Modelos para eventos recorrentes na mensuração da influência da mortalidade entre abelhas em experimentos laboratoriais

Abstract

When bee experiments are conducted in laboratories, the interested features are analyzed in groups of caged bees, and typically, the mortality is evaluated considering specific periods of time. Therefore, since all the data is censored, the exact period of the interested feature is unknown. This happens because bees are insects that live in society, and in order to avoid any physiologic and behavioral changes, they should always be kept in groups. Thus, statistical techniques are required for survival analys is, consisting in a set of methods for data evaluation in which the variable is the time until the occurrence of some event of interest. The death of an individual inside the cage could affect all the other bees, leading to correlated observations. The parametric models in survival analysis are useful when the distribution until the event is supposedly known, and the best -known models are: the exponential, Weibull, lognormal and the Cox semiparametric model, with the latter being robust and flexible in several contexts, such as stratification, time dependent variables and multiple events. In the first part of this research, it was performed the analysis of experiments considering data from Trigona spinipes bees, with two routes of intoxication using the natural Neem repellent: by contact (spray) or oral (ingestion). The data from the experiment were collected at every 12 hours, having the time until the occurrence of bee death as variable and the method of how the repellent was applied as covariate. Non-parametric analysis was performed, adjusting the parametric model of Weibull and a semiparametric technique by proportional models of Cox, using the IceReg package in R. It can be stated that the repellent ingestions causes less damage to T. spinipes than the contact (or spraying) of it, especially in the first 288 hours, with the best adjustments being the semiparametric model. It was concluded that the most significant route for bee intoxication was the way that the repellent was applied; the highest mortalit y was caused by spraying. Thus, it is recommended that the product application time should differ from the foraging time of T. spinipes. In the second part of this research some variations of the Cox model were studied over time for recurrent events in bio-essay data of oral toxicity in Africanized bees. Survival studies using Africanized bees almost never consider proportions of mortalities within experimental units. This is relevant due to the hygienic behavior of this species. The death of each bee created an event of interest and its time interval was recorded. The classic Cox models and their adaptations for recurrent events denominated AG, LWA, GT- UR, PWP-CP, PWP-GT and TT-R were considered. In order to select the model that best fits the data, it was used: the Wald test, the verisimilitude ratio, Logrank, and the AIC information criteria. Moreover, for the basic risk analysis for the use of the Cox regression model, techniques of graphical analysis of accumulated risk - Schoenfeld Residual, Martingale Residual and Deviance Residual - were used. The stratified models, which consider the dependence of the proportion of mortality on Africanized Bees inside the cage, were higher than those that were not stratified, being the The PWP-CP model, with a Counting Process type interval, the best fit.