1
Fo as e oC, e al. BMJ Open 2019;9:e023187. doi:10.1136/bmjopen-2018-023187
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E alua ion o he o e diagnosis in
b eas sc eening p og ammes using a
Mon e Ca lo simula ion ool: a s udy o
he in luence o he pa ame e s de ining
he p og amme con igu a ion
C is ina Fo as e o,1 Luis I Zamo a,2 Damián Gui ado,1,3 An onio M Lallena 4
To ci e: Fo as e oC, Zamo aLI,
Gui adoD, e al. E alua ion
o he o e diagnosis in b eas
sc eening p og ammes
using a Mon e Ca lo
simula ion ool: a s udy o he
in luence o he pa ame e s
de ining he p og amme
con igu a ion. BMJ Open
2019;9:e023187. doi:10.1136/
bmjopen-2018-023187
►P epublica ion his o y o
his pape is a ailable online.
To iew hese iles, please isi
he jou nal online (h p:// dx. doi.
o g/ 10. 1136/ bmjopen- 2018-
023187).
Recei ed 25 Ma ch 2018
Re ised 20 Decembe 2018
Accep ed 8 Janua y 2019
1Unidad de Radio ísica, Hospi al
Uni . San Cecilio, G anada, Spain
2Se icio de Física y P o ección
Radiológica, Hospi al Reg. Uni .
Vi gen de las Nie es, G anada,
Spain
3CIBER de Epidemiología y Salud
Pública (CIBERESP), G anada,
Spain
4Depa amen o de Física
A ómica, Molecula y Nuclea ,
Uni e sidad de G anada,
G anada, Spain
Co espondence o
P o esso An onio MLallena;
lallena@ ug . es
Resea ch
© Au ho (s) (o hei
employe (s)) 2019. Re-use
pe mi ed unde CC BY-NC. No
comme cial e-use. See igh s
and pe missions. Published by
BMJ.
Abs AC
Objec i es To build up and es a Mon e Ca lo simula ion
p ocedu e o he in es iga ion o o e diagnosis in b eas
sc eening p og ammes (BSPs).
Design A Mon e Ca lo ool p e iously de eloped has been
adap ed o ob aining he quan i ies o in e es in o de o
de e mine he o e diagnosis: he annual and cumula i e
numbe o cance s de ec ed by sc eening, plus in e al
cance s, o a popula ion ollowing he BSP, and de ec ed
clinically o he same popula ion in he absence o
sc eening. O e diagnosis is ob ained by compa ing hese
esul s in a di ec way.
esul s O e diagnosis be ween 7% and 20%, depending
on he speci ic con igu a ion o he p og amme, ha e been
ound. These ange o alues is in ag eemen wi h some o
he esul s a ailable o ac ual BSPs. In he cases analysed,
a educ ion o 11% a mos has been ound in he numbe
o in asi e umou s de ec ed by sc eening in compa ison
o hose clinically de ec ed in he con ol popula ion. I has
been possible o es ablish ha o e diagnosis is almos
en i ely linked o duc al ca cinoma in si u umou s.
Conclusions The use o Mon e Ca lo ools may acili a e
he analysis o o e diagnosis in ac ual BSPs, pe mi ing o
add ess he ole played by a ious quan i ies o ele ance
o hem.
In ODuC IOn
B eas sc eening p og ammes (BSPs) ha e
become usual in de eloped coun ies and his
has s imula ed an in ense deba e abou he
po en ial isks and bene i s o he women
in i ed o ollow hem. One o hei main
consequences is he change o he b eas
cance incidence in he popula ion. This is
due o he ad ance in he diagnosis o he
disease, which inc eases he incidence a es
a ea lie ages. In addi ion, o he ac s, such
as hose de i ed om he use o ho mone
eplacemen he apy, may modi y he p e a-
lence and, e en ually inc ease he unde lying
incidence.1
Howe e , his appa en incidence excess
should no be con used wi h o e diagnosis,
an aspec ha , oge he wi h o e ea men ,
has ocused pa o he discussion in he
las yea s.2 BSPs a e supposed o enhance
he abili y o de ec ing umou s in hei
ea ly g ow h s ages, which a e hose asso-
cia ed wi h a be e p ognosis and su i al
o pa ien s. Howe e , some o he cance s
ound in he sc eening g ow so slowly ha
hey would ne e mani es clinical symp oms
be o e he women will die due o causes
o he han b eas cance . The de ec ion o
hese umou s is called o e diagnosis o he
BSP.2 3 Due o he impossibili y o knowing,
a p io i, he cance e olu ion, he a ailable
he apeu ic machine y is swi ched on and he
s eng hs and limi a ions o his s udy
►O e diagnosis alues quo ed in he p esen s udy
may be sligh ly o e es ima ed because we ha e
chosen 70 yea s as he maximum age o he women
ollowing he b eas sc eening p og ammes (BSPs).
