Southgate BA, Yacoub A. The epidemiology of schistosomiasis in the later stages of a control program based on chemotherapy: the Basrah study. 3. Antibody distributions and the use of age catalytic models and log-probit analysis in seroepidemiology. Transactions of the Royal Society of Tropical Medicine and Hygiene. 1987 Jan 1;81(3):468-75.

1. 468
TRANSACTIONS OF THE ROYAL SOCIETY OF TROPICAL MEDICINE AND HYGIENE (1987) 81, 468-475
The epidemiology of schistosomiasis in the later stages of a control
programme based on chemotherapy: the Basrah study.
3. Antibody distributions and the use of age
catalytic models and log-probit analysis in
seroepidemiology
B. A. SOUTHGATE
& ALIM YACOUB
Department of Tropical Hygiene, London School of Hygiene and Tropical Medicine, London, WClE 7HT
Abstract
A comparative seroepidemiological survey of Schistosoma
haematobiuminfection among primary
schoolchildren in areasof different levels and patterns of endemicity in Basrahgovernorate, southern
Iraq, also covered all inhabitants of Al-maadan locality, a known endemic focus in Basrah. Blood
sampleswere tested by the enzyme linked immunosorbent assay.Serological data were analysed to
describe the pattern of distribution of antischistosomal antibodies, to relate the level of infection to
ageand sex, and to estimate the force of infection per year by applying agecatalytic models. The
distributions of antibodies among the study populations were positively skewed; 3 patterns were
revealed by relating serological data to ageand sex, depending on the level of infection. The simple
catalytic model was the best to estimate the force of infection among the younger age groups.
Introduction
In previous papers (YACOUB& SOUTHGATE,
1987;
YACOUBet al., 1987) we reported the results of a
seroepidemiological survey of Schistosomahaemato-
bium infection in Al-maadan locality in Basrah,
southern Iraq. Active and past infection, cercarial
dermatitis and agewere significantly associatedwith
the serological profile of the population. The validity
of the test used, the enzyme linked immunosorbent
assay(ELISA), was evaluated by the application of
relative operating characteristic (ROC) analysis in
addition to the calculation of sensitivity and specificity
figures. The ELISA was of sufficient validity to
measure the cumulative experience of the study
population with respect to &istosomiasis.
In this naoer we oresent results of further statistical
and mathematical a’nalysesapplied to serological data
from the Al-maadan population, and primary school-
children (6-14 years old) in various endemic and
non-endemic areasof Basrah. Specifically, the aimsof
the analyses were (1) to examine the pattern(s) of
distribution of antibodies produced in responseto S.
huemutobiuminfection; (2) to describe the serological
profile of the study populations in relation to age(in
this paper the results of such age analyses are
presented for primary schoolchildren only, since the
association between serology and age has been de-
scribed in detail by YACOUBet al., 1987); (3) to
measure the force of infection by the application of
aeecatalvtic models which bestfit the serologicaldata
(&ch models applied to parasitological -data on
schistosomiasis by HAIRSTON, 1965, revealed in-
teresting information which could not be obtained by
simple observation of age prevalence data).
Correspondence
to be addressed
to: Dr B. A. Southgate,
Department of T.ropical Hygiene, London School of
$g;;g+d Troplcal Me&me, Keppel Street, London,
Study areas
Materials and Methods
The study areaswhere the primary school surveys were
carried out were grouped into the following categories.
Category 1: areasin Basrah endemic, albeit at low level,
for S. haematobium
infection. This group included Al-
majidiyah and Al-audiyah villages.
Category 2: areas non-endemic for infection, but where
sporadic caseshavebeen reported recently among school-
children by the Endemic DiseasesCentre of Basrah. These
included Awesian and Bahadria villages in Abu-al-Khassib
district. The cases have been mainly in children from
Abu-al-Jawzi settlement, inhabited by people who migrated
in the 1970sfrom an endemic area (Kumait) in Mavsan
goVernorate north of Basrah. -
Category 3: areas non-endemic for S. haematobium and
where no caseshave been reported before. Umm-al-naaj
village adjacent to Awesian and Bahadria villages was
selected for the study.
