Submitted to: Estadistica
Publication Type: Peer reviewed journal
Publication Acceptance Date: 9/14/2012
Publication Date: 3/1/2013
Citation: Deroche, C., Villa, J.D., Escobar, L.A. 2013. Statistical methods to quantify the effect of mite parasitism on the probability of death in honey bee colonies. Estadistica. 63(181):95-112. Interpretive Summary: The introduced mite, Varroa destructor, can kill honey bee colonies when parasite populations are allowed to develop. Most beekeepers in the United States treat their colonies preventively, in many cases multiple times per year, to reduce the risk of colony losses. This study followed the survival of colonies left untreated and measured the concentration of mites on adult bees at different times of the season. Three statistical methods were compared to measure how the level of infestation influenced the probability of colony death. The three methods produced very similar results. There is a very clear relationship between the level of mite infestation and the probability of colony death, regardless of time of year. The analyses also suggest that the simplest of the statistical methods can be applied to other data sets collected under different environmental or management conditions. Results from analyses like these can guide beekeepers to time the treatment of their colonies for more rational and sustainable use of treatments against mites.
Technical Abstract: Varroa destructor is a mite parasite of European honey bees, Apis mellifera, that weakens the population, can lead to the death of an entire honey bee colony, and is believed to be the parasite with the most economic impact on beekeeping. The purpose of this study was to estimate the probability of death for a honey bee colony as a function of the concentration of mites in the colony and to explore the influence of other variables (such as genetic origin of the colony and season in the year) on the relationship. Two approaches were considered to account for the lack of failures in colonies from two genetic origins which led to divergence of the logistic likelihood when considering the variable “genetic origin” in the model. In the first approach, we used Firth’s penalized likelihood method which has the double effect of correcting the bias of maximum likelihood estimates and providing estimability of the parameters. The second approach consists of forcing a failure for the largest mite concentration in the two genetic origins without failures. This approach, in general, would tend to provide slightly larger colony-death probability estimates. Because there were multiple observations on the same colony over a period of time, the data are longitudinal and the observations may not be independent. For this reason, we used a Generalized Estimating Equations (GEE) approach, which considers the dependency among the observations, and compared it with the simple logistic regression that ignores the dependency. The GEE analysis showed increasing odds of death with increasing concentration of mites and no influence of season or genetic origin on the relationship. The analysis using simple logistic regression is very similar to the more complex GEE analysis, which indicates that the longitudinal observations can be treated as statistically independent.