An age-related decline in balance, gait and lower-extremity muscle strength measures may lead to increased risk of falls and fractures. Previous studies have reported a possible non-linear age-related decline in these measures, but the choice of methodological approach has limited its interpretation. Healthy community-dwelling women (n=212) 21–82 years of age were evaluated for strength [Nicholas MMT (manual muscle tester)], gait [CSA (clinical stride analyser)], activity [HAP (human activity profile)] and static and dynamic balance [CBS (Chattecx balance system), LBT (Lord's balance test) and the ST (step test)]. A GAM (generalized additive model) was developed for each outcome variable to estimate the functional relationship, with age as a continuous variable. Performance was maintained until 45–55 years of age, depending on the outcome measure. Thereafter a decline in performance was evident with increasing age in all measures. Overall, a significant non-linear relationship with age was demonstrated for lower-extremity strength measures (MMT), velocity and double support duration of gait (CSA) and some clinical and laboratory balance tests [ST, LBT (eyes open) and the CBS]. Linear relationships were demonstrated by the LBT with eyes closed and activity measures. Balance, lower-extremity muscle strength and gait may decline non-linearly with age. Our study suggests possible threshold effects between age and balance, muscle strength and gait measures in women. Further research into these threshold effects may have implications for the optimal timing of exercise and other interventions to reduce the risk of falls and fractures.
- non-linear modelling
Maintenance of independent physical function is important throughout life . Contributors to independent function include adequate lower-extremity muscle strength, safe and efficient gait, and good balance function.
The consequences of balance dysfunction, poor gait and reduced strength include falls and fractures, both of which adversely affect health and independence. Falls are a common problem for women over 65 years of age , although a decline in balance function has been reported in women from 40 years of age . The high incidence of serious falls associated with balance dysfunction, muscle weakness and gait problems highlights the importance of studies investigating age-related changes in these key domains.
A variety of experimental methodologies and analytical approaches have been used to elucidate age-related changes associated with postural control (balance), muscle strength and gait [4–7]. Age is associated with a deterioration in balance, resulting in an increase in body sway [8,9]. Reduced speed and shorter step length [10,11], and a decline in muscle strength, due to skeletal muscle mass reduction [12,13], are also considered characteristic of aging.
Previous studies using a variety of laboratory and clinical measures to describe changes in balance, strength and gait associated with age have had several limitations. Many balance studies involved participants with a pathology affecting the motor system [14–16], living in nursing homes  or with a history of falls . Therefore the reported changes in balance function may not accurately reflect true age-related changes, but instead, a pathology that is more prevalent with age. Most studies have modelled age-related changes in balance and related measures linearly, by age categories (young compared with old), using regression and simple product-moment correlation coefficients [19–22]. These approaches are problematic, as age was not represented as a continuous variable and its effects were not measured across the lifespan. The approaches also preclude identification of non-linear associations between the variable of interest and age. Furthermore, given the heterogeneity across participants of the same age, grouping them into decades is also inadequate because a smooth curve cannot be fitted to categories of a variable.
The present study sought to address the limitations of previous studies to obtain a better understanding of age-related differences in balance, strength and gait performance in healthy community-dwelling younger and older adult women. Determining the age at which a decline in performance occurs is important, so that timely effective strategies can be implemented which focus on improving lower-extremity strength, gait and balance. The aim of the present study was to determine the functional form of a decline between performance measures of balance, strength and gait decline and age (as this may not always be linear).
MATERIALS AND METHODS
A sample of 212 healthy community-dwelling females (21–82 years of age) were included from three sources: (i) a subset comprising 176 first-born members of twin pairs obtained from a larger study investigating the heritability of balance (in order to remove the effect of being a twin) , (ii) five additional participants comprising the older sister (of a sister pair) and four twin-members of the excluded twin pairs as a result of the screening tests (as described below), and (iii) 31 community-dwelling women recruited as part of related reliability studies.
