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Deep learning algorithm reveals probabilities of stage‐specific time to conversion in individuals with neurodegenerative disease LATE

Abstract Introduction Limbic‐predominant age‐related TAR DNA‐binding protein 43 (TDP‐43) encephalopathy (LATE) is a recently defined neurodegenerative disease. Currently, there is no effective way to make a prognosis of time to stage‐specific future conversions at an individual level. Methods After using the Kaplan–Meier estimation and log‐rank test to confirm the heterogeneity of LATE progression, we developed a deep learning–based approach to assess the stage‐specific probabilities of time to LATE conversions for different subjects. Results Our approach could accurately estimate the disease incidence and transition to next stages: the concordance index was at least 82% and the integrated Brier score was less than 0.14. Moreover, we identified the top 10 important predictors for each disease conversion scenario to help explain the estimation results, which were clinicopathologically meaningful and most were also statistically significant. Discussion Our study has the potential to provide individualized assessment for future time courses of LATE conversions years before their actual occurrence.

other types of dementia, including Lewy bodies (LB), vascular dementia, Parkinson's disease, and AD. For AD, in particular, its progression rate is known to be highly heterogeneous, varying from subject to subject, with the duration ranging from a few years to two decades. 16,17 Additionally, many factors, including genetic factors (such as apolipoprotein E ε4 genotype), 18 brain atrophy rates, 19 and patterns of brain region atrophy, 20 have been linked to the rate of cognitive deterioration in AD patients. For LATE, although existing neuropathological studies suggested that its cognitive deterioration at a population level was relatively slower than some common chronic age-related neurodegenerative diseases, such as AD, 1,21 there is no method or technique to assess time to conversion to the next stage in LATE at the stage-specific and individual level. The individualized assessment of stage-specific progression and conversion may facilitate our understanding of the pathophysiological characteristics and risks of LATE.
To unravel the heterogeneity and provide an insightful prognosis for LATE, in this study, we first confirmed the heterogeneity of LATE progression at different stages and then developed a deep learning (DL)-based approach for prognosticating stage-specific LATE conversion for subjects. Our assessment results were well explained with the critical predictors identified from a large number of predictors, such as age, sex, race, genetic factors, and clinical-psychological measurements. By assessing the future LATE conversions at different stages with probabilities over time rather than a binary number (i.e., happening or not), we could provide fine-grained time information of conversion years before the actual occurrence at an individual level.
Our analysis and predictive modeling were established on a large cohort from the National Alzheimer's Coordinating Center (NACC), with subjects' multiple-visit information between 2005 and 2020.
Our assessment in this study is based on a DL-based approach.
In general, DL uses artificial neural networks (ANNs), also known as neural networks (NNs), which are computing models and systems motivated by their biological counterparts in animal brains. An ANN typically has an input layer to receive data, an output layer to output processed information, and at least one intermediate layer called the hidden layer. In particular, deep NNs usually have two or more hidden layers. If one draws a graph showing how these layers are built on top of each other, then a deep NN model has many layers, and the structure looks deep, thus the naming. 22 DL usually uses deep NNs to process data and discover patterns and structures in complex, large datasets. From data out of the previous (or input) layer(s), each layer automatically extracts features/patterns and produces data that subsequent layers would use, eliminating the requirements for human engineers to provide manually extracted features/patterns to a computer. DL is known to enable the models to have strong abilities to handle large-scale data with complex nonlinear relationships. 23,24 Standard survival models, such as the Cox proportional hazards (CPH) model, assume a linear combination of patient covariates, which is known as the linear proportional hazards condition. In many applications, however, it may be too simplistic to assume that the log-risk functions are linear. DeepSurv is a DL-based model that can process survival data to account for linear and nonlinear effects from covariates, reporting performance superior to the CPH. 25  For each of eight scenarios, the concordance index was at least 82%, and the integrated Brier score was <0.14.
Moreover, our approach identified the top predictors to help explain our estimation, further corroborated with statistical significance.
3. Future Directions: Our approach has the potential to increase our understanding of the pathophysiology of LATE and provide an individualized assessment for future disease time courses and events years before their occurrence. To further help improve accuracy, a future direction is to integrate with other types of data from multiple sources, such as multi-omics. the potential to more closely model the true underlying relationship between the input variables and the response, which is likely to be nonlinear due to the high complexity of a form of dementia such as LATE.
To our knowledge, this is the first study to develop a DL-based approach that could accurately assess the probabilities of time-toconversion events for LATE. More specifically, our development of this innovative approach consisted of three major components. First, we

