METHODOLOGY Open Access
Imp o ing es ima es o he bu den o
se e e acu e malnu i ion and p edic ions
o caseload o p og ams ea ing se e e
acu e malnu i ion: expe iences om
Nige ia
Assaye Bul i
1*
, And é B iend
2,3
, Nancy M. Dale
2
, A jan De Wag
1
, Fa aja Chiwile
1
, S anley Chi ekwe
4
,
Ch is Isokpunwu
5
and Ma k Mya
6
Abs ac
Backg ound: The bu den o se e e acu e malnu i ion (SAM) is es ima ed using unadjus ed p e alence es ima es. SAM
is an acu e condi ion and many child en wi h SAM will ei he eco e o die wi hin a ew weeks. Es ima ing SAM
bu den using unadjus ed p e alence es ima es esul s in signi ican unde es ima ion. This has a nega i e impac on
alloca ion o esou ces o he p e en ion and ea men o SAM. A simple me hod o adjus ing p e alence es ima es
in ended o imp o e he accu acy o bu den es ima es and caseload p edic ions has been p oposed. This me hod
employs an incidence co ec ion ac o . Applica ion o his me hod using he globally ecommended incidence
co ec ion ac o has led o p og ams unde es ima ing bu den and caseload in some se ings.
Me hods: A me hod o es ima ing a locally app op ia e incidence co ec ion ac o om p e alence, popula ion size,
p og am caseload, and p og am co e age was de eloped and es ed using da a om he Nige ian na ional SAM
ea men p og am.
Resul s: Applying he de eloped me hod esul ed in e o s in caseload p edic ion o abou 10%. This is a conside able
imp o emen upon he cu en me hod, which esul ed in a 79.5% unde es ima e. Me hods o imp o ing he
p ecision o es ima es a e p oposed.
Conclusions: I is possible o conside ably imp o e p edic ions o caseload by applying a simple model o da a ha
a e eadily a ailable o p og am manage s. This implies ha mo e accu a e es ima es o bu den may also be made
using he same me hods and da a.
Keywo ds: Se e e acu e malnu i ion, Bu den, Caseload, P e alence, Incidence, Nige ia
Backg ound
A child wi h se e e acu e malnu i ion (SAM) has a high
isk o nea e m mo ali y [1, 2]. I has been es ima ed
ha SAM a ec ed mo e han 16 million child en globally
in 2016 [3]. This igu e is based on p e alence es ima es
om c oss-sec ional su eys. SAM is an acu e condi ion
and many child en wi h SAM will ei he eco e o die
wi hin a ew weeks. Es ima ing he numbe o SAM cases
p esen in a popula ion o e a gi en pe iod o ime, he
“SAM bu den”, using unadjus ed p e alence es ima es is
likely, he e o e, o miss many new (inciden ) cases and
signi ican ly unde es ima e he SAM bu den [4]. A ecen
es ima e o he annual global SAM bu den ha a emp s
o accoun o inciden cases sugges s ha 110 million
cases pe yea migh be a mo e accu a e es ima e [5]. Poo
es ima es o SAM bu den a e a p oblem o p og am
manage s a all le els. Unde es ima ion has a nega i e
* Co espondence: [email p o ec ed]
1
Uni ed Na ions Child en’s Fund (UNICEF), Abuja, Nige ia
Full lis o au ho in o ma ion is a ailable a he end o he a icle
© The Au ho (s). 2017 Open Access This a icle is dis ibu ed unde he e ms o he C ea i e Commons A ibu ion 4.0
In e na ional License (h p://c ea i ecommons.o g/licenses/by/4.0/), which pe mi s un es ic ed use, dis ibu ion, and
ep oduc ion in any medium, p o ided you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o
he C ea i e Commons license, and indica e i changes we e made. The C ea i e Commons Public Domain Dedica ion wai e
(h p://c ea i ecommons.o g/publicdomain/ze o/1.0/) applies o he da a made a ailable in his a icle, unless o he wise s a ed.
Bul i e al. A chi es o Public Heal h (2017) 75:66
DOI 10.1186/s13690-017-0234-4
impac on he p io i iza ion o esou ce alloca ion o he
p e en ion and ea men o SAM bo h globally and
locally [6].
Bu den is he sum o p e alen cases a he s a o a
pe iod and inciden cases ha a ise du ing ha pe iod.
The numbe o p e alen cases in a popula ion a a gi en
poin in ime can be es ima ed using a combina ion o a
p e alence es ima e om a c oss-sec ional su ey and
popula ion da a. This in o ma ion is usually al eady
a ailable o p og am manage s. Incidence is mo e com-
plica ed and mo e expensi e o es ima e.
