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We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-time linear state space models and equidistantly observed multivariate Lévy-driven continuous-time autoregressive moving average (MCARMA) processes. In the discrete-time setting, we prove strong consistency and asymptotic normality of the QML estimator under standard moment assumptions and a strong-mixing condition on the output process of the state space model. In the second part of the paper, we investigate probabilistic and analytical properties of equidistantly sampled continuous-time state space models and apply our results from the discrete-time setting to derive the asymptotic properties of the QML estimator of discretely recorded MCARMA processes. Under natural identifiability conditions, the estimators are again consistent and asymptotically normally distributed for any sampling frequency. We also demonstrate the practical applicability of our method through a simulation study and a data example from econometrics.AMS 2000 subject classifications: Primary 62F10, 62F12, 62M09; secondary 60G51, 60G10. Keywords: asymptotic normality, linear state space model, multivariate CARMA process, quasi maximum likelihood estimation, strong consistency, strong mixing.For the present purpose it is enough to know that a Lévy process L has finite kth absolute moments, k > 0, that is E L(t) k < ∞, if and only if x 1 x k ν L (dx) < ∞ (Sato, 1999, Corollary 25.8), and that the covariance matrix Σ L of L(1), if it exists, is given by Σ G + x 1 xx T ν L (dx) Sato (1999, Example 25.11).Assumption L1. The Lévy process L has mean zero and finite second moments, i. e. γ L + x 1 xν L (dx) is zero, and the integral x 1 x 2 ν L (dx) is finite.

Cerebral small vessel disease (CSVD) is a widespread condition associated to stroke, dementia and depression. To shed light on its opaque pathophysiology, we conducted a neuroimaging study aiming to assess the location of CSVD-induced damage in the human brain network. Structural connectomes of 930 subjects of the Hamburg City Health Study were reconstructed from diffusion weighted imaging. The connectome edges were partitioned into groups according to specific schemes: (1) connection to grey matter regions, (2) course and length of underlying streamlines. Peak-width of skeletonised mean diffusivity (PSMD) - a surrogate marker for CSVD - was related to each edge group’s connectivity in a linear regression analysis allowing localisation of CSVD-induced effects. PSMD was associated with statistically significant decreases in connectivity of most investigated edge groups except those involved in connecting limbic, insular, temporal or cerebellar regions. Connectivity of interhemispheric and long intrahemispheric edges as well as edges connecting subcortical and frontal brain regions decreased most severely with increasing PSMD. In conclusion, MRI findings of CSVD are associated with widespread impairment of structural brain network connectivity, which supports the understanding of CSVD as a global brain disease. The pattern of regional preference might provide a link to clinical phenotypes of CSVD.

Background and Purpose— About 50% to 80% of stroke survivors present with somatosensory deficits. Somatosensory deficits because of an ischemic stroke are determined by the infarct location. However, a detailed understanding of the long-term effect of lesions on somatosensory performance is lacking. Methods— This prospective observational study enrolled 101 ischemic stroke patients. For voxel-based lesion-symptom mapping, magnetic resonance imaging fluid-attenuated inversion recovery imaging infarct lesions were segmented within 5 days after stroke. Standardized tests such as the National Institutes of Health Stroke Scale and the Rivermead Assessment of Somatosensory Performance were performed during acute stage, after 3 and 12 months. This included bilateral testing for multiple tactile and proprioceptive somatosensory modalities (pressure, light touch, sharp-dull discrimination, temperature discrimination, sensory extinction, 2-point discrimination, and joint position and movement sense). We further study the association of acute somatosensory deficit with functional outcome 12 months after stroke assessed by the modified Rankin Scale using univariate and multiple linear regression analysis also including acute motor deficit assessed by the arm research action test. Results— Sixty patients (59.4%) showed impairment in at least one somatosensory modality. Light touch was most frequently affected (38.7%), whereas temperature was least frequently affected (21.8%). After 3 months, significant recovery was observed in all somatosensory modalities, with only minor additional improvements after 12 months. Voxel-based lesion-symptom mapping revealed significant associations of lesions in the primary and secondary somatosensory and insular cortex with somatosensory deficits. Acute somatosensory deficit was associated with functional outcome at 12 months. However, including the acute motor deficit, somatosensory deficit was no longer an independent predictor of functional outcome. Conclusions— Our study confirms that somatosensory deficits are frequent in acute ischemic stroke but largely recover over time. Infarct lesions in the primary and secondary somatosensory cortex and insula show a robust association with somatosensory impairment. Long-term disability is influenced by somatosensory deficits but driven by motor symptoms.

