## Abstract

Few studies have been performed on the individual-specific trajectory of left ventricular aging as assessed by echocardiography in an asymptomatic elderly cohort. In the present study, a representative cohort of elderly men, who were long-term asymptomatic for cardiovascular issues, were selected from an ongoing observational aging study. Annual echocardiographic data were used to establish an age-dependent hierarchical model. Based on two-level linear regression results, four echocardiographic indexes [left ventricular mass (LVmass; −1.872 g/yr), posterior ventricular wall thickness (−0.048 mm/yr), fraction shortening (0.097/yr), and transmitral peak A velocity (−0.006 m·s^{−1}·yr^{−1})] changed significantly with increasing age and were age- and subject-dependent. The most characterized results of the study were the significant, age-related, within-individual variances in echocardiographic results, which were observed using the likelihood ratio test at an occasion-dependent level. Of these, fluctuated amplitudes of two systolic variables [i.e., LVmass (con/age = −0.012 ± 0.004; *P* = 0.0007) and fraction shortening (con/age = −0.001 ± 0.004; *P* = 0.05)] were significantly attenuated with increasing age within individuals. On the other hand, the age-related variability of four diastolic Doppler variables [i.e., peak A velocity (con/age = 0.003 ± 0.002; *P* = 0.0009), peak E velocity (con/age = 0.004 ± 0.003; *P* = 0.01), E/A ratio (con/age = 0.007 ± 0.003; *P* = 0.0002), and deceleration time of E wave (con/age = 0.025 ± 0.007; *P* < 0.0001)] significantly increased with increasing age within individuals. The age-related individual variability of left ventricular indexes observed in this continuous asymptomatic cohort may reflect the mechanism of preclinical, individualized heart aging. In conclusion, successfully fitted multilevel models were applied as a valuable tool to determine the mechanism of individual cardiac aging in the elderly.

- asymptomatic
- echocardiogram
- cardiac ageing
- individual variability
- multilevel model

despite the acknowledged importance of age in the increased cardiovascular morbidity and mortality associated with the burgeoning elderly population, how the heart ages while failing remains largely unknown. For example, conventional population-average analysis has indicated that left ventricular diastolic indexes are age dependent in the adult population but do not remain age dependent in the elderly, and this difference is attributed to great between-individual variation among the elderly (24). The oldest age group in men showed a uniquely prevalent manner-based population finding (16). Meta-analysis suggested an indefinite increase in mortality by active antihypertensive therapy in very elderly patients more than 80 yr of age (7). One important reason for this finding is the formidable between-individual heterogeneity in the aged population, which is associated with multiple cardiovascular risks and multi-morbidity. In addition to the ubiquitously used individual medication for cardiovascular prevention and therapy (9), another issue emerged, specifically that the use of efficient patient-centered medication challenges conventional statistics and requires adjustment for between-individual variances. This complicated dilemma may be mirrored by the considerable prevalence of asymptomatic elderly cardiovascular patients (6, 9, 11, 13, 20). Approximately one-half of heart failure patients have been shown to be asymptomatic with preserved ejection fraction or preclinical diastolic dysfunction (6, 9, 11, 13, 20), yet the mechanism behind the progression from asymptomatic to symptomatic diastolic dysfunction is entirely unclear. Therefore, individual-based external regulation and protection have elevated the within-individual heterogeneity of heart aging and failure. Meanwhile, the human lifespan is increasing, which further augments the complexity of age-related heart decline. It is very difficult to disentangle the complicated interrelationship among cardiac physiological aging, pathological heart failure, and external cardiovascular protection using conventional statistics. Conventional statistical analysis has limited applicability in such studies because the mathematical coupling dilemma created by high within-individual variance means that changes from baseline values cannot be simply related or regressed to values measured at later time points. Multilevel modeling has resolved this problem by simultaneously dealing with complex error structures and additional covariates and/or potential confounders (2).In the present study, we used hierarchical modeling, an advanced statistical technique, to trace age-related individual heart aging as assessed by longitudinal echocardiographic parameters in a representative aged cohort who were continuously asymptomatic.

