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The Journals of Gerontology Series A: Biological Sciences and Medical Sciences 58:M1125-M1134 (2003)
© 2003 The Gerontological Society of America

Trajectories of Leg Strength and Gait Speed Among Sedentary Older Adults: Longitudinal Pattern of Dose Response

Jama L. Purser1, Carl F. Pieper1,2, Charles Poole3 and Miriam Morey1,5,4

1 Center for Aging and Human Development
2 Department of Biostatistics and Bioinformatics
5 Department of Medicine, Division of Geriatrics, Duke University, Durham, North Carolina.
3 Department of Epidemiology, School of Public Health, University of North Carolina, Chapel Hill.
4 Geriatric Research, Education and Clinical Center, Department of Veterans Affairs Medical Center, Durham, North Carolina.


   Abstract
Top
 Abstract
Method
 Analysis
 Results
 Discussion
 REFERENCES
 
Background. Current theory about how an older adult's leg strength influences walking speed is based primarily on nonlinear patterns of association observed in cross-sectional data. Compared with adults with normal or high levels of leg muscle strength, weak older adults are thought to have a greater capacity for functional change in response to changes in lower extremity strength. Longitudinal data, however, have not been applied to study this putative pattern of dose response.

Methods. Three repeated measures of leg strength, gait speed, and covariates were evaluated in a cohort of 134 sedentary, community-dwelling male and female participants (aged >64 years) of a randomized exercise intervention. Empirical Bayes methods were used to evaluate the association between trajectories of strength and gait speed during the course of the study.

Results. We observed a potentially clinically important, positive linear association between strength change and gait speed change. Each additional unit increase in the monthly rate of strength change increased the rate of gait speed change by 0.29 meters/minute/month (95% CI [confidence interval] = 0.03, 0.55 m/min/mo). Absolute change in walking velocity due to strength changes in the cohort ranged from a gain of approximately 15 m/min to a loss of approximately 13 m/min over the 9-month period (changes of -18% to +20% relative to a normal walking speed of 72 m/min).

Conclusions. In this cohort, change in functional walking speed depended more on the rate of strength change observed than on the amount of muscle weakness present at baseline. These results have important implications for screening and intervention programs designed to change functional walking ability among sedentary older adults.

USUAL walking speed is an important health outcome measure in geriatric functional assessment research (1). Its measurement is simple, reliable, and inexpensive, and recent work has demonstrated its validity in predicting disability, institutionalization, falls, and death among senior adults (2–4). Studies suggest that less than 5% of community-dwelling adults over age 75 walk at gait speeds necessary to safely perform common functional activities, such as crossing at a signaled traffic intersection (5,6). Research to identify impairments that cause this type of functional limitation is needed (7–9) because walking ability is a critical component of functional independence and quality of life.

Lower extremity muscle weakness is one type of physiologic impairment believed to be a key determinant of geriatric functional change in general, and gait speed change in particular (8,9). If a causal relationship exists, it is of particular interest because strength impairments are modifiable (10–14). Existing knowledge about whether leg strength and gait speed are causally related is based primarily on cross-sectional studies, several of which have described the dose-response relationship between leg strength and walking speed (15–26). For example, Buchner and colleagues have reported a nonlinear pattern of dose response in which cross-sectional measures of strength and gait speed are closely associated only for the weakest older adults (20). For stronger older adults, cross-sectional measures of strength and gait speed do not appear to be as closely associated.

Based on this frequently cited nonlinear pattern of cross-sectional dose response, several authors theorize that, by screening older adults for leg muscle weakness, they may be able to identify those older adults who will experience the largest functional impact of lower extremity strength changes (9,20,23,25). Unfortunately, the longitudinal association between strength and gait speed has been described in only two published studies, neither of which tested this theory, and neither of which presented a longitudinal dose-response curve (21,26).

In the current study, we evaluate the association between trajectories of strength and gait speed in a cohort of older, sedentary adult participants of a previously reported randomized exercise study (27). Our primary goal is to characterize the longitudinal association between strength change and gait speed change, and to describe how baseline levels of lower extremity strength modify the relationship between change in strength and change in gait speed over time.


