Performance of small cluster surveys and the clustered LQAS design to estimate local-level vaccination coverage in Mali

Article (PDF Available)inEmerging Themes in Epidemiology 9(1):6 · October 2012with27 Reads
DOI: 10.1186/1742-7622-9-6 · Source: PubMed
Abstract
Background Estimation of vaccination coverage at the local level is essential to identify communities that may require additional support. Cluster surveys can be used in resource-poor settings, when population figures are inaccurate. To be feasible, cluster samples need to be small, without losing robustness of results. The clustered LQAS (CLQAS) approach has been proposed as an alternative, as smaller sample sizes are required. Methods We explored (i) the efficiency of cluster surveys of decreasing sample size through bootstrapping analysis and (ii) the performance of CLQAS under three alternative sampling plans to classify local VC, using data from a survey carried out in Mali after mass vaccination against meningococcal meningitis group A. Results VC estimates provided by a 10 × 15 cluster survey design were reasonably robust. We used them to classify health areas in three categories and guide mop-up activities: i) health areas not requiring supplemental activities; ii) health areas requiring additional vaccination; iii) health areas requiring further evaluation. As sample size decreased (from 10 × 15 to 10 × 3), standard error of VC and ICC estimates were increasingly unstable. Results of CLQAS simulations were not accurate for most health areas, with an overall risk of misclassification greater than 0.25 in one health area out of three. It was greater than 0.50 in one health area out of two under two of the three sampling plans. Conclusions Small sample cluster surveys (10 × 15) are acceptably robust for classification of VC at local level. We do not recommend the CLQAS method as currently formulated for evaluating vaccination programmes.
ANA L Y T I C PE R S P E C T IVE Open Access
Performance of small cluster surveys and the
clustered LQAS design to estimate local-level
vaccination coverage in Mali
Andrea Minetti
1*
, Margarita Riera-Montes
1
, Fabienne Nackers
1
, Thomas Roederer
1
, Marie Hortense Koudika
2
,
Johanne Sekkenes
2
, Aurore Taconet
3
, Florence Fermon
3
, Albouhary Touré
4
, Rebecca F Grais
1
and Francesco Checchi
1
Abstract
Background: Estimation of vaccination coverage at the local level is essential to identify communities that may
require additional support. Cluster surveys can be used in resource-poor settings, when population figures are
inaccurate. To be feasible, cluster samples need to be small, without losing robustness of results. The clustered
LQAS (CLQAS) approach has been proposed as an alternative, as smaller sample sizes are required.
Methods: We explored (i) the efficiency of cluster surveys of decreasing sample size through bootstrapping analysis
and (ii) the performance of CLQAS under three alternative sampling plans to classify local VC, using data from a
survey carried out in Mali after mass vaccination against meningococcal meningitis group A.
Results: VC estimates provided by a 10 × 15 cluster survey design were reasonably robust. We used them to
classify health areas in three categories and guide mop-up activities: i) health areas not requiring supplemental
activities; ii) health areas requiring additional vaccination; iii) health areas requiring further evaluation. As sample size
decreased (from 10 × 15 to 10 × 3), standard error of VC and ICC estimate s were increasingly unstable. Results of
CLQAS simulations were not accurate for most health areas, with an overall risk of misclassification greater than 0.25
in one health area out of three. It was greater than 0.50 in one health area out of two under two of the three
sampling plans.
Conclusions: Small sample cluster surveys (10 × 15) are acceptably robust for classification of VC at local level. We
do not recommend the CLQAS method as currently formulated for evaluating vaccination programmes.
Keywords: Vaccination coverage, Mali, Meningitis, Lot quality assurance sampling, LQAS, Cluster sampling, Survey
Introduction
Vaccination coverage (VC) estimates are essential to
monitor the performance of immunisation progra mmes
and take action to improve them. In resource-poor set-
tings, administrative estimates of VC, reached by divid-
ing the number of people vaccinated by the population
in the target age group, are often biased due to inaccur-
ate population figures and pressure on programmes
to report favourable indicators. Sample surveys are
thus frequently employed to establish more accurate
estimates.
A specific challenge in these settings is estimation of
VC at the local level (e.g. district, sub-district or health
catchment area), so as to identify communities that may
require additional support (e.g. supplementary cam-
paigns, strengthening of routine vaccination) and allo-
cate limited resources efficiently. To do this, two
survey methods recommende d by the World Health
Organization are available: cluster surveys and lot quality
assurance sampling (LQAS) [1].
Cluster surveys feature simple designs that do not re-
quire accurate population figures or household sampling
frames [2]. However, cluster samples cannot be used to
make inferences for individual communities within the
sampling universe; therefore, for each community of
* Correspondence: andrea.minetti@epicentre.msf.org
1
Epicentre, Paris, France
Full list of author information is available at the end of the article
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interest, one independent cluster sample needs to be
selected. Typical sample sizes for such cluster surveys
are on the order of 30 clusters x 7 individuals [3]. Theor-
etically even smaller samples may be chosen , but there is
insufficient evidence on whether the resulting estimates
are likely to be robust, i.e. whether both the point esti-
mate and the estimated standard error (SE) remain ac-
ceptably stable as sample size decreases [4].
