A machine learning approach for potential Super‐Agers identification using neuronal functional connectivity networks

Abstract

INTRODUCTION

Aging is often associated with cognitive decline. Understanding neural factors that distinguish adults in midlife with superior cognitive abilities (Positive‐Agers) may offer insight into how the aging brain achieves resilience. The goals of this study are to (1) introduce an optimal labeling mechanism to distinguish between Positive‐Agers and Cognitive Decliners, and (2) identify Positive‐Agers using neuronal functional connectivity networks data and demographics.

METHODS

In this study, principal component analysis initially created latent cognitive trajectories groups. A hybrid algorithm of machine learning and optimization was then designed to predict latent groups using neuronal functional connectivity networks derived from resting state functional magnetic resonance imaging. Specifically, the Optimal Labeling with Bayesian Optimization (OLBO) algorithm used an unsupervised approach, iterating a logistic regression function with Bayesian posterior updating. This study encompassed 6369 adults from the UK Biobank cohort.

RESULTS

OLBO outperformed baseline models, achieving an area under the curve of 88% when distinguishing between Positive‐Agers and cognitive decliners.

DISCUSSION

OLBO may be a novel algorithm that distinguishes cognitive trajectories with a high degree of accuracy in cognitively unimpaired adults.

Highlights

• Design an algorithm to distinguish between a Positive‐Ager and a Cognitive‐Decliner.

• Introduce a mathematical definition for cognitive classes based on cognitive tests.

• Accurate Positive‐Ager identification using rsfMRI and demographic data (AUC = 0.88).

• Posterior default mode network has the highest impact on Positive‐Aging odds ratio.

1. INTRODUCTION

Aging is frequently characterized by cognitive decline in several domains. ¹ , ² The negative association between age and performance of cognitive areas like executive function, processing speed, visuospatial skills, and particularly memory are well known. ³ , ⁴ Furthermore, a significant decline in episodic memory is shown in adults with mild cognitive impairment (MCI) and Alzheimer's disease (AD). ⁵ , ⁶ , ⁷ Yet, there is substantial variation in how cognitive function evolves in mid‐ to late‐life adults. Some adults aged 80 years or older, called Super‐Agers, show cognitive performance that is similar to healthy middle‐aged adults, particularly for declarative memory. ⁸ , ⁹ , ¹⁰ , ¹¹ Similarly, we have recently found that roughly 20% of middle‐aged to early aged adults in the UK Biobank show gains over time in fluid intelligence, a form of executive function strongly impacted by aging. ¹² Cognitive health is considered an important factor in successful aging. ¹³ Therefore, it is necessary to investigate the neural correlates of Positive‐Agers, adults in midlife with cognitive gain over time, to determine how brain function may differ compared to cognitively unimpaired adults who nonetheless show age‐related cognitive decline.

Neuroimaging studies focused on Super‐Agers have examined regional brain volumes in areas mostly related to memory. Super‐Agers, based on superior episodic memory, showed minimal differences in cortical thickness compared to middle‐aged adults. Moreover, compared to age‐matched controls, Super‐Agers had more regional cortical thickness in areas critical for memory consolidation and retrieval, including the precuneus, the posterior cingulate, and the prefrontal cortices. ¹¹ Another study found that Super‐Agers had thicker anterior cingulate cortex and the least amount of neurofibrillary degeneration compared to age‐matched controls, as well as participants with MCI and AD. ⁸ Although studies have largely converged on differences in brain structure between adults with various levels of cognitive abilities, these methods are typically limited to comparisons of known groups. For precision medicine, however, developing techniques that distinguish individuals is essential; machine learning and prediction models could play a great role in this matter. ¹⁴

Beyond structural imaging, resting state functional magnetic resonance imaging (rsfMRI) provides the opportunity to understand how neuronal functional connectivity networks contribute to cognitive function. ¹⁵ For example, rsfMRI has frequently been used in classification models for neurodegenerative diseases. ¹⁶ A recent study ¹⁷ found that 32 late‐life Super‐Agers versus 58 age‐matched controls had better functional connectivity among brain areas critical for declarative memory. Ensemble classification using machine learning achieved high discrimination between these groups. However, larger sample sizes are warranted to avoid potential model overfitting and achieve robust solutions. It is also important to establish how intrinsic functional connectivity ¹⁸ explains longitudinal changes in cognitive performance between adults who show cognitive gains versus decline over time.

The current study leveraged brain rsfMRI and multivisit cognitive assessments from the UK Biobank. The goals of this study were to (1) introduce a principal component analysis (PCA)‐based labeling approach for the initial characterization of latent groups with different cognitive trajectories, and (2) create a hybrid algorithm of machine learning and optimization to optimally distinguish between largely middle‐aged participants who showed cognitive gains over time (ie, Positive‐Agers) versus cognitive decline.

2. MATERIALS AND METHOD

In this study, 15,003 participants were a part of the UK Biobank cohort, a long‐term prospective biomedical research study including comprehensive questionnaires, physical measures, cognitive function, imaging, and biological sampling on a cohort of more than 500,000 UK adults. ¹⁹ Participants were aged 55 to 70 years at the baseline visit in 2006 to 2010 ($t_1$). This visit and the first follow‐up visit in 2012 to 2013 ($t_2$) consisted of the following: (1) informed consent; (2) a touchscreen questionnaire; (3) a verbal interview; (4) eye measures; (5) anthropometric measures; and (6) blood/urine sample collection. In the subsequent two follow‐up visits starting in 2014 $(t_3)$ and 2019 $(t_4)$, imaging was done of the brain, heart, and body. ²⁰ , ²¹ Due to sample size concerns, we only utilize $t_3$ brain imaging data. Sociodemographic characteristics, occupation, lifestyle, and cognitive function were gathered by questionnaires using touchscreens or laptops. The UK Biobank protocol was approved by the Northwest Multi‐Centre Research Ethics Committee.