METHODS
We used statistical survival models to confirm the heterogeneity of LATE progression and provide a motivative setting for our study in this paper. We then developed an individualized approach based on a DL model, DeepSurv, for prognosis during a given period. We defined two variables, transition event and transition time, to describe our approach. The former was defined as the occurrence of a subject's change from the current stage to the next stage, which was also referred to as conversion; the latter denoted the period from the start time of the current stage to the earliest event occurrence time. The workflow for our DL-based stage-stratified approach is illustrated in Figure 1. It comprises major steps of data aggregation with subject categorization, data preprocessing such as data cleaning, subject stratification including the specifying transition time and event for each subject, and model-based analysis.

Datasets
Our approach of predictive modeling and analysis was established on the large prospective cohort, the NACC, with subjects' multiple-visit information between 2005 and 2020, which can be accessed upon request and approval by the data owner via the link https://naccdata. org/. The obtained dataset contains 163,199 records, each with 1727 variables. These records correspond to one or more visits of 44,864 subjects.

Subject categorization rules
We used the Clinical Dementia Rating (CDR) grades to label the different stages of LATE, which were calculated on the basis of a semistructured interview of the subjects and the caregivers (informant) and the clinical judgment of the clinicians. [26][27][28] The CDR grade is 0 to 3 (see Table S7 in supporting information). A CDR of 0.5 is usually very mild, and a recent study suggested that it might not be an accurate criterion to specify subjects with mild cognitive impairment (MCI). 29 Therefore, we generally consider CDR = 0 and CDR = 0.5 as one group, that is, the preclinical stage of LATE. We followed the categorization rules in Robinson et al. 2 and Wu et al. 30 to determine subjects with LATE; for more details, see Figure S7 in supporting information. For the data in different scenarios, we further performed data cleaning to remove variables that were repeatedly defined, not relevant, and not defined. In this study we did not perform data imputation but directly deleted the variables with missing values; the main consideration was that most of the missing variables in NACC data are categorical, and imputing categorical variables could cause bias or large error fluctuations. 31 We performed experiments to compare imput-

Subject statistics
For the groups in different scenarios, we show the basic subject statistic information for different transitions in Figure S1 in supporting  Figure S2 in supporting information.

Models/methods used in our analysis
In this study, the KM curve, 32,33 log-rank test, 34,35 and DeepSurv 25 were used for our analysis. The KM and log-rank test are two typical methods for univariate survival analysis, describing survival in terms of one factor but ignoring the impact of the other variables.
The CPH model is a standard semi-parametric regression model widely used in epidemiological studies and clinical trials 36 to assess survival time based on risk variables. In our initial analysis and modeling, we found that CPH did not converge well on the data in Table S1.
One reason might be the potentially complex, nonlinear relationships between variables and LATE stage-stratified transitions. Thus, in this study, we used DeepSurv for modeling purposes, which is a recent DL-based extension for the CPH model and could surpass classical survival models. 25 Additionally, we performed ANOVA to corroborate the significance of identified variables.

DL settings
We set the maximum number of epochs to be 2000. We initialized the weights of the layers with the Xavier normal distribution-based initializer. 37 We adopted the Adam optimizer 38

Evaluation metrics
Two standard metrics were adopted for evaluating the performance of our stage-stratified conversion assessment: (1) CI 41 is widely used to evaluate the ability of survival models to rank individuals by their time-to-event risk assessments. It is a generalization of the area under the receiver operating characteristics curve (AUC) taking into account censored data. The range of CI values is in [0, 1], and the larger the CI value, the better the performance. (2) IBS 42 extends the Brier score to right-censored data for evaluating the accuracy of an estimated survival function at time t. The IBS value is non-negative, and the smaller the value, the better the performance. Statistical significance was set at P < 0.05.

