Sequences of cognitive decline in typical Alzheimer's disease and posterior cortical atrophy estimated using a novel event‐based model of disease progression

Abstract Introduction This work aims to characterize the sequence in which cognitive deficits appear in two dementia syndromes. Methods Event‐based modeling estimated fine‐grained sequences of cognitive decline in clinically‐diagnosed posterior cortical atrophy (PCA) (n=94) and typical Alzheimer's disease (tAD) (n=61) at the UCL Dementia Research Centre. Our neuropsychological battery assessed memory, vision, arithmetic, and general cognition. We adapted the event‐based model to handle highly non‐Gaussian data such as cognitive test scores where ceiling/floor effects are common. Results Experiments revealed differences and similarities in the fine‐grained ordering of cognitive decline in PCA (vision first) and tAD (memory first). Simulation experiments reveal that our new model equals or exceeds performance of the classic event‐based model, especially for highly non‐Gaussian data. Discussion Our model recovered realistic, phenotypical progression signatures that may be applied in dementia clinical trials for enrichment, and as a data‐driven composite cognitive end‐point.

without reference to a given individual's clinical status. It has been applied in both sporadic and familial AD, [8][9][10][11] Huntington's disease, 12,13 and progressive multiple sclerosis. 14 Recently, the event-based model idea has been extended to a new algorithm for finding data-driven subtypes of disease, 15 demonstrated in AD and frontotemporal dementia. These investigations, and others, 16 focused largely on neuroimaging biomarkers, made possible by the increasing availability of large datasets such as from the Alzheimer's Disease Neuroimaging Initiative and the Dominantly Inherited Alzheimer Network.
In contrast to neuroimaging, most analyses of complex cognitive datasets have relied on traditional statistical approaches rather than data-driven methods. Methods of detecting cognitive change are important both for improving disease characterization and prognosis in affected individuals, and for detecting and predicting change in individuals who are asymptomatic and at-risk (of sporadic disease) or presymptomatic (have a familial/genetic disease). 17 Optimizing methods for analyzing cognitive change is especially important in the context of clinical trials, because cognitive and functional outcomes are currently the only accepted means for proving efficacy of a drug. This is relevant to both symptomatic trials and secondary prevention trials, because neuropsychological tests may be sensitive to dementia between 10 and 17 years before diagnosis. 18 Evaluation of longitudinal change within and across cognitive domains presents a number of specific challenges. First, performance across cognitive tasks is not independent. General factors (eg, disease severity) and collateral deficits (eg, visuoperceptual problems limiting performance on a visual memory test) can influence testing across domains. Second, cognitive profiles across tasks are often described qualitatively because test properties and normative samples differ across tasks. Third, the psychometric shape of tests can differ markedly. Tests involving graded difficulty yield relatively linear score distributions among healthy control participants, whereas other tests may yield skewed, highly non-Gaussian score distributions owing to an excess of very-easy or very-difficult items. These properties influence the likelihood of clinical populations showing ceiling or floor effects at any given point in their disease progression. Fourth, practice effects mask longitudinal change, for example, test familiarity and/or reduced anxiety may conceal evidence of cognitive instability or decline. 19 We are motivated to understand disease progression in Alzheimer's and dementia, with a focus on impact for interventional trials and in the clinic. International Working Group criteria now include explicit definition of atypical forms of AD, 20,21 of which posterior cortical atrophy (PCA) is acknowledged to be one of the most common. 22,23 It is of fundamental importance to understand disease progression in both typical and atypical AD if the field is to advance. PCA is a clinicoradiological syndrome characterized by progressive decline in visual processing and other posterior cognitive functions, relatively intact memory and language in the early stages, and atrophy of posterior brain regions. 20,21 PCA is most commonly caused by AD, with greater presence of amyloid plaque and/or neurofibrillary tangles in the posterior cortices than in individuals having the more-typical, amnestic presentation. 24

Neuropsychological tests
We employed a battery of tests that are routinely used in the clinic [31][32][33][34][35] and in pharmacological 36 and non-pharmacological 37 clinical trials involving PCA. We used the same battery of neuropsychological tests on each cohort, which allows direct comparison of cognitive decline across the two dementia syndromes. The battery includes assessments of episodic and working memory, visuoperceptual and visuospatial processing, arithmetic, and general cognition. The full list of tests and the primary cognitive domain tested by each is shown in Table 2, along with abbreviations used in the results section. Descriptive statistics of scores for each test and per patient group are provided in Table S1. We found no significant age-related effects in any of the cognitive tests, which reassures us that group differences are due to disease.