►Simula ions equi e he use o da a co esponding
o a e e ence popula ion (eg, he b eas cance in-
cidence) ha may di e o some ex en wi h hose
o speci ic popula ions and ha in oduces a ce ain
unce ain y in he esul s.
►The use o he p esen Mon e Ca lo ool pe mi s o
in es iga e he in luence o he pa ame e s de ining
he BSP as well as hei esul s (such as o e digano-
sis) wi hou in ol ing ac ual popula ions and a oid-
ing he economical, logis ic and e hical p oblems
ha i usually en ails.
►Speci ically, o e diagnosis may be add essed in an
easy way o e coming he limi a ions o he andom-
ized essays in his espec .
►Possible changes in he diagnos ic o p ocedu al
me hodologies can be included in he simula ion,
hus allowing o an icipa e he esul s o he new
BSPs be o e hei implemen a ion.
750. P o ec ed by copy igh . on Oc obe 14, 2019 a G anada/Medicina/CC Salud PO Boxh p://bmjopen.bmj.com/BMJ Open: i s published as 10.1136/bmjopen-2018-023187 on 9 Feb ua y 2019. Downloaded om
2Fo as e oC, e al. BMJ Open 2019;9:e023187. doi:10.1136/bmjopen-2018-023187
Open access
women o e diagnosed become subjec o o e ea men
(eg, su ge y, adio he apy and e en chemo he apy) wi h
he consequen possible ad e se e ec s, e en in hose
cases ha would no e ol e owa ds malignancy. Besides,
some deg ee o spon aneous emission o asymp oma ic
la ency, in case o in asi e cance s, has been obse ed,
and his would inc ease o e diagnosis.4 5
The de e mina ion o he o e diagnosis ex en is in
p ac ice o a complica ed ask. Some es ima ions ha e
been p o ided on he basis o he esul s ob ained in BSPs
unning a e se e al yea s. In his case, o e diagnosis is
ob ained by compa ing he incidence o b eas cance in
he women ollowing he BSP wi h ha in a popula ion
wi h simila cha ac e is ics (age, exposu e o isk ac o s
o b eas cance , a ailabili y o ea men , ollow-up un il
dea h, e c.) and ha does no unde go sc eening. O e di-
agnosis would be linked o he cance excess in he BSP
g oup bu he di ec in e p e a ion o he incidence da a
in women ollowing a BSP is no s aigh o wa d because
o he luc ua ions in he incidences o he popula ions
ha a e compa ed, he di e ences in he con igu a-
ions o he BSPs conside ed (age anges o he women
ollowing he p og amme, mammog aphy equencies,
ollow-up imes), as well as he ways how he lead ime
(unde s ood as he ime be ween he umou de ec ion
by sc eening and he clinical one) is conside ed.2 6
A p io i, a mos consis en es ima e o o e diagnosis
may be ob ained in combined analyses o he esul s o
a ious andomised con olled ials (RCTs). Howe e , a
huge a iabili y in he quo ed o e diagnosis da a, mainly
due o di e en me hodologies in obse a ional s udies,
has been poin ed ou .6 7 In any case, he RCTs de eloped
o da e8–15 we e no designed o de e mine o e diag-
nosis and, as mos o hem began in he 1980s, ha e no
included mos o he ecen ad ances in he apy and ha e
no aken in o accoun he impac o he highe image
quali y and he educ ion in he de ec ion h esholds on
i .
In hese ci cums ances, Mon e Ca lo simula ion
appea s o be as a good al e na i e o o e come he
di icul ies poin ed ou . In p e ious wo ks,16–18 we ha e
de eloped a mammog aphic sc eening model based
on Mon e Ca lo echniques and aiming a e alua ing
sc eening p og ammes. This simula ion ool has allowed
us o ep oduce he esul s o ac ual BSPs conce ning he
in asi e/in si u umou de ec ion a es wi h and wi hou
sc eening, he anges o in e al cance s, and o he
magni udes associa ed wi h de ec ion. By in oducing he
su i al ollowing local- egional ea men has enabled us
o make es ima es o he mo ali y educ ion a ibu able
o BSPs. Finally, he in e nal alidi y o he main RCTs
included in he Coch ane me a-analysis3 was analysed by
using he Mon e Ca lo ool adequa ely adap ed o ake
in o accoun he speci ic cha ac e is ics o each o hem.
In all he si ua ions s udied, he Mon e Ca lo simula ion
has p o en o be an e icien ins umen .
The pu pose o he p esen wo k is o de elop a new
Mon e Ca lo ool o in es iga e he o e diagnosis o BSPs
acco ding o hei pa icula con igu a ions, hese a e
age anges o he women ollowing he p og amme and
mammog aphy equencies. To do ha we ha e used he
ool p e iously buil up and es ed16 ha in ol es gene ic
dis ibu ions ha may be adap ed o each speci ic popu-
la ion in o de o each enough p ecision in he simula-
ion. The p og amme will p o ide us wi h he annual and
cumula i e numbe o cance s de ec ed by sc eening, as
well as he numbe o cance s clinically de ec ed du ing
he p og amme unning (in e al cance s) o he popu-
la ion unde going sc eening. The compa ison o hese
esul s wi h hose ob ained o he same popula ion in
he absence o sc eening has allowed us o es ima e he
o e diagnosis in a di ec way.