## METHODS

#### Longitudinal project on witnessing aging.

Our cohort of continuously asymptomatic elderly men was selected from those who had taken part in the Longitudinal Project on Witnessing Aging (LPWA) in our Geriatrics Department. The LPWA was a single-center, longitudinal, observational cohort study. These elderly participants were qualified by the local government and assigned to be intensively treated, medicated, and followed up longitudinally in our department from age 60 years onward. Extensive biannual health assessments were performed according to a routine protocol. In the project, all male participants were observed and followed up from enrollment until death. Informed consent was obtained from all participants. The project received ethical approval from the Institutional Review Board of the Faculty of Medicine at Harbin Medical University in accordance with the ethical standard outlined in the 1964 Declaration of Helsinki.

#### Identification of continuously asymptomatic participants.

A step-by-step protocol was used to select individuals who were continuously asymptomatic for cardiovascular conditions for a 5-yr duration from April 2004 to April 2009. Individuals who were free of cardiovascular complaints at the time of a 2005 echocardiogram were initially enrolled. Thereafter, continuity of clinical documents was intensively reviewed, and individuals who continued to be free of cardiovascular complaints and events were enrolled.

#### Annually repeated echocardiography.

Each participant received a standard transthoracic echocardiography by a single experienced cardiologist using the same echocardiography platform (GE LOGIQ5) in April of each year of the study period. Standard M-mode and Doppler echocardiographic measurements were taken according to the American Society of Echocardiography recommendations (21). In the present study, five indexes for left ventricular (LV) systolic performance, including three anatomic indexes (posterior ventricular wall thickness, LV mass, and LV diameter on the end-diastole) and two functional indexes (ejection fraction and fractional shortening), were selected for multilevel modeling. Four transmitral filling Doppler indexes, including early transmitral filling velocity, atrial transmitral filling velocity, E/A ratio, and deceleration time of E velocity (DT), were simultaneously modeled.

#### Multilevel statistical modeling.

All two-level linear regression equations were fitted using the longitudinal data for each echocardiographic index and MLwiN Software (MLwiN 2.23; Centre for Multilevel Modeling, UK; http://www.bristol.ac.uk/cmm/software/mlwin/download/manuals.html) (19). First, *level 1* (subscript *i*) was established as the “occasion” of the echocardiographic measurements, which was arrayed as a sequence of numbers 1, 2, 3, 4, and 5. These numbers were used to indicate the chronological order of the data from the intervals 2004–2005, 2005–2006, 2006–2007, 2007–2008, and 2008–2009. *Level 2* (subscript *j*) was established the as “individual,” which indicated participants who met the continuously asymptomatic selection criteria. Second, Y_{ij} represents an echocardiographic index of interest at the i_{th} measurement for the j_{th} individual. Dependent variable Age_{ij} represents the age at the i_{th} measurement for the j_{th} individual. To improve modeling convergence, Age_{ij} values were initially centralized. Before a basic two-level linear regression equation was established, the hierarchical structure of each term in the multilevel model was pre-identified based on the following research aim. In our present study, as the only dependent variable, Age_{ij} was considered a two-level dependent variable, meaning that the relationship between Age_{ij} and Y_{ij} varied, with both changes in measurement occasion and changes in participants. After the linear functional correlation and hierarchical structure of the model were identified, an “empty” equation was defined as Y_{ij} = β_{0ij} constant. Here, constant was defined as the average intercept of the Y_{ij} matrix and could be changed by both the occasion and the individual. Therefore, the estimated two-level constant indicated an average intercept at average measurements for average individuals. Based on the “empty” model, an Age_{ij}-adjusted regression equation was defined as Y_{ij} = β_{0ij} constant + β_{1} Age_{ij}. Here, both the constant and the Age_{ij} hierarchically varied. Therefore, different from the conventional constant, the mean intercept and the mean slope were varied at two different levels, i.e., both were occasion-dependent and subject-dependent. All two-level equations were estimated by restricted maximum likelihood estimation (REML), with two negative likelihood ratios (−2LL) conducted.