2.1. Demographic data

The demographic data include information on age, gender, body mass index (BMI), socioeconomic class, handedness, education level, skin color, waist circumference, tobacco use, and tobacco type. Age was defined as the age in years of each participant at their baseline visit. Socioeconomic class was defined by the participant's average total household income. There were five options provided based on UK Biobank Data‐Coding to be selected by participants in British pounds, which included “Less than 18,000,” “18,000 to 30,999,” “31,000 to 51,999,” “52,000 to 100,000,” and “Greater than 100,000.” These groups were labeled as Under, Lower, Middle, Upper‐Middle, and Upper class. For education level, a categorical variable was used with the following levels: college or other higher‐level status; postsecondary or vocational; secondary; and none of the previous groups. Finally, tobacco smoking status was defined as a categorical variable with the levels “Never smoked,” “Previously smoked,” and “Currently smoking.” The pair plots for the continuous variables in this dataset are shown in Figure S1. The bar plots for the frequency of the levels of each categorical variable are shown in Figure S2.

2.2. rsfMRI data

Imaging data used in this study, rsfMRI, is an indirect measure of neural activity based on changes in blood oxygenation and neural metabolic demand in the absence of a particular task. ²² In this approach, “network nodes” have been defined as voxel clusters that fluctuate most strongly in corresponding brain regions, while “network edges” have been defined as nodes that have weaker effects. ²³ Since raw imaging data are not useful directly, particularly for nonimaging experts, UK Biobank used a processing pipeline to generate both processed image and image‐derived phenotypes (IDPs). ²⁴ The detailed methods of image processing pipeline and image acquisition protocols are provided by both the UK Biobank imaging project ²⁴ and accompanying brain imaging documentation. ²⁵ This is briefly described as follows.

RESEARCH IN CONTEXT

1. Systematic review: The authors reviewed the literature comprehensively using traditional sources including PubMed, Google Scholar, conferences for both the contextual (aging‐related and neuronal connectivity networks) and technical (algorithm development) aspects. We provided a detailed description of the existing literature and our contribution to this research field. The relevant references are appropriately cited.

2. Interpretation: This study proposes a novel approach for distinguishing between Positive‐Agers and Cognitive Decliners using resting state functional magnetic resonance imaging (rsfMRI) and demographic data. The algorithm utilizes a principal component analysis (PCA)‐based labeling procedure to assign individuals to cognitive classes. The proposed algorithm outperformed baseline models and achieved a precision of 91% and an area under the curve of 88%.

3. Future directions: First, assess the generalizability of the proposed algorithm to other MRI modalities. Second, there is a need to validate the proposed methodology in independent samples. Third, employ more robust labeling procedures instead of PCA to avoid information loss.

UK Biobank brain imaging was done in three centers with identical scanners (3T Siemens Skyra) using the same standards and protocol. ²⁶ Processing steps ²⁵ using the FMRIB Software Library (FSL) first included motion correction, grand mean intensity normalization, high‐pass temporal filtering, echo‐planar image unwarping, gradient distortion correction unwarping, and removal of structured artifacts. ²⁴ Group independent component analysis (ICA) then reduced rsfMRI dimensionality to 25 orthogonalized clusters (D = 25). After removing noise components, 21 non‐noise components remained. ²⁴

Finally, connectivity between pairs of ICA components was estimated by partial correlation matrices. Then L2 regularization was applied to improve the estimated partial correlation matrix. ²⁴ , ²⁵ In rsfMRI, IDPs represent edge connectivity strengths and node fluctuation amplitudes. Key acquisition parameters for rsfMRI were spatial resolution = 2.4 mm, repetition time (TR) = 0.735 seconds, factor = 8 multiband accelerator. Table S1 describes the 21 neuronal components. Supplementary Text provides a detailed description of each rsfMRI feature. Figure S3 shows the Pearson correlation between different components.

2.3. Cognitive testing and latent cognitive groups

For timepoints $t_1$, $t_2$, and $t_3$, there was a roughly 5‐minute series of cognitive tests for fluid intelligence (FI), prospective memory (PM), pairs matching memory (PMM), and reaction time (RT). This corresponds to cognitive performance largely before rsfMRI was conducted at $t_3$ _. Despite their idiosyncratic nature, the general cognitive ability tapped by these tests highly corresponded to standardized neuropsychological tests in a subsample of UK Biobank participants. ²⁷

Fluid intelligence is measured by verbal and numerical reasoning using questions that require logic without any prior acquired knowledge. In this test, participants answered 13 multiple choice questions, including logical, numerical, and combinational types. The score was the number of questions with the correct answer in 2 minutes. ²⁸

For prospective memory, at the beginning of the cognitive test battery, participants were shown this message on the screen: “At the end of the games, we will show you four colored shapes and ask you to touch the Blue Square. However, to test your memory, we want you to actually touch the Orange Circle instead.” In the end, four shapes, including a blue square, pink star, grey cross, and orange circle, were seen by instruction of clicking on the blue square. If the participant touched the blue square, the prompt was restated. The score was one if the participants correctly touched the orange circle and 0 if they touched other shapes. ²⁹

The pairs matching memory task assessed visual memory. In this test, participants were shown a screen with several pairs of matching cards, and they were requested to memorize the matched cards for as many pairs as possible. Then, they were asked to match the cards that were turned face down in the fewest tries. The score was the number of errors made on the second trial of this test. ³⁰

The reaction time test was designed to assess the processing speed based on 12 rounds of a card game. In this test, participants were shown two cards with symbols. If the symbols were matched, they were requested to touch the button‐box on the desk immediately. If cards were different, they were supposed to do nothing. Five rounds were practice trials, and they were not counted. The score was the mean reaction to pressing the button in four rounds with matching cards. ³¹

Due to skewness, the following tests were transformed: pairs matching memory (log(x+1)) and reaction time (log).

