Identification of mild cognitive impairment subtypes predicting 1 conversion to Alzheimer’s disease using a heterogeneous mixture 2 learning 3

Mild cognitive impairment (MCI) is a high-risk condition for conversion to 3 dementias, including Alzheimer's disease (AD) dementia. However, individuals with 4 MCI show heterogeneity in patterns of pathology, and MCI does not always convert to 5 AD dementia. Detailed subtyping of MCI and accurate prediction of the patients in whom 6 MCI will convert to AD dementia may support new trial designs and enable evaluation 7 of the efficacy of drugs within small numbers of patients during clinical trials. We identified five subtypes of MCI using the HML approach and categorized 2 them into three groups: those similar to CN subjects with low conversion rates; those with 3 intermediate conversion rates; and those similar to patients with AD with high conversion 4 rates. Furthermore, the subtypes with intermediate conversion rates were separated into 5 the subtype with CSF biomarker abnormalities or the subtype with brain atrophy. The 6 results from the CSF inflammation marker and gene expression analysis suggested the 7 occurrence of aberrant inflammatory immune responses in the CSF and blood of the 8 subjects in the subtypes with CSF biomarker abnormalities. 9 The subtypes that were identified in this study exhibited varying conversion rates to AD as well as differing levels of biological features. Focusing on specific subtypes in which conversion to AD can be predicted with the most accuracy could enable more 13 efficient clinical trials to be conducted.

whether it is single-or multiple-domain MCI, converts to dementia, mainly AD dementia, 1 at a rate of 10% to 15% per year [4]. Recent studies based on neuropsychological tests 2 have also identified some subtypes of MCI [5,6]. However, clinical diagnoses and 3 neuropsychological testing often include subjective factors. In addition to subjective 4 factors, assessment of objective factors such as brain imaging data, biomarker data, and 5 genomic data may enable more precise determination of a subtype of MCI that converts 6 to AD dementia. 7 In this study, we applied the HML method to identify subtypes of MCI. HML 8 divides individuals into similar groups based on the brain volumes from five brain regions, 9 CSF biomarker including Aβ and tau, and genomic data of apolipoprotein E (APOE) 10 gene obtained from individuals and generates appropriate predictive models for each 11 group (e.g., models for determining whether an individual is a patient with AD dementia 12 or a healthy individual). We characterized the subtypes of MCI identified by HML and 13 examined conversion to AD dementia for each subtype over a given period. The data used in this study were obtained from the Alzheimer's Disease

Structural MRI
Structural MRI was used to assess the following five markers: whole-brain 1 volume, ventricular volume, hippocampal volume, entorhinal cortex volume, and white 2 matter hyperintensity (WMH) volume. These volumes were normalized as fractions of 3 the intracranial volume. Cortical reconstruction and volumetric segmentation were 4 performed with the FreeSurfer image analysis suite. WMH volumes were calculated 5 based on coregistered T1-, T2-, and proton density-weighted structural MRI images. using an APOE genotyping kit. APOE includes 3 alleles (ε2, ε3, and ε4) and 6 genotypes 10 (ε22, ε23, ε24, ε33, ε34, and ε44). We assessed the number of ε4 alleles, as the ε4 allele 11 is known as a risk factor for AD. 12 13 HML model 14 We applied HML to obtain a decision tree for MCI subtyping. HML is a type of 15 hierarchical mixture of experts [8-10] that integrates multiple learners using a decision 16 tree. HML divides individuals into similar groups based on various datasets of the 17 individuals and generates appropriate predictive models for each group. As described below, HML simultaneously estimates the parameters for a decision tree and the 1 prediction models using the expectation-maximization (EM) algorithm based on 2 factorized information criterion (FIC), which is an estimator specific to HML 3 (Supplementally information). Using HML has several advantages, including the 4 following: (1) the decision tree facilitates understanding of how individuals are classified 5 into their subtypes, and (2) HML naturally prunes more complex brunches of a decision 6 tree by the contribution of FIC, providing a decision tree with higher interpretability 7 compared to them from the other methods based on decision tree. A program for HML 8 was provided by NEC Corporation. nodes. The prediction model in the j-th expert node is presented in the following equation: Let us denote the regression target as = (1) , … , ( ) , where ( ) corresponds to 1 ( ) and indicates a weight vector of parameters in the j-th expert node. To obtain a decision tree model via HML, we needed the parameters for the 5 gating nodes (i.e., , , and ) and the expert nodes (i.e., ). These parameters were 6 estimated by EM-like iterative optimization (Algorithm 1 in Supplementally 7 information). The variational distribution, which is derived from FIC, in the E-step has 8 a regularization effect and penalizes the expert nodes that contribute to the formation of 9 complex tree structure and that have more variables with small effects (Supplementally 10 information). Therefore, HML automatically selects an optimal decision tree and optimal 11 model parameters to maximize FIC [9, 10].