LQAS has been promoted as a faster and cheaper al-
ternative to cluster sur veys for monitoring various public
health interventions [5], though it could be potentially
misused due to erroneous statistical assumptions [6]. In
this approach, a random sample N of individuals (or
other ba sic sampling units, depending on the indicator
being monitored) is selected within each community, or
lot. LQAS yields a binary classification decision: in the
case of vaccination, the lot is rejected (i.e. judged to re-
quire supplementary activities) if the number of unvac-
cinated individuals within the sample exceeds a decision
threshold d, and accepted otherwise. Various sampling
plans consisting of a given N and d can be used. How-
ever, in practice where both time and res ources are often
limited, one needs to specify a lower threshold VC (LT),
i.e. the minimum acceptable VC below which supple-
mentary interventions (e.g. re-vaccination) must take
place; and an upper threshold VC (UT), usually fixed at
the target VC. Each sampling plan features a probability
α that the survey will yield an acceptance decision when
in fact the lot has a VC < LT (this is known as the con-
sumer risk, as it deprives beneficiaries of the interven-
tion they need); and a prob ability β that the lot will be
rejected when in fact VC exceeds the UT (this constitu-
tes the provider risk of expending resources need-
lessly). Minimising the consumer risk is the main
criterion for sele cting a sampling plan. Minimising the
provider risk is also important, but in many situations
a relatively high provider risk is tolerated so as to en-
sure that the resulting sample size still makes LQAS
more advantageous than a standard survey. The com-
bination of a large grey zone between LT and UT (a
result of the sampling plan) and a high proportion
of communities falling within this grey zone (a
phenomenon independent of the sampling plan, but
merely reflecting how the variable is distributed in the
population) however results in a high classification
error [7].
The theoretical advantage of LQAS is that it yields the
desired information with much smalle r sample sizes
than cluster surveys. However, the often-overlooked re-
quirement for a fully random sample poses a serious
challenge in resource-poor settings, since updated lists
of households are often unavailable, and since random
sampling will usually require travel to an unfe asibly large
number of sites within the community.
To overcome this problem, Pezzoli et al. and Green-
land et al. [8-10] have recently put forward a more field-
friendly clustered LQAS (CLQAS) approach, whereby
the lot sample is divided into clusters, as in any multi-
stage cluster sample. The critical assumption behind this
approach is that, within any given lot (e.g. a district), the
true VC levels in the different individual primary sam-
pling units (e.g. villages), among which one would ran-
domly select clusters, always give rise to a binomial
distribution, with the mean of this distribution equal to
the overall VC of the lot , and the standard deviation
equal to or less than an a priori assumed level. The
authors propose various sampling plans (e.g. 5 clusters
of 10 individuals) that, for assumed standard deviations
0.05 or 0.10 and typical LT and UT thresholds of
interest, yield reasonably low α and β probabilities.
As estimates of local vaccination coverage are used to
orient subsequent catch-up vaccination activities, the
choice of appropriate survey methodology is essential.
The CLQAS approach has been used in different settings
including Nigeria and Cameroon [8,9]; however, the ac-
curacy of classifications generated by this design and
implications of this accuracy for operational decisions
have not been sufficiently documented [11]. Using data
from a vaccination coverage survey carried out in Mali
in January 2011, we aimed to evaluate the performance
of CLQAS in a typical field setting. We also explored
whether classical surveys using smaller samples than
currently recommended provide results that, although
less precise, are still statistically stable and useful for op-
erational decision-making, and could thus constitute an
alternative to CLQAS.
Methods
Cluster survey
A new, single-dose conjugate vaccine against meningo-
coccal meningitis group A (MenAfriVac®) that confers
long-term immunity has recently completed develop-
ment [12]. Three countries were selected for the initia l
introduction of the vaccine: Burkina Faso, Mali and
Niger. In these countries, mass campaigns were carried
out with a target of 90% VC in the age group 1 to 29
years. Médecins Sans Frontières (MSF) supported the
vaccination campaign in three districts of the Koulikoro
region in Mali during December 2010. We carried out a
VC survey in one of these districts (Kati). The objectives
of the survey were to estimate VC for the district as a
whole and to identify health areas (aires de santé) with
VC < 80%, thus eligible for catch-up activities.
The district of Kati is divided into 41 health areas. We
therefore did a stratified multi-stage cluster survey, with
each health area constitu ting a stratum. All individuals
aged 1 to 29 years at the time of vaccination and living
in Kati were eligible. The basic sampling unit was the
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household (defined as a group of people living under the
responsibility of a single head of household and who eat
and sleep together), with all eligible individuals in a
household included in the survey. We targeted a sample
of 123 individuals per health area, sufficient to estimate
a VC of 80% with precision ± 10% and a design effect
(DEFF) of 2. Assuming 3 persons in the eligible age
group per household, and a 10% household non-
participation rate, we required 46 households to achieve
this sample. We thus sampled 10 clusters of 5 house-
holds per health area. Over all 41 health areas, this
yielded a target sample of 410 clusters containing 6 150
people, sufficient to estimate a VC of 80% with precision
± 2% and a DEFF of 4.
Kati district surrounds the city of Bamako. Ten of the
health areas feature a densely populated peri-urban lay-
out, while the remainders comprise rural areas with
lower population density. In peri-urban areas, clusters
were allocated spatially. Accordingly, we mapped the
contours of each health area using global positioning
system (GPS) devices, and selected the starting point of
each cluster randomly from the intersection points of a
grid overlaid on the map, as in Grais et al. [13]. The first
house (or compound) visited in the cluster was that clos-
est to the selected intersection point. If more than one
household lived in the house or compound, we selected
one of these at random. The se cond house visited was
the second on the left; and so forth until 5 households
containing at least one person in the eligible age group
had been visited.
In rural areas, cluster starting points were selected
using probability proportional to size sampling, based on
a sampling frame of villages and their administrative
population estimates. From the geographic centre of the
village containing the cluster, interviewers numbered all
houses up to the village edge along a random direction
and chose one at random as the starting house in the
cluster (this is known as the Expanded Programme on
Immunization or spin-the-pen method [14]). Further
houses were selected as above.