Kaplan-Meier estimation and log-rank test to examine LATE progression rates on NACC (2005-2020)
After using the KM method to estimate the survival functions from different scenarios, we compared the progression rates pairwise between different stages in Figure 2. Then, we used the log-rank test to calculate their P-values, as given in Table 1.  Table 1 indicates that their differences are both statistically significant (<0.05). These findings quantitatively confirmed that the LATE progression rates at different stages are heterogeneous, and the cognitive deterioration progresses more rapidly from the preclinical LATE stage to the early LATE stage than in other conversions. More results are provided in the supporting information.

DL-based time-to-conversion assessment
The To this end, we developed an approach based on a DL model, DeepSurv, to make a probabilistic time-to-conversion assessment. The results of assessment performance in CI and IBS are presented in Table 2 on the cleaned and preprocessed NACC data in Table S1. To illustrate the convergence of model training, we plotted the loss functions in Figure S4 in supporting information.  Further, we visually compared the estimated survival probabilities with our DeepSurv-based approach and the actual time when the transition event occurred. We presented the estimated survival probabilities for five randomly selected subjects in the test set in Figure 3 (for more results, see Figure S5 in supporting information). The visual comparison indicates that our approach produced good predictive modeling for almost all scenarios. Further, it is observed that com- In addition, the conversion for scenarios {0}⇝{0.5} and {0.5}⇝{1} may be clinically interesting, so we also provided the DeepSurv-based evaluation for these two scenarios; see Table 2. Also, in supporting information, we provided other important information for these two scenarios, including statistics of subjects, visit counts, loss function of DeepSurv, and visualization of the individual patient assessments.

Explainability of the assessment results by our approach
As pointed out by Wada-Isoe et al., 29 the CDR of 0.5 might not be an accurate criterion to specify subjects with mild cognitive impairment.
Also, in our experimental results (see Table 2), it is observed that the standard errors for {0}⇝{0.5} and {0.5}⇝{1} were much larger in both CI and IBS than those in other scenarios. This potentially indicates that the prediction involving these two scenarios was relatively less stable, so in the analysis for the explainability of assessment results, we mainly focused on the previous six typical scenarios. We performed post-processing of the learned weight matrix by the DeepSurv method to obtain feature ranking and selection to facilitate the interpretation of the assessment results. And, we compared the expression levels of significant variables between the conversion group and the nonconversion group in Figure 4. More results can be found in supporting information.

DISCUSSION
As pointed out previously, our approach was based on a recent DL model, DeepSurv, to assess the probabilities of conversion time specific to LATE stages and personalized to each new individual (not in the training set). It can provide the ranking and weights of the predic-tors for facilitating the explanation of how our approach produced the assessment results.

Strengths and limitations
The effectiveness of our approach was rigorously verified with crossvalidation and statistical testing in different metrics. However, our approach still has several limitations, which will be discussed below.  In addition, the multi-state models (MSMs) can also analyze and compare several (two or more) events simultaneously; however, the calculation between states in the model is still based on the assumption of linear structure or shallow structure. 45 Compared to MSMs, DeepSurv readily allows us to implement nonlinear covariate effects; in contrast, how to implement nonlinear covariate effects for multistate approaches is not straightforward. 46 Therefore, to account for the nonlinear covariate effects, we adopted the nonlinear variant of the Cox model, i.e., DeepSurv. It cannot handle multiple event states simultaneously; nonetheless, it can focus on the states of interest in a stage-specific way, thereby revealing complex relationships between the input and the response variables. As far as we know, this is the first study to develop a DL-based approach that could accurately assess the probabilities of time-to-conversion events for LATE.

CONCLUSION
Dementia patients may present with different symptoms, progress at different rates at different stages of the disease, and respond differently to interventions. Therefore, it is critical to understand the heterogeneous characteristics at different stages and develop an ability to reliably assess dementia onset and progression. In this study, we confirmed the population-level progression rates and the heterogeneity of LATE progression, and then we developed a stage-stratified approach by leveraging machine learning to probabilistically estimate the time courses of LATE stage-specific progression for different individuals. Our study has the potential to provide an individualized assessment of future time to LATE disease conversions years before their actual occurrences.

ACKNOWLEDGMENTS
This work was partially supported by the National Institutes of Health