The ela ionship be ween incidence and p e alence
is equen ly desc ibed using a “ba h ub”me apho
[7]. In his model he low o wa e in o he ba h ub
is analogous o incidence, he le el o he wa e in
he ba h ub ep esen s p e alence, and he low o
wa e ou o he ba h ub h ough he d ain ep esen s
eco e y and mo ali y. Incidence in ela ion o p e a-
lence depends, o a la ge ex en , upon he a e age
du a ion o illness (see Fig. 1).
The simple ela ionship be ween p e alence, inci-
dence, and du a ion o illness makes i possible o
c ea e a simple ma hema ical model ha allows he
es ima ion o bu den using p e alence and popula ion
es ima es oge he wi h o he da a (e.g. p og am
co e age and p og am caseloads) ha will usually be
a ailable o p og am manage s.
The Communi y Managemen o Acu e Malnu i ion
(CMAM) Fo um has p oposed a simple me hod o es i-
ma e SAM bu den and p edic he numbe o cases ha
a p og am will ea o e a gi en planning pe iod [8].
The numbe o p e alen cases p esen in a popula ion
a he ime o a p e alence su ey is es ima ed as he
p oduc o p e alence and popula ion size:
Es ima ed numbe o p e alen cases ¼NP
whe e:
Nis he size o he popula ion o in e es
Pis he p e alence o he condi ion o in e es
The popula ion bu den (B) consis s o bo h p e alen
cases and new (inciden ) cases ha a e expec ed o
occu in he p og am a ea o e a gi en planning pe iod:
Bu den BðÞ¼Es ima ed numbe o p e alen cases
þExpec ed numbe o inciden cases
The expec ed numbe o inciden cases can be es i-
ma ed using:
Expec ed nume o inciden cases ¼NPK
whe e Kis a co ec ion ac o [9] calcula ed as:
K¼Du a ion o planning pe iod
A e age du a ion o a disease episode
This allows he popula ion bu den (B) o be es ima ed:
B¼Es ima ed numbe o p e alen cases
þExpec ed numbe o inciden cases
B¼NP þNPK
B¼NP 1þKðÞ
The popula ion bu den (B) can be used o p edic
he numbe o cases ha a p og am will ea o e
he planning pe iod (L) using an es ima e o p og am
co e age (C):
Fig. 1 The “ba h ub”me apho o he ela ionship be ween incidence and p e alence. The a e a which cases lea e he popula ion depends
upon he a e age du a ion o illness
Bul i e al. A chi es o Public Heal h (2017) 75:66 Page 2 o 8
Expec ed p og am caseload LðÞ
¼Expec ed co e age CðÞPopula ion bu den BðÞ
L¼CNP 1þKðÞ
All o he e ms in his es ima o a e subjec o
unce ain y.
Unce ain y ega ding co e age (C) and p e alence (P)
is usually quan i iable and is quan i ied by con idence in-
e als o c edible in e als on poin es ima es. The
p e alence o se e e acu e malnu i ion (SAM) is o en
es ima ed wi h poo ela i e p ecision. Fo example, he
commonly used S anda dised Moni o ing and Assess-
men o Relie and T ansi ions (SMART) p e alence su -
eys ypically ha e e ec i e sample sizes (i.e. he sample
size a e accoun ing o su ey design e ec s) be ween
n= 300 and n= 400 [10]. An e ec i e sample size o
n= 400 yields an exac 95% con idence in e al o
[0.55%; 3.24%] on a 1.50% poin es ima e o SAM p e a-
lence [11]. The ela i e p ecision o his es ima e is:
Rela i e p ecision %ðÞ¼
3:24−0:55
1:50 100 ¼179:3%
Co e age is ypically es ima ed wi h a p ecision o
abou ± 10% on a 50% es ima e [12]. This is a 40% ela-
i e p ecision.
Use ul accu acy o popula ion es ima es can be
achie ed by co ec ing census da a o accoun o popu-
la ion g ow h and mig a ion. I can o en be assumed
ha he popula ion is es ima ed wi h li le o no e o .
This may no , howe e , be he case in eme gencies in
which he e is conside able and ongoing popula ion
mo emen and / o high le els o mo ali y.
Caseload (L) is a simple coun o p og am admissions.
This da a is collec ed and epo ed on a ou ine basis
and can usually be assumed o be measu ed wi h li le
o no e o .
