PsychoAge and SubjAge: development of deep markers of psychological and subjective age using artificial intelligence

Psychological and subjective age estimation

To develop psychological clocks, we trained two DNN’s using anonymized surveys from MIDUS 1 — PsychoAge and SubjAge. The former was designed to estimate human chronological age based on a set of 50 psychosocial features, and the latter — human subjective age using the same set of features.

During CV, PsychoAge reached an MAE of 6.70 years and an epsilon accuracy of 0.78, while SubjAge reached an MAE of 7.32 years and an epsilon accuracy of 0.74 (Figure 2). Both PsychoAge and SubjAge outperformed baseline median age assignment in MIDUS 1 (N_samples=6071). When verified in MIDUS 2 and MIDUS Refresher, these quality scores dropped, although remained better than baseline values (Table 1).

Figure 2. PsychoAge and SubjAge provide better than baseline estimates of chronological age and subjective age, respectively, in MIDUS 1 (N samples = 6071). (A) PsychoAge chronological age predictions in MIDUS 1 (MAE = 6.70 years; epsilon accuracy = 0.78). (B) SubjAge subjective age predictions in MIDUS 1 (MAE = 7.32 years; epsilon accuracy = 0.74).

We further tested the efficiency of our approach on significantly smaller samples by dividing MIDUS 1 into age groups based on chronological age (25-39, 40-64, 65-75 years) and training new DNNs for each one of them with the same set of 50 variables. Among the chronological age predictors, only the one trained on 682 samples from the 65-75 years group showed worse than baseline performance. Meanwhile, among the subjective age predictors only the 25-39 years DNN performed worse than baseline.

Lower chronological age estimation accuracy in the elderly may be attributed to greater lifestyle homogeneity in this cohort. We also hypothesize that younger people have a more fluid concept of aging compared to older adults, which might have affected the 25-39 cohort model performance. These hypotheses, however, were not tested in this work and need to be addressed in a follow-up project.

MIDUS 2 (N=3870 respondents) and MIDUS Refresher (N=2521 respondents) datasets were used for model validation. Both models remained accurate when tested in these datasets (Figure 3). PsychoAge showed an MAE of 7.18 and 7.73 years, respectively, while SubjAge — an MAE of 8.53 and 8.56 years, respectively.

Figure 3. PsychoAge and SubjAge provide better than baseline estimates for chronological age and subjective age, respectively, in MIDUS 2 (N samples = 3870) and in MIDUS Refresher (N = 2521). (A) PsychoAge chronological age predictions in MIDUS 2 (MAE = 7.18 years; epsilon-accuracy = 0.73). (B) SubjAge subjective age predictions in MIDUS 2 (MAE = 8.53 years; epsilon accuracy = 0.66). (C) PsychoAge chronological age predictions in MIDUS Refresher (MAE = 7.73 years; epsilon-accuracy = 0.70). (D) SubjAge subjective age predictions in MIDUS Refresher (MAE = 8.56 years; epsilon accuracy = 0.65). Red lines mark ordinary least squares regressions. R2 stands for “coefficient of determination”, MAE stands for “Mean Absolute Error”, ε-acc stands for “epsilon-accuracy”.

The predictions displayed in the scatter plot were obtained during CV. Red lines mark ordinary least squares regressions. R2 stands for “coefficient of determination”, MAE stands for “Mean Absolute Error”, ε-acc stands for “epsilon-accuracy”.

Psycho-social feature importance analysis

We explored the importance of the features used by PsychoAge and SubjAge using PFI and DFS techniques on MIDUS 1. Scores produced by them were normalized and averaged to yield two feature lists in which all features were ranked according to the magnitude of their effect on model output (Figure 4).