In each household, after gathering verbal consent,
investigators interviewed all eligible individuals (or their
caregivers for children) in the local language using a
standardised questionnaire. Individuals were considered
vaccinated if they provided verbal confirmation or based
on their immunisation card, when available. VC esti-
mates and DEFF were used to classify health areas in
categories to guide mop-up activities.
The study was implemented in collaboration with the
Ministry of Health after obtaini ng permission to carry
out the survey. The survey was con ducted by 18 teams
of two persons after three days of training, including a
pilot field test. Data collection took place from 15 to 24
January 2011. Data were entered in EpiData 3.1 (The
EpiData Association, Odense, Denmark) and analysed
using R software [15]. Stratum-specific VC estimates
were weighted for selection of single households within
houses and for unequal cluster sizes, while the estimate
for the entire district was also weighted for unequal
stratum population sizes.
Exploring the performance of small cluster survey designs
and CLQAS
Using the full survey database, we firstly explored the
stability of health area-specific estimates of VC obtained
through the 10 clusters x 15 individuals cluster design
used in Mali, or smaller sample sizes obtained by further
reducing the number of individuals per cluster. Such
small cluster surveys could provide a reasonable alterna-
tive to (C)LQAS without necessitating the definition of
an upper and lower threshold. Next, we performe d a
simulation of alternative CLQAS designs in order to ex-
plore their performance for all health areas including
those falling in the interval between the UT and LT (grey
zone). Although the choice of the grey zone should bal-
ance feasibility with classification accuracy, a large num-
ber of health areas falling within the grey zone would all
but undo a CLQAS surveys operational usefulness.
First, using the survey database, we created samples of
decreasing size for each health area, from 10 clusters x 15
individuals to 10 × 3, by eliminating observations from the
database, starting from the last person interviewed in each
cluster.
We then investigated the stability of the VC point esti-
mate, SE and intra-cluster correlation coefficient (ICC) of
VC in these progressively smaller samples, as a measure of
their statistical robustness. To do this, for each health area
and sampling design (i.e. from 10 × 15 to 10 × 3), we drew
10 000 bootstrap samples from the original data, using a
bootstrap sampling procedure recommended for cluster
survey data [16], which consists of sampling entire clusters
with replacement, without further re-sampling of observa-
tions within clusters.
We analysed the distribution of bootstrap samples to
compute the precision of VC, SE and ICC, as in Efron
and Tibshirani [17]. Absolute precision was computed
as (97.5% percentile of distribution - 2.5% percentile)/2.
Second, using the full survey database, we simulated a
CLQAS design consisting of 10 clusters of 5 individuals
per health area (lot), i.e. the same sample size recom-
mended by Pezzoli et al. [10], but with double the num-
ber of clusters and half the number of individuals per
cluster, i.e. tending towards lower DEFF and thus greater
precision. Accordingly, for each health area we drew 10
000 independent random samples of 5 individuals within
each of the 10 clusters, with the constraint that sampled
individuals must not belong to the same household. We
computed the number of unvaccinated individuals
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arising from each of these replicate samples, and applied
alternative decision values (d) and LT, UT thresholds
suggested by Pezzoli et al. [9,10] to accept or reject the
area. See Table 1 for the theoretical error risks associated
with these sampling plans, based on Pezzoli et al.sas-
sumption of a binomial distribution of lot VC, with SE
0.10.
For each health area and sampling plan, we computed
the proportion of simulations leading to rejection of the
health area (i.e. re-vaccination). We also compared the
CLQAS classification with that provided by the point es-
timate of the cluster survey to compute the frequency of
correct classification including health areas in the grey
zone.
Results
Cluster survey
In total, 2188 households were visited in the 41 health
areas of the district of Kati. Ten refused to participate
(0.5%) and 117 were absent after two visits (5.3%). We
thus interviewed a total of 2061 households, of which
2050 contained at least one individual from the target age
group (1-29 years old). A total of 21 367 people were
included in the survey, of which 73% (n = 15 668; mean of
7.6 per household) were in the target age group for the
vaccination campaign, with a male to female ratio of 0.9.
Among the target age group, VC (by immuniz ation
card or verbal confirmation) was estimated at 88.4%
(95%CI 85.7-90.6). Table 2 shows VC by age group and
sex. Male adults (15-29 years old) had the lowest VC.
The main reported reasons for non-vaccination were ab-
sence during vaccination activities (29.5%), believing not
to be part of the target population (15.0%) and lack of
information about the campaign (9.6%).
VC among the target age group was also estimated for
each health area. Table 3 shows the 41 health areas
ranked by descending VC point estimate; the standard
deviation of VC across the 10 clusters in the health area;
the value of the design effect (DEFF) and intra-cluster
correlation coefficient (ICC). These values were use d to
re-classify health areas in three categories to guide
mop-up activities: c ategory A included h ealth areas
where the lower bound of the 95%CI of the VC
estimate was above 80%; category B included health
areas where the lower bound of the 95%CI of the VC
estimate wa s below 80% and therefore required add-
itional vaccination activities; and category C , he alth
areas w here the DEFF was a bove 4.0 suggesting pock-
ets of unvaccinated populations and thus requiring
targeted catch-up vac cination activities. See the Dis -
cussion for limitations of this approach. Overall, 26
health areas were ac cepted and not requiring sup-
plemental activities (cat. A); 11 health area s w ere
rejected as requiring additional vaccination activities
(cat. B); a nd 4 health areas were also rejected as re-
quiring targeted catch-up vaccination (cat. C) (Fig-
ure 1). Cluster-level summaries for each health area
are provided in Additional File 1 to facilitate for fur-
ther simulation work based on this dataset.
Performance of small cluster samples and CLQAS
Exploration of alternative sampling plans for the small
cluster design sugg ests that, as sample size decreased
from 10 × 15 to 10 × 3 individuals, the stability (absolute
precision) of the standard error of VC decreased from a
median of ±0.017 to ±0.030 across all 41 strata (Figure 2).