#### Hypothesis testing.

The significance of the linear regression coefficient between Y_{ij} and Age_{ij} was tested by the Wald value. The null hypothesis was that no correlation exists between Y_{ij} and Age_{ij} at both levels in the representative cohort. The null hypothesis of variance at each level must be satisfied separately, because split components of variances on two levels (intercept variance, slope variance, and intercept-slope covariance at each level) were respectively conducted. In the present study, variance at *level 1*, which corresponded to the fluctuating amplitude between five measurement occasions for one participant, was highlighted. To show how and to what extent within-individual fluctuation varied between measurement occasions, likelihood ratio (LR) testing was performed. The null hypothesis for the LR was that no age-related, within-individual fluctuation existed for the echocardiographic index of interest in the representative cohort. Both the Wald value and the LR value were distributed in a χ^{2} pattern. A *P* value of <0.05 was considered to indicate statistical significance. For testing the robustness of the null hypothesis, all echocardiographic data were transformed into a Z score for reduplicative modeling.

## RESULTS

#### Clinical characteristics of the representative elderly cohort.

A total of 62 individuals who met our continuously asymptomatic selection criteria were included in our cohort. Basic clinical features, including age, body mass index (BMI; calculated as weight in kilograms divided by height in meters squared), blood pressure, heart rate, blood assessments, multi-morbidity, and daily regimen, were dynamically estimated using MLwiN software. The average intercept of each parameter of interest, which indicated the mean value at mean measurement occasions for mean individuals, was described by the corresponding “empty” two-level model and shown in Table 1. For comparison, average value at baseline and the “pooled” average of five measurements were simultaneously demonstrated by one-level modeling (Table. 1).

#### General characteristics of the echocardiographic indexes in the representative cohort.

Table 2 showed the general characteristics of the echocardiographic indexes both at baseline by one-level average and dynamically by two-level intercepts. From these data, we identified a representative cohort characterized by mild-to-moderate diastolic dysfunction with well maintained systolic function according to echocardiography.

#### Coefficients of the two-level, age-adjusted models for each echocardiographic index in the representative cohort.

Based on the aforementioned “empty model,” the two-level age-adjusted models were fitted. Table 3 provides the regression coefficient of each echocardiographic index by age at the two-level estimation. The average slope in the present cohort indicated how and to what extent Y_{ij} changed with increasing age when both population-average and individual-specific data are considered. According to our results, three systolic indexes, LVmass at −1.872 g/year, PVWT at −0.048 mm/year, and FS at 0.097/year, changed significantly with increasing age in this cohort. For all diastolic Doppler indexes, there was no variability, but the slight decrease in velocity of peak A (0.006 m/s) with increasing age was statistically significant. To better demonstrate the individual-specific and population-average matrix changes, corresponding trajectories were produced (Fig. 1).

#### Two-level variances of the age-adjusted, two-level models for each echocardiographic index in the representative cohort.

Three proportional variance sections, intercept variance (con/con), slope variance (age/age), and intercept-slope covariance (con/age), at each level were defined. Table 2 presents the proportional amount of within-individual (*level 1*) and between-individual (*level 2*) variation for each echocardiographic index. Although both primary echocardiographic data and Z-score-transformed data were modeled simultaneously, only the analytical results of the Z-score data for between-index comparisons are presented (Table 4). Curves illustrating within-individual variances by age are also clearly shown from analysis completed using MLwiN 2.23 software (Fig. 2). In both Table 2 and Fig. 2, it is clear that the occasion-level (*level 1*) variance is mainly reflected by the constant/age covariance. Because the continuous measuring pattern provided an exact superimposition of the measuring occasion and age per se, the con/age covariance could demonstrate how and to what extent the echocardiographic index of interest fluctuated in individuals with increasing age. Apparently, between-individual constant/age covariance equaled zero, because there was no age-dependent (slope) variance with time between individuals.

