Determination of sample sizes for the estimation of Onchocerca volvulus (Filarioidea: Onchocercidae) infection rates in biting populations of Simulium ochraceum s.l. (Diptera: Simuliidae) and its application to ivermectin control programs

Monthly samples of biting Simulium ochraceum s.l. Walker were collected before and after ivermectin treatment in southern Mexico and analyzed for Onchocerca volvulus Leuckart infection rates, infection intensity, and the characteristics of larval distribution among parous flies. The variance over mean ratio (VMR) indicated that in all cases this distribution departed from Poisson and was strongly aggregated (VMR > 1). The negative binomial was found to be an adequate model with a small value of the aggregation parameter k, but the degree of larval overdispersion increased as the mean larval load decreased, invalidating the use of a common kc value. A linear relationship between k and the mean (micro) was established, k (micro) = k1 micro, which permitted exploration of the relationship between the observed proportion of infected flies, p, and the estimated mean larval burden per fly, m (all larval stages in parous flies). This would allow mean numbers of larvae per parous fly to be predicted from presence-absence data (e.g., from infection rates provided by polymerase chain reaction methods applied to pools of flies), assuming that k1 is a known parameter. Given that both p and m are naturally low in S. ochraceum, their relationship was practically linear within the range of observed values. Predictions were tested with the Mexican data from which the clumping parameter was estimated as well as for Guatemalan data for which this information was not available. Results showed a highly satisfactory degree of agreement between predictions and observations. The sample sizes required to estimate mean larval loads from prevalence data for fixed levels of precision (defined as the ratio between SE[m] and m) were calculated for realistic S. ochraceum infection rates (those found in published pre- and postcontrol field surveys as well as in this work). For the special case in which the relationship between k and the mean is linear and goes through the origin, k(micro) = k1 micro, the number of flies to be examined for O. vulvulus infections does not explicitly depend on the aggregation parameter, but rather on the unknown proportion of infected flies. Practical recommendations for the calculation of sample sizes are discussed. For infection levels <0.2%, a minimum number between 6,000 and 13,000 parous flies would have to be examined to estimate the mean larval load with a precision between 0.20 and 0.30. The linearity between onchocercal infection rate and infection intensity in the fly population indicates that relationships between the former and onchocerciasis patterns in the human population should be further explored for the purposes of monitoring the impact of ivermectin control programs through entomological evaluations.