Gustaf J. Wellhagen (1), Maria C. Kjellsson (1), Mats O. Karlsson (1)
1) Pharmacometrics Research Group, Department of Pharmaceutical Biosciences, Uppsala University, Sweden
Introduction/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 (PSI), by incremental step simulations of the whole disease range for motor subscale, i.e. PSI ranged from -2 to 8 by steps of 0.2. Mean and SD of TS were also mapped to Z score; the latent variable of the BI model. Empirical polynomials of high order (≥ 6), with PSI as independent variable, were used to approximate the relation between PSI and TS or Z, called DPIRT and between SD and TS or Z, called SDIRT.
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 SDIRT, and DPIRT 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 DPIRT and SDIRT were implemented. Improved model fit was assessed using objective function value (OFV).
Results: Sixth- or eighth-grade polynomials were sufficient to adequately map PSI to TS and Z scales. As PSI 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 show 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 functions offered an optimal description of the residual error, with no improvement from estimating or changing the functions.
The mapping functions allow a TS-analysis to inform the latent variable of an IRT model. This allows the information content of a TS observation to be compared to a set of individual item observations. Such a comparison for simulated data from the IRT model and ideal parameter values for both IRT and TS models indicated that on average 20% more observations were needed to achieve the same individual latent variable precision for a TS observation compared to a set of items.
When applied to real data, a linear disease progression was superior on the PSI scale over the TS scale for the CV model (∆OFV 108). However, for the BI model, there was no difference in fit between linear disease progression on PSI scale or Z scale (∆OFV 1). The same trends were seen in the simulated data.
Conclusions: Disease progression and residual unexplained variability in a TS-analysis can be improved by using IRT-informed modelling. The BI model appears to map closer to the IRT model than does the CV model.
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 () Abstr 9554 [www.page-meeting.org/?abstract=9554]
Poster: Oral: Methodology - New Modelling Approaches