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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 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
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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.
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To have high probabilities of detection, large numbers of mosquitoes are required when mosquito infection rates are 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
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Figure 3 depicts the upper bounds of the 80% and 95% confidence intervals of infection rates compatible with zero-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.
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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.
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 Lippman-Hand.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: wgu{at}inhs.uiuc.edu and rjnovak{at}staff.uiuc.edu.
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