TITLE:
Modeling Individual Patient Count/Rate Data over Time with Applications to Cancer Pain Flares and Cancer Pain Medication Usage
AUTHORS:
George J. Knafl, Salimah H. Meghani
KEYWORDS:
Adaptive Regression, Extended Linear Mixed Modeling, Generalized Estimating Equations, Likelihood-Like Cross-Validation, Poisson Regression
JOURNAL NAME:
Open Journal of Statistics,
Vol.11 No.5,
September
30,
2021
ABSTRACT: The
purpose of this article is to investigate approaches for modeling individual
patient count/rate data over time accounting for temporal correlation and non-constant dispersions while
requiring reasonable amounts of time to search over alternative models for
those data. This research addresses formulations for two approaches for
extending generalized estimating equations (GEE) modeling. These approaches use
a likelihood-like function based on the multivariate normal density. The first
approach augments standard GEE equations to include equations for estimation of
dispersion parameters. The second approach is based on estimating equations
determined by partial derivatives of the likelihood-like function with respect
to all model parameters and so extends linear mixed modeling. Three correlation
structures are considered including independent, exchangeable, and spatial
autoregressive of order 1 correlations. The likelihood-like function is used to
formulate a likelihood-like cross-validation (LCV) score for use in evaluating
models. Example analyses are presented using these two modeling approaches
applied to three data sets of counts/rates over time for individual cancer
patients including pain flares per day, as needed pain medications taken per
day, and around the clock pain medications taken per day per dose. Means and
dispersions are modeled as possibly nonlinear functions of time using adaptive
regression modeling methods to search through alternative models compared using
LCV scores. The results of these analyses demonstrate that extended linear
mixed modeling is preferable for modeling individual patient count/rate data
over time, because
in example analyses, it
either generates better LCV scores or more parsimonious models and requires
substantially less time.