would actually demand to be prepared to that people can update their beliefs in a Bayesian man-
implement the intervention, with its associated time, ner, but how the task is framed is important (Giger-
Journal of Dairy Science Vol. 97 No. 6, 2014

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HIGGINS ET AL.
titis control plan to investigate the influence of veterinary prior
beliefs on clinical interpretation. Prev. Vet. Med. 91:209–217.
Green, M. J., K. A. Leach, J. E. Breen, L. E. Green, and A. J. Bradley.
2007. National intervention study of mastitis control in dairy herds
in England and Wales. Vet. Rec. 160:287–293.
Kalton, G. 1987. Introduction to Survey Sampling. Sage Publications,
London, UK.
Kynn, M. 2008. The ‘heuristics and biases’ bias in expert elicitation.
J. R. Stat. Soc. A Stat. Soc. 171:239–264.
Nelder, J. A., and R. Mead. 1965. A simplex algorithm for function
minimization. Comput. J. 7:308–313.
O’Hagan, A., C. E. Buck, A. Daneshkhah, J. R. Eiser, P. H. Garth-
waite, D. J. Jenkinson, J. E. Oakley, and T. Rakow. 2006. Uncer-
tain Judgements: Eliciting Experts’ Probabilities. Wiley, Chich-
ester, UK.
Parmar, M. K. B., D. J. Spiegelhalter, and L. S. Freedman. 1994. The
CHART trials: Bayesian design and monitoring in practice. Stat.
Med. 13:1297–1312.
R Core Team. 2012. R: A language and environment for statistical
computing. R Foundation for Statistical Computing, Vienna, Aus-
tria. http://www.R-project.org/.
Spiegelhalter, D. J., K. R. Abrams, and J. P. Myles. 2004. Bayesian
Approaches to Clinical Trials and Healthcare Evaluation. Wiley,
Chichester, UK.
enzer and Edwards, 2003; Gigerenzer and Hoffrage,
2007). In reality, it may be challenging for veterinarians
to differentiate between evidence of varying strength
and quality. Other factors, such as the perceived repu-
tation of the scientists conducting the work, the final
concluding remarks of the paper, or the point estimate
alone (not in combination with the confidence or cred-
ible interval) may be more influential. More research is
needed to establish how logically veterinarians update
their beliefs about clinical parameters, using informa-
tion published in veterinary journals. This is important
to ascertain, because investing money in larger clinical
trials to convince skeptical clinicians will not provide
a return unless they revise their beliefs in at least a
somewhat logical manner. And, of course, due consid-
eration should be given to all the other factors that
influence veterinary beliefs and other approaches em-
ployed as necessary. This could include communication
strategies, as well as helping veterinarians to interpret
new information appropriately, and facilitating and im-
proving veterinary education (both undergraduate and
postgraduate).
Tversky, A., and D. Kahneman. 1974. Judgment under uncertainty:
Heuristics and biases. Science 185:1124–1131.
Westover, M. B., K. D. Westover, and M. T. Bianchi. 2011. Signifi-
cance testing as perverse probabilistic reasoning. BMC Med. 9:20.
It is also worth noting that, in human medicine, λ
has not been elicited from doctors, even though doc-
tors’ clinical demands have been elicited. A choice for
λ that is less than 0.95 may not be generally accept-
able to the scientific community, because it may not be
regarded as robust enough evidence. However, it is a
subjective choice and clinically useful information may
go unreported if only clinical trials achieving λ ≥0.95
are published.
A potential limitation of this study is the repeat-
ability of the results at a later date in the absence of
any genuine change in veterinarians’ beliefs. There is
no literature reporting the repeatability of the method.
However, during the interviews, extra clarification was
given if required. This reduced misunderstanding, which
is one reason why different results may be obtained on
different dates.
APPENDIX
Standard Elicitation Script
Clinical Expectations: Mastitis Intervention.
My first question is about a clinical mastitis interven-
tion and how successful you think it might be when
implemented on a large number of dairy farms.
Please imagine that all the dairy farms in England
are visited by their own local veterinarian today, spe-
cifically to discuss their current clinical mastitis situ-
ations. As a result, we have identified a large number
of farms, for which both the farmer and their local vet
have agreed there is a clinical mastitis problem and
they have decided that the farmer will go ahead with a
structured clinical mastitis intervention with the help
of their local vet over the next year.
