Data were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database.¹ ADNI is a multicenter longitudinal cohort study with the main research goal of examining whether clinical, neuropsychological, biological, and other neuroimaging markers can be combined to track clinical progression in the Alzheimer’s disease continuum. The ADNI study was approved by an ethical review board of participating study centers and all subjects provided written informed consent.

For the current study, we selected subjects with a baseline clinical diagnosis of either MCI or mild AD dementia who had elevated amyloid as determined by PET imaging (specific methods and cutoff described below) and had at least 1 follow-up measurement available (with ADAS-Cog-13 administration) the next 5 years. Criteria for MCI were (1) memory complaint; (2) abnormal memory function evidenced by the Logical Memory II subscale (Delayed Paragraph Recall) from the Wechsler Memory Scale-Revised; (3) Mini-Mental State Examination (MMSE) score ≥ 24; (4) global Clinical Dementia Rating (CDR) score of 0.5; (5) absence of dementia. Criteria for mild AD dementia were (1) memory complaint; (2) abnormal memory function evidenced by the Logical Memory II subscale from the Wechsler Memory Scale-Revised; (3) MMSE score between 20–26 (inclusive); (4) global CDR score of 0.5 or 1; (5) NINCDS/ADRDA criteria for probable AD dementia (Mckhann et al., 1984). This study included 421 participants with early AD (MCI or mild dementia due to AD). The inclusion criteria for participants with early AD in the current study largely aligned with those used in a recent anti-amyloid AD clinical trial (van Dyck et al., 2023). For detailed sample selection procedures, please see Figure 1.

The ADAS-Cog (Rosen et al., 1984) is a commonly used cognitive outcome for tracking disease progression and measuring the efficacy of antidementia treatments and the most used cognitive outcome measure in AD clinical trials (Cano et al., 2010). Thus, we treated ADAS-Cog as our primary cognitive outcome and used it as the variable for longitudinal cluster analysis (specific procedures for cluster analysis described below). The 13-item version of ADAS-Cog (ADAS-Cog-13) includes 13 tasks that primarily assess the cognitive domains of episodic memory, praxis, and language. Total score ranges from 0 to 85, with higher scores indicating greater cognitive impairment (Rosen et al., 1984).

Apart from the ADAS-Cog, the second and third most frequently used cognitive outcome measures in AD clinical trials were the MMSE (Folstein et al., 1975) and the CDR-sum of boxes (CDR-SB) (Williams et al., 2013; Jutten et al., 2021). The Functional Activities Questionnaire (FAQ) (Pfeffer et al., 1982) is a commonly used instrumental activities of daily living (IADLs) scale that predicts clinical progression (Marshall et al., 2015). Therefore, these cognitive measures (i.e., MMSE, CDR-SB, and FAQ) were taken to assess and validate cognitive and functional changes over time between different cognitive subgroups. The MMSE is a widely used global cognitive screening test, with total scores ranging from 0 to 30, and a lower score indicates greater cognitive impairment (Folstein et al., 1975). The CDR-SB captures 6 cognitive and functional domains, including memory, orientation, judgment and problem-solving, community affairs, home and hobbies, and personal care (Williams et al., 2013). Scores for each domain range from 0 to 3, with higher scores reflecting greater impairment. Adding scores of each domain leads to a total score, which ranges from 0 to 18 (Williams et al., 2013). The FAQ rates 10 functional domains, with total scores ranging from 0 to 30, and higher scores indicate greater impairment (Pfeffer et al., 1982).

Amyloid status (amyloid negative vs. amyloid positive) was determined based on Pittsburgh compound B (PiB) or Florbetapir AV-45 PET imaging (summarized data were pulled from the ADNI Laboratory of Neuroimaging database: ida.loni.usc.edu; the file name is ADNIMERGE.csv). Amyloid positivity was determined by calculating the standardized uptake value ratio of the mean uptake in four cortical regions (frontal, cingulate, parietal, and temporal cortices), which was normalized to the uptake in the entire cerebellum. We used validated tracer-specific cutoff values to determine abnormality, which were > 1.47 for PiB-PET and > 1.10 for AV45-PET (Landau et al., 2013).