We denoted the dataset with the cognitive test information as G. The time points of interest in this study are $t_1$ and $t_3$. Therefore, overall, we had eight features in dataset G:

$$\mathit{G}=\left(\mathit{F}{\mathit{I}}_1\mathbf{F}{\mathit{I}}_3\mathbf{P}{\mathit{M}}_1\mathbf{P}{\mathit{M}}_3\mathbf{PM}{\mathit{M}}_1\mathbf{PM}{\mathit{M}}_3\mathbf{R}{\mathit{T}}_1\mathbf{R}{\mathit{T}}_3\right).$$ (1)

Figure S4 shows the histograms of changes in cognitive test values between timepoints $t_1$ and $t_3$. It is worth noting that the decision to exclude time point $t_2$ in our analysis was primarily driven by a key logistical challenge: the significant loss of data that occurs when it is combined with other time points. By inclusion of cognitive tests for $t_2$, the sample size would dramatically decrease from 6369 to only 962 participants.

2.4. Data preparation

To prepare the data for the modeling phase, we applied multiple preprocessing steps. We denoted the dataset of integrated MRI and demographics as $X$. To bring continuous variables into the same scale, we used standardization as below:

$$x_{ij}^{new}=\frac{x_{ij}-\overline{x_j}}{s_{x_j}},$$ (2)

where $x_{ij}$ is the i‐th observation in the j‐th feature in $X$, and $\overline{x_j}$ and $s_{x_j}$ are the training mean and standard deviation for the j‐th feature, respectively. The final preprocessed dataset is denoted as $\mathbb{X}$.

Next, in dataset $G$ (ie, cognitive tests data), we removed observations for which cognition test results were not available for any of the time points $t_1$ or $t_3$. Then, we randomly split the observations into training $(G_{train}$) and testing ($G_{test}$) sets. We then standardized them using Equation (2) and created ${\mathbb{G}}_{train}$ and ${\mathbb{G}}_{test}$, respectively. The same split was then applied to the dataset $\mathbb{X}$, to ensure that the training and test sets across these two datasets include the same set of participants.

It should be highlighted that participants with missing values in any of the key areas—rsfMRI data, demographic information, or cognitive test values—were excluded from our study from the outset.

2.5. Overview of the method

The predictability of the class labels (ie, latent groups) in this report can be attributed to two sources: (1) the power of the classification model to capture the underlying pattern and distinguish between the classes; and (2) the degree to which the classes are well separated, which depends on how to define the Positive‐Ager group. In our study, initially, we did not have the class labels for participants. In other words, the classes were latent. Therefore, a supervised learning algorithm could not be used. Thus, we needed to have a mechanism for assigning labels to the participants based on some meaningful criteria and then predicting those classes using rsfMRI and demographic data. To achieve this goal, we developed an algorithm, named Optimal Labeling using Bayesian Optimization (OLBO), that automatically assigned labels to the participants using the information from the cognitive tests, such that it maximized the predictive capability of the classification model. We utilized the original cognitive tests in the UK Biobank to find the optimal labeling for distinguishing latent cognitive trajectory groups.

The proposed algorithm enabled superior predictions via an unsupervised labeling procedure. The algorithm consisted of two main components: machine learning and optimization. Logistic regression was used for the predictive side of the algorithm. Beside its simplicity and interpretability, it can be equipped with a feature selection mechanism through regularization. For the other side of the algorithm, to optimize the labeling procedure, we incorporated Bayesian optimization (BO). See Supplementary Text for detailed descriptions of the logistic regression and BO.

2.6. OLBO algorithm

The OLBO algorithm consists of three main procedures, including labeling, prediction, and optimization. OLBO starts with the cognition training set, ${\mathbb{G}}_{train}$. In each iteration, it suggests a set of class labels, Positive‐Agers or Cognitive Decliners, using the threshold values chosen by the BO in that iteration. A detailed description of the labeling procedure can be found in Section 2.7.

In the next step, using the labels assigned, a logistic regression model is trained on the training set and then evaluated using a 5‐fold cross‐validation (CV) approach. The average of the area under the receiver operating characteristic (ROC) curve ($\text{AUC}$), denoted as $\overline{AUC}$, is used as the primary metric for optimization. The objective function for each iteration in the BO is calculated using the following:

$${\mathcal{L}}^{\left(j\right)}=1-{\overline{\mathrm{AUC}}}^{\left(j\right)},\forall j=1,2,\cdots ,J.$$ (3)

Based on the value of the objective function and the uncertainty in the posterior, BO selects the next best set of parameter values, $\theta$, from the feasible space $\mathcal{A}$, and specifies the threshold values for the next iteration along with some other parameters required for tuning the logistic regression model. The algorithm repeats the process $J$ times. The flowchart for the OLBO algorithm is illustrated in Figure 1A. The pseudocode for the algorithm is provided in Figure 1B.

FIGURE 1.

(A) Flowchart of the OLBO algorithm. (B) Pseudocode for the OLBO algorithm. $P{C}_1$ is the first component of PCA‐transformed cognitive test data; ${\mathbb{G}}_{train}$ is the of cognitive tests training set; ${\mathbb{X}}_{train}$ is the predictors training set; ${\theta }^{\ast }$ is the optimal parameter vector found by Bayesian optimization; $J$ is the total number of iterations for the optimization process; $y_{train}^{(j)}$ and $y_{test}^{(j)}$ are the class labels for training and test sets, respectively; ${\mathcal{L}}^{(j)}$ is the objective function value in iteration $j$. FI, fluid intelligence; OLBO, Optimal Labeling using Bayesian Optimization; PCA, principal component analysis; PM, prospective memory; PMM, pairs matching memory; RT, reaction time.