This categorization was based on records and reports of
the Endemic DiseasesCentre of Basrah. A detailed account
of the geographical location of the study areas, the
so&cultural characteristics of their inhabitants and the
results of a recent parasitological survey there have been
described by YACOUB (1985). The locations of the study
areas along the Shatt-al-Arab river and the locations of
schoolswithin the villages are shownin Figs 1 and 2 in paper
1 of this series (YACOUB & SOUTHGATE, 1987).
Blood samples were obtained by finger-prick from all
primary schoolchildren in Al-majidiyah (788) and Al-
audiyah (204)villages; random samples,either 1in 3 or 1in
5, were obtained from schoolchildren in Umm-al-naaj (86),
Awesian and Bahadria (411).
Laboratory procedures
Blood sampleswere stored deep frozen and examined by
ELISA as described by YACOUB et al. (1987).
Statistical and mathematical analyses
The analyseswere carried out in the following sequence.
(1) The frequency distributions of the absorbancevalues
(A 492nm) of schoolchildren in different areas, and of the
Al-maadan total population, were examined. The log-probit
transformation wasapplied to assess
the degreeto which the
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2. B. A. SOUTHGATE AND A. YACOUB 469
data followed a log normal distribution; the probit, used
here, is the standard normal deviate corresponding to agiven
proportion plus 5 (ARMITAGE, 1971).The absorbancevalues
on a log,, scale were plotted on the x axes and the
corresponding values of the probit of cumulative percentage
on the y axesof graphs. Regressionlines were fitted and the
values of the intercept (a), the slope (b) and the correlation
coefficient (r) were calculated for primary schoolchildren in
each area and for the Al-maadan population. The signi-
ficance of r was tested by
n-2 vi
using r
(3
l-2
asat statistic on n-2 degrees of freedom.
(2) The geometric mean of the absorbancevalues and the
proportion of seropositives were used to describe the
serological profile of schoolchildren in relation to age. The
mean of the log transformed data was calculated and the
antilog taken asthe geometric mean; analysisof variance was
carried out using log transformed data.
(3) Age catalytic models were applied to the serological
data. These are mathematical models which estimate the
results of population exposure to infection and allow the
measurement of forces of infection from data obtainable
from cross-sectional surveys. MUENCH (1959) described
several different models and their derivations using basic
calculus. Two models relevant to our study wereapphid, the
reversible and the simple catalytic models. The mathematic-
al formulae for these-models are given below.
(a) The simple catalytic model:
YE 1-p where y is the proportion of positives at
age t (years), r is the force of seroconversion per
year, and e is the base of natural logarithms.
(b) The reversible catalytic model:
Y= u+b (l-e-(“+6)q
where a= rate of seroconversionper year, b= rate of
seroreversion per year, e and t and y are as above.
-L
The first model assumeszero seroreversionwhile the second
model assumesthat those who lose the infection (serorever-
sion) are entirely susceptible to reinfection (seroconversion).
Both models assume that the force of infection remains
constant over a period of time long enough to include the
oldest age group covered by the study, and that migration
and mortality due to the infection are negligible.
It is reasonableto assume,in the caseof schistosomiasis,
that all the population at birth is susceptible to infection. In
Basrah, becauseof the low prevalence and intensity of S.
huenuztobiuminfection, mortality due to schistosomiasisis
negligible. The populations in Al-majidiyah and Al-audiyah
villages and in Al-maadan locality are fairly stable. The
schoolscoveredby the survey in Awesian and Bahadria had a
sign&cant proportion of children from families who had
moved from endemic areasoutside Basrahin the early 1970s.
Thus, schoolchildren 6-14 years old could be considered a
stable segment of the population in these 2 localities. The
validity of the assumption of constant force of infection will
be discussedlater based on the results of the estimation of
the goodness of fit.