The research has been carried out in accordance with the Declaration of Helsinki (2000) of the World Medical Association, and has been approved by both the Institutional Human Research Ethics Committee and the Australian Twin Registry. All subjects gave informed written consent for participation.
Questionnaires completed prior to the testing session provided demographic data and information on risk factors for falls and fractures. The testing session, which lasted 90 min per participant, was conducted at the National Ageing Research Institute, and comprised screening tests and assessment of clinical and laboratory measures of balance, strength, gait and activity.
Participants were excluded if they had a clinically significant impairment or disease affecting their ability to perform the test procedures. Screening tests, with cut-off scores for exclusion shown in parentheses, were as follows: (i) AMTS (abbreviated mental test score)  (<7 out of 10); (ii) visual contrast sensitivity using the Melbourne Edge Test  (<16 out of 24); (iii) proprioception of both great toes, in which three trials were given for each great toe with confounding movements of the toe interspersed (any incorrect response); (iv) Sharpened Romberg Test , where participants were instructed to stand with one foot in front of the other, heel to toe (with whichever foot they preferred in front), and with their arms by their sides and eyes closed for 5 s (being unable to maintain this position for 5 s); and (v) postural blood pressure and pulse rate, where postural blood pressure and pulse rate were recorded in the supine position, after standing for 1 min, and after standing for 3 min, using an automatic electronic blood pressure Sein-6000 device (Sein Electronics) (>20 mmHg fall in systolic blood pressure or >10 mmHg fall in diastolic blood pressure upon standing) .
Four participants were excluded. Three reported musculoskeletal problems which affected their performance on the outcome measures (Scheuermann's disease and poliomyelitis) and one of the three also scored <7 on the AMTS. The fourth participant failed the toe proprioception test.
Eligible participants were then assessed using a comprehensive test battery of balance, strength and gait measures (balance measures were described in detail previously ) with shoes removed (with the exception of gait assessment).
The CBS (Chattecx Balance System; Chattanooga Group) is a computerized force platform used to measure the body's centre of pressure under static and dynamic balance conditions, as either a single or dual task condition (the latter where the participant performed a concurrent distractor task counting backwards in threes from a randomly selected three digit number) . Single and dual task performance was assessed on a stable platform, with the platform tilting F–B (forwards–backwards) or S–S (side to side). CBS measures were adjusted for the participant's height (m).
The ST (step test) is a measure of dynamic single limb stance, involving stepping one foot on and off a 7.5-cm-high block as fast as possible for 15 s . The performance for each leg was assessed separately, and the average score was obtained.
The LBT (Lord's Balance Test) is a series of dual limb static stance tests (feet 10 cm apart) using a sway meter to record displacements of the body at the level of the waist . Four sensory conditions each of 30 s duration were evaluated: firm surface with eyes open and eyes closed, and high-density foam with eyes open and closed. Total sway was calculated manually by counting the number of mm squares traversed by the pen on graph paper in the 30-s period.
Activity level was measured using the HAP (Human Activity Profile) test, a 94 item questionnaire assessing activity levels across a wide range of energy requirements. The AAS (adjusted activity score) was calculated .
Gait was assessed walking at comfortable walking speed using a CSA (clinical stride analyser; B&L Engineering), a computerized footswitch system that measures temporal and distance gait characteristics. Subjects walked across an 8 m walkway, with recording over the central 6 m. No subjects used a walking aid. Gait velocity (m/min) and double support duration (% gait cycle) were recorded.
Lower limb muscle strength testing was assessed in a supine position using a hand-held Nicholas MMT (Manual Muscle Tester; Lafayette Instruments). Hip abductors, knee extensors and ankle dorsiflexors in each leg were evaluated. The MMT recorded the maximum force applied (kg) to overcome the muscle contraction using the ‘break method’ . Three trials were conducted for each muscle. Measurements from the MMT were adjusted to the participant's weight in kg.