Hippocampal atrophy, ventricular enlargement, and cerebral glucose hypometabolism are presumed to reflect neurodegenerative alterations most proximal to the onset of cognitive decline, and valid predictors of disease progression (Jack et al., 2004, 2010a). Therefore, we took these three imaging markers to characterize neurodegenerative changes among cognitive subgroups. Summary data were obtained from the ADNI Laboratory of Neuroimaging database: ida.loni.usc.edu; the file name is ADNIMERGE.csv. The proportional approach [(normalization of regional volumes by intracranial volume (ICV)] was taken to adjust sex differences in head size since women and men differ substantially in ICV. Adjusted ventricular volume (aVV) was calculated using the following equation: aVV = ventricular/intracranial volume × 10³. Adjusted hippocampal volume (aHV) was calculated using the following equation: aHV = hippocampal/intracranial volume × 10³. Cerebral glucose metabolism was measured by Fludeoxyglucose PET (FDG-PET). The global FDG SUVRs were measured by calculating the mean FDG uptake in three brain regions (posterior cingulate, angular gyri, and inferior temporal gyri), which was normalized to the uptake in the pons and cerebellum.

Lumbar puncture was conducted as described in the ADNI manual.² The levels of CSF AD biomarkers, including CSF Aβ 1–42 (Aβ42), total tau (t-tau), and phosphorylated-tau at threonine 181 (p-tau), were measured by the Roche Elecsys Aβ42 CSF, Elecsys t-tau CSF, and Elecsys p-tau CSF immunoassays at the Biomarker Research Laboratory, University of Pennsylvania, USA, as previously described (Bittner et al., 2016). In this study, Elecsys Aβ42 values >1700 pg./mL (upper technical limit) were fixed at 1700 pg./mL. CSF Aβ42 values below 1,098 pg./mL were used to classify individuals as amyloid-positive, based on thresholds established in a previous study (Schindler et al., 2018).

Statistical work and data visualization were conducted using R version 4.1.2 (Team, R.Core, 2014).

First, to identify distinct longitudinal cognitive profiles, a non-parametric k-means longitudinal clustering method from the R package “kml” (Genolini et al., 2015) was used to detect the ADAS-Cog-13 trajectories over a 5-year follow-up period. This method allows for the investigation of how a parameter of interest changes over time and categorizes individual trajectories into distinct groups of participants with homogeneous characteristics. The ADAS-Cog-13 was treated as our clustering variable given its predominant role in AD clinical trials. In the cluster analysis, we only included participants who had undergone at least one follow-up assessment using ADAS-Cog-13 within 5 years since baseline. K-means is an algorithm in the expectation–maximization (EM) (Celeux and Govaert, 1992) class that utilizes a hill-climbing approach. EM algorithms initially assign each observation to a cluster and then achieve optimal clustering by alternating between two phases. In the expectation phase, the centers of the different clusters (known as seeds) are computed. The maximization phase involves assigning each observation to its “nearest cluster.” The alternating between the two phases is repeated until no further changes occur in the clusters. Models were constructed for 1 to 8 clusters, and the 4-cluster solution was chosen based on several factors, including the Bayesian information criterion (BIC) (Schwarz, 1978), the elbow method, and ensuring that each cluster had an adequate sample size. The graph showing the BIC per cluster solution is provided in Supplementary Figure S1. The individual trajectories and resulting 4-cluster trajectories are shown in Figure 2A.

Second, the differences in demographics, APOE4 genotype, clinical diagnosis, cognitive evaluations, neurodegenerative markers, and CSF AD biological markers between 4 clusters at baseline were compared. We used analysis of variance (ANOVA) to assess differences between clusters for continuous variables and Pearson’s x² tests for categorical variables. If group differences were detected using ANOVA or Pearson’s x² tests, we performed pairwise t-tests or x² tests in post hoc analyses and corrected for multiple testing using the false discovery rate (FDR) correction (Benjamini and Hochberg, 1995). To demonstrate group comparisons of means, we also presented visual representations, as shown in Figure 3.

Third, to characterize the longitudinal changes over a 5-year follow-up period in cognitive measures, neurodegenerative markers, and CSF AD biological markers for each cluster, linear mixed-effects models were built using the R package “lme4” (Bates et al., 2014). We constructed nine models for the dependent variables, including MMSE, CDR-SB, FAQ, aVV, aHV, FDG SUVRs, CSF Aβ42, t-tau, and p-tau. These models included time since baseline (in years), clusters, and their interaction as fixed effects, and age, gender, years of education, APOE4 status, and their interactions with time as covariates. Additionally, a random intercept was included for each participant in all models. Each model was fit using maximum likelihood, which is a method used to estimate the parameters of a statistical model by finding the parameter values that maximize the likelihood function. We also used Satterthwaite’s method to estimate the degrees of freedom in the t-tests, which allowed us to test the significance of the fixed effects and calculate the 95% confidence intervals. The models can be summarized as the following equations: Y_change∼ Clusters∗time + Age∗time + Gender∗time + Education∗time +APOE4 status∗time. Y_change represents the annual change in the aforementioned nine dependent variables from the baseline. To further understand the differences in slopes among the four cluster groups, we conducted pairwise comparisons between clusters using estimated marginal means (EMMs). To adjust for multiple testing, we applied the FDR method for correction.

