Modelling the ethanol-induced sleeping time in mice through a zero inflated model

Abstract

In the analysis of data in statistics, it is imperative to select most suitable models. Wrong choice of model selection leads to bias parameter estimates and standard errors. In the ethanol anesthesia data set used in this thesis, we observe more than expected zero counts, usually termed zero-inflation. Traditional application of Poisson and negative binomial distributions for model fitting may not be adequate due to the presence of excess zeros. This zero-inflation comes from two sources; a proportion of mice with an actual zero minute sleeping time and another proportion of mice that had their observations left censored with a fixed detection limit of one minute. The purpose of this thesis is to illustrate how zero-inflated poisson model is used to model the ethanol anesthesia data set. Such a model accounts for the excess zero in the data. With the zero-inflated model we could calculate the probability of nonsleeping mice in the population and further observe the distribution of sleeping mice. After fitting the ZIP model and using maximum log likelihood estimating functions, we found out that the probability of observing a non-sleeping mouse is 1.03%, which is extremely low. We could further calculate the probabilities of observing non-sleeping mice under specific covariates. For example we could calculate the probability of observing a female albino non-sleeping mice. We further checked for the significant effects of our covariates on our response variable. Based on our ZIP model, environmental factors like gender, albinism, birthday, and trial day had a significant influence on the sleeping time after the first trial. The variable, trial day 1 however had a boarder line significant influence (p–value =0.0462) on the sleeping time. The only genetic factor with a significant effect was the chromosome variable.