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Test performance 14 We used the datasets from 156 AD dementia patients and 305 CN subjects as 15 training and validation datasets to determine a decision tree and model parameters via 16 HML ( Figure S2). The data for four-fifths of the AD dementia patients and CN subjects 17 were used as a training dataset. The remaining data were used as a validation dataset to fine-tune the model parameters. The regression target was ( ) = 1 when a subject is 1 AD and ( ) = 0 when a subject is CN. Of 480 MCI subjects, the dataset from the 396 2 MCI subjects who were followed for more than three years was used as test data. The 3 regression target was ( ) = 1 when an MCI subject converted to AD dementia within 4 three years and ( ) = 0 otherwise.

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Using the training dataset, we first set the tree depth d to a value ranging from 6 three to six. Then, we estimated parameters via HML. As we mentioned above, HML 7 optimizes the parameters based on the EM-like iterative optimization. It is well known 8 that the EM iterative optimization generally converges to a local optimum depending on 9 an initial value and is not guaranteed to converge to the global optimum. To avoid a local 10 optimum, we generated 500 models with different initial values at each depth. We next 11 applied the validation dataset to the 2,000 models (= 4 depths × 500 models) generated 12 from the training data and adopted the decision tree model with the highest accuracy in 13 the validation dataset as the model with optimal parameters (Figure S2). We finally 14 calculated the test performances of the model using the test data. These procedures were 15 repeated for 5-fold cross-validation (CV).

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An HML decision tree model generated from the training data classified the MCI subjects into AD dementia patients (the predicted ADs) or CN subjects (the predicted 1 within three years were defined as true positives (TPs). The predicted ADs in whom MCI 2 did not convert were defined as false positives (FPs). In the same way, the predicted CNs 3 who developed AD dementia within three years and those who did not develop AD 4 dementia were defined as false negatives (FNs) and true negatives (TNs), respectively.

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We calculated sensitivity, specificity, precision, and accuracy using the four outcomes as

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The AD conversion in each MCI subject is presented as a time-to-event value, that is, the 12 number of days from age at baseline to age at onset. In this study, we defined the data for 13 the MCI subjects in whom MCI did not convert to AD dementia during follow-up period 14 as censoring data. The log-rank test was performed to evaluate the difference in 15 conversion between the predicted ADs and the predicted CNs or among the MCI subtypes.

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The conversion rate at time t (CRt) was given by the following: where nt is number at risk at time t and ct is the number of the individuals converted to 1 AD dementia during the period from time t-1 to time t. The test performances by CART were calculated using the same 5 training/validation/test datasets with HML ( Figure S2). We set the tree depth d to a value 6 ranging from three to six. A function GridSearchCV provided by the Python scikit-learn 7 package [11] optimized the following parameters in CART: the maximum depth of the 8 tree (3, 4, 5, and 6); the criterion ("the Gini impurity" or "the information gain"); the 9 minimum number of samples required to be at a leaf node (1,…,11); the minimum number 10 of samples required to split an internal node (2,…,11); the random state (0,…,101); the 11 strategy used to choose the split at each node ("best" or "random"). We adopted the model 12 with the highest accuracy in a validation dataset and calculated the test performances of 13 the adopted model using the test dataset.

