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Am. J. Trop. Med. Hyg., 71(5), 2004, pp. 636–638
Copyright © 2004 by The American Society of Tropical Medicine and Hygiene
SHORT REPORT: DETECTION PROBABILITY OF ARBOVIRUS INFECTION IN
MOSQUITO POPULATIONS
WEIDONG GU AND ROBERT J. NOVAK
Illinois Natural History Survey, Medical Entomology Laboratory, Champaign, Illinois
Abstract. An important component of arbovirus surveillance is monitoring the vector for presence of the pathogen.
Intervention and preventive programs need early detection of arboviral activity in mosquito populations. In this report,
we examine the factors affecting the probability of detection of mosquito infections. Since arbovirus infection rates in
mosquito populations are very low, observations of zero-infected mosquito samples are common. Using statistical
models, we describe methods to estimate the probability of detection and upper bounds of confidence intervals of
mosquito infection rates as measures of confidence for observations of zero infection. Our results show that detection
of low levels of mosquito infections requires large samples (greater than 1,600 individuals) for a high probability (0.8)
of detection. Due to focal transmission of arboviruses, grouping samples over different sampling sites and times is often
inappropriate for detection of mosquito infection. We emphasize sample size as a key determinant in detection of
mosquito infections and recommend intensified entomologic surveys at sentinel sites to detect arboviral activity.
rates compatible with observations with zero infected individuals in sample size N as 3/N. For example, zero-infected
mosquitoes in a sample of 100 has an upper bound of the 95%
confidence interval of 3%. This general rule is valid under the
circumstances when sample size is not less than 30. Because
arboviral infection rates in mosquito populations are low (often measured in infected individuals per 1,000), especially in
early periods of the transmission season, non-detection can be
a severe problem. Therefore, an investigation of statistical
issues regarding non-detection of mosquito infections due to
sampling variation is warranted.
For simplicity, we assume that arbovirus testing is perfect,
i.e., the sensitivity and specificity of the test are 100%. We
further assume that infected and non-infected mosquitoes are
equally likely to be captured by a sampling method. Thus, the
probability of detection (P) of any infected individuals in a
sample of N mosquitoes can be calculated based on the binomial distribution
Mosquito-borne arbovirus diseases, such as West Nile virus
(WNV) and St. Louis encephalitis (SLE), pose severe threats
to public health. For implementation of intervention and prevention programs, early detect arbovirus activity in mosquito
populations is important. Factors affecting detection of arboviruses in mosquito samples include the sensitivity and specificity of the testing method, sample size, infection rates, and
statistical significance levels.1 Advanced laboratory techniques, such as the reverse transcriptase−polymerase chain
reaction TagMan (Applied Biosystems, Foster City, CA),
have been developed to screen pools of mosquito samples for
arboviruses and facilitate examination of a large amount of
mosquitoes. Since arboviral infections in mosquito populations are low, observations of zero infection in mosquito
samples are common. Probability statements are needed to
attest a measure of confidence to observations of zero infection. The statistical theories underlying detection of mosquito
infections are different for those governing estimation of infection rates. For the former, we are concerned with whether
mosquito infections are present or not based on examination
of a mosquito sample. For estimation of infection rates, we
consider various estimators and pooling methods of mosquito
samples.2−5 For example, the minimum infection rate (MIR)
and maximum likelihood estimation (MLE) of infection rates
are commonly used in arbovirus surveillance. Recently, we
demonstrated that both MIR and MLE are highly biased for
constant pool size of 50 individuals when mosquito infection
rates are high, e.g., greater than 30 per 1,000.5 Under this
circumstance, variable size pooling aiming at reducing proportions of positive pools is more important than the choice
of different estimators for reliable estimation of infection
rates.
Although estimation of infection rates is important for determining risk of transmission, for many surveillance programs early detection is necessary for focusing control efforts.