The OLBO algorithm has a parameter vector $\theta$ that is optimized for improving the overall performance. The vector $\theta$ can be written as:

$$\theta =\left({\tau }_1,{\tau }_2,\psi ,\phi \right),\theta \in \mathcal{A},$$ (4)

where $\mathcal{A}$ is the user‐defined parameter space from which the sampling is drawn. The parameters ${\tau }_1$ and ${\tau }_2$ are lower and upper percentile thresholds, respectively, by which the labeling procedure is done. In this study, the domain of ${\tau }_1$ and ${\tau }_2$ is set as below:

$${\tau }_1\in \left\{0.05,0.45\right\},{\tau }_2\in \left\{0.55,0.95\right\}.$$ (5)

The two thresholds are initially sampled independently and uniformly, as shown below:

$${\tau }_1\sim uniform\left(0.05,0.45\right),{\tau }_2\sim uniform\left(0.55,0.95\right).$$ (6)

In addition to the parameters described above, we have two specific parameters pertinent to the logistic regression model: the cost, $\psi$ (inverse of regularization strength), and $\phi$, which is the mixing parameter that controls the balance between L1 and L2 regularization in the elastic net loss function (see Supplementary Text). We used log‐uniform and uniform distributions for $\psi$ and $\phi$, respectively:

$$\psi \sim loguniform\left(\exp \left(-10\right),100\right),$$ (7)

$$\phi \sim uniform\left(0,1\right).$$ (8)

BO is regarded as a black‐box optimization tool, particularly effective when the internal workings of the objective function (here, $\mathcal{L}$, which is dependent on AUC), are complex or unknown. Its strength lies in its ability to efficiently navigate the optimization landscape without requiring explicit gradients or other detailed information about the function. By constructing a probabilistic model, BO intelligently predicts which points in the parameter space are likely to yield better outcomes, based on past evaluations. This approach is especially valuable in scenarios where each evaluation of the objective function is costly or time‐consuming. BO's method of balancing exploration (testing new possibilities) and exploitation (refining known good areas) ensures a more targeted and efficient search for the optimal parameters.

2.7. Labeling procedure

In order to label participants, we used the cognitive dataset ${\mathbb{G}}_{train}$ including $F{I}_1,F{I}_3,P{M}_1,P{M}_3,PM{M}_1,PM{M}_3,R{T}_1$, and $R{T}_3.$ For this purpose, after applying PCA to ${\mathbb{G}}_{train}$, and extracting the first component ($P{C}_1$), we need to find the direction of $P{C}_1$. In other words, we want to know whether higher values of $P{C}_1$ are accompanied by a higher chance of being in the Positive‐Ager or Cognitive Decliner classes.

In Figure 2, we plotted the first two components of PCA (scaled) with the loading vectors. As shown, $FI$ and $PM$ are negative in $P{C}_1$ while $PMM$ and $RT$ are positive. We also know that higher values of $FI$ and $PM$ are followed by a higher likelihood of being a Positive‐Ager, while for PMM and RT the opposite is true. Therefore, we can conclude that the relation between $P{C}_1$ and Positive‐Ager is contrariwise, meaning that participants with smaller values of $P{C}_1$ are more likely to be in the Positive‐Ager class.

FIGURE 2.

First two components of principal component analysis with the loading vectors. FI, fluid intelligence; PM, prospective memory; PMM, pairs matching memory; RT, reaction time.

Now, with the knowledge of the $P{C}_1$ direction, we can use the sampled ${\tau }_1^{(j)}$ and ${\tau }_2^{(j)}$ in iteration j to obtain the class labels:

$$y_i^{\left(j\right)}=\left\{\begin{array}{c}0,if{u}_i\ge P_{{\tau }_2^{\left(j\right)}}\left(P{C}_1\right)\\ 1,if{u}_i\le P_{{\tau }_1^{\left(j\right)}}\left(P{C}_1\right)\end{array}\forall j=\left\{1,2,\text{…},J\right\}\right.,$$ (9)

where $y_i^{(j)}$ is the class label for $x_i\in \mathbb{X}$ in iteration $j$ of the algorithm, $u_i$ is the $i$‐th element (observation) in $P{C}_1$ quantifying the cognitive performance of participant $i$, $P_{{\tau }_1^{(j)}}(P{C}_1$) is the ${\tau }_1^{(j)}$‐percentile of $P{C}_1$, and $P_{{\tau }_2^{(j)}}(P{C}_1$) is the ${\tau }_2^{(j)}$‐percentile of $P{C}_1$. In this study, class label 0 was used to denote Cognitive Decliner and class label 1 represents Positive‐Ager.

2.8. Baseline models

We compared the performance of the OLBO algorithm when using rsfMRI data along with the demographics against three sets of baseline models. For the first set of baseline models, we modified the labeling procedure by utilizing only one type of cognition test at a time. This resulted in four different models, each corresponding to one of the cognitive tests: $FI$, $PM$, $PMM$, or $RT$. For each model in this category, we used both timepoints $t_1$ and $t_3$. The second set of baseline models utilized only a single time point, either $t_1$ (baseline) or $t_3$ for labeling. The third group restricted input features to be only one of the rsfMRI‐ or demographic‐related features. For consistency, the same procedure was used for tuning and training all models, including the main OLBO algorithm and all baseline models.

2.9. Evaluation metrics

Different metrics were used to evaluate the algorithms. Terms were defined as follows:

• True Positives, or $tp$: Number of Positive‐Agers that were predicted as Positive‐Agers

• False Positives, or $fp$: Number of Cognitive Decliners that were predicted as Positive‐Agers

• True Negatives,or $tn$: Number of Cognitive Decliners that were predicted as Cognitive Decliners

• False Negatives, or $fn$: Number of Positive‐Agers that were predicted as Cognitive Decliners

The evaluation metrics and their equations are the following:

$$Accuracy=\frac{tp+tn}{tp+tn+fp+fn},$$ (10)

$$Precision=\frac{tp}{tp+fp},$$ (11)

$$Recall\left(Sensitivity\right)=\frac{tp}{tp+fn},$$ (12)

$$Specificity=\frac{tn}{tn+fp},$$ (13)

$$F1\mathrm{Score}=\frac{2\ast Precision\ast Recall}{Precision+Recall}.$$ (14)

3. RESULTS

In this section, first, we explore the demographics of the participants in the final optimal grouping. We also examine differences between the Positive‐Agers and Cognitive Decliners across different neural components and cognition tests. Then, we show the numeric results obtained from the set of baseline models and the full OLBO algorithm, where the full OLBO performed best. A sensitivity analysis is conducted in a separate subsection to investigate the behavior of the algorithm more thoroughly. Finally, we describe the algorithm's performance with respect to the set of parameters selected in each trial.