The maximum likelihood estimate was used to solve the
differential equations representing these models through
computer programs basedon the generalized linear interac-
tive modelling (GLIM) package to estimate r of the simple
catalytic model, and the MINUIT to estimate a and b of the
reversible catalytic model. The MINUIT is a package of
moerams written to minimize a function of multiule
;a&bles, to calculate the covariancematrix and to find t;ue
errors. The GLIM alsoprovides an estimate of the goodness
of fit and can be usedfor agegroups not necessarilystarting
from birth (truncated data). The method of moments,
described by ~LJENCH (1959);would produce similar results;
although the fit of the model to the observed data can be
assessedvisually only by the technique of curve fitting. In
addition, the procedure to apply the models to truncated
data using the method of moments is very complicated and
requires multiple trials.
Cm-square, F and standard normal deviate (SND) tests
were applied to age and sex analysis of serological data.
I I I I I I I I 1 I I I I I I I I 1
0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.65
ABSORBANCE VALUE
Fig. 1. Distribution of absorbance values among primary schoolchildren of Al-audiyab village (arrow indicates the 0.4 cut-off point).
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3. 470 EPIDEMIOLOGY OF SCHISTOSOMIASIS IN BASRAH. 3.
Results
Distribution of absorbance values
The frequency distribution of the absorbance
values among primary schoolchildren of Al-audiyah
village is shown in Fig. 1. The distribution of
antibodies was positively skewed; about 81% of
children had values below 0.4 (the selected cut-off
point). The distribution of absorbancevalues among
children in other areas and Al-maadan locality fol-
lowed a similar pattern and is not shown here. For
example, 64% of males in Al-majidiyah village had
values below 0.4, compared to 77% of femalesin the
samevillage. The corresponding values were 73%for
malesof Bahadria, 79%for malesof Awesian, 83%for
0 AL-AUDIY AH
l AL-MAJIDIY AH .
0
8
7
6
t
Ei
5E
4
3
2
0.2 0.5 1.0
ABSORBANCE VALUE
(LOG ,. SCALE)
Fig. 2. Log-probit transformation of absorbancevalues of primary
schoolchildren of Al-audiyah and Al-majidiyah villages.
females of Awesian and Bahadria (the figure is
combined becausefemalesfrom both areas,which are
adjacent to each other, studied at the sameschool).
Log-probit transformation
The plotted points and the fitted regressionlines for
children of Al-audiyah and Al-majidiyah areshown in
Fig. 2. Those of males and females of Al-majidiyah
separatelyare shown in Fig. 3 while Fig. 4 showsthe
results of the log-probit transformation of the absor-
bance values of Bahadria and Umm-al-naaj. An
almost linear relationship was obtained by such
transformation, confirming the log normal distribu-
tion of the absorbancevalues; the y axesin Figs 2 to 4
are drawn to the right of the x axes, since all
absorbancevalues recorded were lessthan 1.0, giving
negative logI values.
The values of a, b, and r for the different areasare
o FEMALES
. MALES
7
.
6
3
2
0.2 0.5 1.0
ABSORBANCEVALUE
(LOG ,. SCALE)
Fig. 3. Log-probit transformation of absorbancevalues of male and
female primary schoolchildren of Al-majidiyah village.
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4. B. A. SOUTHGATE AND A. YACOUB 471
0 FEMALES (BAHADRIA) ..-
.
0 UMM-AL-NAAJ :1
:I
A MALES (BAHADRIA) : ’
9,
: I
.‘I.
O-1
t
.
I
r
8
/
7
6
t
8
E
5
4
3
0.2 0.5 1.0
ABSORBANCEVALUE
(LOG ,. SCALE)
Fig. 4. Log-probittransfotmation
of absorbance
valuesof primary
schoolchildren
of Babadria(malesand females)andUmn-al-naaj.
given in Table 1. The use of thesequantities is well
established in epidemiological studies of lymphatic
filariasis (SASA, 1967; SOUTHGATE, 1974)applied to
microfilarial densities per tmit volume of blood; they
have proved of great value as sensitive indicators of
levels of endemicity in different geographical areas,
and of changing epidemiological patterns following
the institution of control programmes. The intercept
and the slope are inversely related to the level of
endemicity; malesof Al-majidiyah, for example, have
lower values than females,indicatmg ahigher level of
infection. The highest value of the intercept was
calculated for Umm-al-naaj, a non-endemic area,and
the lowest for Al-maadan, the most highly endemic
area.