MA e IAl AnD Me hODs
Ou Mon e Ca lo ool allows ca ying ou simula ions
based on a minimum numbe o pa ame e s ha ing
clinical o physical signi icance: umou a e age size o
symp oma ic de ec ion, mammog aphy sensi i i y (as a
unc ion o he hickness, his ological ype and densi y
o he b eas ) and he p opo ion o in asi e/in si u
umou s. I is wo h eminding he di e ences be ween
hese wo his ological ypes o cance s en e ing in ou
analysis. Duc al ca cinoma in si u (DCIS), o in aduc al
ca cinoma, in ol es he clonal p oli e a ion o malig-
nan cells. They g ow in he mamma y duc lumens, do
no in ade he adjacen b eas s oma and a e usually
diagnosed by mammog aphy. On he con a y, in asi e
umou s do mul iply in no mal issues and cons i u e
much o he cases o he clinically de ec ed b eas cance s.
Besides, we do no include any ad-hoc assump ion such as
ha ela ed o he highe agg essi i y o umou s in hei
ea ly g ow h s ages.
O he simula ion models a e ei he o e pa ame e ised
o based on dis ibu ions o pa ame e s ha a e di icul
o obse e o show non-negligible co ela ions wi h he
mammog aphy sensi i i y.19 O he app oaches, such as
hose linked o Ma ko models, may gene a e esul s ha
s ongly depend on he de ined s a es.20
In he simula ion ool we de eloped,16 ha is he base
o he p esen Mon e Ca lo app oach, he his o y o each
woman pa icipa ing in a BSP is simula ed indi idually,
conside ing a model ha includes pa ame e s and cha -
ac e is ics ha may be ga he ed in one o he ollowing
ca ego ies.
►Pa ame e s desc ibing he a ge popula ion o he
BSP. He e we ha e he incidence dis ibu ion o
b eas cance as a unc ion o he age o he women.
In ou simula ions we ha e used ha o he Cana y
Islands be o e BSP as ep esen a i e o an occiden al
popula ion no submi ed o sc eening. As he inci-
dence ac ually needed is ha o he umou onse ,
he incidence cu e was shi ed owa ds smalle ages
using he a e age ime be ween he umou de ec ion
by any diagnos ic echnique and he umou onse ,
employing a logis ic g ow h model.
750. P o ec ed by copy igh . on Oc obe 14, 2019 a G anada/Medicina/CC Salud PO Boxh p://bmjopen.bmj.com/BMJ Open: i s published as 10.1136/bmjopen-2018-023187 on 9 Feb ua y 2019. Downloaded om
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Fo as e oC, e al. BMJ Open 2019;9:e023187. doi:10.1136/bmjopen-2018-023187
Open access
►Tumou p ope ies ha in luence he p obabili y o
de ec ion by mammog aphy. Tumou size, his olog-
ical ype and b eas densi y a e he h ee undamen al
cha ac e is ics in his g oup. In addi ion, a model
desc ibing he e olu ion o he umou size as a unc-
ion o ime and a model o he de ec ion p obabili y
o b eas cance by mammog aphy a e equi ed.
►Con igu a ion o he BSP. He e we included he
equency o mammog aphy, he age ange o he
women pa icipa ing in he p og amme and he
ollow-up ime o each pa icipan .
The simula ion o a his o y begins by sampling, wi hin
he co esponding popula ion dis ibu ion, he age o a
candida e o pa icipa e in he BSP. I he age ob ained
is wi hin he ange es ablished o he i ual BSP, he
women his o y con inues by sampling whe he he
woman has de eloped a cance a some momen since
he bi h. This is done acco ding o he cumula i e inci-
dence dis ibu ion. I he answe is a i ma i e, hen he
women b eas densi y, he ini ial his ological ype o he
umou , he momen when i occu ed and i s size when
he woman en e s in o he BSP a e ob ained by sampling
he co esponding dis ibu ions. I is wo h poin ing ou
ha bo h he umou his ological ype and he b eas
densi y may change h oughou he simula ed his o y.
The his ological ype may e ol e om DCIS o in asi e
cance s. Also he b eas densi y may educe wi h age.
These ansi ions a e hypo heses aken in o accoun in
ou model.
The momen a which he umou a ises is sampled
acco ding o he incidence cu e, which shows he
p obabili y o umou occu ence as a unc ion o he
woman age. The umou size is es ima ed by using a eal-
is ic umou g ow h model ha desc ibes he inc ease
o he umou diame e wi h he ime elapsed since i s
incep ion. This g ow h is simula ed by using a model21
wi h a single ee pa ame e ha we assume o ollow a
log-no mal dis ibu ion, an ini ial p opo ion o in asi e/
DCIS umou s, and gi en ansi ion p obabili ies be ween
hese wo umou his ological ypes. This p opo ion is
chosen acco ding he esul s ob ained o de ec ion in
he a ious sc eening ounds. No addi ional hypo heses
abou umou e olu ion a e included.