Each of the gait, strength, activity and balance measures were continuous, and were defined as the outcome variables. Age (in years) as a single continuous variable was entered into each model. The smooth representation of age-related differences on these measures was obtained by the adoption of a non-parametric smoothing method, which enabled the structure of the observed data to influence the functional form between age and outcome measures. For each outcome variable, an additive model was developed to estimate the functional relationship with age . Additive models are a flexible regression-type modelling approach where the fitted functions are curves that best represent the relationship between an outcome variable and a continuous covariate. In the present study, they have been developed for each outcome variable to estimate the functional relationship with age as a continuous variable by the use of spline smoothers to determine whether data are linear or non-linear. For example, a linear regression with a single continuous covariate (age) can be represented by the form: y=α+βx+ϵ, where y is the outcome measure, i.e. any one of the balance, gait, strength or activity measures, and x is age (years). If βx is replaced by a non-linear function f(x), we get an additive model: y=α+f(x)+ϵ. The f functions are termed smooth functions, α the intercept and ϵ the error term. Smoothing splines (piecewise polynomials) are used where a number of polynomial curves are joined together at points termed as knots . The functions were fitted using the additive model function with a default choice of DF (degrees of freedom) for the smooth term. An estimated DF of 1 suggests a linear fit is adequate in describing the age-related changes in the outcome measures. Diagnostic plots of residuals against fitted, normal Q-Q plots and Cook's distance plots were used to assess the adequacy of each fitted additive model. Results are presented as plots with fitted smooth functions and approx. 95% point-wise confidence intervals.
All analyses were completed using the R implementation of the S language program (R Development Core Team, 2004; http://www.R-project.org). The R statistical package uses a GAM (generalized additive model) procedure . The GAM procedure fits a cubic spline to the data. After fitting a model to the data, the adequacy of the respective model can be checked using deviance residuals. Deviance residuals are based on the χ2 distribution property that is derived as the sum of squares of normal variables. The deviance residual for an observation reflects its contribution to the overall goodness of fit (deviance) of the model. Analysis of the relationships between age and each of the variables described were undertaken.
Characteristics of participants are shown in Table 1. The distribution of age among participants consisted of 10% (n=22) of the sample between 21–30 years, 15% (n=31) between 31–40 years, 28% (n=59) between 41–50 years, 24% (n=51) between 51–60 years, 13% (n=28) between 61–70 years and 10% (n=21) between 71–82 years. The majority (67%) of participants were from urban areas of Victoria, with most living at home with family (16% were living home alone) and only 6% required community services (mostly home help). The majority of the overall sample perceived their general health as good, with one-third reporting the presence of neurological, cardiac or musculoskeletal problems not affecting their performance on physical measures of balance and strength. A total of 13% of participants reported taking more than four medications. None of the participants were taking medication known to have an effect on motor or sensory performance (for example, benzodiazepines).
Performance on balance, strength, gait and activity measures across the age groups
The performance of the participants on the balance, strength, gait and activity measures are shown in Tables 2, 3 and 4. Scatter plots of balance, strength, gait and activity measures with age suggested that the performance on these measures declined significantly with increasing age (plots not shown). This was evident by the increase in postural sway on both the CBS and the LBT, the decrease in the number of steps on the ST, decreased muscle strength and decreased activity levels. Moreover, the plots suggested non-linear relationships of some of these measures with age.
Analysis of the relationships between age and balance, strength, gait and physical activity measures
Additive models were developed to estimate the mean curve, i.e. E(y/x), where y is one of the balance, gait, strength or activity measures and x is age as a continuous variable in years.
Results of the analysis of the relationships between age and balance, strength, gait and activity measures are shown in Table 5. Overall, a significant non-linear relationship with age was demonstrated for lower-extremity strength measures (MMT), velocity and double support duration of gait (CSA) and some clinical and laboratory balance tests [ST, LBT (eyes open, with and without foam) and the CBS]. The smooth term for all of the measures described was significant, with age explaining 5.5–40.1% of the deviance residuals.