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Composite scores of cognitive domains 16 We used the composite scores of four cognitive domains (memory, executive 17 function, language, and visuospatial function) in a bi-factor model [12,13]  time. Separate models were run for the four cognitive functions. We used the false 7 discovery rate (FDR) method to correct for multiple testing. were selected as the genes whose differences in expression had non-adjusted p-values < 15 0.05. We first set the significance level of the FDR-adjusted p-value to < 0.05, but we 16 found no genes at this significance level. We adopted a significance level based on a non-17 adjusted p-value to assess the overall alterations in gene expression by gene functional enrichment analysis. Next, we classified the DEGs into clusters using agglomerative 1 hierarchical clustering based on Ward's method and the Euclidean distance. The number 2 of clusters was set to six based on the gap statistic [14]. Gene functional enrichment 3 analysis of the DEGs was performed using the Metascape database 4 (http://metascape.org/) [15]. 5 We performed linear regression analysis to examine the association between CSF with CSF YKL-40 were selected as the genes with non-adjusted p-values < 0.05.

Test performance of a decision tree model obtained by HML
We generated decision tree models via HML using the dataset from 156 AD 1 dementia patients and 305 CN subjects, and assessed the test performance of the models 2 using the dataset from 396 MCI subjects by 5-fold CV (see Materials and methods, 3 Figure S2). The data for four-fifths of the AD dementia patients and CN subjects were 4 used as a training dataset. The remaining data were used as a validation dataset to fine-5 tune the model parameters. Using the training dataset, we tried decision trees with four 6 depths ranging from three to six and generated 500 models based on the different initial 7 conditions at each depth. Next, we applied the validation dataset to the 2,000 models (= 8 4 depths × 500 models) generated from the training data. We selected the decision tree 9 model with the highest accuracy in the validation dataset as the model with optimal 10 parameters. We further used the data for 396 MCI subjects as test data to evaluate the 11 decision tree model and calculated the test performance of the model. These procedures 12 were repeated for 5-fold CV. The results from 5-fold CV showed a sensitivity of 13 0.751±0.027, a specificity of 0.810±0.020, a precision of 0.682±0.022, and an accuracy 14 of 0.789±0.014. In the same way, we also used the CART method, which is known as a 15 traditional decision tree method, and compared the test performance. The comparison of 16 the models obtained from the two methods showed that the models from the HML had 17 higher accuracy than those from CART ( Table 2). In addition, the comparison of model complexities showed that the models from HML had fewer leaf nodes (expert nodes in 1 HML) than those from the CART method, providing higher interpretability.

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Characteristics of each subtype 4 We next focused on construction of a decision tree to examine MCI subtypes 5 ( Figure 1A). This decision tree was generated from all 461 subjects, including 156 AD 6 dementia patients and 305 CN subjects, and had five expert nodes. After the 396 MCI 7 subjects were applied, the decision tree model had an accuracy of 0.804. We next applied 8 all 480 MCI subjects to the decision tree. This decision tree model predicted 170 of the 9 MCI subjects as AD dementia patients (the predicted ADs) and 310 of the MCI subjects 10 as CN subjects (the predicted CNs). We compared the conversion rates to AD dementia 11 between the predicted ADs and the predicted CNs. The predicted ADs exhibited a higher 12 percentage of progression to AD dementia over three years from baseline (61.6%) than 13 the predicted CNs (11.5%) ( Figure 1B). 14 The individuals included in an expert node on a decision tree are a group of 15 individuals with similar features. We then considered the MCI subjects who were 16 classified into a specific expert node as one subtype. The MCI subjects were divided as 17 follows: 68 subjects were in subtype 1, 173 were in subtype 2, 188 were in subtype 3, 14 were in subtype 4, and 37 were in subtype 5 (Table 3). We compared the conversion rates 1 of MCI to AD dementia in the subjects in each subtype to characterize each subtype 2 (Figures 1C and 1D). The Kaplan-Meier curves showed different conversion patterns in 3 each subtype. Notably, 67.9% of MCI cases in the subjects in subtype 5 progressed to AD 4 dementia within three years. On the other hand, the conversion rates in subtypes 1, 3, and 5 4 were moderate at approximately 40%. Subtype 2 had a comparatively low conversion 6 rate.