Figure 4. PsychoAge and SubjAge use the same variables to predict chronological and subjective age, but assign different importance to them. (A) Top-25 important features for estimating chronological age with PsychoAge. Features not present in the SubjAge top-25 list (marked by arrows): “health compared to others your age”, “neuroticism personality trait”, “middle age upper limit (men)”, “control over life in general now for psychological age prediction. (B) Top-25 important features for estimating subjective age with SubjAge. Features not present in the PsychoAge top-25 list (marked by arrows): “rate current work situation”, “extraversion personality trait”, “openness personality trait”, “shortness of breath while walking up a slight hill”, “rate sex life currently”, “positive reappraisal (secondary control)”. Mean importance is the normalized mean of PFI and DFS importance scores.

The most important PsychoAge and SubjAge features belonged to the categories of closer relationships and health. More specifically, top-5 important features in both these aging clocks contained variables describing “rate sex life in 10 years” and “marital status” (closer relationships category), as well as “health limits on vigorous activity”, “prescription medications for blood pressure” (health category). The “headaches frequency (30 days)” variable was ranked fifth most important for PsychoAge, while in SubjAge it was ranked only ninth.

Interestingly, the top-25 feature lists are quite dissimilar between PsychoAge and SubjAge. We explored these dissimilarities to see which features determine the difference between psychological aging and human idea of it (subjective aging). Variables such as (i) “health compared to others your age”, (ii) “neuroticism personality trait”, (iii) “middle age upper limit (men)”, and (iv) “control over life in general” are identified as important only in PsychoAge (Figure 4A). Conversely, some variables were important only for SubjAge predictions: “rate current work situation”, (ii) “extraversion personality trait”, (iii) “openness personality trait”, (iv) “shortness of breath while walking up a slight hill”, (v) “rate sex life currently”, and (vi) “positive reappraisal (secondary control)” (Figure 4B).

Note that neuroticism was the only big five personality trait present in the top-25 features for PsychoAge. In the meantime, openness and extraversion are the only big five personality traits important for SubjAge prediction. This finding can be interpreted as neurotic tendencies being inherent to psychological aging, while changes in openness and extraversion are much less significant parts of this process. They, however, greatly affect the personal perception of age.

Feature importance analysis with PFI and DFS is sufficient to determine the significance of features in absolute terms, but it does not convey any information on the direction of change. Other methods should be employed to associate psychological aging, for example, with increasing or decreasing neuroticism (see “Results: Psychological aging across different age groups”).

Psychological aging across different age groups

Psychological aging core and uniquely important features

To describe how different variables contribute to psychological aging throughout human life, we trained DNNs on MIDUS 1 age group subsamples (25-39, 40-64, 65-75 years). These models contained the same 50 features as PsychoAge and Subjage, but their relative importance was not constant. In other words, a variable’s contribution to psychological aging was not static and its influence may vary with time.

First, we explored important variables (top-25 mean normalized PFI and DFS scores) shared by all age-group specific clocks to define the “psychological aging core” — features that significantly shift throughout one’s lifespan (Table 2). Core features that determined the chronological aspect of psychological aging in MIDUS 1 contained neuroticism, seeing the community as a source of comfort and defining the lower boundary of male middle age. These features are expected to have life-long trends that let DNNs tell an old and a young person apart. Personality traits that were rendered important for human perception of age included aspirations scale, extraversion, openness, being career-oriented, and the prevalence of the positive reappraisal coping mechanism. Changes in these traits are expected to drive the internal psychological clock in humans of all ages.

The psychological core defines what aspects of human personality are constantly evolving and thus qualify as lifelong markers of psychological aging. But some features may quickly shift in a certain life period and be important for measuring psychological aging in this period only. These variables are called “uniquely important” in Table 2. They identify which aspects of psycho-social life change the most reliably within an age group and thus get assigned higher importance within the corresponding age predictor.

To illustrate, agency is a uniquely important feature for accurate chronological age estimation in elderly people. This does not mean that being more or less willing to shape one’s own life is a trait only seen (or uniquely lacking) in the elderly. Most probably, agency was considered important in this age group, since people experience a major shift in this psychological attribute while going from 65 to 75 years. The DNN may have learned this possibly non-linear pattern to move a person closer to the upper or the lower boundary. In contrast, younger people may maintain more consistent agency throughout their lives, which makes DNNs seek aging-related patterns in other features.