3.1. Optimal labeling

Using the first component of the PCA‐transformed cognition data, the optimal group of Cognitive‐Agers and Cognitive Decliners were operationally defined as participants scoring in the bottom 11% (${\tau }_1=0.11)$ and top 5% (${\tau }_2=0.95$), respectively, where ${\tau }_1$ and ${\tau }_2$ are lower and upper thresholds (see Figure 3 for a visual definition of the optimal Positive‐Ager and Cognitive Decliner classes).

FIGURE 3.

Visual representation of the optimal Positive‐Agers versus Cognitive Decliners.

To have a more precise definition of Positive‐Agers and Cognitive Decliners, we provided the mathematical definition obtained from the algorithm. In order to use equation (9), we need to define $u_i$, $P_{{\tau }_1^{(j)}}(P{C}_1)$, and $P_{{\tau }_2^{(j)}}(P{C}_1)$:

$$u_i=w.{\mathcal{g}}_{\mathcal{i}},$$ (15)

where

$$w=\left(w_{F{I}_1},w_{F{I}_3},w_{P{M}_1},w_{P{M}_3},w_{PM{M}_1},w_{PM{M}_3},w_{R{T}_1},w_{R{T}_3}\right)$$ (16)

is the weight vector obtained from PCA loadings for the first component (see Table S2, column $P{C}_1$ for the values), and ${\mathcal{g}}_{\mathcal{i}}$ is the $i$‐th observation (participant) in $\mathbb{G}$, comprising of the scaled cognitive test values. The mean and standard deviation used to scale the cognitive tests are shown in Table S3. Therefore,

$$y_i^{\ast }=\left\{\begin{array}{c}CognitiveDecliner,if{u}_i\ge 2.60\\ PositiveAger,if{u}_i\le -1.70\end{array}\right.,$$ (17)

where $y_i^{\ast }$ is the optimal class label assigned to $i$‐th observation (participant).

One interesting finding from the proposed labeling definition was that the algorithm assigned larger weights in magnitude to cognitive tests at time point $t_3$ compared to those at $t_1$ (see Table S2). This tendency to prioritize recent cognitive test values is likely due to the closer temporal alignment of these tests with the rsfMRI data, which is aligned with the expectation as the rsfMRI data are collected at the third visit. OLBO seems to intuitively understand and incorporate the significance of the latest cognitive assessments, hence adjusting the weights to give more emphasis on the recent time point.

3.2. Demographic information of latent cognitive groups

Table 1 shows the descriptive statistics of the initial sample of participants as well as the final sample (after labeling), for each cognitive class. Univariate comparisons were done using either the chi‐square independence test for the categorical variables or two‐sample two‐sided Kolmogorov–Smirnov tests for the continuous variables. Briefly, Positive‐Agers were more likely to be men, of higher socioeconomic status, achieved more education, and were 3.51 years younger. Critically, age relative to other features was a modest factor for model fit when classifying latent groups.

TABLE 1.

Descriptive statistics of the demographic features in the initial and final (after labeling) sample.

Variable	Level	Unit	Initial sample (6369)	Optimal labeling (965)		p value
				Decliners	Positive‐Agers
Sex	Male Female	No. (%)	3333 3036	137 (24.3) a 139 (34.6)	426 (75.7) 263 (65.4)	< 0.001 b
Household income	Under class Lower class Middle class Upper‐middle class Upper class	No. (%)	889 1778 1897 1414 391	91 (62.8) 100 (40.8) 35 (19.3) 27 (11.5) 5 (7.6)	54 (37.2) 145 (59.2) 222 (80.7) 207 (88.5) 61 (92.4)	< 0.001
Handedness	Ambidextrous Left‐handed Right‐handed	No. (%)	78 618 5673	6 (60.0) 36 (36.0) 234 (27.4)	4 (40.0) 64 (64.0) 621 (72.6)	0.017
Education	Secondary education post‐secondary or vocational college or similar other education	No. (%)	664 1005 4346 354	32 (55.2) 60 (44.8) 121 (17.1) 63 (96.9)	26 (44.8) 74 (55.2) 587 (82.9) 2 (3.1)	< 0.001
Skin color	Brown‐Skinned Olive‐skinned Pale‐skinned	No. (%)	12 1201 5156	2 (66.7) 61 (33.0) 213 (27.4)	1 (33.3) 124 (67.0) 564 (72.6)	0.11
Tobacco use	Non‐smoker Prior smoker Smoker	No. (%)	3768 2324 277	169 (28.6) 99 (28.7) 8 (27.6)	422 (71.4) 246 (71.3) 21 (72.4)	0.99
Tobacco type	Cigars pipes Hand‐rolled cigs Manufactured cigs Non‐smoker	No. (%)	43 25 118 3768	1 (20.0) 1 (25.0) 5 (38.5) 269 (28.5)	4 (80.0) 3 (75.0) 8 (61.5) 674 (71.5)	0.84
Age	–	Years	60.88 ± 3.8 c	71.46 ± 4.3	67.95 ± 3.8	< 0.001
Body mass index	–	Kg/m2	18.19 ± 2.9	18.26 ± 2.9	18.36 ± 2.9	0.99
Waist circumference	–	cm	88.97 ± 11.9	89.07 ± 11.6	89.88 ± 11.7	0.69

^a Values in parentheses show the percentage of participants in a cognitive class.

^b The bold values show statistical significance (p values less than 0.05).

^c Mean ± standard deviation.

3.3. Neuronal functional connectivity networks comparisons

First, we examined differences in intrinsic functional connectivity for 21 neuronal networks (ie, independent components) among two latent cognitive classes: Positive‐Agers and Cognitive Decliners (see Figure 4A). Except for components 7 and 10, Positive‐Agers showed a significantly higher mean intrinsic functional connectivity. The numerical output for this Figure is summarized in Table S4.

FIGURE 4.