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To provide a more detailed characterization of each subtype, we compared the 8 levels of 12 variables among the subtypes (Figure 2). Subtype 2 showed high levels of 9 CSF Aβ(1-42) (Figure 2A), suggesting low deposition of Aβ in the brain. The levels of 10 CSF tau (CSF tTau, CSF pTau, tTau/Aβ(1-42) ratio, and pTau/Aβ(1-42) ratio), which 11 indicate the degree of Aβ-dependent neurofibrillary tangles, were high in subtypes 4 and 12 5 (Figures 2B-E). These biomarker pattern suggests that individuals classified subtypes 13 4 and 5 have AD pathology in the brain. Interestingly, these subtypes did not have 14 upstream gating nodes associated with tau on the decision tree. Subtype 1 had a high 15 ventricular volume, suggesting brain atrophy ( Figure 2F). This subtype also had low 16 hippocampal, whole-brain and entorhinal cortex volumes in accordance with enlargement of the ventricles (Figures 2G-H). Low hippocampal and entorhinal cortex volumes were also observed in subtype 5 (Figures 2G and 2I). Regarding WMH volumes, which reflect 1 white matter lesions caused by cerebral ischaemia, there were no differences among the 2 subtypes ( Figure 2J), implying that most MCI subjects in this study did not present with 3 vascular dementia. Comparison of ages showed that subtypes 1 and 4 included relatively 4 older and younger MCI subjects, respectively ( Figure 2K). Not surprisingly, the MCI 5 subjects in subtypes 1 and 2 did not have APOE ε4 alleles, which are genetic risk factors, 6 and all of the subjects in subtypes 3, 4, and 5 had one or two APOE ε4 alleles because the 7 decision tree had the gating nodes with APOE ε4 alleles ( Figure 2L). 8 The spot matrix in Figure 3 more clearly shows the differences among the 9 subtypes. The spot matrix characterized the subtypes with the conversion rates shown in 10 Figures 1C and 1D: subtype 2, with no abnormalities had a low conversion rate; subtype 11 1, which had some brain atrophy, and subtypes 3 and 4, which had no abnormalities in 12 CSF biomarkers, had intermediate conversion rates; and subtype 5, which had both CSF 13 biomarker abnormalities and brain atrophy, had a high conversion rate.

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Cognitive functions in each subtype 16 We compared the four composite scores for memory, executive function, 17 language, and visuospatial function at baseline among the subtypes. A high composite score in each cognitive domain indicates high cognitive function. Comparisons among 1 subtypes showed that the scores for memory, executive function, and language of the 2 subjects in subtype 2 were basically significantly higher than those of the subjects in the 3 other subtypes (Figures 4A, 4D, and 4G). The scores for visuospatial function did not 4 show significant differences among the subtypes (Figure 4J). We next examined the 5 trajectories of these scores during the follow-up time. Figures 4B, 4E, 4H, and 4K shows 6 the temporal changes in each subtype. Individual cognitive declines are illustrated in 7 Figure S3. We performed LMM analyses with subtype 2 (no abnormalities) as the 8 reference to compare the association between follow-up time and each score. The scores 9 of memory and executive function in subtypes 1, 3, 4, and 5 declined significantly more 10 steeply than those in subtype 2 over time. Subtypes 1 and/or 4 did not show significant 11 associations for the language and visuospatial function scores. Subtype 5 consistently 12 showed the most rapid decreases in all scores. In addition, subtype 1 exhibited slower 13 declines than subtypes 3, 4, and 5, particularly for the memory and executive function 14 scores. These results show that the rate of exacerbation of cognitive decline differs 15 depending on the subtype.

