Gustaf J. Wellhagen (1), Sebastian Ueckert (1), Maria C. Kjellsson (1), Mats O. Karlsson (1)
(1) Pharmacometrics Research Group, Department of Pharmacy, Uppsala University, Sweden
Objectives: Composite scales are commonly used in many disease areas, such as CNS disorders. Often these scales were developed for diagnosis, but in lack of reliable biomarkers they also function as clinical endpoints to evaluate disease progression and treatment efficacy. Such scales consist of many questions/items, that are summarised to a total score (TS) through an algorithm, where the TS is discrete and bounded. One example is the MDS-UPDRS scale for Parkinson’s disease [1].
Item level data contains all the information and therefore adequately designed Item Response Theory (IRT) models are the best way to handle composite scales. These include item characteristic curves for each item and handle correlation between items through a latent variable. However, IRT models may be cumbersome to develop, include many parameters and take long time to estimate. Also, they require that data on the item level are available.
Alternatively, the TS can be modelled; several approaches are used such as continuous variable (CV), bounded integer (BI) [2], beta regression [3] or coarsened grid models [4]. None of these methods use the information from item level data. However, if there exists an IRT model for the same composite scale as the TS data it might be used to inform TS-analyses. The aim of this work was to investigate if disease progression and variability from an IRT model could improve TS-analyses.
Methods: A published IRT model [5] for MDS-UPDRS was used to map the mean and standard deviation (SD) of TS to the latent variable (Ψ), through exact link functions. Mean and SD of TS were also mapped to Z score; the latent variable of the BI model. Empirical Chebyshev polynomials of high order (≥ 12), with Ψ as independent variable, were used to approximate the relation between Ψ and TS or Z, called E(Y|Ψ), and between Ψ and SD of TS or Z, called SD(Y|Ψ).
The approach of IRT-informed TS-analysis was investigated on simulated data and a real data set. Simulations were performed (n=1000), with IRT baseline at 0.654 and 1) no disease progression or 2) a linear disease progression of 0.449 year-1. These data sets were analysed with CV and BI models both with and without SD(Y|Ψ), and E(Y|Ψ) when there was a disease progression. The real data set was the same as in the published IRT model [5], from the Parkinson’s Progression Markers Initiative (PPMI) [6]. Both CV and BI models were used to fit the data where both E(Y|Ψ) and SD(Y|Ψ) were implemented. Model fit was assessed using objective function value (OFV).
The Fisher information for different models was computed as a function of the latent variable to illustrate which part of data were considered most informative.
Results: Polynomials of high order (12-23) were sufficient to adequately map Ψ to TS and Z scales. As Ψ increased from low to high values, the TS scores increased with an S-shape, whereas Z scores increased linearly across the relevant disease severity range. The SD in TS showed strong deviation from homoscedasticity, with decreasing SD towards the extremes and symmetry around the score mid-point. The SD for the Z score also showed symmetry but with the lowest SD at the mid-point and higher SD towards the extremes. When analysing the TS data simulated from an IRT model, predictably, these derived SD(Y|Ψ) functions offered an optimal description of the residual error, with no improvement from estimating or changing the functions.
When applied to real data, a linear disease progression was superior on the Ψ scale over the TS scale for the CV model (?OFV 74). However, for the BI model, there was no difference in fit between linear disease progression on Ψ scale or Z scale (?OFV -5). The same trends were seen in the simulated data. Also, the SD(Y|Ψ) required a scaling factor and inter-individual variability to achieve better fit than a homoscedastic SD, since real data has additional sources of variability.
The link functions allow a TS-analysis to inform the latent variable of an IRT model. This means that different model types (item-level or total score) can be compared in terms of parameter precision, but also information. The Fisher information of IRT-informed models was similar to, but slightly lower than, an IRT model.
Conclusions: Disease progression and residual unexplained variability in a TS-analysis can be improved by using IRT-informed modelling. The approach requires no additional parameters to be added. Also, different model types can be directly compared.
References:
[1] Goetz CG, Fahn S, Martinez-Martin P, Poewe W, Sampaio C, Stebbins GT, et al. Movement Disorder Society-sponsored revision of the Unified Parkinson’s Disease Rating Scale (MDS-UPDRS): process, format, and clinimetric testing plan. Mov Disord. 2007.
[2] Wellhagen GJ, Kjellsson MC, Karlsson MO. A Bounded Integer Model for Rating
and Composite Scale Data. AAPS J. 2019.
[3] Conrado DJ, Denney WS, Chen D, Ito K. An updated Alzheimer’s disease
progression model: incorporating non-linearity, beta regression, and a
third-level random effect in NONMEM. J Pharmacokinet Pharmacodyn. 2014.
[4] Lesaffre E, Rizopoulos D, Tsonaka R. The logistic transform for bounded
outcome scores. Biostatistics. 2007.
[5] Buatois S, Retout S, Frey N, Ueckert S. Item response theory as an efficient tool to describe a heterogeneous clinical rating scale in de novo idiopathic Parkinson’s disease patients. Pharm Res. 2017.
[6] http://www.ppmi-info.org/data
Reference: PAGE 29 (2021) Abstr 9831 [www.page-meeting.org/?abstract=9831]
Poster: Methodology - New Modelling Approaches