#### Within-individual significance of age-related variances for each echocardiographic index.

To illustrate the significance of within-individual level (*level 1*) variances, LR tests were performed. To testify to the robustness of the presented null hypothesis, two LR algorithms, which produced the same residuals (σ_{e01} + σ_{e12}), were applied separately. LR1 equaled double levels minus the *level 2* value, whereas LR2 equaled *level 1* minus zero-level (“empty”) estimation. Although a slight distinction was observed between LR1 and LR2, the statistical significance was exactly the same (Table 5). Therefore, the significance of within-individual occasion/age-related variances for LVmass, FS, A, E, E/A ratio, and DT was confirmed by two distinct algorithms of two-level modeling in our asymptomatic cohort. The interpretation of this significance is that the within-individual variability was drastically changed by occasion (along a similar age trajectory) for these six test indexes. The robustness of the addressed hypothesis was further proven by the repeated estimation using Z-score-transformed data. Exactly the same significance was observed from these two data series. Detailed results are available on request.

## DISCUSSION

Echocardiography has been proven to be predictive of functional assessment for LV indexes in asymptomatic individuals within a population-based study (10, 22). Therefore, we used annually repeated echocardiographic parameters to reveal the age-related LV changes in an asymptomatic elderly male cohort. As a part of our ongoing observation project on aging, continuously asymptomatic elderly men were rigorously selected. We selected and analyzed a homogeneously asymptomatic cohort using an advanced statistical model to identify the underlying mechanism of preclinical heart aging among those with high between-individual heterogeneity and considerable risk for cardiovascular conditions. Age was used as the only dependent variable not only for improved feasibility and interpretability but also to obtain patient-centered insight.

Although previous studies have reported age-related cardiac anatomic and functional changes by echocardiographic assessment, none have focused on the individual-centered view. According to our hierarchical results, the significance of age-related changes was both population-averaged and individual-specific. Two systolic indexes of LV anatomic indexes, PWVT and LVmass, were significantly decreased. The underlying mechanism was assumed to be primarily regression induced by efficient antihypertensive treatment (4, 17). LV pump functional indexes, which showed a slight age-related increase in FS and a well maintained EF at rest, changed subtly with increasing age. Simultaneously, all transmitral Doppler indexes showed little age-dependent correlation. Except for the population-based study on age-related echocardiographic changes, studies on representative individuals were commonly performed among those who were considered “normal” elderly (i.e., asymptomatic elderly). However, the single-level results were somewhat controversial due to high between-individual variability. For example, correlations between age and Doppler indexes of LV diastolic function were observed in some “normal” individuals (1, 3) but not in others in another published study (23). Our distinctive results could highly mimic the age-related traces of echocardiographic indexes in this continuously asymptomatic cohort of elderly men. Due to the time-continuous two-level estimation, the epidemic distribution of echocardiographic indexes in this rigidly selected cohort, which was characterized by mild-to-moderate diastolic dysfunction and well maintained systolic function, was interestingly consistent with that from another population-based study (5).