Other variables recognized as uniquely important in Table 2 should be interpreted in a similar fashion. They represent the variables that go through a major shift within the specified age range, yet the direction of this shift cannot be determined using PFI or DFS techniques only. We address the directionality of age-related changes in the next section.

Apart from agency, other psychological traits such as positive reappraisal, persistence in goal striving, and living for today were found to be key features in the older generation. Meanwhile, aspirations scale and forcefulness turned out to be more significant attributes for accurate chronological age prediction in the 25-39 years cohort.

Among the big five personality traits, neuroticism was found to be important for subjective age prediction in the 65-75 years cohort, while in the 25-39 years cohort conscientiousness was a unique significant big five trait. Interestingly, optimism is also considered important to accurately estimate the subjective age in the 65-75 years cohort.

Contrary to the other age groups, psychological aging in the middle-aged (40-64 years) people were driven not by personality traits, but by the measures of social success and expectations of future life: overall education, career satisfaction now and in 10 years, having any unique contributions to the public good, as well as the expected contribution towards the well-being of others in 10 years.

Some health-related features also differed in significance across age groups. For example, self-evaluated mental health was uniquely important for accurate subjective age prediction in the 25-39 years cohort. Current opinion on health was uniquely important for accurate chronological age prediction in the 65-75 years cohort.

Directionality of age-related changes

To interpret the available variables in terms of the effect they have on psychological aging, we employed an approach based on linear models with mixed effects (Table 3). Most variables used by PsychoAge and SubjAge have a discordant effect on the predictions in MIDUS 1. In other words, variables associated with higher PsychoAge are also associated with lower SubjAge.

Thirteen health-related variables were tested, among them all were significantly (effect coefficient above 3σ) associated with SubjAge, but only 11 — with PsychoAge. Having chronic conditions, as well as being physically challenged, did not affect PsychoAge prediction. But these specific health problems were more frequent in those who felt older than their actual age.

Variables corresponding to other health problems, such as headaches, hypertension, shortness of breath, and obesity displayed a pattern in which less severe conditions decreased SubjAge and increased PsychoAge. Similar patterns were observed for the self-evaluated mental and physical health scores.

Among the health-related features, external locus of health control was the only feature that was significantly increased in people with both high SubjAge and high PsychoAge (Figure 5). Noteworthy, its linearly positive effect on SubjAge was twice as large. Internal locus, being a by definition opposite health mindset, was not associated with lower PsychoAge. It was, however, associated with lower SubjAge. Internal locus thus showed behavior typical of most other health-related variables, in which less severe problems were associated with lower SubjAge and higher PsychoAge.

Figure 5. Mixed-effects linear models were used to observe how changing a variable affects PsychoAge and SubjAge predictions in MIDUS 1. (A) Confusion matrix of MIDUS 1 samples divided based on their PsychoAge and SubjAge predictions (see Supplementary Figure 1 for SubjAge × Real Age and PsychoAge × Real Age confusion matrices). (B–D) Heatmaps of mean values for three important features (neuroticism, internal and external locus of health control) in SubjAge × PsychoAge confusion groups. Groups with <25 samples were excluded from the mixed-effects analysis and left blank on the Confusion matrices for all psychosocial variables are listed in Supplementary Figure 2.

Most tested personality traits and beliefs also displayed a connection to psychological aging. All traits from the big five, except for neuroticism, (openness, conscientiousness, extraversion, agreeableness) were associated with higher PsychoAge and lower SubjAge. Neuroticism had an opposite effect on age prediction: decreasing PsychoAge and increasing SubjAge (Figure 5).