In hose cases in which women ha e de eloped a
umou , he de ec ion p obabili y is sampled o conside
whe he he umou is de ec ed o no a e he mammog-
aphy. Fo women who do no p esen disease, he spec-
i ici y is used. I a ue posi i e case occu s, he his o y
is inished and a new one is s a ed. In any o he case,
successi e ounds a e simula ed ei he because he
umou was no de ec ed in he p e ious one ( alse nega-
i e) o he woman is heal hy bu con inues in he BSP
un il he age limi is eached ( ue nega i e). I , in his
las case, he woman was e oneously classi ied as posi i e,
we would deal wi h a alse posi i e case and i is unde -
s ood ha he woman is called again o a u he es ha
will con i m he e o in he diagnosis and ha she will
con inue wi hin he BSP.
In alse nega i e cases, which suppose he con inu-
a ion o he his o y, he simula ion akes in o accoun
he g ow h o he umou be ween he di e en ounds,
including he p obabili y o clinical de ec ion be ween
hem. This means ha in e al cance s a e conside ed.
Also he possible changes in he umou his ological ype
and b eas densi y a e aken in o accoun . Likewise, o
he cases o heal hy women, he p obabili y o cance
occu ence du ing ollow-up is simula ed.
Wi h his me hodology, he Mon e Ca lo ool pe mi s
o simula e he in oduc ion o a BSP in a gi en popu-
la ion, ca y ou i s ollow-up du ing a ce ain ime and
de e mine wi h he selec ed pe iodici y he o al numbe
o umou s de ec ed by sc eening in he sample o women
ha a end he p og amme, as well as hose de ec ed clin-
ically (in e al cance s i hey occu in women who ollow
he BSP). I he p e alence o b eas cance is s able o e
ime, he incidence cu es co esponding o he popu-
la ion unde going sc eening should con e ge, a e a
ime o he o de o he lead ime, o hose ound o
he same popula ion wi hou sc eening, and he whole
p ocedu e would no show o e diagnosis. I his does no
happen, and a e he lead ime, he wo cumula i e inci-
dence cu es would emain pa allel and he di e ence
be ween bo h would p o ide us wi h an es ima e o he
o e diagnosis.
Speci ically, he o e diagnosis was calcula ed as2:
S
=
N
sc een
(
c
+
l
)−N
clin
(
c
+
l
)
N
sc een(
c)
(1)
whe e
Nsc een ( )
is he cumula i e numbe o cance s
de ec ed in women who ha e ollowed he BSP du ing
a o al ime
, including in e al cance s,
Nclin ( )
is he
cumula i e numbe o umou de ec ed clinically in an
equi alen g oup o women who ha e no ollowed a BSP,
c
is he du a ion o he BSP o ime cou se and
l
is a
ime equi ed o a oid he ansien pe iod associa ed o
he lead ime. Excep o a e y small numbe o cance s,
he a e age lead ime is ~3–4 yea s2 and we ha e consid-
e ed
l= 10 yea s
.
In ou simula ions we an 50 million o woman his o ies
in each BSP. Two age anges [al,au] = [50,70] and [40,70]
(wi h age alues gi en in yea s) we e analysed wi h
c= 10
and 20 yea s, espec i ely. Time in e als be ween consec-
u i e mammog aphies o
in =1
, 2 and 3 yea s we e
conside ed. In all cases simula ed, an a endance a e o
100% was assumed, hough es ima ions o 80% a en-
dance we e also pe o med.
The i s unning yea o he BSP, all women wi h ages
in he selec ed age ange [al,au] en e he p og amme; in
he ollowing yea s, women who each he minimum age
o pa icipa ion al a e inco po a ed. They a e ollowed
wi hin he BSP un il hey each au. I he p og amme
inishes, woman’s his o ies con inue o be simula ed,
conside ing he possibili y o umou clinical de ec ion.
In ou simula ions we chose 20 yea s o his pe iod a e
he p og amme: his pe mi ed es ima ing he ime neces-
sa y o he p og amme e ec s o disappea .
750. P o ec ed by copy igh . on Oc obe 14, 2019 a G anada/Medicina/CC Salud PO Boxh p://bmjopen.bmj.com/BMJ Open: i s published as 10.1136/bmjopen-2018-023187 on 9 Feb ua y 2019. Downloaded om
4Fo as e oC, e al. BMJ Open 2019;9:e023187. doi:10.1136/bmjopen-2018-023187
Open access
Pa ien and public in ol emen
The p esen s udy deals wi h a Mon e Ca lo simula ion.
