Eleven ordered categories data: which modelling options?
Elodie Plan, Yang Sun, Mats O. Karlsson
Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University, Uppsala, Sweden.
Objectives:
Ordered categorical responses are common pharmacodynamic outcomes; models dealing with these data using the non-linear mixed-effects approach have been successfully developed. However when the number of categories reaches 11, like in the case of the visual analogue scale (VAS), the number of needed parameters become high; therefore there might be other types of models to consider. Treating such data as continuous seems to be done frequently and needs to be evaluated, but treating them as counts is an option considering the flexibility of the probability distribution models.
The aim of this study was to explore different modelling approaches candidates for fitting simulated discrete VAS data.
Methods:
This methodological study consisted of stochastic simulations followed by re-estimations performed in NONMEM VI FOCE or Laplace. A first set of 100 simulations was performed with an ordinal model including a baseline; parameters values were derived from a real case study on 231 patients recording 100 observations each on average [1]. A second set of 100 ordinal simulations included 3 dose levels in parallel with the placebo arm; the drug effect was linear with a slope of 0.045 (30% interindividual variability).
Estimations of the simulated data sets were performed with an ordinal, a continuous (with logit transformation of predictions and data), a truncated Poisson and a truncated generalized Poisson model [2]. Performances were evaluated by comparison of re-simulated score distributions with the true distributions at different doses.
Results:
The ordinal model was composed of 11 parameters for the baseline profile, whereas all the other models had 2 or 3. The continuous model required a discretization of the simulated values.
In simulations from the four models the truncated Poisson model was clearly worst. The continuous model showed some discrepancy compared to the true values at the highest dose whereas the generalized Poisson model showed good agreement at all doses. The ordered categorical model showed good estimation properties and simulations mimicked closely the true score distribution at different dose levels.
Conclusions: VAS data can accurately be analysed with an ordinal model, at least with rich data sets and, as here, a lack of Markovian patterns. A logit-transformed model for continuous data performed reasonably and a generalized truncated Poisson model well. These latter models may be alternatives for sparser data sets and in the presence of serial correlations.
References:
[1] Plan EL, Karlsson MO: New models for handling correlated underdispersed Likert pain scores. PAGE. 2009.
[2] Plan EL, Maloney A, Trocóniz IF, Karlsson MO: Maximum likelihood estimation methods: performances in count response models population parameters. PAGE. 2008.