Other variables that describe whether a person is optimistic and proactive showed a pattern similar to the four out of five big five traits. The prevalence of positive reappraisal, being outgoing, optimistic, forceful, and goal-oriented decreased SubjAge and increased PsychoAge in the mixed-effects models. A similar pattern was observed for the optimistic beliefs that “community is a source of comfort” and that “the world is becoming a better place”. Meanwhile, lower aspirations and “live for today” attitude only increased SubjAge with no significant effect on PsychoAge.

Another set of beliefs we tested concerned the question of when middle age starts and ends. People who were predicted to be older by PsychoAge responded to specified higher boundaries of this life period. For example, people whose PsychoAge matched their SubjAge estimated male middle age period to start at 39-47 years on average. In the meantime, people from the same SubjAge groups but with PsychoAge 20 years larger suggested that men’s middle age started at 45-50 years. Despite the large effect on PsychoAge, the concept of middle age did not affect SubjAge. People from the same PsychoAge group were extremely consistent in their definitions of male and female middle age, even when coming from different SubjAge cohorts.

The last 17 features not yet discussed belonged to the categories of personal well-being, accomplishment, and close relationships. Variables describing marital status and sex life were a rare occurrence of concordant effect on both PsychoAge and SubjAge. More fulfilling sex life or being married decreased the predictions of both these aging clocks.

The level of life satisfaction and personal accomplishment correlated with lower SubjAge, and in some cases — with higher PsychoAge. Among the variables that did not affect PsychoAge were effort put into work, expectations of work, and contributing to the well-being of other people in 10 years.

Psychological aging and mortality

We inspected whether SubjAge and PsychoAge prediction errors were indicative of all-cause mortality risk using Cox regression. In models adjusted for gender, age, and either PsychoAge or SubjAge error both predictors were shown to be significant (p-value<0.05) risk factors (Figure 6). SubjAge delta above +5 years was associated with a more than two-fold increase in mortality rate (HR=2.11), and SubjAge delta below -5 years was recognized as a major protective factor (HR=0.54). HRs produced by the PsychoAge survival model were much less significant and carried less weight: HR for PsychoAge delta above +5 years was 1.14 (p-value=0.04) and HR for delta below -5 was 0.93 (p-value=0.40).

Figure 6. SubjAge is a more significant all-cause mortality risk factor than PsychoAge. Hazard ratios were obtained with Cox regression. Delta is the difference between actual age (chronological for PsychoAge or subjective for Subjective) and their DNN-derived estimations. Each row represents a hazard ratio and the 95% confidence interval associated with a specific feature. Note: “***” for P-value of 0.001; “**” for P-value of 0.01; “*” for P-value of 0.05.

We then compared the 50 features used by both PsychoAge and Subjage plus chronological age within one Cox regression (Figure 7 and Supplementary Figure 2). The 10 most powerful risk factors based on HR magnitude belonged to the categories of:

Figure 7. Ten most important features associated with mortality risk in a Cox regression adjusted for 49 psychosocial variables, sex, and chronological age. Most significant risk factors include variables describing personality traits and health status.

• - Health (“Rate current health”, “Health compared to others your age”, “Shortness of breath while walking up a slight hill”);

• - Personality (“Conscientiousness”, “Agency”);

• - Psychological beliefs (“Live for today”, “Positive reappraisal”, “Lower aspirations”);

• - Personal well-being (“Satisfied with life at present”);

• - Demographics (“Chronological age”).

Among these risk factors only “Live for today”, “Health compared to others your age”, “Chronological age”, “Rate current health”, “Lower aspiration” and “Shortness of breath” were deemed significant.

Surprisingly, the optimistic outlook associated with higher “Live for today values” was the largest contributor to the mortality risk (HR=1.35), while lower aspirations were a significant mortality protector variable (HR=0.84). These results, however, are in line with the previous findings in the mixed-effects analysis, in which both these features were shown to increase SubjAge, while only insignificantly affecting PsychoAge.