The e is conside able unce ain y abou he alue o he
incidence co ec ion ac o (K). The a e age du a ion o an
un ea ed SAM episode ha is cu en ly being used globally
is 7.5 mon hs. This is based on da a om wo coho s ud-
ies and p o ides an incidence co ec ion ac o (K)o 1.6
o a one-yea planning pe iod [13]. I was assumed ha
his alue o Kwould apply in all con ex s. Go e nmen s,
Uni ed Na ions agencies, non-go e nmen al o ganiza ions
(NGOs), and o he SAM ea men p og am implemen ing
pa ne s ha e, in he absence o o he e idence, been using
his alue o K o es ima e he bu den and expec ed case-
load and o ad oca e o esou ces o ea child en wi h
SAM. Repo s om SAM ea men p og ams sugges ha
he use o K= 1.6 has led o p og ams unde es ima ing
caseload in some Wes A ican se ings. Recen wo k indi-
ca es ha a single alue o K o use globally may no be
use ul (see Table 1) [6, 14–16].
Da a om he Nige ian Communi y-based Manage-
men o Acu e Malnu i ion (CMAM) p og am om
2014 and 2015 a e p esen ed in his a icle. This p o-
g am s a ed ope a ions in 2009 and has ea ed be-
ween 300 housand and 500 housand SAM cases
each yea . Du ing he cou se o implemen a ion i
was ecognized ha he use o K=1.6hadled o
conside able unde es ima ion o SAM bu den and
p og am caseload. Gi en he public heal h and secu -
i y si ua ion in Nige ia i is an icipa ed ha he Ni-
ge ian CMAM p og am will un o many yea s and
accu a e es ima es o expec ed caseloads will be e-
qui ed o secu e adequa e con inued unding.
This a icle p esen s a me hod o adjus o calib a e
he alue o Kusing he popula ion o he p og am a ea,
he numbe o p og am admissions, es ima es o p o-
g am co e age, and es ima es o he p e alence o SAM
in o de o p o ide mo e accu a e es ima es o bu den
and expec ed caseload du ing p og am implemen a ion.
The me hod is illus a ed using da a om he Nige ian
CMAM p og am. The e ised es ima e o Kmay also be
use ul o p edic SAM bu den and caseload om p e a-
lence su eys in simila se ings.
Me hods
The caseload es ima ion o mula:
L¼CNP 1þKðÞ
can be ea anged o ind Kgi en he o he e ms:
L¼CNP 1þKðÞ
1þK¼L
CNP
K¼L
CNP
−1
A sui able alue o Kcan be ound by subs i u ing
known alues o L,C,N, and Pwi h Lbeing he ob-
se ed p og am caseload (i.e. he numbe o admissions).
The me hod ou lined he e assumes ha bo h popula-
ion (N) and caseload (L) a e measu ed wi h li le o no
e o al hough he me hod can be easily ex ended o ac-
commoda e unce ain y in hese e ms. The p incipal
sou ces o unce ain y in his analysis a e, he e o e,
p e alence (P) and co e age (C). This can lead o con-
side able unce ain y in hei p oduc (PC) used in he
es ima o (Addi ional ile 1).
An app oxima e 95% con idence in e al o he p od-
uc o wo p opo ions (i.e. p e alence (P) and co e age
(C) in his applica ion):
θ
b¼PC
is gi en by:
Bul i e al. A chi es o Public Heal h (2017) 75:66 Page 3 o 8
θ
be1:96SE logθ
bÞ

whe e:
SE logθ
b¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1−P
nPPþ1−C
nCC

and n
P
and n
C
a e he sample sizes used o es ima e
p e alence (P) and co e age (C) espec i ely [17]. This
o mula is no immedia ely applicable o he so s o
da a likely o be a ailable o p og am manage s because
he e ec i e sample sizes used o es ima e bo h p e a-
lence and co e age (n
P
and n
C
) will di e om epo ed
sample sizes due o design e ec s in oduced by he use
o complex samples and / o he use o p io in o ma-
ion [12,18,19].
P e alence is usually es ima ed using su eys employing
complex sample designs. The p e alence es ima es used in
his epo we e made by combining esul s om se e al
c oss-sec ional household su eys ha used a wo-s age
clus e sample design ep esen a i e a he s a e le el ol-
lowing he SMART me hodology [10, 20, 21].
Co e age o CMAM p og ams is o en es ima ed using
spa ially s a i ied samples [12, 22–24]. Semi-Quan i a i e
E alua ion o Access and Co e age (SQUEAC) co e age
assessmen s use a Bayesian be a-binomial conjuga e
analysis in which he conjuga e p io con ains in o -
ma ion ha con ibu es “pseudo-obse a ions” o he
analysis [12, 19].
