Use of a mixture statistical model in studying malaria vectors density

Abstract

Vector control is a major step in the process of malaria control and elimination. This requires vector counts and appropriate statistical analyses of these counts. However, vector counts are often overdispersed. A non-parametric mixture of Poisson model (NPMP) is proposed to allow for overdispersion and better describe vector distribution. Mosquito collections using the Human Landing Catches as well as collection of environmental and climatic data were carried out from January to December 2009 in 28 villages in Southern Benin. A NPMP regression model with "village" as random effect is used to test statistical correlations between malaria vectors density and environmental and climatic factors. Furthermore, the villages were ranked using the latent classes derived from the NPMP model. Based on this classification of the villages, the impacts of four vector control strategies implemented in the villages were compared. Vector counts were highly variable and overdispersed with important proportion of zeros (75%). The NPMP model had a good aptitude to predict the observed values and showed that: i) proximity to freshwater body, market gardening, and high levels of rain were associated with high vector density; ii) water conveyance, cattle breeding, vegetation index were associated with low vector density. The 28 villages could then be ranked according to the mean vector number as estimated by the random part of the model after adjustment on all covariates. The NPMP model made it possible to describe the distribution of the vector across the study area. The villages were ranked according to the mean vector density after taking into account the most important covariates. This study demonstrates the necessity and possibility of adapting methods of vector counting and sampling to each setting.

Figure 1. Means and standard deviations of the number of mosquitoes collected per site and per night at each of the 28 villages of the study.

Figure 2. Mean-variance diagrams of the number of malaria vectors collected per village (Panel A), per mission (Panel B), and per village-mission (Panel C).

Panel D shows a bar diagram of the distribution of mosquito counts at each collection site (the scale of the X-axis was limited to 14). On panels A, B and C: the dotted lines represent a linear link between the means and the variance ( with  = 7.4, 6.48 and 5.9 respectively); the curves represent a quadratic link between mean and variance ( with  = 4.4, 8.9 and 1.1 respectively).

Figure 3. Observed and expected proportions of mosquito counts according to Poisson, ZIP, NPMP and NB distributions.

Figure 4. Changes in the values of the Bayesian Information Criterion (BIC), the entropy, and the Integrated Complete-data Likelihood (ICL-BIC) according to the number of latent classes.