Fourth, the bootstrap was used to quantify the uncertainty associated with the coefficients and to test the robustness of the results from the aforementioned linear mixed-effects models. We generated 1,000 bootstrapped samples by randomly resampling the data with replacement and refitting the linear mixed-effects models. The random effects were included to generate bootstrapped samples and a semiparametric bootstrap method was performed. The bootstrapped estimates were used to estimate the sampling distribution of the fixed effects, and the 95% confidence intervals (CIs) for the fixed effects were also calculated. A forest plot demonstrating the effect difference relative to Cluster 1 (the reference group) was also created to conduct bootstrap inference.

Fifth, to examine whether cluster membership was predictive of progression from MCI to dementia over a 5-year follow-up period, a Kaplan–Meier plot was utilized to demonstrate the conversion rate to dementia in the four clusters, and log-rank tests were employed to carry out pairwise comparisons of the survival curves and the FDR method was used to correct for multiple testing. Initially, we segregated MCI participants from each cluster, yielding a sample size of 130 in Cluster 1, 119 in Cluster 2, 40 in Cluster 3, and 2 in Cluster 4. Due to the limited number of MCI participants in Cluster 4, we merged MCI participants from Clusters 3 and 4 into a revised Cluster 3. Subsequently, we performed survival analysis utilizing the newly configured cluster variable (consisting of 3 clusters) as the primary predictor. The duration of follow-up was calculated as the interval between the baseline evaluation and the diagnosis of dementia at the last visit. For those subjects who did not develop dementia during the 5-year follow-up period, their data were censored at the time of their last visit.

Sixth, to estimate associations between baseline predictors and cluster membership, multivariable multinomial logistic regression models by the R package “nnet” (Venables and Ripley, 2002) were performed, with Cluster 1 as the reference category. To handle missing values among predictors, 5 complete-data replicates were computed by Multivariate Imputation by Chained Equations using the R package “mice” (Buuren and Groothuis-Oudshoorn, 2011). The overall variable-level missingness is shown in Table 1. We imputed a score using the “predictive mean matching” method, and the imputation model included all predictors that were part of the multinomial logistic regression models, while the outcome variable (cluster membership) was not included in the predictor matrix of the imputation scheme. The multinomial logistic regression modeling was then applied to the 5 imputed data sets and results were pooled utilizing Rubin’s rules to yield estimates and confidence intervals that incorporate the imputed values’ uncertainty (Rubin, 1989). A total of four multinomial logistic regression models with cluster membership as the dependent variable were constructed: the base model included age, gender, years of education, APOE4 genotype, and clinical diagnosis as predictor variables; the cognition model included all the predictors from the base model and additionally incorporated MMSE; the neurodegeneration model further included aHV and FDG-PET at the basis of the cognition model; the AD biomarker model included all the predictors from the neurodegeneration model and additionally incorporated CSF Aβ42 and p-tau proteins. Adjusted odds ratios (ORs) with 95% CIs were computed for all other three clusters by comparing them with Cluster 1 (the reference category).

Seventh, given that cluster 1 showed negligible decline and cluster 2 only exhibited a slightly higher decline, while clusters 3 and 4 demonstrated similar rates of cognitive decline, we decided to combine clusters 1 and 2 into a group called “non/slow decliners,” and merge clusters 3 and 4 into a group referred to as “steep decliners.” Binary logistic regression models were built with same predictors included in the AD biomarker model and the two groups (non/slow decliners vs. steep decliners) as the outcome. To select the predictors that explain the bulk of variance in cognitive decline and create a simplified model for practicality, we employed a fast backward variable selection method (Lawless and Singhal, 1978), using the total residual Akaike’s information criterion (AIC) (Akaike, 1974) as the stopping rule. A nomogram was created to facilitate an easy and visual estimation of probabilities of steep cognitive decline based on the reduced model. Finally, in order to examine whether the inclusion of our nomogram for enrichment can reduce sample size, simulation of clinical trials were performed using the longpower R package, with a 25% treatment effect on cognitive performance over time, a statistical power of 80%, 1:1 allocation of placebo and treatment groups, and a total duration of 18 months with cognitive assessments at 0, 3, 6, 9, 12, 15, and 18 months. Bootstrap with 500 iterations was conducted.