By a structured clinical mastitis intervention over the
next year, I mean the following:
ACKNOWLEDGMENTS
Initially, the vet tries to identify the main cause (s) of
the mastitis problem. The vet carries out some strategic
laboratory testing, assesses any available milk recording
data and any other relevant farm data that is available
(e.g., clinical mastitis records). The vet then makes a
specific visit to walk round the farm and assess the
risks that may be contributing to the problem. The vet
quantifies the risks using our current best evidence for
clinical mastitis. As a result the vet produces a list of
recommendations, prioritizes them and discusses them
with the farmer. Over the next year, the vet revisits the
farm at least every quarter, reassesses any data avail-
able and the on-farm risks, and modifies the recom-
Our thanks go to all the veterinarians who partici-
pated in this study. H. M. Higgins was funded by a
Wellcome Trust Research Fellowship [087797/Z/08/Z]
and hosted by the University of Nottingham, UK.
REFERENCES
Gigerenzer, G., and A. Edwards. 2003. Simple tools for understanding
risks: From innumeracy to insight. BMJ 327:741–744.
Gigerenzer, G., and U. Hoffrage. 2007. The role of representation in
Bayesian reasoning: Correcting common misconceptions. Behav.
Brain Sci. 30:264–267.
Green, M. J., W. J. Browne, L. E. Green, A. J. Bradley, K. A. Leach,
J. E. Breen, and G. F. Medley. 2009. Bayesian analysis of a mas-
Journal of Dairy Science Vol. 97 No. 6, 2014

3407
So, your plausible range for the average effect of a
QUANTIFYING BELIEFS AND BAYESIAN UPDATING
mendations as necessary. These are discussed with the
farmer, and the vet supports and encourages the farmer mastitis intervention is between X and Y. Please take
to implement the required changes. This approach, over time to consider if this properly reflects the amount of
a year, is what I mean by a “structured clinical mas- uncertainty you have in what the average effect of this
titis intervention.” Note: the recommendations can be mastitis intervention might be? You can revise your
anything, including major farm reinvestment, but the answer if you wish. Note that the more uncertainty you
vet is realistic and will not make suggestions that will have, the wider your range should be.
outstrip the current labor and capital resources of this
particular farm.
Median: Given your range, please tell me your “best
guess” (median value, M) for the average effect of the
When we think about this large number of farms, clinical mastitis intervention. This should be a value
despite the fact that the farmers have all decided to such that you believe it is just as likely that the true
implement a mastitis intervention and they have all answer will turn out to fall somewhere between your
had a first initial visit by their vet, nevertheless some worst possible value (which was X) and this number,
of them may not actually implement any of the recom- and this number and your best possible value (which
mendations either at all or sufficiently well over the was Y). Please let me know if you have any queries
year, such that their intervention had no chance of hav- about this.
ing any effect at all simply due to farmer compliance.
Lower and upper quartiles: Please can you give me a
Question: What is your best estimate for the per- value for your lower quartile for the average effect. This
centage of farms that, in reality, would fall into this is a number such that you think it is equally likely that
category?
the actual answer will fall between your worst possible
Now we are going to think about how successful the value (X) and this value, and this value and your best
mastitis interventions will be on average, across all the guess (which was M). Please let me know if you have
farms. However, when doing this we are going to exclude any queries about this.
the farms we have just talked about; that is, those who
will do nothing or so little that their interventions have tile for the average effect. This is a number such that
no chance of working at all.
you think it is equally likely that the actual answer will
Please can you give me a value for your upper quar-
[Scale:] We will be working in terms of the percentage fall between your best guess (which was M) and this
reduction (or percentage increase) of the original masti- value, and this value and your best possible answer
tis problem. By this I mean that in the year before we (which was Y). Please let me know if you have any
start the mastitis intervention, we have measured (for queries about this.
each farm) the number of clinical cases of mastitis per
Fitted probability distribution: [Researcher fits prob-
100 cows per year. And in the year after the interven- ability distribution to the 5 values (range, median,
tion, we will again measure the number of clinical cases lower and upper quartile) and produces a graph using
of mastitis per 100 cows per year. So for example, a SHELF software. The graph is shown to veterinarian
50% reduction in the farms original clinical mastitis (with explanation). The fitted probabilities are com-
problem means that a farm with 120 clinical cases per pared with the elicited values. Researcher feeds back 2
100 cows occurring in the year before the intervention implied probabilities (10th and 90th percentiles) from
would have 60 clinical cases per 100 cows in the year the fitted distribution].
after the intervention. Do you have any questions about
this?
If we don’t intervene, we will assume that the masti-
tis problems on the farms will not change on average.