(A) Boxplots of neuronal functional connectivity network values for Positive‐Agers (green) versus Cognitive Decliners (red). A t‐test was conducted for each component to examine any significant difference in the average neural component values representing degree of intrinsic functional connectivity. (B) Comparison of cognitive tests between Positive‐Agers and Cognitive Decliners. An independent t‐test was conducted for fluid intelligence, pairs matching memory, and reaction time cognitive tests separately at timepoint $t_1$ (ie, baseline) and $t_3$. We used a proportion z‐test for the prospective memory cognitive test, where we wanted to test whether the success rate (ie, percentage of participants with a correct initial answer) is the same between Positive‐Agers and Cognitive Decliners or not. ns, nonsignificant (p > 0.05); rsfMRI, resting state functional magnetic resonance imaging. *p < 0.05, **p < 0.01, ***p < 0.001, ****p < 0.0001.

3.4. Cognitive test comparisons

We also investigated the difference in cognitive tests among the Positive‐Agers and Cognitive Decliners, as shown in Figure 4B. As expected, Cognitive Decliners had worse FI and memory scores, as well as slower reaction time.

3.5. Classification of latent cognitive groups

In this section, we compared the performance of three sets of baseline models versus the full OLBO algorithm using all available demographic and rsfMRI features. Each baseline model examined the effect of an altered component, which is one of the labeling inputs (eg, cognitive tests) or predictor variables (eg, rsfMRI and demographics). Baseline models in groups one and two assessed the predictability of labels generated through the utilization of partial labeling inputs from rsfMRI and demographic data (ie, same predictors as full OLBO but altered labeling inputs). By contrast, baseline models in group three examine the impact of exclusion of one of the rsfMRI or demographic variables in predicting the cognitive classes generated from the complete cognitive data (ie, same labeling inputs as full OLBO but altered predictor subset). The main goal of this study was to find a classification model that best predicted who would be in the Positive‐Ager versus Cognitive Decliner groups. Table 2 shows that the full OLBO algorithm outperformed all baseline models. This set of comparisons revealed that (1) using the combination of all cognition tests is more robust than one test alone; (2) labeling based on a single time point leads to inferior results compared to the labeling with both $t_1$ and $t_3$ time points; (3) between single time point labeling procedures, the time point using the most recent cognition tests showed better performance; (4) using rsfMRI and demographics combined leads to superior performance overall; and (5) the OLBO algorithm is a promising tool to assign individuals to cognitive groups, given a feature input.

TABLE 2.

Evaluation metrics for the baseline models versus full OLBO for classifying Positive‐Agers versus Cognitive Decliners.

#	Model	Altered component	Accuracy	Precision	Sensitivity	Specificity	F1	AUC	Size	Ratio a
1	Baseline 1: FI‐based	Labeling inputs	0.80 b	0.77	0.82	0.78	0.80	0.86	689	369/320
2	Baseline 2: PM‐based labeling	Labeling inputs	0.60	0.15	0.42	0.63	0.23	0.57	6239	1319/4920
3	Baseline 3: PMM‐based labeling	Labeling inputs	0.63	0.32	0.55	0.65	0.41	0.63	2057	540/1517
4	Baseline 4: RT‐based labeling	Labeling inputs	0.62	0.69	0.63	0.61	0.66	0.68	865	508/357
5	Baseline 5: $t_1$‐based labeling	Labeling inputs	0.63	0.62	0.63	0.64	0.62	0.73	706	350/356
6	Baseline 6: $t_3$‐based labeling	Labeling inputs	0.78	0.70	0.80	0.76	0.75	0.84	882	373/509
7	Baseline 7: rsfMRI Only	Predictors	0.60	0.91	0.61	0.53	0.73	0.61	2915	2562/353
8	Baseline 8: Demographics only	Predictors	0.77	0.70	0.76	0.77	0.73	0.84	905	577/328
9	Full OLBO	–	0.77	0.91	0.76	0.80	0.83	0.88	965	689/276

Abbreviations: AUC, area under the curve; FI, fluid intelligence; OLBO, Optimal Labeling using Bayesian Optimization; PM, prospective memory; PMM, pairs matching memory; rsfMRI, resting state functional magnetic resonance imaging; RT, reaction time.

^a Ratio of Positive‐Agers to Cognitive Decliners.

^b Values in bold font show the highest value for each metric.

Overall, the proposed algorithm showed equal or better performance in all metrics except for accuracy and sensitivity. However, OLBO with all features had the highest AUC (88%), which was the primary criterion for optimization. Critically, rsfMRI data were needed to ensure by far the largest proportion of correctly identified participants in latent cognitive groups (ie, 91% precision). Indeed, the maximal precision value was attained with all of the cognitive tests utilized, and only when rsfMRI data were incorporated into the set of predictors. Therefore, the likelihood that individuals classified by the algorithm as Positive‐Agers actually belong to this category, as per the employed labeling definition, was considerably high for these cases (models 7 and 9). Figure 5 shows the ROC curves for the final OLBO algorithm compared to the baseline models.

FIGURE 5.

Receiver operating characteristic curves. The true positive rate is plotted against the false positive rate for the full OLBO algorithm (red line) and all baseline models. FI, fluid intelligence; OLBO, Optimal Labeling using Bayesian Optimization; PM, prospective memory; PMM, pairs matching memory; rsfMRI, resting state functional magnetic resonance imaging; RT, reaction time.

In the first group of baseline models detailed in Table 2 (models 1 to 4), the model employing $\mathrm{FI}$‐based labeling exclusively demonstrated superior performance. The $\mathrm{RT}$‐based labeling model yielded mediocre results. However, models that relied solely on the $\mathrm{PM}$ or $\mathrm{PMM}$ test for labeling exhibited notably low precision and sensitivity. Regarding the second set of models (Table 2, models 5 and 6), the one that utilized $t_3$ cognition test data for labeling surpassed its counterpart, which relied only on baseline data, in all performance metrics. For the final group of baseline models (Table 2, models 7 and 8), the model that used only demographic features outperformed the one with rsfMRI features in all metrics, with the exception of precision and F1‐score. The full OLBO model (Table 2, model 9), which incorporated both rsfMRI and demographic features, and utilized cognition test data from both $t_1$ and $t_3$ time points for labeling, was deemed the most effective. This model excelled in terms of precision and overall fit, making it the most robust among the evaluated models.