Relation between serology and age
The relations between the level of antibodies and
age among primary schoolchildren are shown in
Tables 2-9. In most cases,except when the sample
size was small or the exact agewas not available, the
analyses have been carried out with respect to
individual years of age for the 6-10 year age group.
This is important since YOGOREet al. (1983) pointed
out a danger in grouping children in prevalence
surveys at S-year intervals: infection rates at single
years of age, especially from 5-9 years, may vary
enough to produce fallacious comparisons.
3 patterns were identified as a result of these
analyses. (1) A significant increase with age in the
level of antibodies, as measured by the geometric
mean, and the proportion of seropositives. Such a
pattern wasobservedamongmale and femaleprimary
schoolchildren of Al-maiidivah (Tables 2-3’1. and
malesof Bahadria (Tablesb-73. This pattern indicates
a definite increasedlevel of infection aschildren grew
older in these areas.
(2) A significant increase of the geometric mean
with age, but not of the proportion of seropositives.
Such a pattern was observed among males of Al-
audiyah (Tables 4-5) and males of Awesian (Tables
6-7). This could be explained by an increase in the
level of antibodies sufficient to give a significant
difference with respect to the geometric means but
not marked enough to produce a higher proportion of
seropositives at the selected cut-off point:
(31No sienificant difference wasobservedwith aee
in the geometric mean or the proportion of seropoz-
tives. This pattern was observed among children of
Umm-al-naaj (Tables 8-9) and femalesof Al-audiyah
(Tables 4-5) and Bahadria and Awesian (Tables 6-7);
in general, it indicates the groups with the lowest level
of infection. In fact, only 9 out of 86(10%)children of
the non-endemic areaof Umm-al-naaj were above0.4,
possibly due to exposure to non-human schistosome
cercariae.
Application of age catalytic models
The forces of seroconversion per year, their 95%
confidence intervals and the goodnessof fit calculated
from the application of the simple catalytic model to
the serological data of schoolchildren in Basrah are
shown in Table 10. Among children of Al-majidiyah
village, the model fitted the data for those agedb-8
vearsonlv. The force of infection was 2% ner vear. A
comparable figure was estimated among ‘children of
Al-audiyah 6-14 yearsold with good fit of the data to
the model. The corresponding figures for males of
Awesian and Bahadria were 3% and 4% respectively.
The 95%confidenceintervals were calculated only for
data which fitted the model.
It was also found that serological data from O-14
year old children of Al-maadan localitv fitted the
simple catalytic model with a 10%force ofseroconver-
sion oer vear (r*=3.2, df=2. 0*25>P>O*lO). The
results of- the aiplication of the reversible catalytic
model to the samesetof data are shown in Table 11.
The forces of seroconversion estimated by this
method are similar to those estimated by the simple
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5. 472 EPIDEMIOLOGY OF SCHISTOSOMIASIS IN BASRAH. 3.