Neuronal dysfunction and inflammatory responses in each subtype
We examined the levels of CSF proteins reflecting neuronal injury, synaptic 1 dysfunction, and inflammation within the brain. The CSF markers were measured in the 2 following subjects: 10 subjects in subtype 1, 18 in subtype 2, 26 in subtype 3, and 8 in 3 subtype 5. The CSF markers were not measured in any of the subjects in subtype 4. The 4 levels of the neuronal injury marker VILIP-1 and the synaptic dysfunction markers 5 SNAP-25 and NGRN were elevated in the subtypes in the following order: 1, 2, 3, and 5 6 ( Figure 5). The levels of VILIP-1 in subtype 3 and 5 were significantly higher than that 7 in subtype 1 ( Figure 5A). Additionally, the levels of SNAP-25 in subtypes 3 and 5 were 8 significantly higher than those in subtypes 1 and 2 ( Figure 5B). On the other hand, the 9 level of the inflammation marker YKL-40 was the highest only in subtype 5 ( Figure 5D).

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Taken together, these results show that although subtypes 3 and 5, which exhibited CSF 11 biomarker abnormalities, displayed progression of neurological damage, the 12 inflammatory response was observed only in subtype 5, which exhibited both CSF 13 biomarker abnormalities and brain atrophy. These findings suggest that the accumulation 14 of Aβ and tau proteins within the brain leads to neuronal dysfunction followed by an 15 inflammatory response. Additionally, as we will mention in the Discussion, the CSF 16 markers such as VILIP1 reflect Aβ-and tau-induced neuronal cell death. Therefore, these 17 markers might not have been elevated in subtype 1. inflammation marker levels shown in Figure 5D. The genes in cluster 6 were prominently 15 upregulated in subtype 4 and moderately upregulated in subtype 5 and were obviously 16 related to B cell activation ( Figure 6C). The genes in cluster 3 represented were 17 upregulated in subtype 4 and downregulated in subtype 5. The genes in cluster 3 were significantly associated with terms related to the immune response, such as 1 "Immunoglobulin production mediated immune response", in addition to RNA 2 localization ( Figure 6C). These results showed that the expression levels of genes in 3 immune response pathways were drastically changed in subtypes 4 and 5 and that 4 pathways evoked by immune responses such as autophagy were also altered in subtype 5 5. In the above analysis, although we could not analyse the level of the inflammation 6 marker YKL-40 in subtype 4 because this marker was not measured in the subjects of this 7 subtype, our results suggested the occurrence of aberrant immune responses in the blood 8 of the subjects in subtype 4 similar to that occurring in the subjects in subtype 5. However, 9 we could not directly relate the events in the blood and CSF. We then searched the genes 10 whose expression levels correlated with the levels of YKL-40 (see Materials and 11 Methods). Overall, the expression levels of 952 genes were found to be associated with 12 the levels of YKL-40. Interestingly, these genes were predominantly associated with 13 immune system process (Figures 6D and 6E). This result implies that the inflammation 14 arising in the CSF or brain propagates to the blood and triggers immune responses. These 15 associations may indirectly reflect events within the brains of the subjects.

Discussion
We constructed a decision tree model to predict the conversion of MCI to AD 1 dementia within three years via the HML approach. Our decision tree model predicted 2 the MCI subjects in whom MCI converted to AD dementia with higher accuracy than an 3 existing decision tree algorithm ( Table 2). Furthermore, the decision tree model divided 4 the MCI subjects into five subtypes based on the characteristics of that data ( Figure 1A).

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Detailed analysis showed a relationship between the speed of transition to AD for each 6 subtype and its biological characteristics.