The data presented in Table 2 indicate disparity in the class frequencies between Positive‐Agers and Cognitive Decliners. This disparity is particularly evident in certain models, such as models 3 and 7, where the imbalance ratio is significantly high. To mitigate potential bias favoring the majority class in these instances, a cost‐sensitive approach was employed during the training of all logistic regression models: The weighting assigned to each class was considered to be inversely proportional to its frequency in the data. Consequently, this approach places a greater penalty on the misclassification of the less prevalent class, a factor that is directly incorporated into the loss function. This strategy ensures a more balanced and equitable treatment of both classes during model training.

Next, for the full OLBO model, as explained in the Supplementary Text, we analyzed the importance of each feature using their coefficient in the OLBO algorithm (see Figure S5).

Figure 6 shows the odds ratio of Positive‐Aging. For the set of neuronal functional connectivity networks, a 1‐unit increase in the posterior default mode network (component 20) has the highest positive impact on the odds of being a Positive‐Ager (odds ratio = 1.4). Conversely the affect processing network (component 10) had the largest negative impact on the odds of Positive‐Aging (odds ratio = 0.643).

FIGURE 6.

Odds ratios of the predictor variables in the full OLBO model. The blue color shows a positive impact, gray has no significant effect, and orange represents variables with negative effect on the odds of Positive‐Aging. OLBO, Optimal Labeling using Bayesian Optimization.

3.6. Sensitivity analyses

We conducted a comprehensive set of sensitivity analyses with respect to the value of percentile thresholds for classification metrics. First, we plotted the achievable AUC for different combinations of threshold percentiles ${\tau }_1$ and ${\tau }_2$ (see Figure S6).

It can be observed that as the algorithm chooses more extreme values for ${\tau }_1$ and ${\tau }_2$, the AUC improves. A more detailed analysis of the threshold effect on different metrics can be found in Figure S7.

We also investigated the relationship between the final sample size and the values of ${\tau }_1$ and ${\tau }_2$ (see Figure S8). This depicts a trade‐off between generalizability (sample size) and predictability (AUC). As the algorithm becomes stricter and opts for more extreme values for the thresholds, model performance improves but sample size is reduced. In other words, more stringent thresholds for identifying an observation as Positive‐Ager or Cognitive Decliner removes borderline cases and decreases generalizability to a community population. Fortunately, this analysis enabled us to decide between thresholds that optimally matched performance and robustness. Because the focus of this study was model's performance, the OLBO algorithm followed the stricter approach.

3.7. OLBO details

Finally, we explored the results pertaining to the proposed algorithm. In each iteration of the OLBO algorithm, a combination of parameters sampled from the feasible domain was used. The loss function corresponding to that trial was recorded. To examine the effect of each variable in our algorithm, including ${\tau }_1$, ${\tau }_2$, $\psi ,$ and $\phi$, we plotted the values sampled for each variable against the loss function resulted in that iteration (see Figure S9).

4. DISCUSSION

Aging is often considered an inexorable journey to decreased function in several cognitive domains and a higher risk of dementia. ¹ , ² However, there is the hope of successful cognitive aging seen in older Super‐Agers, who have comparable cognitive function versus considerably younger adults. ⁹ By studying middle‐aged adults who show better cognition over time and relative to their peers (ie, Positive‐Agers), we can better understand biomarkers and potential mechanisms. In turn, this may lead to improvements in cognitive function through targeted lifestyle or pharmacological therapies before clinically significant cognitive decline occurs.

We previously found that vascular and metabolic blood biomarkers achieved good performance in distinguishing between UK Biobank participants showing cognitive gains or decline over 7 to 10 years. ¹² The current study focused on whether the neuronal functional connectivity network, an indirect measure of neural activity, successfully predicted different cognitive trajectory types over time in UK biobank adults. We propose a novel hybrid algorithm, OLBO, that incorporates machine learning and BO to distinguish between Positive‐Agers and Cognitive Decliners using demographics and rsfMRI data. Compared to baseline models, the full OLBO model showed excellent overall performance of 88% AUC. Further, the algorithm successfully predicted Positive‐Agers with a precision of 91%.

First, by examining baseline models, it is possible to understand which cognitive domains best reflected the overall pattern of cognitive function among latent groups and relevant neuronal functional connectivity network correlates. $\mathrm{FI}$‐ and to a lesser degree $\mathrm{RT}$‐based labeling approaches showed better model performance compared to memory indices. The $\mathrm{FI}$ score, which corresponds to verbal and numeric reasoning, correlates with default mode network (DMN) resting state connectivity. ³² Interestingly, higher posterior DMN connectivity was the strongest network predictor for being a Positive‐Ager. $\mathrm{RT}$ is related to raw processing speed and has been correlated with rsfMRI outcomes in several reports. ³³ , ³⁴ , ³⁵ Specifically, with higher $\mathrm{RT}$ values (ie, longer processing time), dorsal anterior cingulate cortex showed weaker functional dissociation relative to the precuneus. ³⁶ We found that more intrinsic functional connectivity in a dorsolateral prefrontal and anterior cingulate network (component 16) corresponded to a greater likelihood of being a Cognitive Decliner. $\mathrm{PM}$ and $\mathrm{PMM}$ cognitive tests, which measure prospective and visual memory, respectively, performed poorly according to precision and sensitivity metrics. Executive control network and default DMN regions are associated with poor episodic memory. ³⁵ Furthermore, stronger connectivity in DMN is related to better working and episodic memory. ³⁵ , ³⁷ Also, spatial working memory may show an increase after hyperbaric oxygen administration. ³⁸

One of the analyses conducted in this study was feature importance evaluation. We described the metric used as the feature importance in Section 3.5. We observed that components 1, 2, 5, 6, 11, 12, 13, 14, 17, 18, 19, and 20 are influencing the odds of being a Positive‐Ager versus Cognitive Decliner in a positive way, meaning that a unit increase in the value of any of these components is followed by an increase in the odds ratio. On the other hand, components 3, 4, 7, 8, 9, 10, 15, 16, and 21 turned out to be negatively influential on the odds of Positive‐Aging. In particular, the posterior and anterior DMN component labeled 20 was the best performing index. Preservation of both anterior and posterior DMN is associated with a reduced likelihood of developing cognitive decline in participants with MCI. ³⁹

Among demographic features, the odds of being Positive‐Ager are 1.595 as high for males compared to females and having “other education” levels drops the odds of Positive‐Aging the most by a factor of 0.817, given that all other variables stay the same. For household income, being in the upper, middle, and upper‐middle socioeconomic classes increases the odds ratio, while being in the underclass group negatively influences the Positive‐Aging odds. As expected, age negatively affects the odds of being a Positive‐Ager, and this was found to be by a factor of 0.902 when other variables are kept constant.