Table l-Values of intercepts (a), slopes (b) and correlation coefficients (r) of regression lines of log-probit
transformed absorbance values, and their statistical analyses
Area
Al-majidiyah
(males & females)
Al-majidiyah
(males)
Al-majidiyah
(females)
Al-audiyah
(males & females)
Bahadria
@W
Awesian
(males)
Bahadria & Awesian
(females)
Umm-al-naaj
(males & females)
Al-maadan
(all age groups)
a b r t P
7.0158 3.0760 0.994 36.27 <O.OOl
6.8530 3.1353 0.989 27-83 <O*OOl
7.3206 3.1388 0.998 72.80 <O*OOl
7.7583 4.2710 0.995 37-28 -Co*001
7.4096 3.7893 0.988 23.06 <O~OOl
7.3092 3.2750 O-992 2940 <O*OOl
8.4114 5.7017 0.992 19.01 co*001
8.5840 5.3440 0.991 20.94 CO*001
6.6600 3.3096 o-950 9.62 <O*OOl
Table 2-Geometric mesns and 95% confidence intervals of the
absorbaace values for males aad females of Al-majidiyab village
witb respect to age (m completed years)
Age
(Y-4
M&S
6
7
8
9
10
11-14
Total
(95% confidence
Number Geometric mean intervsl)
94 0.23 (O.ZO-0.25)
62 0.25 (0.22~@29)
64 0.24 (0.21-0.28)
58 0.34 (0~29-040)
92 044 (0.39~@49)
78 040 (0.34-0.45)
448 0.31 (0.29-0.33)
F= 19.808, EYO.001
Females
6
7
8
9
10
11-14
Total
90 0.23 (0.20-0.25)
65 0.18 (@ 15-0.20)
44 0.20 (0.17-0.23)
47 0.24 (0.20-0.29)
54 0.31 (0.26-0.35)
40 0.40 (0.34-0.48)
340 024 (0.23-0.26)
F= 16252, P<O.OOl
catalytic model for the younger age group of the
population with zero seroreversion per year.
Discussion and Conclusions
One of the main usesof serological surveys is to
establish the pattern of infection in the community
(LUCAS, 1979). They can be used to obtain informa-
tion on various epidemiological quantities required to
permit optimal use of available resources in public
Table %Ptoportion of seropositives with respect to age
among primary schoolchildren of Al-majidiyah
Age
(Ye=@ No. tested Number positive(o/o)
9
Kl4
Total
Females
Z! ‘:‘Ki
44 8 (18.1‘)
160 (35.7)
x2=98.6, P<O901
health programmes (LOBEL & KAGAN, 1978). In
schistosomiasis,examining the variation of the pat-
tern of infection between different communities and
in the samecommunity over time is necessaryfor the
assessmentof the impact of control programmes.
Serologyis particularly useful for this in areasof low
transmission and among minimally infected popula-
tions, where perfect treatment efficiency may produce
very small changesin prevalenceand other indices of
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6. B. A. SOUTHGATE AND A. YACOUB 473
Table Aeometric means and 95% confidence intervals
of ELISA readings among primary schoolchildren of
Al-audiysh
Age (95% confidence
(Yard Number Geometric mean interval)
Males
Table S-Proportion of set0
. ~it$esM-i~g~;gg~iite
among primary school clul
Age
(Ye4 Number tested Number positive (%)
Males
6 24 0.21 (0.17-0.26) 4 I’: : (ii::;
7 21 0.15 (0~10-~20) S (26.3)
8 19 0.27 (0.22-0.34)
t :;
9 29 0.28 (023-0.34)
10 22 0.29 (0.24-0.35) :t14
22 1; i;;.:;
s (45:s)
11-14 11 0.38 (0.26-054) Total
1::
Total 126 0.25 (0.22-027) x’=8.*43,‘0%~zJ>0.10
F=6.139, P<O401
FernaleS Females
6 13 0.20 (0.16-0.27)
7 9 0.14 (0.11-0.19)
f 13 1 (7.7)
9
8 12 0.18 (0~12-02s) z 12 ! ,C:5{
9 17 0.23 (0.19-0.28)
;:
1 (5.9)
10 12 0.23 (0.18~0.30) 10
11-14 15 0.21 (0.16-0.28) 11-14 t g::j
Total 78 0.20 (0.18-0.22) Total 8 (10.3)
F=1.919, P<Wl x2=0.13, F>O.975
Table 6-Geomet.k means and 95% confidence intervals with respect to age for males and females of
Babadria and Awesian
Age
(ye4 No. tested Geometric mean (95% confidence interval)
Males
(Bahadria)
6 t; 0.19 (0.16-0.23)
3 24 0.29
0.34 (0.23-0.36)
(0.29-0.39)
z-14 :: 0.37
0.36 (0.32-044)
(O-32-0.42)
Total 122 0.30 (0.27-O-32)
F= 11*66,P<O~OOl
Males
(Awesian)
4
f
10
11-14
Total
103 0.22 (0.19-0.25)
28 0.25 (0.20-0.32)
9 0.13 (Of@-0.17)
:t 0.25
0.25 (0.20-0.31)
(0.21-0.30)
2:x 0.29
0.24 (0.25-0.34)
(0.23-0.25)
F=3-33, 0f1O1<P<0~01
Females
(Bgaghadria& Awesian)
10114 :: 0.28 (0.25-0.31)
0.30
Total 70
(0.27-O-33)
0.29 (0.27-O-32)
SND=0.561, two-tailed P=O-57
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7. 474 EPIDEMIOLOGY OF SCHISTOSOMIASIS IN BASRAH. 3.
