| dc.description.abstract | This dissertation extends statistical methods in two distinct directions. The first concerns the automation of intravenous drug delivery during anesthesia through "closed-loop" systems. Systems are termed closed-loop when a response signal (i.e., a measurement of a patient’s depth of hypnosis) is fed directly back to the mechanism that controls the input delivery (i.e., the drug infusion rate), thereby "closing" the feedback loop. Implementation of closed-loop control, however, is confounded by variability in how patients process and respond to anesthetics. We introduce a framework for optimizing closed-loop control of anesthetic delivery within a population during the induction of anesthesia according to a user- specified criterion. This criterion could reflect any number of quantities of clinical interest, such as of over- and under-shoot of the target depth of hypnosis, time to stably reach the target, or the amount of drug delivered. We propose the specification of a "reference function" to be used by the closed-loop controller. This reference function determines the value of the response variable that is targeted by the controller as a varying function over time and, in doing so, effectively implements a protocol for determining infusion rates. By optimizing the parameters of the reference function according to a population-level criterion, we can identify a protocol that is optimal for the criterion within the population of patients. We additionally introduce the software package “tci” in the R programming language that flexibly implements target-controlled infusion algorithms for open- and closed-loop control with compartmental PK and PK-PD models. These algorithms allow the user to target specific drug concentrations for a patient, rather than specifying infusion rates directly. The second direction of the dissertation is to extend a promising, but little-used, methodology called “data squashing.” The goal of squashing is to summarize a large data set with a much smaller, “squashed” version that contains synthetic pseudo-data on the same variables and a corresponding set of frequency weights. The squashed data set is constructed to preserve the statistical information of the original data set, so a model fit to both squashed and full data sets will have highly similar results. One limitation of the original squashing method is that it did not provide a mechanism for accommodating missing values. We propose two different methods to handling missing data within data squashing, which we term "propagation squashing" or "p-squashing", and "expectation squashing" or "e-squashing." In the first, missingness from the original data set is propagated on to the p-squashed data set while the information required for maximum likelihood-based missing data techniques is preserved in the p-squashed data set. In e-squashing the squashed data set is constructed to preserve the expectation of an arbitrary log-likelihood. | |
