Statistical methods for optimal design and information preservation in pharmacokinetics and data squashing with missing values

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.