Four clusters were identified. Figure 2A demonstrates the categorization of participants with symptomatic early AD based on their ADAS-Cog-13 trajectories over a 5-year follow-up period into the following clusters: Cluster 1 (n = 131, 31%), characterized by stable cognitive performance; Cluster 2 (n = 141, 34%), characterized by a mild cognitive decline; Clusters 3 (n = 108, 26%) and 4 (n = 41, 9%), characterized by moderate to rapid rates of cognitive decline, with Cluster 4 showing more impaired cognitive performance at baseline and greater rates of cognitive decline than Cluster 3 as shown by the intercepts and slopes.

As shown in Table 1 and Figures 2B–D, 3, the baseline sociodemographic and clinical characteristics were compared between clusters. For age, Cluster 3 was older than Cluster 1, and Cluster 4 was younger than Cluster 3, but no other pairwise difference was observed. For years of education, APOE4 status (Figure 2B), and gender (Figure 2C), clusters did not differ significantly. For clinical diagnosis (Figure 2D), the distribution of mild AD dementia was significantly different between each cluster, with Cluster 4 having the highest percentage of patients with mild AD dementia. For follow-up duration, four clusters differed significantly, with Cluster 1 having the longest follow-up duration. Regarding cognitive and functional measures, all tests (MMSE, CDR-SB, and FAQ) showed significant differences between the four clusters. For neurodegenerative markers (aVV, aHV, and FDG-PET), four clusters showed significant differences, except no difference in aVV between clusters 1 and 2 and no difference in aHV between clusters 3 and 4. Regarding CSF Aβ42 levels, Clusters 2–4 had lower levels of CSF Aβ42 than Cluster 1, while no other pairwise difference was observed. Regarding CSF tau proteins, Clusters 2–4 had higher levels of CSF t-tau and p-tau than Cluster 1, and Cluster 4 had higher levels of CSF t-tau and p-tau than Cluster 2, while no other pairwise difference was observed.

The results of the linear mixed-effects models, which investigated the relationship between cluster membership and longitudinal changes in other cognitive measures, neurodegenerative markers, and CSF AD pathologies over a 5-year follow-up period, are presented in Table 2 and Figure 4.

Concerning the models that involve cognitive and functional assessments (MMSE, CDR-SB, and FAQ), our analysis revealed that Clusters 2 through 4 experienced significantly greater decline (or worsening) relative to Cluster 1 (refer to Table 2 and Figures 4A–C). Utilizing EMMs for pairwise comparisons, we observed that the differences in slopes were statistically significant between each cluster (with all FDR-adjusted p-values being less than 0.0001).

For the aVV model (see Table 2 and Figure 4D), the cluster × time interactions were all significant, indicating that Clusters 2–4 had greater slopes (i.e., faster rates of ventricular enlargement) compared to Cluster 1. Pairwise comparisons showed that the slope difference was significant between each cluster (all FDR-adjusted p < 0.0001). For the aHV model (see Table 2; Figure 4E), the cluster × time interactions were all significant, indicating that Clusters 2–4 had steeper slopes (i.e., faster rates of hippocampal atrophy) compared to Cluster 1. Pairwise comparisons showed that the slope difference was significant between each cluster (all FDR-adjusted p < 0.05), except for a comparable level between Clusters 3 and 4 (FDR-adjusted p = 0.289). For the FDG-PET model (see Table 2 and Figure 4F), Clusters 2 and 3, but not Cluster 4, had steeper slopes (i.e., faster decline in brain glucose metabolism) compared to Cluster 1. Pairwise comparisons showed that the slope difference was significant between Clusters 1 and 2 (FDR-adjusted p = 0.0026), and between Clusters 1 and 3 (FDR-adjusted p = 0.007), while no other pairwise comparison was significant (all FDR-adjusted p > 0.05).

Regarding the models that invovle CSF AD biological markers (CSF Aβ42, t-tau, and p-tau levels), the cluster × time interactions were not significant, except for a slope difference on CSF p-tau between Clusters 4 and 1 (see Table 2 and Figures 4G–I). These findings suggested that the changes in CSF AD biomarkers over time were consistent across clusters, with the exception of CSF p-tau, where a difference in the rate of change was observed between Clusters 4 and 1. Pairwise comparisons showed that there were significant slope differences in CSF p-tau between Clusters 4 and 1 (FDR-adjusted p = 0.04), and between Clusters 4 and 2 (FDR-adjusted p = 0.04), while no other pairwise comparison was significant (all FDR-adjusted p > 0.05).

