Correcting for serial dependence in studies of respiratory dynamics

Understanding the physiological impact of drug treatments on patients is important in assessing their performance and determining possible side effects. While this effect might be best determined in individual subjects, conventional methods assess treatment performance by averaging a physiological measure of interest before and after drug administration for n subjects. Summarizing large numbers of time-series observations in two means for each subject in this way results in significant information loss. Treatment effect can instead be analyzed in individual subjects. Because serial dependence of observations from the same animal must then be considered, methods that assume independence of observations, such as the t-test and z-test, cannot be used. We address this issue in the case of respiratory data collected from anesthetized rats that were injected with a dopamine agonist. In order to accurately assess treatment effect in time-series data, we begin by formulating a method of conditional likelihood maximization to estimate the parameters of a first-order autoregressive (AR) process. We show that treatment effect of a dopamine agonist can be determined while incorporating serial effect into the analysis. In addition, while maximum likelihood estimators of a large sample with independent observations may converge to an asymptotically normal distribution, this result of large sample theory may not hold when observations are serially dependent. In this case, a parametric bootstrap comparison can be used to approximate an appropriate measure of uncertainty.