ICC was markedly unstable at low sample sizes
(Figure 3), ranging from a median absolute precision of
±0.047 (10 × 15 design) to a median precision of ±0.204
(10 × 3 design).
As expected, for the CLQAS, the proportion of simu-
lations leading to rejection of each health area (i.e. re-
vaccination) varied considerably and was dependent on
the distribution of the number of unvaccinated indivi-
duals resulting from the simulation runs and on the
sampling plan (Table 4).
When looking at health areas with a VC > UT, the
CLQAS wrongly rejected, with a probability β greater
than expected, two areas for sampling plan 1, one area
for sampling plan 2 and one area for sampling plan 3.
When looking at health areas with VC < LT, none was
wrongly accepted and all probabilities α were below the
expected maximum. However, when looking at health
areas that were rejected with a VC > UT or accepted
with VC < LT and also including health areas in the grey
zone, at least one third of health areas had a risk of
Table 1 CLQAS sampling plans included in the evaluation
Sampling plan Lot sample
size (N)
Lower VC
threshold (LT)
Upper VC
threshold (UT)
Decision
threshold (d)
Consumer error
risk (α)
Provider error
risk (β)
1 50 (10 × 5) 85% 95% 3 10% 30%
2 50 (10 × 5) 80% 95% 4 5% 19%
3 50 (10 × 5) 75% 90% 7 8% 20%
These sampling plans assume that vaccination coverage in the 10 clusters is distributed according to a binomial distribution centred at the point estimate for the
entire lot, and with SD 0.10. If the number of unvaccinated individuals > d, the lot is rejected.
Probability of classifying the lot as acc eptable when in fact VC < LT. Probability of classifying the lot as unacceptable when in fact VC UT. Probabilities for
plan A are taken from Table one of Pezzoli et al. [9], and for B and C from Tables two and three in Pezzoli et al., [10] respectively. Note that all calculations in
these publications refer to a 5 × 10 (i.e. theoretically less precise) plan.
Minetti et al. Emerging Themes in Epidemiology 2012, 9:6 Page 4 of 11
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misclassification 0.25, irrespective of sampling plan.
Under plans A and B, about half of lots had a risk
greater than 0.50 of being misclassified (Figure 4).
Nearly all misclassification error was on the provider
side, thereby potentially resulting in unwarranted re-
vaccination of health areas with good VC.
Discussion
Cluster survey
VC for the entire district of Kati was high and close to
the target of 90%. Data collected for each stratum of
the cluster survey allowed us to interpret results for each
health area and classify areas accordingly into categories:
health areas not requiring further corrective measures
(VC 80%); health areas requiring additional vaccin-
ation activities (VC possibly under 80%); health areas
without an acceptable precision of VC estimates (high
degree of heterogeneity or DEFF over 4.0), indicating the
existence of pockets of unvaccinated individuals. For
these areas the recommendation was to carry out further
investigations through local informants in order to iden-
tify specific communities with low VC to be targeted by
catch up campaigns. The above classification system is
also potentially flawed: confidence intervals, particularly
for proportions, are known to have imperfect coverage
(e.g. 95% intervals rarely contain the true value 95% of
the time as expected) [18]; moreover, the DEFF cut-offs
we used are arbitrary and, while they seemed useful in
this setting, would have to be formally tested in a variety
of other scenarios, with classification properties evalu-
ated against a known gold standard. While we dont sug-
gest that our classification system should be adopted
uncritically instead of CLQAS, we nonetheless believe
that one need not to look to LQAS alone a s a way to
meaningfully use small survey data, and that both the
confidence interval and the observed degree of cluster-
ing provide useful information for classification. In par-
ticular, we suggest that the estimated ICC value could be
used in the future to refine cla ssification as opposed to
relying only on DEFF.
In order to provide information at the local (health
area) level, we opted for small stratum surveys of 10
clusters, far lower than the recommended 30 clusters.
Investigation of the statistical robustness of this design
and increasingly smaller cluster samples suggested that,
with fewer than 10 clusters x 15 individuals, standard
error and ICC estimates were increasing ly unstable.
However, the 10 × 15 design appeared to provide rea-
sonably robust estimates in most health areas: an abso-
lute precision of ±0.015 to ±0.025 in the standard error
of VC roughly means that, 95% of the time, confidence
intervals returned by the 10 × 15 design in this setting
would have been accurate within about ±3 to ±5%. Our
analysis suggests that, for local classification of VC
within the context of a larger survey aiming to estimate
VC across a district or region, small stratum cluster
samples of 10 clusters provide a reasonable balance be-
tween feasibility and statistical robustness. However, our
findings do not support a 10 cluster design for accurate
estimation of VC.
Performance of the clustered LQAS design
When considering the aim of providing information for
decision-making at local level, the overall recommended
sample size for a CLQAS design in the district was three
times smaller (N=2 050 assuming a 10 × 5 design) than
the sample size needed for our cluster survey. Further
improvements in efficiency would have resulted from early
stoppage of LQAS surveys when the number of unvaccin-
ated individuals exceeded d, even before completing the
lot sample.
Our simulation based on real field data showed that,
in this setting, the CLQAS design always classified
health areas with VC < LT correctly, and mostly classi-
fied correctly health areas with VC UT - that is, it al-
most always achieved the classification accuracy
specified by each of the sampling plans tested. Moreover,
all misclassifications were of a conservative nature, i.e.
provider risk leading to unwarranted re vaccination.