Although the majority of measures had non-linear relationships with age, activity level [both MAS (maximum activity score) and AAS] measured by the HAP questionnaire and components of the LBT with eyes closed (with and without foam) had linear relationships.
Examples of the non-parametric models of measures of balance (CBS) and strength (MMT) are shown in Figures 1 and 2 respectively. Fitted values from an additive model for the CBS (F–B perturbations with a distractor task) had a non-linear relationship with age (as a continuous variable) (Figure 1). The fitted curve suggests stability in postural sway until approx. 40 years of age, and an increase thereafter. The fitted smooth term with 3DF was highly significant (P<0.001).
A fitted curve for the additive model for right hip abductor strength and age is shown in Figure 2. The fitted smooth curve is overlaid on the residuals. The smooth term with 4 DF is highly significant (P<0.001). The fitted model suggests a smooth increase in hip strength between 20 and 45 years of age, a rapid deceleration to age 70 and then stability thereafter.
For all measures, the observed increase in the fitted function for women over 75 years of age and between 20 and 40 years of age may be an overfit of the model due to the small numbers in the study. This is also evident in the wider confidence intervals for these age groups.
The results from the present study support the hypothesis that the majority of balance-related measures investigated have a non-linear relationship with age.
For most of the outcomes, performance was maintained until 45–55 years of age, depending on the outcome measure. Thereafter a gradual decline in performance with age was evident. Results from a previous study demonstrated a non-linear relationship between muscle strength and gait velocity in older men and women . Our present findings that most of the balance-related measures investigated had a non-linear relationship with age are consistent with the results from that study, as both musculoskeletal and sensory systems are key contributors to effective balance performance. Although these changes are described throughout the present study as effects of age, it is also possible that these effects reflect differences between age cohorts.
A significantly non-linear relationship with age was demonstrated by all lower-extremity strength measures (MMT), velocity and double support duration of gait (CSA) and clinical and laboratory balance tests [ST, LBT (eyes open, with and without foam) and the CBS]. The smooth term for all measures described was significant with age, explaining 5.5–40.1% of the deviance residuals. The LBT measures with eyes closed (with and without foam) and both the MAS and AAS of the HAP questionnaire had linear relationships. For inferential purposes, it may be instructive to adjust the models for other factors, other than age, that contribute to physical performance, such as nutrition and lifestyle factors; however, this was not within the scope of the present study.
An important feature in determining the specific nature of the relationship between age and each of the balance-related variables is in identifying the timing of the onset of decline (threshold effect) and the rate of decline of each function with respect to age. This information may be useful in indicating an optimal time for targeting health promotion behaviours, such as balance training or strength training programmes. These approaches have been shown to be effective in reducing falls in older subjects [35–37], although the present findings suggest that these options should be considered at an earlier stage to coincide with the observed decline in performance, which appears to commence between 40 and 55 years of age in a number of the measures evaluated .
Aging is an important determinant of balance, strength and gait outcomes and is the primary focus of many studies. Research evidence using a range of methodologies and measurement approaches has demonstrated a clear relationship between aging and these outcome measures. However, limitations in many of these studies include that they have either used ANOVA or a regression-type approach to assess age-related differences. When ANOVA is used, age is stratified into younger and older [4,6,21], and sometimes into 10–20 year age groups, for example, 20–40, 40–60, 60–70 etc . An overall test is used to determine the differences in outcome measures between groups, with some studies adopting a post-hoc test to determine exactly where this age difference may occur . These tests underestimate the relationships between age and outcome measures, and age is treated as non-continuous, thereby making it difficult to examine exactly where age-related differences in outcome measures may occur.
Hence one of the advantages of the present study is that age is treated as a continuous variable, rather than lumping age groups together (for example by decade). Despite the large heterogeneity across participants of the same age, using age as a continuous variable is critical as it demonstrates the relationship with a particular variable to the year level (as opposed to the decade level). Hence the accuracy of the differences with age may be lost to a degree when grouped by decades.