In this report, we focus on statistical issues regarding the
detection of mosquito infections and examine variables affecting detection of mosquito infections in the context of arboviral infections of low infection rates and focal dynamics.
Non-detection issues have been extensively investigated in
wildlife research6−8 and medical research.1,9 Hanley and
Lippman-Hand9 recommended a role of thumb for estimating
the upper bound of the 95% confidence limit of infection
P = 1 − 共1 − r兲N
(1)
where r is the infection rate. The infection rate r needs to be
specified to calculate the probability of detection. The smaller
r is, the smaller P is for a given sample N. For example, the
probabilities of detecting infected individual(s) in a sample of
500 mosquitoes given infection rates of 1 and 5 per 1,000 are
0.39 and 0.91, respectively (Figure 1). In arboviral surveillance, we suggest to use the infection rate of 1 of 1,000 as the
detection threshold for calculation of the probability of detection. This infection rate has been used as the criterion for
defining the epicenters of WNV transmission in the New
York City10 and identifying conditions that “favor epidemic
SLE transmission in south Florida”.11,12 Choice of this infection rate is a compromise between the need to detect low
levels of mosquito infection and the overwhelming difficulty
associated with obtaining large mosquito samples for detecting lower levers of infection rates.
For sampling design, we can calculate, a priori, the minimal
sample size for a specified probability of detection and infection rates by manipulation of equation 1 as
N = log共1 − P兲 Ⲑ log共1 − r兲
(2)
To have high probabilities of detection, large numbers of
mosquitoes are required when mosquito infection rates are
636
PROBABILITY OF DETECTION OF ARBOVIRUS TRANSMISSION
637
FIGURE 3. Upper bounds of 80% and 95% confidence intervals of
infection rates compatible with observations of zero-infected individuals in mosquito samples. cl ⳱ confidence limit.
FIGURE 1. Probability of detection of infected mosquitoes as a
function of sample sizes (infection rates per 1,000: solid line ⳱ 1;
dashed line ⳱ 5).
low (Figure 2). For example, 1,609 and 2,301 mosquitoes are
needed for detection probabilities of 0.8 and 0.9, respectively.
Even a medium detection probability of 0.5 requires 693 mosquitoes. Of course, definition of a high probability of detection depends on the researcher’s view. Conventionally, 0.8
has been recommended as a high power (equivalent to high
probability of detection) in environmental management.13
To estimate the upper bound of infection rates, rupper, compatible with observations of a zero-infected individual and a
specified confidence interval, equation 1 can be transformed
into
rupper = 1 − 公1 − P
N
(3)
Figure 3 depicts the upper bounds of the 80% and 95% confidence intervals of infection rates compatible with zero-
FIGURE 2. Relationship between minimum numbers of mosquitoes required for prescribed detection probabilities and infection
rates of mosquitoes.
infected individuals in mosquito samples. For small sample
sizes (< 300), it is not surprising (probability > 5%) to observe
zero-infected individuals even when true infection rates are
relatively high, e.g., 5 per 1,000.
In arbovirus surveys, researchers tend to analyze mosquito
data by grouping samples from several sites and times to
evaluate the role of various potential vector species and to
estimate infection rates.10,14−16 However, transmission of
arboviruses typically exhibit considerable spatial and
temporal variability in mosquito infection rates.12 Therefore,
grouping samples over sites scattered across a large area
and extended periods of time provides little information
about the dynamics of focal transmission and confounds
estimation of the detection probability and infection rates.
For example, Bernard and others10 reported MIRs for Culex
pipiens as 3.53 and 11.42 per 1,000 by grouping samples
from all sites and from sites in Staten Island, New York
alone, respectively. To identify the focal structure of arbovirus transmission, ideally, samples collected from each sampling site and occasion should be analyzed separately. Grouping samples should be restricted to sites and times where
homogeneity in mosquito infection rates can be reasonably
justified.
