%0 Journal Article
%T Regression Modeling of Individual-Patient Correlated Discrete Outcomes with Applications to Cancer Pain Ratings
%A George J. Knafl
%A Salimah H. Meghani
%J Open Journal of Statistics
%P 456-485
%@ 2161-7198
%D 2022
%I Scientific Research Publishing
%R 10.4236/ojs.2022.124029
%X <strong>Purpose:</strong><span style=\"font-family:&quot;\"><span style=\"font-family:Verdana;\"> To formulate and demonstrate methods for regression modeling of pr</span><span style=\"font-family:Verdana;\">obabilities and dispersions for individual-patient
longitudinal outcom</span><span style=\"font-family:Verdana;\">es taking on discrete numeric values. </span><b><span style=\"font-family:Verdana;\">Methods:</span></b><span style=\"font-family:Verdana;\"> Three alternatives for modeling of outcome probabilities are considered.
Multinomial probabilities are based on different intercepts and slopes for
probabilities of different outcome values. Ordinal probabilities are based on
different intercepts and the same slope for probabilities of different outcome
values. Censored Poisson probabilities are based on the same intercept and
slope for probabilities of different outcome values. Parameters are estimated
with extended linear mixed modeling maximizing a likelihood-like function based
on the multivariate normal density that accounts for within-patient
correlation. Formulas are provided for gradient vectors and Hessian matrices
for estimating model parameters. The likelihood-like function is also used to
compute cross-validation scores for alternative models and to control an
adaptive modeling process for identifying possibly nonlinear functional
relationships in predictors for probabilities and dispersions. Example analyses
are provided of daily pain ratings for a cancer patient over a period of 97
days. </span><b><span style=\"font-family:Verdana;\">Results: </span></b><span style=\"font-family:Verdana;\">The censored Poisson approach is preferable for modeling
these data, and presumably other data sets of this kind, because it generates a
competitive model with fewer parameters in less time than the other two
approaches. The generated probabilities for this m</span><span style=\"font-family:Verdana;\">odel are distinctly nonlinear in time while the dispersions are
distinctly</span><span style=\"font-family:Verdana;\"> nonconstant over time, demonstrating the need for adaptive
modeling of such data. The analyses also address the dependence of these daily
pain ratings on ti</span><span style=\"font-family:Verdana;\">me and the daily numbers
of pain flares. Probabilities and dispersio</span><span style=\"font-family:Verdana;\">ns change differently over
time for different numbers of pain flares. </span><b><span style=\"font-family:Verdana;\">Conclusions: </span></b><span style=\"font-family:Verdana;\">Adaptive
modeling of daily pain ratings for
%K Cancer Pain Ratings
%K Discrete Regression
%K Extended Linear Mixed Modeling
%K Likelihood-Like Cross-Validation
%K Nonlinear Moderation
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=119122