Table 7-Proportions of seropositives witb respect to age
for primary school children of Bahadria and Awesian
Table II-Forces of seroconversion (a) and seroreversion
(b) per year, estimated by the maximum likelihood method
(using the MINUIT)
Age
bars) No. tested No. oositive (%‘I
Males
(Bgahadria)
li
9
IO-14
Total
Males
(Awesian)
6
i
:;
24 8 (33.3)
:: 14
4 (25.0)
(45.2)
122
x2=11.84, 0.05,3;!~~0~)
103
28
9
9 6 (i3.oj
::.14 :; 9
3 (13.0)
(30.0)
Total 2:: 45 (20.5)
x2 (calculated for 6-7,8-9 and lo-14 agegroups to avoid less
than 5 expected frequencies) = 0.391, 0*75>P>O.50
Females
(Bg$adria & Awesian)
2 (8.7)
IO-14 :: 10 (21.3)
Total 70 12 (17.1)
x2=2*721, 0.lO>P>O.O5
Table g-Geometric means with respect to age among
primary school children of Umm-al-naaj (both sexes
combined)
Age
(years) Number
Geometric mean
(95% confidence
interval)
6 18 0.26 (0.22-0.29)
7 14 0.28 (0.21-0.35)
8 10 0.22 (0.17-0.28)
9 15 0.25 (0.21-0.30)
10 14 0.26 (0.22-0.30)
11-14 15 0.27 (0.21-0.32)
Total 86 0.26 (0.24-0.28)
F=0.59, P>O.l
Table 9-Proportions of seropositives by age in Umm-al-
naaj (both sexes combined)
Age
(YeW No. tested No. positive (%)
E4
57 7 (12.3)
Total ii:
x2=0.159, 0.75>P>O.50
Area
Al-maadan
Al-maadau
Al-majidiyah
Al-audiyah
Bahadria
Age group
(years)
all groups
o-14
6-14
6-14
6-14
a(%)
13.064
10.123
4.326
2.345
3.584
b(%)
6.188
0.0
;:;
0.0
infection level asmeasuredby parasitological techni-
ques. As prevalencedecreases,the proportion of false
negatives to all apparent negatives by urine or stool
examination will not always decrease uniformly.
GODDARD (1977) showed that this was particularly
true on the assumptionof non-constant sensitivity of a
parasitological test. Thus, even with an apparent
complete cure rate following a population survey and
treatment of thosefound infected?the remaining true
positives undiagnosed by parasitology (false nega-
tives) comprise the prevalence for the next survey.
The results presented in this paper attempt to
describe by serology the existing pattern of S.
haematobium infection in various areas of Basrah
where a control programme based on selective che-
motherapy is in operation. They prmide baselinedata
for monitoring changesin the statusof the infection as
a result of control measures. The methods used
provide a framework for the analysis of serological
data on schistosomiasisobtained from other areasor
from future surveys.