Another common and frequently misused approach is linear regression. Some reported analyses have assumed a linear relationship between a continuous measure of age and outcome without adequately testing the assumption for linearity [38–40]. Violating this assumption results in invalid estimates of the effects of age, and inferences made from these models may be misleading. Others have extended this approach to estimate quadratic  or cubic (polynomial) terms , or piece-wise linear  terms for age-related differences. Although including an additional term for age may explain more of the variability in outcome measures, the parametric models constrain the age effects particularly at the end points of the age distribution and, thus, may not adequately describe the structure of the observed data.
We adopted a non-parametric smoothing method allowing the structure of observed data to dictate the functional form between age and outcome measures, resulting in a smooth representation of age-related differences. These methods accommodated both parametric (e.g. linear) and non-parametric relationships with the outcome. Furthermore, these methods allow us to determine possible threshold effects most evident in studies of age-related physiological changes.
The smoothing techniques adopted in the present study use smoothers to represent the relationship between age (continuous) and outcome measures, as displayed visually on a scatter plot. The models make no a priori assumptions concerning the functional form so that the method of fitting can be easily transported to another dataset. The methods also accommodate linear relationships as demonstrated in many other studies [5,40] that should not be ruled out entirely. During the model fitting process, if the smooth term is not statistically significant and the scatter plot of fit compared with the data suggests a linear function form, then it would be wise to proceed with a linear regression approach.
Several factors may limit the generalizability of our present results. Most of the participants were healthy community-dwelling volunteer twins, registered with the Twin Bone Research Program. Therefore there was potential for recruitment bias. However, performance achieved on outcome measures by the older twins in the present study was similar to that reported for healthy older women . It is possible that balance performance differs between the sample in the present study (twins) and the broader non-twin population. Only data from the first-born twin were included to avoid the need to adjust for twinness. Further limitations include the imbalance in the number of participants in the various age categories and that the study was cross-sectional and not longitudinal. However, comprehensive longitudinal studies of aging-related measures are extremely challenging and take many years to complete. Future studies also need to evaluate these outcomes in males. We chose to study females in this instance because falls are a clinical problem mainly affecting older women.
Selection bias could have arisen if fitter subjects participated in the present study. A comparison of activity levels between women from the Twin Bone Research Program who were participants and non-participants indicated no differences in the number of hours of general sports or walking for the last 12 months. Moreover, the subset sample of women over 65 years of age in our present study was similar to a randomly generated sample of older people living in the community , in that the majority lived at home with others, approximately one-quarter were taking more than four medications and most of the participants rated their general health as good. Therefore the results of the present study are likely to be generalizable to the wider female population of the same age.
Further studies are required to investigate the possible threshold levels observed in the present study while adjusting for potential confounders, such as gender, nutrition, weight, height etc.
In conclusion, we have demonstrated that the majority of balance, muscle strength, gait and activity measures investigated in the present study decline non-linearly with age. Adoption of a non-parametric smoothing method resulted in a smooth representation of age-related differences with variation in the age at which a decline in performance commences and possibly in their rates of decline.
We acknowledge the role of the Australian Twin Registry. The Australian Twin Registry is supported by an Enabling Grant (ID 310667) from the National Health & Medical Research Council administered by The University of Melbourne. This project was supported by grants from The Australasian Menopause Society and The University of Melbourne Research Grant Scheme, and two scholarships (to N. E. H.) from Osteoporosis Australia and The University of Melbourne.
Abbreviations: AAS, adjusted activity score; AMTS, abbreviated mental test score; CBS, Chattecx Balance System; CSA, clinical stride analyser; DF, degrees of freedom; F–B, forwards–backwards; GAM, generalized additive model; HAP, Human Activity Profile; LBT, Lord's Balance Test; MAS, maximum activity score; MMT, Manual Muscle Tester; S–S, side to side; ST, step test
- © The Authors Journal compilation © 2008 Biochemical Society