Integer-valued antedependence models for longitudinal count data

Many scientific studies involve counting things repeatedly over time for the same individual— for example, the number of seizures a patient has each week, the number of times an animal presses a lever in successive intervals, or the number of pain-relief requests recorded across the hours following a medical procedure. Such repeated count measurements typically depend on one another in ways that change as time passes, and standard statistical methods often struggle to capture this evolving pattern of dependence in a faithful and interpretable way.

This dissertation develops a new family of statistical models, called integer-valued antedependence (INAD) models, for analyzing repeated count data of this kind. The central idea is to describe how each new count is generated from a portion of the previous counts together with a fresh random contribution, while allowing both the strength of the connection to the past and the distribution of the new contribution to change over time. This perspective preserves the whole-number nature of the data, accommodates situations in which counts vary more widely than a simple Poisson model would predict, and yields straightforward interpretations of how dependence evolves across time.

The dissertation derives the mathematical properties of these models, develops methods for estimating their parameters and testing scientifically meaningful hypotheses, and studies their behavior in simulation experiments. The methodology is then applied to a classical dataset from a study of morphine bolus analgesia, where it provides a more parsimonious and better-supported description of the data than several widely used alternatives. To make the methods accessible to other researchers, the dissertation also describes an accompanying R software package, antedep, that implements estimation, testing, and diagnostics for the proposed models.