The e ec i e sample size associa ed wi h he es ima e
o a p opo ion can be calcula ed om he epo ed
poin es ima e (p) and i s associa ed uppe and lowe
95% con idence limi s (UCL and LCL).
Va iance (VAR) is calcula ed as:
VAR ¼UCL−LCL
21:96

2
The e ec i e sample size (n
e ec i e
) is calcula ed as:
ne ec i e ¼p1−pðÞ
VAR
ounded o he nea es whole numbe .
This calcula ion is pe o med o ind bo h n
P
and n
C
be o e calcula ing SE logθ
b .
We used he app oach ou lined abo e o ind a
sui able alue o K o he Nige ian CMAM p o-
g am. Da a ela ing o p og am admissions (i.e. case-
load) in 2014 and 2015 we e aken om ou ine
p og am moni o ing epo s. Popula ion es ima es
we e made using da a om he 2006 Nige ian Census
co ec ed o popula ion g ow h and mig a ion [25].
P e alence es ima es o SAM we e a ailable o 2014
and 2015 [20, 21]. An es ima e o p og am co e age
was a ailable om a wide-a ea Simpli ied Lo -quali y-
assu ance E alua ion o Access and Co e age
(SLEAC) su ey comple ed in ea ly 2014 [12, 26, 27].
The epo ed co e age om his su ey was used o
Table 1 Values o incidence co ec ion ac o s (K) ound in ecen s udies
a
Coun y Yea (s) K
b
SAM case de ini ion(s)
c
W/H
Re e ence
c
Da a Sou ce(s) Me hod Sou ce
Nige 2010–2013 4.30–9.50 W/H < −3 z-sco es o
MUAC <115 mm o bi-
la e al pi ing edema
WGS Su eillance sys em (weekly)
Rou ine p og am da a (weekly)
Rou ine p og am da a (mon hly)
Simple ma hema ical
models
Deconinck
e al., 2016
[14]
Nige 2006–2007 5.37–11.78 W/H < −3 z-sco es o
MUAC <115 mm o bi-
la e al pi ing edema
WGS Communi y coho (mon hly) Compa men al model
o es ima e mean
du a ion o SAM
episodes
Isanaka e
al., 2011 [6]
Mali 2010–2013 2.10–2.50 W/H < −3 z-sco es o
MUAC <115 mm o bi-
la e al pi ing edema
WGS Communi y coho (qua e ly)
Su eys (occasional)
Simple ma hema ical
models
Isanaka e
al., 2016
[15]
Nige 2010–2011 5.00–8.10 W/H < −3 z-sco es o
bila e al pi ing edema
WGS Communi y coho (mon hly)
Su eys (mon hly)
Simple ma hema ical
models
Bu kina Faso 2009–2010 7.30–17.00 MUAC <110 mm
(p e alence) MUAC
<120 mm (incidence)
WGS Su eys (annual) Rou ine
p og am da a (mon hly)
Simple ma hema ical
models
Va ious
d
2005–2009 11.21 W/H < 70% o median NCHS Su eys Caseloads o 5 mon hs
a e su ey
Linea eg ession Dale e al.,
2017 [16]
a
A ange o me hods and da a sou ces we e used (su eillance sys ems, wo kload e u ns, coho s udies, epea ed c oss-sec ional su eys, compa men al models,
and eg ession o obse ed caseload agains p e alence) we e used o es ima e he incidence co ec ion ac o s (K). Re e o he o iginal a icles o de ails
b
A ange o alues (i.e. om di e en me hods, da a sou ces, se ings, and case-de ini ions o se e e acu e malnu i ion) is gi en when a ailable
c
SAM = se e e acu e malnu i ion, W/H = weigh - o -heigh , MUAC = mid-uppe -a m ci cum e ence, WGS = Wo ld Heal h O ganiza ion child g ow h s anda ds,
NCHS = Na ional Cen e o Heal h S a is ics child g ow h e e ence
d
24 da ase s (su eys and p og am admissions) om DRC (8), Bu undi (2), Somalia (2), Sudan (7), Myanma (2), and Nige (3). The incidence co ec ion ac o (K)
gi en in he able is o pooled da a assuming co e age (C) o 38% ( om Roge s e al., 2015). Conside able a ia ion in Kbe ween se ings was obse ed
Bul i e al. A chi es o Public Heal h (2017) 75:66 Page 4 o 8
bo h 2014 and 2015 since i was he only co e age
da a a ailable. Da a we e en e ed and analyzed using
Mic oso Excel. This so wa e was used because i is
likely o be a ailable and amilia o CMAM p og am
manage s. A Mic oso Excel sp eadshee ha pe -
o ms he equi ed calcula ionsisp o idedasonline
suppo ing ma e ial. All calcula ions we e checked
using he RLanguage and En i onmen o S a is ical
Compu ing e sion 3.3.3 [28].