Purpose The aim of this study was to analyze sex differences in outcome after thrombectomy for acute ischemic stroke in clinical practice in a large prospective multicenter registry. Methods Data of consecutive stroke patients treated with thrombectomy (June 2015–April 2018) derived from an industry-independent registry (German Stroke Registry–Endovascular Treatment) were prospectively analyzed. Multivariable binary logistic regression analyses were applied to determine whether sex is a predictor of functional independence outcome (defined as a modified Rankin scale [mRS] 0–2) 90 days after stroke. Results In total, 2316 patients were included in the analysis, 1170 (50.5%) were female and 1146 (49.5%) were male. Women were older (median age 78 vs. 72 years; p < 0.001) and more frequently had a prestroke functional impairment defined by mRS >1 (24.8% vs. 14.1%; p < 0.001). In unadjusted analyses, independent outcome at 90 days was less frequent in women (33.2%) than men (40.6%; p < 0.001). Likewise, mortality was higher in women than in men (30.7% vs. 26.4%; p = 0.024). In adjusted regression analyses, however, sex was not associated with outcome. Lower age, a lower baseline National Institutes of Health Stroke Scale score, a higher Alberta Stroke Program Early CT score, prestroke functional independence, successful reperfusion, and concomitant intravenous thrombolysis therapy predicted independent outcome. Conclusion Women showed a worse functional outcome after thrombectomy for acute ischemic stroke in clinical practice; however, after adjustment for crucial confounders sex was not a predictor of outcome. The difference in outcome thus appears to result from differences in confounding factors such as age and prestroke functional status.

The time course of topological reorganization that occurs in the structural connectome after an ischaemic stroke is currently not well understood. We aimed to determine the evolution of structural brain networks in stroke patients with motor deficits and relate changes in their global topology to residual symptom burden and functional impairment. In this prospective cohort study, ischaemic stroke patients with supratentorial infarcts and motor symptoms were assessed longitudinally by advanced diffusion MRI and detailed clinical testing of upper extremity motor function at four time points from the acute to the chronic stage. For each time point, structural connectomes were reconstructed, and whole-hemisphere global network topology was quantified in terms of integration and segregation parameters. Using non-linear joint mixed-effects regression modelling, network evolution was related to lesion volume and clinical outcome. Thirty patients were included for analysis. Graph-theoretical analysis demonstrated that, over time, brain networks became less integrated and more segregated with decreasing global efficiency and increasing modularity. Changes occurred in both stroke and intact hemispheres and, in the latter, were positively associated with lesion volume. Greater change in topology was associated with larger residual symptom burden and greater motor impairment 1, 3 and 12 months after stroke. After ischaemic stroke, brain networks underwent characteristic changes in both ipsi- and contralesional hemispheres. Topological network changes reflect the severity of damage to the structural network and are associated with functional outcome beyond the impact of lesion volume.

Cerebral small vessel disease is a common finding in the elderly and associated with various clinical sequelae. Previous studies suggest disturbances in the integration capabilities of structural brain networks as a mediating link between imaging and clinical presentations. To what extent cerebral small vessel disease might interfere with other measures of global network topology is not well understood. Connectomes were reconstructed via diffusion weighted imaging in a sample of 930 participants from a population based epidemiologic study. Linear models were fitted testing for an association of graph‐theoretical measures reflecting integration and segregation with both the Peak width of Skeletonized Mean Diffusivity (PSMD) and the load of white matter hyperintensities of presumed vascular origin (WMH). The latter were subdivided in periventricular and deep for an analysis of localisation‐dependent correlations of cerebral small vessel disease. The median WMH volume was 0.6 mL (1.4) and the median PSMD 2.18 mm2/s x 10−4 (0.5). The connectomes showed a median density of 0.880 (0.030), the median values for normalised global efficiency, normalised clustering coefficient, modularity Q and small‐world propensity were 0.780 (0.045), 1.182 (0.034), 0.593 (0.026) and 0.876 (0.040) respectively. An increasing burden of cerebral small vessel disease was significantly associated with a decreased integration and increased segregation and thus decreased small‐worldness of structural brain networks. Even in rather healthy subjects increased cerebral small vessel disease burden is accompanied by topological brain network disturbances. Segregation parameters and small‐worldness might as well contribute to the understanding of the known clinical sequelae of cerebral small vessel disease.

The class of multivariate Lévy-driven autoregressive moving average (MCARMA) processes, the continuous-time analogs of the classical vector ARMA processes, is shown to be equivalent to the class of continuous-time state space models. The linear innovations of the weak ARMA process arising from sampling an MCARMA process at an equidistant grid are proved to be exponentially completely regular (β-mixing) under a mild continuity assumption on the driving Lévy process. It is verified that this continuity assumption is satisfied in most practically relevant situations, including the case where the driving Lévy process has a non-singular Gaussian component, is compound Poisson with an absolutely continuous jump size distribution or has an infinite Lévy measure admitting a density around zero.