“Health compared to others your age” also increased SubjAge (coef = 1.91) but also decreased PsychoAge predictions (coef = -2.14). Despite this compensatory effect of reduced PsychoAge, “Health compared to others your age” (1=”Much better”, 6=”Much worse”) was recognized as a significant risk factor (HR=1.16). This may be attributed to the previously established higher mortality associated with increased SubjAge predictions (Figure 6). “Rate current health” behaved similarly, although due to its reversed scale (0=”Worst”, 10=”Best”) its HR was below one — 0.86.

Significantly low HR for “Shortness of breath” may also be misleading, since it is a binary variable, in which “1” signifies no problems with breathing, while “2” — shortness of breath when walking uphill. In the mixed-effects analysis having short breath was associated with, on average, 2.91 years larger SubjAge predictions and only 0.88 years smaller PsychoAge predictions. This furthers the point that the most significant all-cause mortality risk factors are associated with disproportionately larger SubjAge predictions.

Column “range” describes the range of possible values for each variable. For a full list of hazard ratios and associated MIDUS variable names see Supplementary Figure 3.

Data

The MIDUS series was funded by the John D. and Catherine T. MacArthur Foundation Research Network on Successful Midlife Development. MIDUS 1 data was collected between 1995 and 1996. The study consisted of two parts – In Part 1, the participants were asked to undertake a 30-minute telephone interview while Part 2 consisted of a self-administered questionnaire, which included sociodemographic characteristics, physical health, biomarkers, and psychosocial information, including the estimation of the subjective age. In total, the dataset contained surveys from a total of 7,108 participants.

In order to verify our findings, the MIDUS 2 (https://www.icpsr.umich.edu/web/NACDA/studies/4652, 2004-2006) and MIDUS Refresher datasets (https://www.icpsr.umich.edu/web/NACDA/studies/36532, 2011-2014) were used. MIDUS 2 (2002-2009) is a follow-up of the MIDUS 1 study (1995-1996), while the MIDUS Refresher (2011-2014) is a next-wave study with new participants. To examine the predictive power of trained models on the publicly available data, we analyzed the MIDUS 2 and Refresher datasets and tested our DNN on these datasets retrospectively.

To perform each analysis, MIDUS 1 was split into training and test datasets. The training cohort of MIDUS 1 consisted of 7,106 participants (3,176 females). Following preprocessing, the dataset consisted of 6,071 participants (2,523 females). The testing dataset consisted of 1,214 participants (644 females). An overview of the process is given in Figure 2.

The validation dataset – MIDUS 2 – consisted of participants 4,963 (2,647 females). After preprocessing, the dataset consisted of 2131 participants. The validation dataset MIDUS R consisted of participants 3,576 (2,647 females). After preprocessing, the dataset consisted of 2,521 participants (1,337 females).

For reporting purposes, all datasets were divided into three age-cohorts: 25-39, 40-64, 65-75 years, as per MIDUS 1 specifications.

To perform mortality analyses, we explored the MIDUS 2 and MIDUS Core Sample Mortality datasets (1,767 confirmed deaths: https://www.icpsr.umich.edu/web/NACDA/studies/37237, 2016).

Feature selection and data preprocessing

The original MIDUS 1 dataset had a total of 2,097 defined features. To perform feature engineering and data preprocessing we excluded the following features: explanatory and ID features and highly age-related features (e.g. age group). Then, the samples with either target variable (subjective or chronological age) outside the 0-100 years range were excluded. Next, we calculated a feature correlation matrix and highly correlated (Pearson’s r > 0.9). We selected features that have the most predictive power, other correlated features were excluded. Features were then filtered to remove those that contained >80% missing values. All categorical features were binarized using one-hot encoding. Finally, outliers were filtered and removed using the Isolation Forest outlier detection algorithm.

After the filtering and exclusion processes, the final dataset contained 6,071 participants with a total of 954 features, of which 573 were defined as categorical and 382 as numerical.

Training procedure

First, we trained a chronological age predictor on a full list of features remaining after feature engineering and data preprocessing (here, “features” were defined as those that imply preprocessed or raw input data). Then feature importance analysis was applied to select the 100 most important features (see “Methods: Feature importance analysis”). After another round of training 50 most important features were selected to build the final models: PsychoAge for chronological age prediction and SubjAge for subjective age prediction.

