Background/Purpose: Cognitive impairment (CI) is usually operationalized on the American College of Rheumatology Neuropsychological Battery (ACR-NB) as a z-score of ≤-1.5 on ≥2 domains or z ≤-2 on ≥1 domain.

Given that this binary classification may miss participants who have CI but score just below the cut-off, we explored using continuous z-scores, instead of the binary approach of the ACR-NB, to facilitate the interpretability of the results. This framework is developed based on Hidden Markov Models (HMMs) and on existing data over time.

Methods: 301 consecutive consenting SLE patients aged 18-65 years attending a single center were assessed for CI at baseline using the ACR-NB and 187 patients completed visits at 6 and 12 months.

ACR-NB includes 19 tests and 6 cognitive domains. Age and gender matched normative data were used to obtain z-scores.

The 1^st step of our approach reduces the high-dimensional aspect of the ACR-NB tests using principal component analysis (PCA) to create a single component score which explains the most variance (1^st dimension). The 2^nd step builds a 2-state cognitive status based on a discrete-time HMM with the dimensionality reduction gained in the first step. The HMM assumes that the change of the component score over time in patients with SLE can be segmented into 2 distinct cognitive states, where each state captures if a patient is CI or not at time t, using the component score obtained at each time point. We assumed that the component score is Normal with unknown mean and variance, and the mean and variance are different between the two hidden states (CI or non-CI). Additionally, we specified that the mean of the Normal outcome depends linearly on education level; this adjustment means that the hidden states will capture the unobserved heterogeneity not explained after controlling by education level. All the statistical analysis was done from a Bayesian perspective using Stan through R which implements the Hamiltonian Markov Chain Monte Carlo method.

Results: Of 301 patients, 89.0% were women, mean age 40.9 ± 12.1 and mean disease duration 14 ± 10.1 years at study entry. Figure 1 shows the results of the PCA; at baseline, 1^st dimension separates patients into CI and non-CI and 2^nd dimension was mainly explained by measures of simple information processing or motor speed.

From the HMM analysis, the estimated mean for the CI state was -1.78 (95% Credible Interval [Crl]: -4.47, 0.91) and 1.78 (95% CrI: -0.92, 4.46) for the non-CI state. A patient will be classified as CI if their observed component score lies on the area of mu[1] (Fig. 2) and as non-CI if it lies on the area of mu[2].

We found higher education level associates with an increase mean component score (implies less CI). We also found that patients did not transition between CI and non-CI over time (Fig. 3).

Conclusion: This is the first framework which aimed to classify patients with SLE as CI or not using an unsupervised method. This approach relies on the observed z-scores from the 19 tests on the ACR-NB and not on the binary classification. We found that the probability of changing between CI and non-CI over 1 year is low.

Figure 1. Biplot at baseline. PCA where patients’ component scores are colored by ACR-NB CI binary definition (turquoise for CI and orange for non-CI). The 1st dimension separates patients into CI and non-CI at baseline. Axis x represents the first dimension (explaining 28.3% of the variance) and axis y represents the second dimension. The length of each arrow represents the strength of the relationship between the ACR-NB subtests, and the cognitive components found in our PCA. The angle between variables represents the strength of the correlation between them. The ACR-NB included the following domains: Manual motor speed and dexterity, simple attention and processing speed, visual-spatial construction, verbal fluency, learning and memory, executive function.

Figure 2. Posterior estimates from the HMM. X axis represents the distribution of the parameters of interest. Y axis represents the parameters where inference is made. The dark shaded region represents the point estimate from a frequentist point of view and the light shaded region represents the 95% uncertainty interval, i.e., with 95% of probability the estimate would lie in that region. As an example mu[1] represents the inference made on the unknown mean of the observed component score given that it comes from the CI state after adjusting for education level. The point estimate is -1.78 with 95 % CrI (-4.47, 0.91).

Figure 3. Posterior uncertainty intervals for the transition probabilities in the HMM. X axis represents the transition probability and Y axis represents the parameters where inference is made. We labeled ‘1’ as the CI state and ‘2’ as the non-CI. Therefore, over discrete time points, P11 is the probability of remaining in the CI state, P12 is the probability of moving from the CI state to non-CI state and so on (P21 and P22). The dot on the graph represents the point estimate and the line represents the 95% CrI.

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ACR Meeting Abstracts - https://acrabstracts.org/abstract/identifying-cognitive-impairment-in-patients-with-systemic-lupus-erythematosus-using-hidden-markov-models-a-bayesian-approach/