It is worth noting that the high odds ratio linked to certain demographic factors like handedness, tobacco use, and skin color, warrants careful interpretation due to potential influences arising from the limited number of participants in specific subcategories. For example, in our sample, the distribution of right‐handed, left‐handed, and ambidextrous participants was 89.1%, 9.7%, and 1.2%, respectively. While this distribution mirrors the usual patterns seen in the general population, suggesting no bias in our sample study, it is crucial to approach the interpretation of these variables with caution. This caution is necessary because the relatively small proportion of left‐handed and ambidextrous participants might skew the results, particularly in relation to the odds ratio. Therefore, while such demographic variables provide interesting insights, their implications should be considered within the context of the study's sample limitations.

It is important to differentiate the suggested algorithm from traditional machine learning methodologies in two aspects. First, in supervised learning, the class labels are provided to the models in advance, enabling them to discern patterns between the input features and labels. Contrarily, in the context of the algorithm under discussion, class labels are initially unknown. Throughout each optimization cycle, with the provision of proposed parameters and the consequent class labels, the scenario simplifies to a conventional supervised learning paradigm. Second, in traditional machine learning, given the same population, different feature sets are used to evaluate the efficacy of each feature set in correct predictions; however, here, finding the optimal subpopulation is an intrinsic part of the methodology. The algorithm concentrates on identifying the optimal subpopulation that most effectively delineates the classes given a specific set of features. It is important to emphasize that our analysis maintains a constant baseline—the initial sample of 6369 participants—across all models. This approach allows for a fair and meaningful comparison of the algorithm's performance under different labeling and predictor scenarios. For further details on differences between the proposed algorithm and traditional machine learning models, refer to the Supplementary Text, Section 5.1.

This study offers several significant contributions, as follows:

1. First, we introduced cognitive classes (Positive‐Ager and Cognitive Decliner) through a mathematical expression using multiple cognitive tests. This straightforward representation showcases how these cognitive tests can be utilized to classify cognitive classes, devoid of any supplementary information. Moreover, the resultant equation elucidates the individual contribution of each test to this cognitive separation.

2. The proposed algorithm effectively discerns between the two distinct classes by employing the rsfMRI and demographic information. This classification task illuminates the extent to which rsfMRI components and demographic attributes influence Positive‐Aging.

3. Leveraging the power of BO within the algorithm equips us with an optimal configuration to effectively segregate the cognitive classes.

4. While the primary goal of this study was to achieve peak performance, the algorithm enables analysts to choose any level of trade‐off between performance (AUC) and generalizability (sample size). We provided the trade‐off and the pareto frontier for these two objectives.

This study has a few limitations. Relying primarily on the first principal component could lead to the omission of significant information which, if retained, could augment predictive power. Furthermore, it would be beneficial to replicate the procedure used in this study using other principal components for comparative analysis. Finally, in this study, we assessed the effectiveness of our algorithm using specific performance evaluation metrics. Future analysis could focus on external criteria beyond performance metrics, to assess the quality of cognitive class separation or predict future cognitive decline. Such research would contribute to a deeper understanding and refinement of cognitive labeling methodologies.

In summary, this study utilizes rsfMRI data and demographic information to distinguish between Positive‐Ager and Cognitive Decliner groups. For this purpose, we proposed the OLBO algorithm that finds the cognitive class labels according to the cognitive information such that it maximizes the classification performance of the predictive model (here, logistic regression). To evaluate the performance of the proposed algorithm, we compared it against three sets of baseline models, one group with a restricted set of features, and the two other groups with a modified labeling procedure. OLBO demonstrated a superior performance with an AUC of 88%, precision of 91%, accuracy of 77%, sensitivity of 76%, and specificity of 80%. This study not only proposes a solution to find the best performing model to distinguish between the Positive‐Ager and Cognitive Decliner groups, but also provides a trade‐off between generalizability (sample size) and predictability (AUC) through a sensitivity analysis of the labeling procedure.

AUTHOR CONTRIBUTIONS

All authors contributed to conceptualization; Mohammad Fili and Parvin Mohammadiarvejeh performed data curation; Mohammad Fili and Parvin Mohammadiarvejeh performed formal analysis; Auriel A. Willette conducted funding acquisition; Auriel A. Willette and Guiping Hu conducted the investigation; Mohammad Fili designed the methodology; Mohammad Fili and Auriel A. Willette were responsible for project administration; Mohammad Fili was in charge of software; Guiping Hu and Auriel A. Willette conducted supervision; Guiping Hu, Brandon S. Klinedinst, and Auriel A. Willette performed validation; Mohammad Fili oversaw visualization; Mohammad Fili, Parvin Mohammadiarvejeh, and Auriel A. Willette wrote the original draft; all authors reviewed and edited the final version of the manuscript.

CONFLICT OF INTEREST STATEMENT

This study uses UK Biobank data. UK Biobank has ethical approval from the North West Multi‐centre Research Ethics Committee (MREC) (https://www.ukbiobank.ac.uk/learn‐more‐about‐uk‐biobank/about‐us/ethics). Written informed consent was obtained from all participants.

STATEMENTS AND DECLARATIONS

Author disclosures are available in the Supplementary Files.

Supporting information

Supporting Information

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Supporting Information

Fili M, Mohammadiarvejeh P, Klinedinst BS, et al. A machine learning approach for potential Super‐Agers identification using neuronal functional connectivity networks. Alzheimer's Dement. 2024;16:e12595. 10.1002/dad2.12595