Hamdan et al., 2024: Item performance of the scale for the assessment and rating of ataxia in rare and ultra-rare genetic ataxia

Course exam presentation – Generalized Linear Models

Ataxia

Rare neurodegenerative disease
Impairs coordination and movement

Principal clinical rating scale:
Scale for the Assessment and Rating of Ataxia (SARA)

SARA

Item	Possible responses
1) Gait	0 - 8
2) Stance	0 - 6
3) Sitting	0 - 4
4) Speech disturbance	0 - 6
5) Finger chase	0 - 4
6) Nose-finger test	0 - 4
7) Fast alternating hand movements	0 - 4
8) Heel-shin slide	0 - 4
Total	0 - 40

Research question

Is SARA, and its individual items,

A good performing clinical outcome assessment?
Applicable across rare and ultra-rare ataxia subpopulations?

Graded response model (IRT)

\[ P\left( Y_{ij} \ge k \mid \Psi_i \right) = \mathrm{logit}^{-1}\left( a_j \left( \Psi_i - b_{jk} \right) \right) \]

\(i\)	Number of participant
\(j\)	Number of SARA item
\(k\)	A score for an item
\(Y_{ij}\)	Observed score for participant \(i\) and item \(j\)
\(\Psi_i\)	Latent disease severity for participant \(i\), with \(\Psi_i \sim \mathcal{N}\left( 0, 1 \right)\) assumed
\(a_j\)	Discrimination parameter of item \(j\), to be estimated
\(b_{jk}\)	"Difficulty" parameter of score \(k\) of item \(j\), to be estimated

\[ P\left( Y_{ij} = k \mid \Psi_i \right) = P\left( Y_{ij} \ge k \right) - P\left( Y_{ij} \ge k + 1 \right) \]

Graded response model (IRT)

\[ P\left( Y_{ij} \ge k \mid \Psi_i \right) = \mathrm{logit}^{-1}\left( a_j \left( \Psi_i - b_{jk} \right) \right) \]

Proportional Odds Model , with \(q = 1\) and reparameterized:

\[ \mathrm{logit}\left( P\left( X_i \le s \mid \mathbf{y} \right) \right) = \alpha_{i0(s)} - \sum\limits_{j=1}^q \alpha_{ij} y_j\]

Limitations

\(\Psi_i \sim \mathcal{N}\left( 0, 1 \right)\) warranted?

Authors:

The same has been done for other clinical rating scales
No evidence of misspecification in model fit assessments

Data was longitudinal, thus not i.i.d.

Authors published longitudinal IRT model later in 2024

Assumption that all response categories for an item share the same slope is often violated in clinical scales

Not discussed in article, supplements, or follow-up article

Thank you!

Full reference:
Hamdan A, Hooker AC, Chen X, et al.
Item performance of the scale for the assessment and rating of ataxia in rare and ultra-rare genetic ataxias.
CPT Pharmacometrics Syst Pharmacol. 2024;13(8):1327-1340.
doi:10.1002/psp4.13162