Does the shape and distribution of this graph repre-
sent what you believe? (yes/no)
[If yes, proceed. If no, invite them to vary some values
to fit others that are believed to be more pivotal. Re-fit
Range: It is natural that you will have some uncer- a new distribution and feedback until the veterinarian
tainty about the average effect of the mastitis inter- is satisfied that the distribution is an accurate reflec-
vention. Therefore, please can you give me a plausible tion of their belief.]
range for the average effect, as a percentage increase
Clinical Demands: Mastitis Intervention. So
or reduction of the original clinical mastitis problem? far, we’ve discussed what we expect might actually
That is, tell me the worst (X) and the best (Y) possible happen if we were to implement a clinical mastitis in-
answer for the average, such that you think it exceed- tervention on a large number of dairy farms, in terms
ingly unlikely that the actual answer could turn out to of the average effect. For my next question, I just want
fall outside of this range?
Take time to think about your answer. Feel free to we’ve said previously about what we are expecting to
ask any questions or talk it through.
happen!
a single answer and it has nothing to do with what
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We are interested in what you want the average re-
HIGGINS ET AL.
My next 2 questions are identical in format to this
duction in clinical mastitis to be, in order for you to feel clinical mastitis intervention question, except that they
that the intervention itself typically provides what you relate to a lameness intervention and a Johne’s disease
consider a clinically worthwhile and important reduc- intervention. Let’s start with lameness first.
tion and therefore should be implemented on a large
number of farms.
Rolling out an intervention onto thousands of farms
has costs to the whole industry but also benefits. This
Lameness Intervention
Repeat the above text, but substitute “lameness” for
question is about weighing up all the costs and all the “clinical mastitis” and “ 3 years” for “1 year.” For the
benefits. description of the structured lameness intervention,
If I told you that the average effect of a mastitis the text is modified to include mobility (locomotion)
intervention is an increase in the original disease prob- scoring the milking cows. For the scale, substitute the
lem, say 10% on average, we wouldn’t consider it a following text:
good intervention! Similarly if I told you that the aver-
age effect of a mastitis intervention is zero change on tion (or percentage increase) of the original lameness
average, we wouldn’t consider it a good intervention! problem. So at the start of the lameness intervention,
We will be working in terms of the percentage reduc-
For this 1-yr clinical mastitis intervention, please tell we mobility (locomotion) score the entire herd for lame-
me, what is the minimum that you would want the ness and hence we know, for every farm (reliably) what
average reduction in clinical mastitis to be in order for percentage of the herd is lame. Note: by “lame” we
you to feel that the mastitis intervention itself is clini- mean observably lame in one or more limbs, with any
cally useful when implemented on a large number of severity of limp. At the end of the 3-yr intervention,
farms? This can just be a single answer (or you can give we will again mobility (locomotion) score the entire
me a range if you prefer).
herd for lameness and hence we know, for every farm
In reality, all researchers can do is estimate the aver- (reliably) what percentage of the herd is lame. So, for
age effect of a mastitis intervention when implemented example, a 50% reduction in the farm’s original lame-
on a large number of farms, by carrying out a clinical ness problem means that a farm with 40% of the herd
trial. They would implement the mastitis intervention lame has 20% of the herd lame after 3 yr.
on a small number of farms and compare the average
reduction observed to a small number of control farms.
Hence, researchers cannot prove to us with absolute
certainty that the average reduction will definitely be
Johne’s Disease Intervention
Repeat the above text, but substitute “Johne’s dis-
greater than what you wanted. There will always be ease” for “clinical mastitis” and “8 years” for “1 year.”
some uncertainty.
λ: My next question is about how certain you per-
For the scale, substitute the following text:
We will be working in terms of the percentage re-
sonally would need to be (as percentage chance), that duction (or percentage increase) of the original Johne’s
the average reduction is going to be at least what you problem. So, we blood sample all the adult cattle (over
said you wanted, in order that you personally would be 24 mo old) and hence we will know, for every farm,
convinced that the mastitis intervention is useful and what percentage of the adults are blood test positive for
worthwhile implementing on many farms, based on the Johne’s at the start. After the end of the 8-yr interven-
results of a clinical trial alone.
tion, we will again blood test the adults and hence we
By this I mean that if you considered the evidence know, for every farm, what percentage of the herd is
that some researchers had produced, and as a result blood test positive for Johne’s at the end. So for ex-
you are now sure enough that the average reduction is ample, a 50% reduction in the farms original Johne’s
going to be at least what you wanted, then you would problem after an 8-yr Johne’s intervention means that a
be convinced that the mastitis intervention is clinically farm with 40% of adults testing positive for Johne’s at
useful. How sure would you personally need to be (as the start has 20% of adults testing positive after 8 yr.
a percentage chance) in order for you to be convinced
that the mastitis intervention is clinically useful and
worthwhile implementing on many farms?
Journal of Dairy Science Vol. 97 No. 6, 2014