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The identified subtypes revealed varying conversion rates to AD dementia as 9 well as differing levels of CSF biomarkers and brain atrophy (Figures 1C, 1D, 2, and 3). 10 The MCI subjects were mainly categorized into three groups in terms of AD conversion: 11 those similar to CN subjects with low conversion rates (subtype 2); those with 12 intermediate conversion rates (subtypes 1, 3, and 4); and those similar to AD dementia 13 patients with high conversion rates (subtype 5). Furthermore, the subtypes with 14 intermediate conversion rates were separated into subtypes with CSF biomarker 15 abnormalities (subtypes 3 and 4) and a subtype with brain atrophy (subtype 1). One of 16 the differences among these subtypes was the presence or absence of APOE ε4 alleles. consistent with our results. As expected, the trajectory analysis of cognitive functions 1 showed that subtype 5, which had both CSF biomarker abnormalities and brain atrophy, 2 had the steepest declines over the follow-up time (Figures 4B, 4E, 4H, and 4K). On the 3 other hand, we observed different exacerbation rates for each score in subtypes 1, 3, and 4 4, even though these subtypes had similar conversion rates. Previous studies have shown that the CSF level of VILIP-1 is associated with the 7 CSF Aβ and p-tau levels, suggesting that VILIP-1 is a marker of neuronal degeneration 8 related to Aβ and tau pathologies [27,28]. In addition, a comparison of CSF VILIP-1 9 levels among CN subjects, MCI subjects, and AD dementia patients showed that VILIP-10 1 levels increased year-over-year only in MCI subjects; they did not increase in the CN 11 subjects and AD dementia patients [29]. The VILIP-1 levels in the CSF may increase 12 during inflammation and neurodegeneration triggered by Aβ and tau, but they may 13 decrease after neurons have already died and brain atrophy has occurred. Based on the 14 findings of these studies, we concluded that subtype 1 did not exhibit increases in the 15 levels of these neuronal degeneration markers because there were no prominent CSF 16 biomarker abnormalities. Additionally, our results suggested that the MCI subjects in 17 subtype 1 convert to the other dementia as discussed above because they did not show relatively CSF biomarker abnormalities specific to AD pathologies.

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Subtypes 3 and 5 showed high levels of CSF markers for neuronal and synaptic 3 injury such as VILIP-1 and SNAP-25 (Figures 5A and 5B). The levels of these markers 4 gradually increased with the dose of APOE ε4, consistent with the findings of recent 5 studies reporting associations between these markers and APOE ε4 [30,31]. On the other 6 hand, the levels of the inflammation marker YKL-40 in the CSF were increased only in 7 subtype 5 among the subtypes except for subtype 4 ( Figure 5D). Additionally, gene 8 expression analysis using blood tissues also showed that genes associated with the 9 inflammatory immune response were up-or downregulated specifically in subtype 4 and 10 5 ( Figure 6C). To clarify the potential link between the CSF and the blood, we examined 11 the genes with blood expression levels that correlated with the CSF YKL-40 level and 12 found that they were enriched in inflammatory immune response pathways ( Figures 6D   13   and 6E). However, the direct relationship between CSF and blood is unclear. The blood-14 brain barrier (BBB) and the blood-CSF barrier play roles as boundaries between the blood 15 and the brain or CSF. The BBB strictly regulates the passage of select blood molecules 16 through various channels into the brain. It has been considered that the central nervous system, including the brain, has immune privilege (which protects it from inflammation and the immune response) because of the existence of the BBB. However, recent studies 1 have shown that the immune privilege of the brain is not always assured [32,33] corresponds with the alterations in gene expression in the autophagy pathway in subtype 10 5. In summary, BBB impairment may progress in MCI subjects in subtypes 5.

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Our study has several limitations. First, we were not able to analyse all MCI 13 patients in some analyses. For example, the MCI subjects in subtype 4 did not have the 14 CSF markers for neuronal, synaptic injury, and inflammation markers. Second, although 15 we examined the comprehensive mRNA levels in the blood, the levels of mRNA in the 16 blood may change depending on lifestyle and other factors. To verify our results, detailed 17 analysis using animal models is necessary.

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The Tukey's HSD test was used to verify the differences in CSF levels between two 13 subtypes and was applied as a multiple comparison procedure. *p < 0.05, **p < 0.01, 14 ***p < 0.001.