Then, nei he pa ien s no public we e in ol ed.
esul s
Figu e 1 shows he cumula i e incidences o in asi e
plus DCIS umou , no malized o he a e age numbe o
women pa icipa ing in he BSP, (pe housand women),
as a unc ion o he ime elapsed since he beginning o
he BSP, o he con igu a ions o [50-70] wi h
c= 10
yea s (panel 1a) and [40-70] wi h
c= 20
yea s (panel
1b). Fo hese con igu a ions, he esul s ob ained o
mammog aphy equencies
in =1
(g een solid ci cles),
2 (blue solid squa es) and 3 ( ed solid iangles) yea s
a e shown. The a endance is assumed o be 100%. Open
squa es co espond o he alues ound o he popula-
ion o women who do no ollowed he BSP.
The o e diagnosis es ima es o 100% a endance,
calcula ed acco ding o equa ion (1), a e shown in able 1.
The co esponding incidences o in asi e plus DCIS
umou s, no malised o he a e age numbe o women
pa icipa ing in he BSP and o 100% a endance, a e
shown in igu e 2.
Finally, in igu e 3 he cumula i e incidence o in asi e
cance s in he sc eened woman sample o
in =1
yea and
100% a endance (g een solid ci cles) is compa ed o he
esul s ob ained o a popula ion o women who did no
ollow a BSP (open squa es). The alues a e no malised
o he a e age numbe o women pa icipa ing in he BSP.
DIsCussIOn
The e ec o he o e diagnosis is clea ly seen in igu e 1:
once a ime equal o he lead ime
l= 10
yea s has passed
a e he BSP inished ( his means, espec i ely, 20 and 30
yea s a e he beginning o he p og amme o he wo
con igu a ions s udied), he esul s ob ained in he case
o he women who ha e ollowed he BSP beha e pa allel
o hose o he unsc eened woman.
As shown in able 1, he co esponding o e diag-
nosis es ima es ound o he [50–70] con igu a ion a e
signi ican ly la ge (be ween 15% and 21%) han hose
ob ained o he [40–70] one. This is due o he ac ha
he umou de ec ion by sc eening a ea lie ages, as i
occu s in he second con igu a ion, would ha e mo e
ime o g ow and each a size exceeding he clinical de ec-
ion h eshold in he absence o sc eening.
On he o he hand, and as i was expec ed, he inc ease
o he ime in e al be ween mammog aphies educes
he o e diagnosis, he educ ion being ~40% when
in
changes om 1 o 3 yea s.
Figu e 1 Cumula i e in asi e+duc al ca cinoma in
si u  umou incidence, no malised o he a e age numbe
o women pa icipa ing in he b eas sc eening p og amme
(BSP), as a unc ion o he ime elapsed since he beginning
o he BSP. Solid symbols show he esul s ob ained o
he con igu a ions (A) [50–70] wi h a BSP du a ion o
c= 10
yea s and (B) [40–70] wi h
c= 20
yea s, wi h 100%
a endance. The alues co esponding o in e als be ween
mammog aphies o 
in =1
, 2 and 3 yea s a e shown wi h
g een solid ci cles, blue solid squa es and ed solid iangles,
espec i ely. Open squa es indica e he esul s ound o he
woman popula ion who do no ollow he BSP.
Table 1 Values o o e diagnosis, as de ined in equa ion (1), o he wo con igu a ions s udied and he h ee mammog aphy
in e als
in
conside ed in each case
in
O e diagnosis
[50,70] yea s;
c= 10
yea s [40,70] yea s;
c= 20
yea s
100% a endance 80% a endance 100% a endance 80% a endance
1 yea 0.200±0.009 0.14 0.168±0.005 0.13
2 yea s 0.150±0.010 0.10 0.123±0.005 0.07
3 yea s 0.115±0.007 0.06 0.100±0.005 0.07
Values shown o 100% a endance we e ob ained wi h he Mon e Ca lo simula ion ool; hose o 80% a endance a e es ima ions (see ex
o de ails). Unce ain ies a e gi en wi h a co e age ac o k=3.
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Fo as e oC, e al. BMJ Open 2019;9:e023187. doi:10.1136/bmjopen-2018-023187
Open access
When he BSP inishes (a e 10 yea s in he case o he
con igu a ion [50–70] and 20 yea s o he [40–70] one o
i s beginning), a ansien pe iod occu s. In igu e 1 his is
be e seen in he case o
in =1
yea (g een solid ci cles)
and i shows up as a change in he slope o he co e-
sponding da a. This beha iou may be obse ed in a mo e
clea way by looking a he co esponding incidences, shown
in igu e 2. The ein he end desc ibed appea s as a s ong
educ ion o he incidence a e and is a consequence o he
de ec ion de ici once he BSP is no longe ac i e. As we
can see, he incidence a e equi es abou 10 yea s o each
he incidence co esponding o he unsc eened popula ion
(shown wi h open squa es). I is wo h men ioning ha he
educ ion obse ed is inhe en o he BSP i sel and i occu s
e en i o e diagnosis is absen . To isola e in he incidence
cu es hese changes om hose due o o e diagnosis, i is
manda o y wai ing o he lead ime
l= 10
yea s a e he
BSP has inished.
