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.

S u b j A g e ~ V a r i a b l e + ( 1 | P s y c h o A g e g r o u p ) P s y c h o A g e ~ V a r i a b l e + ( 1 | S u b j A g e g r o u p )

The mixed-effects analysis was carried out on the complete MIDUS 1 data set while using the predictions obtained in CV. The implementation additional reading was written in R 3.6.2, mixed-effects models were implemented with lme4 package (v1.1.21;

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; 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

Coefficient of determination: R 2 = 1 ? ? i = 1 N ( y ^ i ? y i ) 2 ? i = 1 N ( y i ? y ? ) 2 ; y i is the real value, y ^ i is the predicted value and y ? is the mean of y. R 2 shows the percentage of variance explained by the regression between predicted and actual value.

Mean absolute error: MAE= 1 N ? i = 1 N | y ^ i ? y i | ; where 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.

? ? a c c u r a c y = ? i = 1 N 1 A ( y ^ i ) N where A = [y_i – ?; y_i + ?] and 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.