However, in practice, decision makers on the field
need to adopt a binary decision for each health area -
that is, either to carry out supplementary vaccination ac-
tivities or to treat the area as sufficiently vaccinated. This
means that the classification reached by the CLQAS
Table 2 District-wide estimates of vaccination coverage, by age group and sex
Age
group
Male Female Total
N % (95%CI) N % (95%CI) N % (95%CI)
<1 year 252 3.8 (1.0-12.7) 235 11.5 (5.0-24.3) 489 10.9 (5.4-20.8)
1-4 years 1682 92.5 (88.8-95.0) 1767 91.0 (87.7-93.4) 3455 92.0 (89.5-93.9)
5-14 years 3489 95.8 (94.0-97.1) 3589 94.4 (91.4-96.4) 7087 95.1 (92.7-96.7)
15-29 years 2046 70.0 (66.0-73.8) 3070 81.2 (76.5-85.2) 5126 77.4 (74.0-80.4)
>29 years 2713 12.7 (10.8-14.8) 2481 20.3 (18.6-22.1) 5210 16.3 (15.0-17.6)
Total 10,182 65.3 (63.5-66.9) 11,142 71.8 (69.4-74.1) 21,367 68.7 (66.7-70.6)
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Table 3 Estimates of vaccination coverage by health area
Health area VC point
estimate
(%)
95%
confidence
interval
Standard
deviation
of VC
Design
effect
Intra-cluster
correlation
coefficient
Classification
for
decision*
Neguela 98.3 95.0-99.4 0.030 1.6 0.014 A
Nana-Kenieba 96.7 92.0-98.7 0.048 1.9 0.018 A
Sandama 95.7 92.4-97.6 0.040 1.2 0.005 A
Kati Coro 95.6 89.7-98.2 0.062 1.7 0.021 A
Diago 95.4 93.0-97.0 0.031 0.9 0.001 A
Kalifabougou 94.9 90.6-97.3 0.051 1.3 0.007 A
Dombila 94.4 88.5-97.4 0.067 2.1 0.024 A
Niouma-Makana 94.4 86.9-97.7 0.079 2.0 0.029 A
Faladie 94.3 90.5-96.6 0.048 1.3 0.008 A
Tanima 93.7 87.0-97.1 0.076 1.7 0.021 A
Falani 93.5 88.9-96.3 0.058 1.4 0.007 A
N'Gouraba 93.5 88.1-96.5 0.065 1.8 0.019 A
Yelekebougou 93.5 89.4-96.1 0.053 1.2 0.006 A
Kati Sananfara 93.2 85.6-96.9 0.085 1.8 0.025 A
Doubabougou 93.1 89.6-95.5 0.047 1.0 0.001 A
Djoliba 92.8 87.2-96.0 0.068 2.0 0.022 A
Kanadjiguila 91.7 80.3-96.8 0.123 2.1 0.034 A
Sonikegny 91.5 87.2-94.4 0.057 1.2 0.007 A
Siby 91.0 84.1-95.1 0.086 2.0 0.022 A
Kabalabougou 90.9 85.3-94.5 0.072 1.7 0.022 A
Dogodouma 89.8 83.5-93.8 0.150 1.6 0.024 A
Sanankoroba 89.8 76.2-96.0 0.082 2.5 0.050 B
Siracoro Meguetana 89.5 80.4-94.7 0.111 2.3 0.033 A
Safo 89.3 81.1-94.2 0.102 1.8 0.024 A
Bancoumana 88.7 80.7-93.6 0.102 2.6 0.033 A
Moutougoula 88.6 82.9-92.5 0.077 1.8 0.018 A
Malibougou 87.6 73.3-94.8 0.165 3.4 0.059 B
Baguineda 87.3 80.0-92.2 0.097 2.0 0.027 A
Diedougou Torodo 83.6 56.4-95.2 0.085 5.3 0.091 C
Sangarebougou 83.6 77.7-88.3 0.303 1.3 0.009 B
Farada 83.2 74.6-89.3 0.118 2.0 0.025 B
Kalabancoro 82.9 76.9-87.6 0.086 1.4 0.012 B
Dialakorodji 82.1 56.1-94.3 0.303 5.6 0.170 C
Kalabancoro Koulouba 80.8 70.7-88.0 0.139 2.0 0.038 B
Kalabancoro Adeken 79.8 69.7-87.1 0.140 1.8 0.035 B
Daban 79.1 52.6-92.8 0.327 4.9 0.091 C
Kati Koko 77.9 60.8-88.9 0.229 3.5 0.084 B
N'Gabacoro-Droit 76.3 69.3-82.2 0.104 1.4 0.015 B
Dio-Gare 76.1 41.5-93.5 0.441 6.1 0.134 C
Moribabougou 73.6 63.7-81.6 0.146 2.3 0.030 B
Kalabancoro
Heramakono
71.7 61.8-79.9 0.148 1.6 0.027 B
*A= accepted;B=rejected, requiring overall additional vaccination activities; C= rejected, requiring targeted catch-up vaccination activities.