The me hod used o calcula e he 95% con idence limi s
o he p oduc o p e alence and co e age (PC)isap-
p oxima e. A less app oxima e 95% con idence in e al
(i.e. an in e al ha con ains he ue alue close o 95% o
he ime) may be calcula ed using a boo s ap es ima o
[29, 30]. Es ima es o he incidence co ec ion ac o (K)
we e made using a boo s ap es ima o o he p oduc o
p e alence and co e age (PC). A pe cen ile boo s ap es i-
ma o wi h one million eplica es o p e alence and co e -
age d awn om app op ia e binomial dis ibu ions was
used [29]. Da a we e analyzed using he RLanguage and
En i onmen o S a is ical Compu ing e sion 3.3.3 [28].
Resul s
Table 2 shows he obse ed and expec ed (i.e. calcu-
la ed using K=1.6)caseloadsand he e isedinci-
dence co ec ion ac o s (K) o 2014 and 2015
oge he wi h he da a on which he calcula ions we e
based. Use o K= 1.6 o p edic caseload had esul ed
in g oss unde es ima es in bo h yea s. The esul ing
e ised es ima es o Kwe e K= 14.39 (95% CI = 6.64;
30.02) and K= 11.66 (95% CI = 5.94; 22.10) o 2014
and 2015 espec i ely. These es ima es we e pooled
gi ing K= 13.02 (95% CI = 6.80; 19.25). The inal
wo ows o Table 2 show he expec ed caseloads o
2014 and 2015 using he pooled es ima e o Kand
di e ence be ween he obse ed and expec ed case-
loads. Table 3 compa es es ima es o he incidence
co ec ion ac o (K) calcula ed using he app oxima e
me hod and he boo s ap es ima o .
Discussion
The app oach ou lined in his documen can p o ide use ul
es ima es o locally app op ia e incidence co ec ion ac-
o s. Applying he alue o Kes ima ed o 2014 o he
popula ion, p e alence, and co e age da a o 2015 yields a
p edic ed caseload o 484,766 cases. This is a 21.6% o e -
es ima e o he obse ed caseload o 2015. Some o his
e o may ha e been due o lowe han speci ied co e age
du ing he implemen a ion phase o addi ional CMAM
p og amming ini ia ed in ea ly 2015 as pa o he ongoing
eme gency esponse in No he n Nige ia. This deg ee o
e o in caseload p edic ion is a conside able imp o emen
Table 2 Incidence co ec ion ac o s o no he n Nige ia CMAM p og am 2014 and 2015 and he da a used o calcula e hem
Yea
2014 2015 Da a sou ces
Popula ion N3,550,827 4,281,700 Nige ia census 2006 co ec ed o popula ion g ow h
and mig a ion. Popula ion is o child en aged be ween
6 and 59 mon hs in dis ic s in which CMAM se ices
we e deli e ed.
P e alence
a
P1.60% (0.50%; 2.71%) 2.01% (0.82%; 3.19%) Pooled p e alence om s a e le el SMART su eys
P og am Co e age
b
C36.6% (32.3%; 40.9%) 36.6% (32.3%; 40.9%) Wide-a ea SLEAC su ey
Obse ed caseload L320,047 398,676 Rou ine p og am moni o ing da a
Expec ed caseload
(using K= 1.6)
E
K= 1.6
=CNP(1 + K) 54,063 81,897 C,N, and Pas abo e (C and P exp essed as
p opo ions). Calcula ions a e based on K= 1.6
Di e ence (obse ed −
expec ed)
L−E
K= 1.6
265,984 316,779 Calcula ed as he di e ence be ween obse ed
caseload (L) and expec ed caseload (E).
P e alence × Co e age PC 0.59% (0.29%; 1.18%) 0.74% (0.40%; 1.34%) Calcula ed (see ex )
Incidence co ec ion
ac o
c
K¼L
PCN
−1 14.39 (6.64; 30.02) 11.66 (5.94; 22.10) Calcula ed (see ex )
Expec ed caseload (using
pooled adjus ed
incidence co ec ion
ac o )
E
K= 13.02
=CNP(1 + K) 291,527 441,612 C,N, and Pas abo e (C and P exp essed as
p opo ions). Calcula ions a e based on K= 13.02 (see
ex ).
