New models for handling correlated underdispersed Likert pain scores
Elodie Plan and Mats O. Karlsson
Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University, Uppsala, Sweden.
Objectives: Pain intensity is principally assessed using rating scales comprising eleven categories, like the Likert scale. Population models available to analyse such data don’t usually treat scores as ordinal but as continuous [1].
Frequent observations of pain are generally dependent within each other and present low variability. The inclusion of features handling correlation and underdispersion into non-linear mixed-effects scores models remains to be done.
The aim of this study was to develop a model adapted to fit 11-point data.
Methods: Likert pain records were collected on a daily basis over 18 weeks from 231 individuals. These patients suffering from painful distal diabetic neuropathy were under placebo treatment. An exponential placebo model was used to describe the mean score time course.
A truncated generalized Poisson model [2], with four levels of probabilities inflated by Markov elements, was implemented in NONMEM VI. It was compared to a continuous model including a logistic transformation of the individual predictions and data, and an auto-correlation factor for the residual error model.
Capacities for handling underdispersion were assessed by computing the variability of the observations within individuals. Evaluation of the ability of the models to handle serial correlation was done through the number of transitions between scores.
Results: The placebo effect was estimated to be of 22 % of the baseline with a half-life of 30 days with the count model. Very similar estimates were obtained with the continuous model. The correlation half-life was 0.75 days in the continuous model. In the count model the probability of an observation to be identical to the previous one was a function over the scores with a maximum of 76 %.
Diagnostics plots, with respect to time course, distribution of the scores and transitions, displayed concordance between observed and simulated data for both the continuous and the count models.
Conclusions: Two models have been developed that adequately describe observed Likert pain scores. Novel features to handle underdispersion and serial correlation were proposed.
References:
[1] Anderson BJ, Holford NH, Woollard GA, Kanagasundaram S, Mahadevan M: Perioperative pharmacodynamics of acetaminophen analgesia in children. Anesthesiology 1999, 90(2):411-421
[2] Yang Z, Hardin JW, Addy CL, Vuong QH: Testing approaches for overdispersion in poisson regression versus the generalized poisson model. Biometrical journal 2007, 49(4):565-584.