Event-based model
The event-based model 7 is designed to estimate a data-driven, probabilistic sequence of biomarker "events" that represents an underlying cumulative process, using a cross-sectional set of observations.
These can be any biomarkers. In the context of neurodegenerative Graded Difficulty Arithmetic (total) GDA (tot) a For further details on many of these tests, we refer the reader to [31][32][33][34][35][36][37] diseases, an event corresponds to a group-level statistical deviation from normality/health (defined by data from controls) toward abnormality/disease (defined by data from patients), with the full sequence of events representing the cumulative effects of neurodegenerative disease progression. The ordering of events is determined probabilistically, in a data-driven manner, by pooling biomarker severity (event probability) across individuals. Conceptually, higher prevalence corresponds to an earlier position in the sequence. The event-based model estimates both the sequence and uncertainty in the sequence. Event probability is a function of the likelihood of an event having occurred Assuming independent observations and biomarkers, the likelihood of an ordered sequence S is [8] Pr where measurements x ∈ X come from i ∈ M event markers and j ∈ N individual samples, such as participants in a disease cohort.
In the absence of prior information, a uniform prior distribution over sequences is used and the characteristic orderingŜ is the sequence that maximizes the likelihood Pr(X|S) in (1)  We emphasize that events are inherently probabilistic. While we use the language of events having "occurred" or not, this is in an explicitly probabilistic sense. This is one of the event-based model's key benefits -that explicit biomarker cutpoints are not required.

Mixture modeling and our new event-based model
We now discuss how the mixture modeling is used to calculate event probabilities. with an independent and identically distributed sample {x j } drawn from a distribution with an unknown density is given bŷ

Parametric, Gaussian mixture modeling
where K is a non-negative zero-mean kernel function that integrates to unity and h is a positive smoothing factor called a bandwidth.

Cross-validation
We performed cross-validation of our event-based models by re-estimating each full model (event distributions and maximumlikelihood sequence) on 100 bootstrap samples (sampling with replacement). The resulting bootstrapped model tends to overestimate positional variance in the event sequence.

RESULTS
Here we present results from our experiments on real data in two dementia syndromes using our new event-based model incorporating     Figure 1B. This warrants further investigation. which may reflect heterogeneity within tAD.

Patient staging and longitudinal self-consistency of models
We use patient staging to assess model self-consistency.

DISCUSSION
We have revealed fine-grained representations of deterioration across cognitive domains in two dementia syndromes: PCA and tAD. This was enabled by a novel event-based model for estimating data-driven sequences of cognitive decline in neurodegenerative diseases, as well as uncertainty in the sequences.
We estimated sequences of cognitive decline that are broadly con- We validated our models by assessing longitudinal self-consistency of patient staging on a separate test set: the follow-up data in each cohort. In PCA, we observed 93% longitudinal consistency (nondecreasing patient stage at follow-up), and in tAD we observed 89%.
We further assessed the robustness of our results by comparing the maximum-likelihood models with their bootstrapped counterparts, the latter of which tends to overestimate uncertainty. The estimated sequences are robust, with the 2D positional density maps remaining consistently close to the diagonal.
A number of previous studies in PCA found broadly supportive results. Our finding that visual and visuospatial deficits (eg, A Cancellation time/Object Decision) precede those in memory (MMSE) was also found in refs. [40][41][42]. Our finding of early mathematical difficulty (GDA) agrees with ref. [42].
In  In summary, our results verify clinical opinion on disease progression while revealing new insight into the fine-grained sequence of clinical decline in memory-led tAD and vision-led PCA. This fine-grained understanding promises clinical utility for informing earlier differential diagnosis, and prognosis through data-driven disease staging -both are relevant for clinical trials and patient management.

ACKNOWLEDGMENTS
We thank all participants in the PCA longitudinal study for donating their time to research. We also thank everyone at the Dementia

FUNDING
The funding agencies had no involvement in the research itself, including: study design; data collection, analysis, and interpretation; writing of this report; nor the decision to submit this article for publication.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.