Additionally, a semiparametric bootstrap method was performed to quantify the uncertainty associated with the coefficients and to test the robustness of the results from the linear mixed-effects models (Supplementary Figure S2). For example, as shown in Supplementary Figures S2A–C, the findings from the models involving cognitive and functional measures can further be evidenced by visually examining the forest plots showing the slope difference relative to Cluster 1 (the reference group). The plots demonstrate how much the effect of interest in each of the three clusters differed relative to Cluster 1. All effects were significant relative to the reference group because none of the 95% confidence intervals contained 0. Additionally, the coefficients of Clusters 2–4 fell outside each other’s intervals, indicating that they were significantly different from each other. For other models, the results were largely unchanged and consistent with the pairwise comparisons described above.

Of the 291 MCI participants, two participants initially assigned to Cluster 4 in the cluster analysis (see Table 1) were reclassified as Cluster 3 due to the inadequacy of their small size as an independent group. Therefore, the cluster variable used in the survival analysis included 3 subgroups rather than 4 subgroups. Over a 5-year follow-up period, 103 (35%) participants converted to dementia. Figure 5 demonstrates the conversion rate to dementia using the Kaplan–Meier curves. A significant cluster difference in the conversion rate was observed using a log-rank test (x²[2] = 124; p < 0.001). All pairwise comparisons between the 3 clusters were significant (all FDR-adjusted p < 0.001). With regard to the type of dementia, of the 103 MCI participants who progressed to dementia, 98 (95.1%) participants were diagnosed with AD dementia, while 5 (4.85%) progressed to non-AD dementias, including 2 with primary progressive aphasia, 1 with Parkinson’s disease and Lewy body dementia features, 1 with progressive supranuclear palsy, and 1 who had experienced delirium in the past after being infected with the West Nile Virus.

Multinomial logistic regression models were performed to examine the associations between potential predictors at baseline and cluster membership. Table 3 shows the summary of multinomial logistic regression models. We built four models and assessed model fit using Nagelkerke’s R² (Nagelkerke, 1991). In the base model, all predictors captured 47.5% of the variability in the Cluster outcome (R² = 0.475). The cognition model explained 56.7% of the variability in the Cluster outcome (R² = 0.567), indicating that the MMSE explained an additional 9.2% of the total Cluster variability. In the neurodegeneration model, all predictors captured 67.4% of the variability in the Cluster outcome (R² = 0.674), suggesting that aHV and FDG-PET explained an additional 10.7% of the total Cluster variability. Meanwhile, the AD biomarker model explained 68.8% of the variability in the Cluster outcome (R² = 0.688), indicating that CSF Aβ42 and p-tau explained only an additional 1.4% of the total Cluster variability. Table 3 displays the adjusted odds ratios (aOR) and their 95% confidence intervals (CIs) for each model. For instance, in the AD biomarker model (the full model), compared with Cluster 1, there were consistent associations of membership to Cluster 2–4 with a clinical diagnosis of AD (aOR [95% CI]: 5.41 [2.54, 11.5], 12.6 [5.85, 27.1], and 44.9 [16.6, 121], respectively). MMSE, aHV, FDG-PET, and CSF p-tau were also consistently associated with cluster membership to Cluster 2–4. However, there were no significant associations between CSF Aβ42 levels and cluster membership.

Model simplification was conducted using stepwise variable selection with AIC as the stopping rule (see the seventh point in the statistical analyses section). The variables screened for inclusion were the same predictors as those in the AD biomarker model (see Table 3). The reduced model included clinical diagnosis, MMSE score, and FDG-PET, and partial effects plots with 95% pointwise confidence bands are presented in Figure 6A. This model resulted in an Area Under the Curve (AUC) of 0.912 (95% confidence intervals: 0.88–0.94; using DeLong statistics; Figure 6B). To evaluate the reliability of the model, a bootstrap overfitting-corrected calibration curve was generated with 1,000 iterations. Figure 6C demonstrates the excellent calibration of the model on the probability scale, as indicated by the close alignment of the calibration curve with the 45° line. Internal validation was performed using the bootstrap technique with 1,000 iterations, resulting in an optimism-corrected AUC of 0.910. A nomogram was created to facilitate an easy and practical estimation of the probabilities of experiencing steep cognitive decline in early AD (Figure 6D). Finally, simulated clinical trials were performed to investigate whether the nomogram would be used to enrich for trial populations in order to reduce sample size for a clinical trial involving individuals with early AD. As shown in Figure 6E, when including all eligible patients (no restrictions), the required sample sizes were 926.8 (95% CI: 822.6–1057.5). However, when including individuals predicted to experience steep cognitive decline using the nomogram, the required sample sizes were decreased to 400.9 (95% CI: 306.9–516.8).