A complete list of the fifty features is provided in Supplementary Table 1. All features were divided into the following categories, according to their MIDUS description: (i) health, (ii) closer relationships, (iii) images about life changes, (iv) occupational features, (v) community involvement, (vi) personality traits, (vii) psychological beliefs, (viii) demographic features, and (ix) well-being.

Final models were trained with five-fold cross-validation (CV) using all MIDUS 1 samples. MIDUS 2 and MIDUS Refresher were used for model validation purposes (Figure 8). Final model performance was visualized using Seaborn for Python (v0.10.0; https://seaborn.pydata.org).

Figure 8. Building a deep psychological age predictor. MIDUS 1 dataset was filtered to contain only relevant features and samples with <20% missing values. DNNs were built with all the available features in a cross-validated manner to select the best hyperparameters. After establishing feature importance, top-100 features were selected, which were further filtered down to top-50 features. The selected top-50 features were used to build the final PsychoAge and SubjAge models.

DNN architectures

In this study age prediction was treated as a regression tasks, i.e., the model utilized vectors to calculate values for both psychological and subjective age estimation task. A single value was then returned for one of the selected age’s targets. Here we used a deep model composed of multiple layers to permit the fitting of data with high-level dependencies between the input features (biopsychological markers) and the output features (different types of ages).

Multilayered, feed-forward neural networks were used as deep models (i.e., models that had more than 3 hidden layers) with Python implementation using the Keras library (https://keras.io/) with Tensorflow backend (https://www.tensorflow.org) to build and train the neural networks. A grid search over the space of model parameters was applied to find the best performing network architecture. The MAE loss function was used as an objective for neural networks. The best performing neural network had 5 hidden layers with 512 neurons each. Mish activation non-linear pointwise functions were used to introduce non-linearity to the linear transformed input in each hidden layer of the neural network. Radam, with lookahead, was used to leverage a dynamic rectifier to adjust the adaptive momentum of Adam based on the variance applied to optimize the cost function. A dropout with 45% probability was used after each layer for regularization. L2 regularization was applied on the weights of all hidden layers with a coefficient equal to 0.0001. Neural networks were trained using five-fold cross-validation to compensate for overfitting and to obtain more robust performance metrics. All experiments were conducted using an NVIDIA RTX 2080Ti graphics processing unit.

Feature importance analysis

To address the interpretability problem of DNNs, one model-agnostic (Permutation Feature Importance, PFI) and one DNN-specific (Deep Feature Selection, DFS) feature importance analysis method were used [37].

DFS was applied as a DNN-specific feature importance method. DFS was used to select features at the input level of a DNN. The primary role of DFS was to add a sparse one-to-one linear layer between the input layer and the first hidden layer of an MLP. To select input features, weights of the DFS layer were required to be sparse, to satisfy this requirement elastic net regularization was applied. DFS importance score was defined as the DFS weight of the input features.

PFI was applied as a model-agnostic feature importance method. PFI was applied to identify the best performing models for each dataset. PFI assigns an importance score to a feature by measuring the drop in model accuracy upon randomly permuting its values. A larger drop in model accuracy is associated with greater importance. To carry out PFI analysis on categorical features, which were encoded as one-hot columns, “1” was placed in a random column and other columns for the corresponding feature were turned to “0”.

The final importance score we report here is the mean of normalized PFI and DFS scores.

To identify which variables were most important for accurate prediction in specific age groups, a separate set of DNNs was trained using the predefined set of 50 features. Each of these DNNs was trained using only the samples that belong to one of the following age groups: 25-39, 40-64, 65-75 years (Table 2).

Variable effect estimation

To interpret the available variables in terms of the effect they have on psychological aging, we employed an approach based on linear models with mixed effects.