As seen in igu e 3, o he con igu a ion [50-70], he
cumula i e incidence o in asi e cance s in he sc eened
woman sample (shown by g een solid ci cles in he panel
3a) coincide wi h ha ob ained o he e e ence popula-
ion o women no ollowing a BSP (open squa es) a e
a pe iod o ~5 yea s once he p og amme has inished. As
he numbe o in asi e umou s is he same in he popula-
ions wi h and wi hou sc eening, he o e diagnosis abo e
discussed elies comple ely on DCIS umou s. The same
does no occu in he case o he con igu a ion [40-70]
(panel 3b) whe e a de ici o 11% in he cumula i e inci-
dence o in asi e umou s wi h espec o he unsc eened
popula ion is ound a e BSP inished.
Once he impo ance o DCIS umou s in o e diag-
nosis has been poin ed ou , i is wo h no ing ha i is
no a consequence o a slowe g ow h o hese umou s
compa ed wi h in asi e ones, since ou model does no
include any di e ence acco ding o hei his ological
ype. The eason is a he ha he e is a g ea e abun-
dance o DCIS cance s in he ea ly s ages in which hey
can be e icien ly de ec ed by sc eening.
Figu e 2 In asi e+duc al ca cinoma insi u umou
incidence, no malised o he a e age numbe o women
pa icipa ing in he b eas sc eening p og amme (BSP),
as a unc ion o he ime elapsed since he beginning o
he BSP. Solid symbols show he esul s ob ained o he
con igu a ions (A) [50–70] wi h a BSP du a ion o
c= 10
yea s and (B) [40– 70] wi h
c= 20
yea s, wi h 100%
a endance. The alues co esponding o in e als be ween
mammog aphies o  in =1, 2 and 3 a e shown wi h g een
solid ci cles, blue solid squa es and ed solid iangles,
espec i ely. Open squa es indica e he esul s ound o he
woman popula ion who do no ollow he BSP.
Figu e 3 Cumula i e incidence o in asi e umou s,
no malised o he a e age numbe o women pa icipa ing
in he b eas sc eening p og amme (BSP), as a unc ion o
he ime elapsed since he beginning o he BSP. G een solid
ci cles show he esul s ob ained o he con igu a ions (A)
[50–70] wi h a BSP du a ion o
c= 10
yea s and (B) [40–70]
wi h
c= 20
yea s, wi h an in e al be ween mammog aphies
o
in =1
yea and 100% a endance. Open squa es indica e
he esul s ound o he woman popula ion who do no ollow
he BSP.
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6Fo as e oC, e al. BMJ Open 2019;9:e023187. doi:10.1136/bmjopen-2018-023187
Open access
As said abo e, o e diagnosis es ima ions om ac ual
BSPs a e di icul . Puli i e al22 analysed 13 obse a ional
s udies and concluded ha o e diagnosis would each up
o 10%. In he case o he B i ish Na ional Heal h Sys em
BSP, wi h a ollow-up o 20 yea s and o women olde han
50 yea s,2 he mammog aphic sc eening a oided a dea h
each 250 in i ed women. The e o e, assuming an accep-
ance/pa icipa ion a e o a ound 80% and a de ec ion
a e in he incidence ounds o 4 cance s de ec ed pe
1000 women and yea , one would ha e 3 cases o o e di-
agnosis/o e ea men pe dea h a oided, ha is, 1% o
women in i ed o BSP a e expec ed o be o e diagnosed.
The si ua ion o he RCT es ima ions is also unclea .
The Coch ane epo es ablished an absolu e isk o
o e diagnosis/o e ea men o 0.5%.3 Much smalle
alues,~0.025% pe yea , we e es ablished by Moss23
acco ding again o he da a o he Canadian ials,9 10 while
o he ela i e isk in he in e en ion a ms o hese RCTs
he ound alues be ween 11% and 14%. The easons o
hese disc epancies may be linked o he se ious me hod-
ological p oblems shown by hese RCTs.24
On he o he hand, he 2009 e ision o he US P e en-
i e Task Fo ce25 quo ed ha o e diagnosis was wi hin 1%
and 10%.
Tes ing he esul s o hese ac ual BSPs o RCTs wi h
ou Mon e Ca lo ool would equi e de ailed simula ions
in which he a ious speci ica ions o each o hem a e
included. In he case o BSPs, one o he main inpu s is
he a endance ha in ou calcula ions has been assumed
o be 100%. Howe e , i is possible o es ima e he o e di-
agnosis o lowe a endances using he esul s we ha e
ob ained by assuming ha he numbe o de ec ed
umou s emains app oxima ely cons an a e he
sc eening has inished. In able 1 he alues ob ained in
his way o 80% a endance a e shown. A smalle a en-
dance gi e ise o lowe alues o he o e diagnosis: a
educ ion o ~5% has been ound o 80% a endance wi h
espec o 100% one, he o e diagnosis anging be ween
7% and 14% depending on he con igu a ion. These es i-
ma ions gi e an idea o he magni ude o o e diagnosis in
BSPs wi h a endances a ound 80%.