Di e ence (obse ed −
expec ed)
L−E
K= 13.02
28,520 −42,936 Calcula ed as he di e ence be ween obse ed
caseload (L) and expec ed caseload (E
K = 13.02
).
a
P e alence is o MUAC <115 mm o bila e al pi ing edema. This case-de ini ion accoun s o c. 98% o all p og am admissions based on an analysis o ou ine
p og am moni o ing da a om wo s a es o no he n Nige ia (n= 102,245 admissions om Janua y 2010 o Decembe 2013). P e alence es ima es o he s a es
in which he p og am was ope a ing a e epo ed. This was calcula ed as he popula ion weigh ed a e age o SMART su ey esul s om indi idual s a es
b
Co e age e e s o poin co e age (i.e. he p opo ion o cu en SAM cases ound by he su ey ha we e en olled in he CMAM p og am). Resul s om a wide-a ea
SLEAC su ey om Feb ua y 2014 a e used o bo h yea s [Banda e al., 2014]
c
The o mula o he es ima o o Kis ea anged o e lec he ac ha PC was calcula ed p io o use
Bul i e al. A chi es o Public Heal h (2017) 75:66 Page 5 o 8

upon he 79.5% unde es ima e expe ienced when using
K= 1.6. Applying he pooled es ima e o K(i.e. K= 13.02)
o he popula ion, p e alence, and co e age da a yields p e-
dic ed caseloads o 291,257 cases and 441,612 cases o
2014 and 2015 espec i ely. These a e a 9.0% unde es ima e
and 10.8% o e es ima e o he ue cases o 2014 and
2015. E o a e likely o dec ease o e ime as mo e annual
es ima es o Kbecome a ailable. No all e o s ha e he
same consequences. Fo example, o e es ima ion may ha e
posi i e consequences i p og am co e age is limi ed by
s op-s a unding and supply b eaks caused by unde es i-
ma ion o bu den and / o p edic ed caseload. Unde es i-
ma ion may lead o an unde - esou ced p og am in which
p og am ac i i ies essen ial o achie ing and main aining
co e age (e.g. communi y mobiliza ion, communi y
sensi iza ion, and communi y-based case- inding ac i i ies)
a e neglec ed in o de o main ain co e clinical ac i i ies.
Unde es ima ion, in some cases, may lead o supply b eaks
necessi a ing he empo a y closu e o p og ams.
Con idence in e als o he boo s ap es ima es o he
incidence co ec ion ac o s a e wide han when he ap-
p oxima e me hod is used. Es ima es made using he ap-
p oxima e me hod a e likely o be spu iously p ecise.
The use o app oxima e me hods o calcula e con idence
in e als is, howe e , a widely accep ed p ac ice o
many public heal h applica ions. The app oxima e
me hod has he ad an age o being easy o implemen
using so wa e, such as Mic oso Excel, ha is a ailable
and amilia o CMAM p og am manage s.
Es ima es o he incidence co ec ion ac o (K) lack
p ecision e en when he app oxima e me hod is used.
Fo example, he 95% con idence in e al o he 2015
es ima e o he incidence co ec ion ac o (K) using he
app oxima e me hod anges be ween K= 5.94 and
K= 22.10. This ansla es in o a 95% con idence in e al
o he caseload p edic ion o be ween abou 218 hou-
sand and 728 housand. This deg ee o imp ecision may
limi he u ili y o he me hod as a planning ool.
The p incipal sou ces o imp ecision a e in es ima es
o p e alence and co e age. Imp o ing he p ecision o
es ima es o p e alence and / o co e age will imp o e
he p ecision wi h which he incidence co ec ion ac o
(K) is es ima ed.
SAM p e alence is usually es ima ed wi h poo ela i e
p ecision. Rela i e p ecision o he p e alence es ima es
a e 138% o he 2014 SAM p e alence es ima e and
118% o he 2015 p e alence es ima e. The lack o p e-
cision in p e alence es ima es is due, in pa , o he use
o sample designs ha educe he e ec i e sample sizes
o su eys. I is likely ha p ecision could be imp o ed
using, o example, s a i ied sample designs and la ge
sample sizes. This would, howe e , equi e conside able
changes o cu en p ac ice. Lack o p ecision is also due
o he way ha su ey da a a e analyzed. Replacing he
classic es ima o :
P e alence ¼Numbe o SAM cases ound in he su ey sample
Su ey sample size
wi h a PROBIT es ima o has been demons a ed o e-
duce he hal -wid h o 95% CIs by abou 60% wi h only
small losses o accu acy [31–33]. Sligh ly La ge gains in
p ecision ha e been demons a ed using a Bayesian-
PROBIT es ima o [19,34]. The ad an age o da a ana-
ly ic app oaches o imp o ing p ecision a e ha hey
can be applied o da a collec ed wi h cu en ly used su -
ey me hods including his o ical da a a li le ex a cos .