Minetti et al. Emerging Themes in Epidemiology 2012, 9:6 Page 6 of 11
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Table 4 Results of the CLQAS simulation (10 000 runs), for three alternative sampling plans
Sampling plan 1 Sampling plan 2 Sampling plan 3
(LT = 85%, d = 3) (LT = 80%, d = 4) (LT = 75%, d = 7)
Health area Survey VC
estimate (%)
CLQAS median
number unvaccinated
individuals (95%
percentile)
VC region Frequency
of "reject"
classification
Frequency
of correct
classification
VC region Frequency
of "reject"
classification
Frequency
of correct
classification
VC region Frequency
of "reject"
classification
Frequency of
correct
classification
Neguela 98.3 1 (02) >UT 0.002 0.999 >UT 0.000 1.000 >UT 0.000 1.000
Nana-Kenieba 96.7 3 (15) >UT 0.235 0.765 >UT 0.067 0.933 >UT 0.000 1.000
Sandama 95.7 3 (16) >UT 0.368 0.632* >UT 0.157 0.843 >UT 0.001 0.999
Kati Coro 95.6 3 (16) >UT 0.498 0.502* >UT 0.239 0.761* >UT 0.004 0.996
Diago 95.4 3 (06) >UT 0.272 0.728 >UT 0.097 0.904 >UT 0.001 0.999
Kalifabougou 94.9 4 (17) Grey 0.614 Grey 0.374 >UT 0.019 0.981
Dombila 94.4 3 (16) Grey 0.428 Grey 0.201 >UT 0.004 0.996
Niouma-Makana 94.4 5 (28) Grey 0.755 Grey 0.517 >UT 0.038 0.962
Faladie 94.3 3 (16) Grey 0.442 Grey 0.202 >UT 0.003 0.998
Tanima 93.7 4 (17) Grey 0.550 Grey 0.292 >UT 0.009 0.991
Falani 93.5 3 (06) Grey 0.364 Grey 0.162 >UT 0.002 0.998
N'gouraba 93.5 3 (17) Grey 0.436 Grey 0.216 >UT 0.007 0.993
Yelekebougou 93.5 4 (17) Grey 0.573 Grey 0.343 >UT 0.018 0.982
Kati Sananfara 93.2 5 (38) Grey 0.900 Grey 0.683 >UT 0.064 0.936
Doubabougou 93.1 3 (16) Grey 0.400 Grey 0.194 >UT 0.005 0.995
Djoliba 92.8 4 (27) Grey 0.697 Grey 0.417 >UT 0.018 0.982
Kanadjiguila 91.7 8 (511) Grey 1.000 Grey 0.992 >UT 0.553 0.447*
Sonikegny 91.5 4 (17) Grey 0.585 Grey 0.348 >UT 0.018 0.982
Siby 91.0 5 (29) Grey 0.864 Grey 0.702 >UT 0.133 0.867
Kabalabougou 90.9 5 (28) Grey 0.761 Grey 0.520 >UT 0.038 0.963
Dogodouma 89.8 6 (39) Grey 0.947 Grey 0.799 Grey 0.108
Sanankoroba 89.8 6 (39) Grey 0.964 Grey 0.863 Grey 0.193
Sirac. Meguetana 89.5 7 (311) Grey 0.958 Grey 0.874 Grey 0.331
Safo 89.3 6 (310) Grey 0.957 Grey 0.847 Grey 0.235
Bancoumana 88.7 6 (29) Grey 0.888 Grey 0.725 Grey 0.150
Moutougoula 88.6 6 (310) Grey 0.912 Grey 0.772 Grey 0.178
Malibougou 87.6 8 (412) Grey 0.992 Grey 0.966 Grey 0.550
Baguineda 87.3 8 (512) Grey 0.999 Grey 0.988 Grey 0.640
Diedoug. Torodo 83.6 9 (612) <LT 1.000 1.000 Grey 1.000 Grey 0.804
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Table 4 Results of the CLQAS simulation (10 000 runs), for three alternative sampling plans (Continued)
Sangarebougou 83.6 10 (614) <LT 1.000 1.000 Grey 0.996 Grey 0.850
Farada 83.2 9 (514) <LT 0.997 0.997 Grey 0.982 Grey 0.736
Kalabancoro 82.9 8 (412) <LT 0.983 0.983 Grey 0.947 Grey 0.546
Dialakorodji 82.1 7 (410) <LT 0.997 0.997 Grey 0.962 Grey 0.314
Kalab. Koulouba 80.8 10 (614) <LT 0.999 0.999 Grey 0.996 Grey 0.866
Kalab. Adeken 79.8 12 (816) <LT 1.000 1.000 <LT 1.000 1.000 Grey 0.985
Daban 79.1 10 (713) <LT 1.000 1.000 <LT 1.000 1.000 Grey 0.937
Kati Koko 77.9 8 (512) <LT 0.999 0.999 <LT 0.987 0.987 Grey 0.673
N'gabacoro-Droit 76.3 10 (614) <LT 1.000 1.000 <LT 0.997 0.997 Grey 0.877
Dio-Gare 76.1 10 (713) <LT 1.000 1.000 <LT 1.000 1.000 Grey 0.955
Moribabougou 73.6 14 (1018) <LT 1.000 1.000 <LT 1.000 1.000 <LT 0.998 0.998
Kalab. Heramak. 71.7 16 (1320) <LT 1.000 1.000 <LT 1.000 1.000 <LT 1.000 1.000
Using the VC point estimate as a reference.
*Error higher than expected (>β).
Minetti et al. Emerging Themes in Epidemiology 2012, 9:6 Page 8 of 11
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method for areas that in reality fall within the grey
zone is also highly relevant for operations : areas that
are rejected would go on to receive additional vaccin-
ation interventions. Our simulation shows that, in our
Mali scenario, all three of the sampling plans tested
leave a large proportion of health areas in the grey zone,
where the risk of misclassification is very high. For many
health areas, CLQAS appeared no better than flipping a
coin. The consequence of this high risk of misclassifica-
tion would mainly have been to allocate resources for
catch up cam paigns in areas where they were not
needed. It seems plausible that the 5 × 10 design put
forward by Pezzoli et al., while reaching the same sample
size, would have performed even worse given the lower
ratio of clusters to individuals. In operational terms, our
results suggest that, in choosing to save resources up-
front by reducing the cost of surveys throu gh LQAS,
vaccination progra mmes may in fact end up committing
even greater resources down the line by having to carry
out remedial vaccination in a far greater proportion of
the community than in fact needed.