The validity of a test needs to be assessed
before
proceeding to interpret the results. A sensitivity of
83% can be used for epidemiological surveys of
schistosomiasisin Basrah. The specificity of the test,
basedon screeningschoolchildren in the non-endemic
area of Umm-al-naaj, was 90% (see Table 9).
The pattern of infection in each study area of
Basrah was established by examining the frequency
distribution of the absorbance values and fitting
regression lines to the log transformed data, relating
the level of infection to ageand sexand estimating the
force of infection by applying age catalytic models.
The distribution of antibodies, produced in re-
sponseto schistosomalinfection and measuredby the
ELISA, was positively skewed. This has been con-
firmed and quantified by log-probit analysis. The
fitted regression lines and the values of the intercept
and slope provided a useful tool for comparing
endemic and non-endemic areas; they would also be
Table lo-Forces of seroconversion per year (Y), the 95% confidence intervals and the goodness of fit for the
data of primary schoolchihlren in various areas of Basrah (using GLIM)
Age
group
Area b-d
Al-majidiyah 6-14
Al-majidiyah 6-10
Al-majidiyah 6-9
Al-majidiyah 6-8
Al-audiyah 6-14
Awesian (males) 6-14
Bahadria (males) 6-14
*df = degrees of freedom
r
o-04
o-04
0.03
0.02
0.02
0.03
0.04
95% confidence
interval
-
-
0*018-0*029
0*017-0.030
0*020-0.040
0~030-0-050
df* X2 P
5 51.8 -Co*001
4 44.0 -Co.001
: ;:; 0~025>P>0-01
o-90 >P>O*75
: ;:; o-75 >P>O*50
O-25 >P>O*lO
5 6.1 0.50 >P>O-25
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8. B. A. SOUTHGATE AND A. YACOUB 475
valuable as baseline figures at the start of control Medicine and for his advice on certain technical issues,and
campaigns: efficient control measureswould increase to Mr D. Dunn for statistical advice.
the values of a and b. However, the observed Part of the material in this paper was included in a thesis
distribution can be related to areasof low endemicity by A. Yacoub acceptedfor the award of aPhD degreeby the
only; YOGOREetal. (1983)found that the distribution
University of London.
of absorbancevalues among schoolchildren in an area
highly endemic for S. japonicum was bimodal.
The geometric mean and the proportion of sero-
positives were used to summarize the serological data
and to relate the level of infection to ageand sex. The
geometric meanis more appropriate than the arithme-
tic mean because of the high degree of variation
between individual absorbance values and their
skewed distribution.
In applying the ELISA to discriminate between
areas of different levels of endemicity, it is important
to examine the variation in the patterns of infection
with age and sex in addition to examining the
differences between the absolute values of the geomet-
ric meansor the proportion of positives. We were able
to identify 3 such patterns describing the level of
infection in the study areas. Since the approach
depends on the validity of the statistical techniques
applied, it is essential that proper sampling proce-
dures should be used in selection and determination
of size of the study populations.
Finallv. the studv shows that the simnle catalvtic
model is-the most appropriate one for serological data.
Since the control programme in Basrah is mainly
basedon screeningprimary schoolchildren 6-14 years
old, the estimation of forces of infection among this
group provides another useful tool for monitoring the
impact of such aprogramme. The model wasfound to
fit data from schoolchildren in all study areas except
those from Al-majidiyah village, where a good fit
applied to children 6-8 years old only; this indicates
that children 9- 14 years old were exposed to a force of
infection different from those 6-8 years old. This
further emphasizes the importance of the point, made
in the results section, that even within a narrow band
of agegroups it is essential, when relating serology to
age among schoolchildren, to use as far as possible
individual years of age.
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Acknowledgements
We thank all staff at the Endemic DiseasesCentre, Basrah
for their help during the field work. We arevery grateful to
all schoolchildren and inhabitants of Al-maadan locality,
without whose cooperation this study would not have been
possible. Thanks alsogo to Dr C. C. Draper for allowing us
to process the blood samples at the Seroepidemiology
Laboratory of the London School of Hygiene and Tropical
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Accepted for publication 9 June 1986
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