The p ecision o he co e age es ima e was no an
issue in he wo k epo ed he e because a la ge s a i ied
sample was used o es ima e co e age wi h good ela i e
p ecision (i.e. 23.5%). P ecision o co e age es ima es
may, howe e , be a p oblem o smalle p og ams. We
in es iga ed his issue using da a om 227 SQUEAC
co e age assessmen s o dis ic -le el NGO-deli e ed
CMAM p og ams pe o med be ween Janua y 2010 and
July 2015 and p o ided o us by he Co e age Moni o -
ing Ne wo k. The median ela i e p ecision o co e age
es ima es be ween 40% and 60% was 42.6% (IQR = 38.4%;
48.5%). This is an expec ed esul as SQUEAC co e age
assessmen s a e usually designed o es ima e co e age
wi h his le el o p ecision [12].
The poo e ela i e p ecision o SAM p e alence es i-
ma es means ha e o s o imp o e he p ecision o hese
es ima es a e likely o yield g ea e imp o emen s in he
p ecision wi h which he incidence co ec ion ac o (K)is
es ima ed han may be achie ed by e o s o imp o e he
p ecision o co e age es ima es. This is illus a ed in
Table 4 using he da a om 2015. I is impo an o no e
ha imp o emen in he p ecision o p e alence es ima es
can be achie ed wi h e y li le inc ease in cos s bu ha
imp o emen s in he p ecision o co e age es ima es
would en ail conside able inc eases in cos s.
Limi a ions
A key limi a ion o he wo k epo ed he e is ha co e -
age da a was no cu en , pa icula ly o 2015.
A limi a ion o he me hod desc ibed he e is ha bu den
and caseload may be in luenced by mig a ion in o and ou
o he p og am a ea. Rapid and subs an ial changes in he
popula ion o he p og am a ea a e likely o a ec
Table 3 Es ima es o he incidence co ec ion ac o made
using wo me hods o calcula e he p oduc o p e alence and
co e age
Yea K (app oxima e) K (boo s ap)
2014 14.39 (6.64; 30.02) 14.72 (7.73; 40.44)
2105 11.66 (5.94; 22.10) 11.91 (6.17; 27.08)
Pooled 13.02 (6.80; 19.25) 13.32 (6.10; 20.53)
Bul i e al. A chi es o Public Heal h (2017) 75:66 Page 6 o 8
popula ion size (N), p e alence (P), and p og am co e age
(C). Mig a ion may, he e o e, esul in g ossly inaccu a e
p edic ions o bu den (B) and caseload (L) ha a ebased
on es ima es o popula ion size (N), p e alence (P), and
p og am co e age (C). Moni o ing popula ion mo emen s
and adjus ing bu den and caseload p edic ions may help o
add ess his p oblem. Adjus men may also equi e ha
addi ional p e alence and co e age su eys be unde aken.
In he case o he Nige ian CMAM p og am he e ha e
been epo s o SAM cases en e ing Nige ia om Nige
and being admi ed o CMAM si es in dis ic s ha bo de
Nige . The e ec o his on he wo k epo ed he e is likely
o be small since da a o he whole coun y we e used. I is
impo an o no e ha his may ha e la ge e ec s on bu -
den (B) and caseload (L) p edic ions o (e.g.) small NGO-
deli e ed p og ams ope a ing in bo de dis ic s.
The assump ion ha caseload (L)ismeasu edwi h
li le o no e o may also be a limi a ion. In he case
o he Nige ian CMAM p og am he e ha e been e-
po s om 3 o he 114 dis ic s in which he p o-
g am is ope a ing o bene icia ies being egis e ed a
mo e han one CMAM si e wi h he assumed
in en ion o ecei ing addi ional ood and d ugs. New
CMAM si es we e opened in hese dis ic s and some
o he double egis a ion may ha e been due o in-
o mal ans e s be ween si es. An in o mal ans e
would ha e been epo ed as a new admission a he
des ina ion si e and, some weeks la e , as a de aul ing
pa ien a he o igina ing si e. The e ec o his
would ha e been o inc ease epo ed caseload (L). I
seems likely ha double egis a ion will ha e had
only a small e ec on caseload (L)usedin hewo k
epo ed he e. This would ha e caused only a small
inc ease in he es ima es o K epo ed he e. The
co e na u e o some double egis a ions does mean
ha he magni ude o any inc ease will always be di -
icul o quan i y.
