We used data from 2011 to 2015 waves of the National Health Aging Trends Study (NHATS), a nationally representative longitudinal cohort study that has collected a sample of Medicare beneficiaries ages 65 or older in the United States. Our study sample consists of 2,592 community-dwelling older adults with complete data on main outcome variables (subjective age and frailty) from 2011 to 2015 waves. Compared to participants who were included in this study, the excluded participants felt older, had less education, and had more ADL/IADL impairment, chronic diseases, hospitalizations, and falls with poorer health status. The excluded participants were also less obese, engaged in less vigorous activity, but more demented. The NHATS was approved by the Johns Hopkins Bloomberg School of Public Health IRB. NHATS participants completed written informed consent prior to being interviewed.
Frailty was assessed using the modified frailty phenotype paradigm  based on five criteria: unintentional weight loss, exhaustion, weakness, slow gait and low physical activity. Criteria were operationalized from NHATS interviews and performance assessments. (1) unintentional weight loss: involuntarily losing 10 pounds or more in the last year; (2) exhaustion: self-reported low energy or being easily exhausted to limiting activities; (3) weakness: grip strength measured by dominant hand over 2 trials as being at or below the 20th percentile within eight sex-by-body mass index (BMI) categories; (4) slow gait: gait speed from the best of two timed 3-meter walk tests being at or below the 20th percentile within four sex-height categories; and (5) low physical activity: self-reported not having taken part in vigorous activities or never walked for exercise in the last month. Participants who met three or more criteria were considered as “frailty.” Those with one or two criteria were considered as “pre-frailty,” and those without any criterion as “robust.”
Subjective age was measured by the question, “Sometimes people feel older or younger than their age. During the last month, what age did you feel most of the time?” Participants answered a number in years to estimate the age they felt. We calculated proportional discrepancy scores by subtracting chronological age from felt age and divided by chronological age . A negative score indicates a younger subjective age, while a positive score indicates an older subjective age. We coded equal = 0, younger subjective age = 1, older subjective age = 2. Values three standard deviations above or below the mean were considered outliers and excluded from the analysis.
Demographic characteristics included chronological age; sex (coded 0 for female and coded 1 for male); race/ethnicity (coded 0 to 4 for “non-Hispanic White, non-Hispanic Black, Indian/Asian/Native/Hawaii, Hispanic, other”); education (coded 0 to 3 for “less than high school, high school graduates, some college or vocational school, bachelor or higher”); living arrangement (coded 0 to 3 for “alone, with spouse/partner only, with others only, with spouse/partner and with others”).
Health-related variables included the following: (1) bothersome pain was measured by the question “In the last month, have you been bothered by pain?” (0 = no; 1 = yes); (2) depressive symptoms, assessed by the Patient Health Questionnaire-2 (PHQ-2), which measured how often the participant had been bothered by (a) “little interest or pleasure in doing things” and (b) “feeling down, depressed or hopeless” over the last month. Responses were on a 4-point Likert scale (0 = not at all; 1 = several days; 2 = more than half the days; 3 = nearly every day). We summed scores on both of the PHQ-2 questions to create a score from 0 to 6, with scores > 3 were classified as depressive symptom (0 = no; 1 = yes); (3) ADL impairments, we computed the number of activities (eating, dressing, bathing and toileting) in which participants had any difficulty in the past month; (4) IADL impairments, we calculated the number of activities (doing laundry, shopping, preparing meal, managing money and taking medication) in which participants had difficulty in the past month; (5) body mass index (BMI) (coded 0 for normal with BMI < 30 kg/m2 and coded 1 for obesity with a BMI ≥ 30 kg/m2); (6) self-rated health status (code 0 to 4 for “excellent, very good, good, fair, poor”); (7) the number of chronic illnesses (high blood pressure, heart attack/heart disease, arthritis, osteoporosis, diabetes, lung disease, stroke, and cancer) diagnosed by a doctor (coded 0 for no disease, coded 1 for have 1–3 diseases and coded 2 for have more than 4 diseases); (8) hospitalized in the last 12 months (0 = no; 1 = yes); (9) fall was measured with the question “In the past 12 months, have you fallen down?” (0 = no; 1 = yes); (10) smoking (coded 0 for never smokers and coded 1 for current/former smokers); (11) dementia was assessed by asking participants to report whether they had ever been diagnosed by a doctor with dementia or Alzheimer’s disease (0 = no; 1 = yes); (12) vigorous activities, was assessed by asking participants to report whether they ever spend time on vigorous activities that increased their heart rate and made them breathe harder in the last month (0 = no; 1 = yes).
Descriptive statistics were presented as mean ± SD (standard deviation) for continuous variables or absolute number and percentage for categorical variables. Chi-square tests or ANOVAs were used to compare the baseline characteristics of the sample according to subjective age categories (younger than chronological age, equal to chronological age, and older than chronological age) and frailty categories (robust, pre-frailty, and frailty). We used generalized estimating equation (GEE) models to test the concurrent and lagged association between subjective age and frailty. GEE is an extension of the generalized linear model that accounts for the within-subject correlation across repeated measurements and is appropriate to estimate population-averaged effects over time . Since missing values on covariate variables were less than 1 %, we did not apply any techniques to handle them.
Subjective age as a predictor of pre-frailty or frailty
We estimated two sets of GEE models, specifying the logit link function with a binomial distribution [34, 35]. We assumed an exchangeable correlation structure and used robust standard errors to account for the correlation between measures for each measure. First, we assessed the concurrent association between subjective age and frailty. Subjective age at wave w was related to frailty at wave w with adjustment for frailty at wave w-1. The adjustment for frailty at wave w-1 was made to account for the recurrent frailty and compensate for our inability to adjust for frailty history. Then, lagged GEE models were analyzed, in which subjective age at wave w was related to frailty at wave w + 1 with adjustment for frailty at wave w. We presented the crude associations initially (Model 1), then we adjusted for demographics (chronological age, sex, race, education, and living arrangement) (Model 2), and finally further adjusted for health-related variables (pain, depression, number of ADL/IADL impairments, BMI, health status, number of chronic illnesses, hospitalized, fall, and smoking) (Model 3).
Pre-frailty or frailty as predictors of subjective age
We estimated another two sets of GEE models, specifying the identity link function with a gaussian distribution. The modeling strategy was similar to the analysis of the first two sets of GEE models. First, we assessed the concurrent association between frailty at wave w and subjective age at wave w with adjustment for subjective age at wave w-1. Then, lagged GEE models were analyzed, in which frailty at wave w was related to subjective age at wave w + 1 with adjustment for subjective age at wave w.
All P values were two-sided and statistical significance was determined at p < 0.05. Statistical analyses were conducted using STATA 15.