Different from previous results of population-averaged coefficients by age, our hierarchical results demonstrate within-individual changes with age. The value of this individual-centered modeling is apparent, because the processes of individual cardiac aging, remodeling, and failing are inextricably entangled due to the age-related complications of physiological aging, pathological dysfunction, and individual pharmaceutical prevention, especially in a continuously asymptomatic elderly cohort. The representative cohort was characterized by an average 2.2 multi-morbidities and administered a mean 5.2 NNTs, which could indirectly mirror the important impact of individualized therapy during heart aging. Apparently, the contextual individualized treatment benefits on heart aging could not be observed by single-level statistics (a contributing factor to the aforementioned mathematical dilemma). Therefore, our hierarchical results provide data on how cardiac aging progresses individually while fluctuating with time or age, independent of the simultaneously changing average of the population. Our models resolved the individual issue under the premise that age was exactly superimposed over the repeated measuring occasion. According to our individual variance estimation, a very slight fluctuation was observed for the LV pump function index (i.e., EF) with age, by which the practical cardiac protection principle was reinforced. This conclusion is consistent with a published clinical observation that declining systolic indexes rather than diastolic indexes are commonly found in individuals who have complaints and limitations in activities of daily living among the oldest-old (14).

From our hierarchical results, a marked age-related reduction of individual fluctuation was seen for LVmass, which is one of the most important anatomic LV indexes. The interpretation of this result is that the mean amplitude of the fluctuation of LVmass decreases with increasing age within an individual elderly man in our representative cohort. This means that, in this cohort, an old-old man demonstrated milder individual variability in LVmass with age than a young-old man. On the contrary, the most notable age-related increase in individual variance was found for DT, which suggests that greater fluctuation with age is seen in an old-old man than in a young-old man in the same cohort. Simultaneously, individual variability of all four transmitral Doppler indexes increased significantly with age, irrespective of the concurrent age-related diastolic population-averaged deterioration. Although the physiological significance of prolonged DT in asymptomatic elderly subjects has been previously addressed (15), the underlying mechanism of the age-dependent individual fluctuation of the cardiac anatomic and functional echocardiogram indexes remains unexplored. It was also reported that changes in Doppler indexes of diastolic function could be observed in a normal healthy aging population, yet the origin of these changes remains controversial (8, 12, 18). At the same time, how and for what reason the prevailing preclinical heart failures develop into clinical events in the elderly is also largely unknown (13). The premise of our hypothesis is that age-related pathological changes within individuals are neglected due to asymptomatic homogeneity. We further infer that the presented age-related, within-individual variance, which is independent of the population-averaged, age-related tendency, could proportionally reflect the vector impact of compensated capability both internally and externally. It is explicit that the external regulations are efficient and potent in referring to the consistent preclinical and event-free status for the present cohort. Thus the characterized systolic-diastolic “dichotomy” of within-individual cardiac fluctuation with age, which is attributed to the “vector sum” between the reduced physiological compensatory ability and the external pharmaceutical improvement in the present cohort, may largely depict an efficient impact of external regulation on cardiac aging in a given population, irrespective of its diversity.

In conclusion, our study revealed that successfully fitted multilevel modeling has the potential to disentangle the physiopathological mechanism(s) of the correlations between internal cardiac aging and external individualized treatments in asymptomatic elderly men and is especially important for determining the mechanism(s) by which preclinical heart failure develops into clinical heart failure.

## GRANTS

This study was supported by a grant from the HeiLongJiang Province Scientific & Technology Commission (no. GC07C335).

## DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

## AUTHOR CONTRIBUTIONS

Author contributions: Y.-h.W., Y.-p.J., S.-s.L., and F.-f.Q. analyzed data; Y.-h.W., Y.-p.J., F.-f.Q., and H.H. interpreted results of experiments; Y.-h.W., Y.-p.J., and H.H. prepared figures; Y.-h.W. and H.H. drafted the manuscript; Y.-h.W. and H.H. edited and revised the manuscript; Y.-h.W. and H.H. approved the final version of the manuscript; Y.-p.J. and S.-s.L. performed experiments; H.H. conception and design of research.

## ACKNOWLEDGMENTS

The authors thank the participants of the LVAW and the entire project staff of the LVAW, including other investigators, coordinators, physicians, and nurses who made invaluable contributions to this study. The authors also thank Dr. Jie Ge and Dr. Han Wang for helpful discussions and technical aid on two-level modeling.

- Copyright © 2012 the American Physiological Society