To inish, i should be no ed ha ou simula ions may
be a ec ed by some limi a ions because we ha e no he
incidence cu es co ec ed by he a e age de ec ion ime
o women o e 70 yea s and he simula ed his o ies
s opped a ha age. This may imply a small o e es ima-
ion o o e diagnosis. On he o he hand, he ac ha
he simula ions ca ied ou equi e in o ma ion co e-
sponding o a e e ence popula ion (eg, he b eas cance
incidence) in oduces a ce ain unce ain y in he esul s
because hese da a may di e o some ex en wi h hose
o he speci ic popula ions in es iga ed.
COnClusIOns
We ha e de eloped a model based on Mon e Ca lo simu-
la ion echniques ha allows us o ep oduce consis en ly
he known esul s abou o e diagnosis on BSPs. I a ies
om 7% o 20% depending he p og amme con igu-
a ion (age ange o women in ol ed and equency o
mammog aphy).
I has been ound ha , a e he end o he sc eening
p og amme, he incidence o in asi e cance s is simila o
ha ound o an unsc eened con ol g oup: his implies
ha o e diagnosis is mainly associa ed wi h DCIS umou s.
This is due o he ac ha his ype o cance s a e mo e
abundan han he in asi e ones when hey each he size
ha make hem o be de ec able by mammog aphy.
In any case, Mon e Ca lo ools appea o be e y help ul
o analysing he ole o he a ious pa ame e s de ining
he BSP con igu a ions as well as hei esul s (such as
o e diagnosis) wi hou in ol ing ac ual popula ions and
a oiding he economical, logis ic and e hical p oblems
ha i usually en ails. E en mo e, changes in he diag-
nos ic o p ocedu al me hodologies can be included in
he simula ion, hus allowing o an icipa e he esul s o
he new p og ammes be o e hei implemen a ion.
Con ibu o s All he au ho s con ibu ed o he concep ion and design o he s udy.
CF and LIZ w o e he simula ion codes and an hem o he a ious con igu a ions
analysed. All he au ho s pe o med he analysis o he simula ion esul s,
con ibu ed o he w i ing and edi ing o he o iginal e sion o he manusc ip ,
esponded o he e iewe s’ epo s and w o e he e ised e sion o he a icle.
Funding Wo k pa ially suppo ed by he Biomedical Resea ch Ne wo king Cen e -
CIBER de Epidemiología y Salud Pública (CIBERESP), he Spanish Minis e io de
Ciencia y Compe i i idad (FPA2015-67694), he Eu opean Regional De elopmen
Fund (ERDF) and he Jun a de Andalucía (FQM0387).
Compe ing in e es s None decla ed.
Pa ien consen o publica ion No equi ed.
P o enance and pee e iew No commissioned; ex e nally pee e iewed.
Da a sha ing s a emen The e a e no addi ional da a om he p esen s udy o
be sha ed. In o ma ion abou he de ails o he simula ions can be ob ained om
any o he au ho s.
Open access This is an open access a icle dis ibu ed in acco dance wi h he
C ea i e Commons A ibu ion Non Comme cial (CC BY-NC 4.0) license, which
pe mi s o he s o dis ibu e, emix, adap , build upon his wo k non-comme cially,
and license hei de i a i e wo ks on di e en e ms, p o ided he o iginal wo k is
p ope ly ci ed, app op ia e c edi is gi en, any changes made indica ed, and he use
is non-comme cial. See: h p:// c ea i ecommons. o g/ licenses/ by- nc/ 4. 0/.
eFe enCes
1. Du y SW, Lynge E, Jonsson H, e al. Complexi ies in he es ima ion
o o e diagnosis in b eas cance sc eening. B J Cance
2008;99:1176–8.
2. Independen UK Panel on B eas Cance Sc eening. The bene i s and
ha ms o b eas cance sc eening: an independen e iew. Lance
2012;380:1778–86.
3. Gø zsche PC, Nielssen M. Sc eening o b es cance wi h
mammog aphy (Re iew). The Coch ane Collabo a ion. Copenhagen:
John Wiley & Sons, 2009.
4. Zahl PH, Maehlen J, Welch HG. The na u al his o y o in asi e b eas
cance s de ec ed by sc eening mammog aphy. A ch In e n Med
2008;168:2311–6.
5. Zahl PH, Gø zsche PC, Mæhlen J. Na u al his o y o b eas cance s
de ec ed in he Swedish mammog aphy sc eening p og amme: a
coho s udy. Lance Oncol 2011;12:1118–24.
6. Biesheu el C, Ba a A, Howa d K, e al. E ec s o s udy me hods
and biases on es ima es o in asi e b eas cance o e de ec ion
wi h mammog aphy sc eening: a sys ema ic e iew. Lance Oncol
2007;8:1129–38.