Conclusion
The wo k epo ed he e shows ha i is possible o consid-
e ably imp o e p edic ions o CMAM caseload by applying
a simple ma hema ical model o da a ha a e eadily a ail-
able o p og am manage s. This implies ha mo e accu a e
p edic ions o bu den may also be made using he same
me hods and da a. The p ecision o es ima es o caseload
and bu den may be imp o ed by using PROBIT o
Bayesian-PROBIT es ima o s o SAM p e alence.
The implica ion o his s udy, and o simila epo s
based on a a ie y o app oaches (see Table 1), is ha
he cu en es ima es o SAM bu den a e likely o be
g oss unde es ima es. Applying he pooled incidence
co ec ion ac o ound in his s udy o he 16 million
es ima e made using p e alence da a yields an es ima ed
global SAM bu den o 208 (95% CI = 109; 308) million
cases annually. I seems unlikely, howe e , ha he inci-
dence co ec ion ac o es ima ed o he Nige ian
CMAM p og am will be globally applicable. Local es i-
ma es o Kwill be needed o make local p edic ion o
bu den and caseload. These local es ima es o Kcould
be applied o local es ima es o p e alence and popula-
ion wi h he esul s summed in o de o es ima e global
SAM bu den.
Gi en he public heal h impo ance o ha ing eliable
es ima es o bu den and caseload and he unce ain ies o
his app oach based on p og am da a, a con i ma ion o
es ima es o Kusing di ec es ima es o incidence om
con inuous moni o ing o open coho s and su eillance
sys ems in simila se ings may be wa an ed. Compa ison
wi h o he indi ec me hods may also p o e use ul.
Addi ional ile
Addi ional ile 1: Caseload me hod. (XLSX 36 kb)
Acknowledgemen s
The au ho s wish o hank Fede al Minis y o Heal h o Nige ia o p o iding
p og am da a o he analysis.
Funding
No unding was ob ained o his s udy.
A ailabili y o da a and ma e ials
Da a will be a ailable upon eques om he co esponding au ho s.
Au ho s’con ibu ions
AB, ABR, MM concei ed he s udy and d a ed he manusc ip . All au ho s
ead and app o ed he inal manusc ip .
Table 4 E ec o imp o ed p ecision o SAM p e alence es ima es and co e age es ima es o he p ecision o he es ima e o he
incidence co ec ion ac o (K) using 2015 da a om he Nige ian CMAM p og am
Incidence co ec ion ac o (K)
Scena io Poin es ima e 95% LCL 95% UCL Rela i e p ecision
a
No change 11.66 5.94 22.10 139.59%
Reduce hal -wid h o 95% CI o p e alence by 60%
b
11.66 7.72 17.37 82.76%
Reduce hal -wid h o 95% CI o co e age by 60%
c
11.66 6.00 21.88 136.19%
a
Rela i e p ecision is calcula ed as 95%UCL−95%LCL
Poin Es ima e 100. Smalle alues indica e be e p ecision
b
This le el o imp o emen is achie able using a PROBIT es ima o wi h exis ing su ey designs and su ey da a
c
This le el o imp o emen could only be achie ed by a conside able inc ease in su ey sample sizes
Bul i e al. A chi es o Public Heal h (2017) 75:66 Page 7 o 8
E hics app o al and consen o pa icipa e
No applicable.
Consen o publica ion
No applicable.
Compe ing in e es s
The au ho s decla e ha hey ha e no compe ing in e es s.
Publishe ’sNo e
Sp inge Na u e emains neu al wi h ega d o ju isdic ional claims in
published maps and ins i u ional a ilia ions.
Au ho de ails
1
Uni ed Na ions Child en’s Fund (UNICEF), Abuja, Nige ia.
2
Uni e si y o
Tampe e School o Medicine and Tampe e Uni e si y Hospi al, Uni e si y o
Tampe e, Cen e o Child Heal h Resea ch, Lääkä inka u 1, A o Building,
FI-33014 Uni e si y o Tampe e, Tampe e, Finland.
3
Depa men o Nu i ion,
Exe cise and Spo s, Facul y o Science, Uni e si y o Copenhagen,
Roligheds ej 30, DK-1958 F ede iksbe g, Denma k.
4
Uni ed Na ions Child en’s
Fund (UNICEF), Nepal Coun y O ice, UN House, Pulchowk, Lali pu ,
Ka hmandu, Nepal.
5
Depa men o Family Heal h, Head o Nu i ion/SUN
Focal Poin , Fede al Minis y o Heal h, Abuja, Nige ia.
6
B ix on Heal h,
All goch Ucha , Llaw yglyn, Powys, Wales SY17 5RJ, UK.
Recei ed: 2 June 2017 Accep ed: 28 Sep embe 2017
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