Our theoretical analyses show that detecting low levels of
arboviral infections in mosquitoes requires abundant mosquito samples. Therefore, it is not surprising that many surveys failed to uncover positive mosquito pools in the early
stages of arboviral transmission. Occurrence of dead birds or
human cases may precede the reports of positive mosquito
pools. For example, 14 of the 21 patients had illness onsets
preceded detection of the first virus-infected mosquito pools
in their counties by at least 15 days in the northeastern United
States in 2000.17 Early detection of mosquito infection requires intensified sampling and screen large samples of mosquitoes. For example, intensive sampling in the vicinity (3.2
km) of WNV-positive dead birds in three locations in New
York City resulted in detection of levels of mosquito infection
as low as an MIR of 0.2 per 1,000.18 The high probabilities of
detection from their study were attributed to large mosquito
samples of 4,728, 6,150, and 6,342 collected in three locations,
respectively.
638
GU AND NOVAK
A typical pattern of arbovirus surveillance is to sample
mosquitoes from numerous sites over a broad geographic
area, such as a mosquito abatement district or an entire
county. This often results in small mosquito collections from
each site, which is inadequate to achieve early detection at
any reasonable levels of probability of detection for the
threshold of the infection rate (1:1,000). It may not be feasible
to expand intensified surveys to all these sites because of
resource restraints. Therefore, cost-effectiveness of various
monitor schemes and selection of potential foci for intensified
sampling should be prioritized. Instead of sampling numerous
sites, each with limited sampling effort, we suggest that for
early detection of mosquito infection agencies should focus
on sentinel sites with intensified sampling to allow timely detection of low infection rates. The sentinel sites can be environs where potential vector mosquitoes are abundant, or in
areas with a history of arbovirus activities of positive mosquito pools, dead birds, and human cases. Advantages of intensified entomologic surveillance at the sentinel sites are elevated probabilities of detection while not increasing overall
sampling efforts. For illustration purpose, we designed a hypothetical sampling survey of 10 sites in an area where the
mosquito infection rate was 1:1,000. A general sampling protocol collected mosquito samples using light traps at the ten
sites with one trap at each site. Assuming average collection
at 8 sites of low mosquito abundance are 30 individuals per
trap per night, while 150 individuals per trap per night are
captured at 2 sites of high density. Weekly sampling at all of
the 10 sites results in, on average, 540 mosquitoes. In contrast,
selection of the two sites of high mosquito abundance as the
sentinel sites and conduction of daily sampling for consecutive 5 days would collect a total of 1,500 mosquitoes with the
overall sampling effort of 10 trap-nights. Based on equation 1,
the estimated probability of detection with the intensified
sampling at sentinel sites is 0.78, which almost doubles the
probability of detection, 0.42, with the general sampling protocol.
We echo the reformulation of the views of a zero numerator as highlighted for physicians by Hanley and LippmanHand.9 For observations of zero infection in a mosquito
sample, the detection probability and/or the upper bound of
infection rate should be used as measures of confidence and
reported for major vector species in mosquito arboviral surveys. For early warning systems of WNV transmission based
on mosquito surveys, sample size is a primary determinant of
detection of viral activity in mosquito populations. Intensified
entomologic sampling at sentinel sites is a cost-effective alternative to inadequate sampling at numerous sites over
broad areas.
Received January 26, 2004. Accepted for publication May 30, 2004.
Acknowledgments: We thank Drs. Richard Lampman and Robert
Wiedenmann for comments on the manuscript. We are grateful to
three anonymous reviewers for valuable inputs and comments.
Financial support: This work was supported in part by CDC Grant
U50/CCU520518-02 (RJN) and the Department of Natural Resources Illinois Waste Tire Fund (Robert J. Novak).
Authors’ address: Weidong Gu and Robert J. Novak, Illinois Natural
History Survey, Medical Entomology Laboratory, 182 Natural Resources Building, 607 E. Peabody Drive, Champaign, IL 61820, Telephone: 217-333-1186, Fax: 217-333-2359, E-mails: [email protected]
and [email protected].
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