All samples were assigned to one of the five PsychoAge or SubjAge groups (25-34, 35-44, 45-54, 55-64, 65-74 years predicted). For each variable assessed a random intercept for each age group was added to the model:

$SubjAge~Variable+\left(1|PsychoAge\hspace{0.17em}group\right)$

$PsychoAge\hspace{0.17em}~\hspace{0.17em}Variable+\left(1|SubjAge\hspace{0.17em}group\right)$

The mixed-effects analysis was carried out on the complete MIDUS 1 data set while using the predictions obtained in CV. The implementation was written in R 3.6.2, mixed-effects models were implemented with lme4 package (v1.1.21; https://cran.r-project.org/web/packages/lme4/index.html).

Visualization of effects was conducted with Plotly (v.4.5.0; https://plotly.com) for Python.

Model validation was carried out using MIDUS 2 and MIDUS Refresher datasets. This pipeline was repeated independently for PsychoAge and SubjAge.

Survival analysis

To investigate the predictive ability of deep psychological aging clocks in terms of all-cause mortality, we employed Cox-regression models for both psychological age and subjective age. To evaluate the association of the predicted age with all-cause mortality, hazard ratios (HR) were calculated. Survival time data (defined as the age at examination until the age of death or last follow-up) was analyzed. For hazard analysis by group, the CoxPHFilter method was used from lifelines for Python (v.0.23.9; https://github.com/CamDavidsonPilon/lifelines). Cox models were adjusted for chronological age and sex.

For survival analysis purposes, the rate of aging was expressed as a set of one-hot binary variables representing the sample’s delta — the difference between predicted and the actual age of the samples (either chronological or subjective). One-hot columns were filled based on whether a sample’s delta was below -5 years, above +5 years, or within the ±5 year error range.

Statistical analysis

The following metrics were used to evaluate the accuracy of the age prediction models:

• 1)

  Coefficient of determination: $R^2=1-\frac{{\displaystyle {\sum }_{i=1}^N{({\widehat{y}}_i-y_i)}^2}}{{\displaystyle {\sum }_{i=1}^N{(y_i-y^{\prime })}^2}};y_i$ is the real value, ${\widehat{y}}_i$ is the predicted value and $\underset{¯}{y}$ is the mean of y. R² shows the percentage of variance explained by the regression between predicted and actual value.

• 2)

  Mean absolute error: $\text{MAE=}\frac{1}{N}{\displaystyle {\sum }_{i=1}^N|{\widehat{y}}_i-y_i|};$ where ${\widehat{y}}_i$ is a predicted age, y_i is a real value and N is the total number of samples. MAE demonstrates average disagreement between predicted and actual target value.

• 3)

  $\epsilon -accuracy=\frac{{\displaystyle {\sum }_{i=1}^N{1}_{A\hspace{0.17em}}({\widehat{y}}_i)}}{N}$ where A = [y_i – ε; y_i + ε] and ${\widehat{y}}_i$ is a value predicted by the model, y_i is a true value. For example, if the DNN model predicted 55 for the sample with the actual target value ranging from 50 to 60, then this sample would be considered as correctly classified if the case epsilon equals 5.

Limitations and future investigation

To develop a methodology for psychological and subjective age prediction we trained our models using the MIDUS data set based on participants in the United States. Future investigations that use more recent, and other national studies should be used to enhance the accuracy of the models Psychological deep clocks may be dependent on the socio-cultural values in a society. For example, if a society tends to shy away from a topic like sexual health, that factor may not show up as important for that culture’s psychological deep clock. Knowing the commonalities across psychological deep clocks will further refine the most important factors.

As these psychological deep clocks are integrated into clinical practice, hospitals and insurance companies may find these tools valuable in offering cost-effective medical care in addition to being able to obtain more value for the same amount of financial investment. Additionally, participants will spend less time answering 200+ survey questions and instead be able to focus on answering the most highly-ranked 50 questions. Clinicians will then know what are the best treatment protocols rather than relying on a blanket prescription (Supplementary Figure 4).