7. Puli i D, Miccinesi G, Paci E. O e diagnosis in b eas cance : design
and me hods o es ima ion in obse a ional s udies. P e Med
2011;53:131–3.
750. P o ec ed by copy igh . on Oc obe 14, 2019 a G anada/Medicina/CC Salud PO Boxh p://bmjopen.bmj.com/BMJ Open: i s published as 10.1136/bmjopen-2018-023187 on 9 Feb ua y 2019. Downloaded om
7
Fo as e oC, e al. BMJ Open 2019;9:e023187. doi:10.1136/bmjopen-2018-023187
Open access
8. Ande sson I, Aspeg en K, Janzon L, e al. Mammog aphic sc eening
and mo ali y om b eas cance : he Malmö mammog aphic
sc eening ial. BMJ 1988;297:943–8.
9. Mille AB, To T, Baines CJ, e al. Canadian Na ional B eas Sc eening
S udy-2: 13-yea esul s o a andomized ial in women aged 50-59
yea s. J Na l Cance Ins 2000;92:1490–9.
10. Mille AB, To T, Baines CJ, e al. The Canadian Na ional B eas
Sc eening S udy-1: b eas cance mo ali y a e 11 o 16 yea s o
ollow-up. A andomized sc eening ial o mammog aphy in women
age 40 o 49 yea s. Ann In e n Med 2002;137:305–12.
11. Tabà L, Gad A. Sc eening o b eas cance : he Swedish ial.
Radiology 1981;138:219–22.
12. Shapi o S, Vene W, S ax P, e al. Selec ion, ollow-up, and analysis
in he Heal h Insu ance Plan S udy: a andomized ial wi h b eas
cance sc eening. Na l Cance Ins Monog 1985;67:65–74.
13. F isell J, Glas U, Hells öm L, e al. Randomized mammog aphic
sc eening o b eas cance in S ockholm. Design, i s ound esul s
and compa isons. B eas Cance Res T ea 1986;8:45–54.
14. Bju s am N, Bjö neld L, Du y SW, e al. The Go henbu g b eas
sc eening ial: i s esul s on mo ali y, incidence, and mode o
de ec ion o women ages 39-49 yea s a andomiza ion. Cance
1997;80:2091–9.
15. Moss SM, Wale C, Smi h R, e al. E ec o mammog aphic sc eening
om age 40 yea s on b eas cance mo ali y in he UK Age ial
a 17 yea s’ ollow-up: a andomised con olled ial. Lance Oncol
2015;16:1123–32.
16. Fo as e o C, Zamo a LI, Gui ado D, e al. A Mon e Ca lo ool o
simula e b eas cance sc eening p og ammes. Phys Med Biol
2010;55:5213–29.
17. Zamo a LI, Fo as e o C, Gui ado D, e al. A Mon e Ca lo ool o s udy
he mo ali y educ ion due o b eas sc eening p og ams. Med Phys
2012;39:7215–23.
18. Zamo a LI, Fo as e o C, Gui ado D, e al. A Mon e Ca lo analysis o
b eas sc eening andomized ials. Phys Med 2016;32:1609–14.
19. Cong XJ, Shen Y, Mille AB. Es ima ion o age-speci ic sensi i i y
and sojou n ime in b eas cance sc eening s udies. S a Med
2005;24:3123–38.
20. Uh y Z, Hédelin G, Colonna M, e al. Mul i-s a e Ma ko models
in cance sc eening e alua ion: a b ie e iew and case s udy. S a
Me hods Med Res 2010;19:463–86.
21. Sp a JA, on Fou nie D, Sp a JS, e al. Decele a ing g ow h and
human b eas cance . Cance 1993;71:2013–9.
22. Puli i D, Du y SW, Miccinesi G, e al. O e diagnosis in
mammog aphic sc eening o b eas cance in Eu ope: a li e a u e
e iew. J Med Sc een 2012;19:42–56.
23. Moss S. O e diagnosis and o e ea men o b eas cance :
o e diagnosis in andomised con olled ials o b eas cance
sc eening. B eas Cance Res 2005;7:230–4.
24. Njo SH, Ga ne JP, Lynge E. O e -diagnosis es ima e om he
Independen UK Panel on B eas Cance Sc eening is based on
unsui able da a. J Med Sc een 2013;20:104–5.
25. Nelson HD, Tyne K, Naik A, e al. Sc eening o b eas cance :
sys ema ic e idence e iew upda e o he U. S. P e en i e Task
Fo ce. E idence e iew upda e No. 74. AHRQ publica ion No. 10-
05142-EF-1. Rock ille: Agency o Heal hca e Resea c and Quali y,
2009.
750. P o ec ed by copy igh . on Oc obe 14, 2019 a G anada/Medicina/CC Salud PO Boxh p://bmjopen.bmj.com/BMJ Open: i s published as 10.1136/bmjopen-2018-023187 on 9 Feb ua y 2019. Downloaded om