To a large extent, the above findings reflect a known
limitation of LQAS: its specificity is high only if few of
the lot s fall within the grey zone [19]. However, add-
itional inaccuracy in our results also arose from the vio-
lations of two key assumptions of CLQAS that are
irrelevant if the traditional LQAS method featuring
Figure 1 Classification of health areas (n=41) according to
vaccination coverage estimates (95%CI lower bound) and
design effect in Kati district.
Figure 2 Absolute precision of estimates of the standard error
of VC, for different survey designs. Box plots indicate the median
and inter-quartile range of the median absolute precision values
from 10 000 bootstrap replicates of each of the 41 stratum surveys.
Whiskers denote the range.
Figure 3 Absolute precision of estimates of the intra-cluster
correlation coefficient of VC, for different survey designs. Box
plots indicate the median and inter-quartile range of the median
absolute precision values from 10 000 bootstrap replicates of each
of the 41 stratum surveys. Whiskers denote the range.
Figure 4 Distribution of CLQAS misclassification risk, for three
sampling plans, among all health areas.
Minetti et al. Emerging Themes in Epidemiology 2012, 9:6 Page 9 of 11
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simple or systematic random sampling (SRS) is carried
out. The first assumption is that the standard deviation
of VC in any cluster within each lot does not exceed a
given value (0.10 in the sampling plans we studied). This
assumption has been shown to be violated for 25-50% of
lots in applications of the CLQAS to date [8,9], meaning
that variability of VC within the lot is in fact often
greater than expected. In this study, 17/41 (41.4%) of
health areas featured a standard deviation > 0.10
(Table 3), reinforcing the above findings. It should be
noted, however, that standard deviation values presented
in this study may or may not reflect the true standard
deviations of VC in villages within each health area,
since the cluster-level samples were collected through a
sampling process (i.e. random walk) that is not des igned
to return a representative sample of the community
within which the cluster falls.
The second, more fundamental assumption is that VC
within each lot follows a binomial distribution. In devel-
oping countries, multi-modal or over-dispersed (left- or
right-skewed) distributions of VC are more likely given
the known difficulties in accessing remote communities
and the very uneven performance of local health services
[20]. The distribution of VC across health areas in our
district of inter vention also suggests a pattern other than
binomial, though for an administrative level higher than
the one at which we evaluated the CLQAS (Figure 5).
If cluster sampling is to be used with LQAS, the meth-
ods accuracy could be increased by reducing inter-
cluster variability within lots. This can be done by either
(i) increasing the number of clusters or (ii) working at a
smaller geographic resolution (e.g. lots defined as sub-
districts or villages, within which VC may be more
homogeneous). Both solutions would howe ver negate
the main advantage of LQAS, as the resulting survey
would be neither faster nor cheaper than a stratified
cluster survey. Furthermore, in our study we already
considered the smallest administrative division of rele-
vance for vaccination programmes. A third solution
would be to restrict the application of the method to
evaluate immu nisation programmes that tend to per-
form well or to scenarios when the territory under
study is somewhat homogeneous in terms of vaccination
coverage [8]. However, highly performing areas are
rarely known in advance, and inter-cluster variability is
difficult to predict; furthermore, such an approach would
seem to negate the very purpose of carrying out VC
studies.
Study limitations
Limitations of the cluster survey, common to most VC
surveys in developing countries, include potential mis-
classification bias due to the retrospective nature of data
collection , and inability in many cases to verify vaccin-
ation status through immunisation card review, relying
instead on the individuals or caregivers verbal declaration.
Similarly, verifying the age of the person interviewed
was not possible in most cases. This can also be a
source of misclassification between target or non-target
population especially for children around 1 year old and
adults around 30 years old, although the direction of
any bias is difficult to predict. The proportion of chil-
dren under 5 years was 18.5% in the interviewed sam-
ple, equal to the national estimate [21], suggesting little
directional bias. Additional selection bias may have
resulted from inaccurate population estimates in the
cluster sampling frame: these were based on a 1998
census adjusted for estimated growth rates. All the
above limitations might have biased VC estimates that
we have used as a gold standard for classifying results
of CLQAS simulations. Furthermore, these VC estimates
were themselves subject to considerable imprecision.
Our reference values for comparison of the CLQAS
classification are thus imperfect, and weaken the
strength of inference of our study.
Our CLQAS simulation also had limitations. We could
only explore a 10 × 5 design due to the nature of our
original survey dataset. It is known that higher sample
sizes would achieve better accu racy of the CLQAS
method, although, as discussed above, they would tend
Figure 5 Distribution of vaccination coverage in Kati district (n = 41 health areas).
Minetti et al. Emerging Themes in Epidemiology 2012, 9:6 Page 10 of 11
http://www.ete-online.com/content/9/1/6
to negate its efficiency benefit over classical surveys. Fur-
thermore, our original survey featured a sampling step
of two between houses visited during the last stage of
cluster selection; by contrast, CLQAS applications to
date have used various sampling steps (nine or 18 for
yellow fever in rural and urban areas respectively; three
or six for polio [9]); because close proximity of house-
holds may increase the ICC, our findings may somewhat
unfairly penalise the CLQAS method as it has been
implemented. However, in practice our sampling step
was such as to span nearly the full width of most villages
in our sampling frame, which tende d to be small. Fur-
thermore, it is likely that most variability in VC is not
within villages themselves, but at a higher administrative
level, i.e. that differences in sampling steps may not
greatly affect the ICC.
Conclusions
This study suggests that small sample cluster surveys of
10 clusters x 15 individuals may be acceptably robust for
practical applications of classifying VC at the local level.
However, further studies are needed to establish the stat-
istical robustness of these small samples in other set-
tings. Based on this study, we do not recommend the
CLQAS method as currently formulated for evaluating
vaccination programmes.
Additional file
Additional file 1: Cluster-level data for each health area.
Competing interests
Authors declare no conflict of interest.
Authors contributions
Conceived and designed the study: AM MRM ATa FF AT RFG FC. Performed
the study: AM MRM FN MHK JS. Analyzed the data: AM MDM TR FC. Wrote
the first draft of the manuscript: AM MRM FC. Contributed to the writing of
the manuscript: all authors. Agree with manuscript results and conclusions:
all authors. All authors read and approved the final manuscript.
Funding Discloser
This work was supported by Médecins Sans Frontières.
Acknowledgments
We wish to thank the population of Kati district in Koulikoro region of Mali
for their participation in this study, the Ministry of Health of Mali for
collaboration and support during the survey, the MSF teams on the field for
their outstanding work and the MSF teams at HQ level for their precious
advice and support. We are also extremely grateful to an anonymous
reviewer for very useful comments and for suggesting the present version of
Table 4 in the paper.
Author details
1
Epicentre, Paris, France.
2
Médecins Sans Frontières, Bamako, Mali.
3
Médecins
Sans Frontières, Paris, France.
4
National Centre for Immunization, Ministry of
Health, Bamako, Mali.
Received: 24 January 2012 Accepted: 8 October 2012
Published: 12 October 2012
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    • "This inflation of the risks occurs because σ and ρ decrease as a function of p but the average coverage across SAs is lower than 75%. The risks are not inflated in the example from [27] because the range of vaccination coverages is similar to the 75–90% couplet thresholds. "
    [Show abstract] [Hide abstract] ABSTRACT: Lot quality assurance sampling (LQAS) surveys are commonly used for monitoring and evaluation in resource-limited settings. Recently several methods have been proposed to combine LQAS with cluster sampling for more timely and cost-effective data collection. For some of these methods, the standard binomial model can be used for constructing decision rules as the clustering can be ignored. For other designs, considered here, clustering is accommodated in the design phase. In this paper, we compare these latter cluster LQAS methodologies and provide recommendations for choosing a cluster LQAS design. We compare technical differences in the three methods and determine situations in which the choice of method results in a substantively different design. We consider two different aspects of the methods: the distributional assumptions and the clustering parameterization. Further, we provide software tools for implementing each method and clarify misconceptions about these designs in the literature. We illustrate the differences in these methods using vaccination and nutrition cluster LQAS surveys as example designs. The cluster methods are not sensitive to the distributional assumptions but can result in substantially different designs (sample sizes) depending on the clustering parameterization. However, none of the clustering parameterizations used in the existing methods appears to be consistent with the observed data, and, consequently, choice between the cluster LQAS methods is not straightforward. Further research should attempt to characterize clustering patterns in specific applications and provide suggestions for best-practice cluster LQAS designs on a setting-specific basis.
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    • "Sometimes a simple random sample is not available—for example, geographic spread may make a simple random sample infeasible [7-9]— and one must resort to other sampling designs. One such instance is the data quality assessment of the community health worker (CHW) program in southern Kayonza, Rwanda. "
    [Show abstract] [Hide abstract] ABSTRACT: Traditional Lot Quality Assurance Sampling (LQAS) designs assume observations are collected using simple random sampling. Alternatively, randomly sampling clusters of observations and then individuals within clusters reduces costs but decreases the precision of the classifications. In this paper, we develop a general framework for designing the cluster(C)-LQAS system and illustrate the method with the design of data quality assessments for the community health worker program in Rwanda. The C-LQAS sample sizes provided in this paper constrain misclassification risks below user-specified limits. Multiple C-LQAS systems meet the specified risk requirements, but numerous considerations, including per-cluster versus per-individual sampling costs, help identify optimal systems for distinct applications.To determine sample size and decision rules for C-LQAS, we use the beta-binomial distribution to account for inflated risk of errors introduced by sampling clusters at the first stage. We present general theory and code for sample size calculations. We show the utility of C-LQAS for data quality assessments, but the method generalizes to numerous applications. This paper provides the necessary technical detail and supplemental code to support the design of C-LQAS for specific programs.
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  • [Show abstract] [Hide abstract] ABSTRACT: Background: Implementation of trachoma control strategies requires reliable district-level estimates of trachomatous inflammation-follicular (TF), generally collected using the recommended gold-standard cluster randomized surveys (CRS). Integrated Threshold Mapping (ITM) has been proposed as an integrated and cost-effective means of rapidly surveying trachoma in order to classify districts according to treatment thresholds. ITM differs from CRS in a number of important ways, including the use of a school-based sampling platform for children aged 1-9 and a different age distribution of participants. This study uses computerised sampling simulations to compare the performance of these survey designs and evaluate the impact of varying key parameters. Methodology/principal findings: Realistic pseudo gold standard data for 100 districts were generated that maintained the relative risk of disease between important sub-groups and incorporated empirical estimates of disease clustering at the household, village and district level. To simulate the different sampling approaches, 20 clusters were selected from each district, with individuals sampled according to the protocol for ITM and CRS. Results showed that ITM generally under-estimated the true prevalence of TF over a range of epidemiological settings and introduced more district misclassification according to treatment thresholds than did CRS. However, the extent of underestimation and resulting misclassification was found to be dependent on three main factors: (i) the district prevalence of TF; (ii) the relative risk of TF between enrolled and non-enrolled children within clusters; and (iii) the enrollment rate in schools. Conclusions/significance: Although in some contexts the two methodologies may be equivalent, ITM can introduce a bias-dependent shift as prevalence of TF increases, resulting in a greater risk of misclassification around treatment thresholds. In addition to strengthening the evidence base around choice of trachoma survey methodologies, this study illustrates the use of a simulated approach in addressing operational research questions for trachoma but also other NTDs.
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