   METHOD
Top
 Abstract
 Method
Analysis
 Results
 Discussion
 REFERENCES
 
Study Design
This was a longitudinal cohort study using participants from a randomized exercise trial, conducted at Duke University Medical Center (DUMC) from 1993–1997. The primary study methodology and results of the underlying interventions have been reported elsewhere (27). Briefly, 70 participants were randomized to a progressive aerobic exercise group consisting of brisk walking or biking for 40 minutes 3 times per week. Sixty-four people were randomized to 20 minutes of progressive aerobic exercise (brisk walking or biking), followed by 20 minutes of spinal flexibility exercises 3 times per week. Treadmill exercise tolerance tests and measures of functional outcome were administered at baseline, at the end of the interventions 3 months later, and 6 months later after a home-based version of the relevant exercise intervention. In the original study, both groups demonstrated positive change on primary measures of outcome, but neither group demonstrated more improvement than the other (27). The comparability of the underlying treatment effects allowed us to combine the two treatment groups into a single cohort for the current analysis of the association between strength change and gait speed change. This study utilized 3 repeated measures of lower extremity strength, gait speed, and covariates originally collected from each of the 134 sedentary older adult participants of the original study.

Participants
Recruitment and selection procedures have been described previously (27). Briefly, community-dwelling residents of Durham, Wake, or Orange counties (North Carolina) aged 65 years or older were recruited. Residents were invited to participate if classified by telephone interview as "non-exercisers" or "non-vigorous exercisers" using Reuben's Advanced Activities of Daily Living Scale (28). Individuals with any of the following were excluded: unstable angina, myocardial infarction in the last 6 months, blindness (>20/100 corrected vision), unstable chronic obstructive pulmonary disease (acute flair requiring hospitalization or prednisone taper within 12 months), history of stroke or other fixed hemiparesis, uncontrolled hypertension (diastolic >100 mmHg), any active, progressive neurological diagnosis (Parkinson's, myelopathy), congestive heart failure in the previous 12 months, lower extremity amputation, total spinal rotation less than 60° or greater than 120°, or presence of mental status deficits as assessed by the Short Portable Mental Status Questionnaire (29). Participants with exercise-induced ventricular tachycardia, ventricular fibrillation, or syncope were excluded as well as those with a 2 mm or greater ST segment depression during their baseline exercise tolerance test. Those with a maximum oxygen uptake greater than 27 ml/kg/min (for men) or 25 ml/kg/min (for women) were also excluded.

Data Collection
Informed consent was obtained from all participants, who were tested at DUMC's outpatient clinical research unit. Data were collected by a staff of physical therapists and research assistants using a written protocol.

Lower Extremity Muscle Strength
Lower extremity strength testing was performed using a Chatillon strain gauge dynamometer (Chatillon Medical Products, Greensboro, NC). Peak isometric hip abduction and ankle dorsiflexion torque were recorded using a standard written protocol (30). Hip abduction was tested in a supine position, with the hip in neutral with respect to flexion/extension, abduction/adduction, and internal/external rotation. Ankle dorsiflexion was recorded in a seated position, with the knee flexed to about 45°, and the ankle in about 30° of plantar flexion. Segment lengths were recorded for each extremity tested, using standard methodology to record from the approximate axis of rotation to the point of application of the dynamometer. Participants were given 1 practice and 2 test trials using a 5-second isometric "make test." Peak force (lb) was multiplied by the length of the limb segment to obtain joint torques (ft-lb). We previously reported 24-hour and 1-week test–retest reliability of strength scores obtained using this method (30). Our 24-hour test–retest intraclass correlation coefficients were 0.88 and 0.91 for the left and right hip abductors, and 0.88 and 0.90 for left and right ankle dorsiflexion. The 1-week test–retest intraclass correlation coefficient was 0.86 for both left and right hip abduction, and 0.94 for left and right ankle dorsiflexion.

Usual Walking Speed
Gait velocity was measured using digital stopwatch recordings of a timed 10-meter walk (31). Two trials of walking at a normal, comfortable pace on a level walking surface were recorded, and walking velocities were averaged.

Demographics, Comorbidity, and Anthropomorphic Data
At baseline, all participants self-reported their race (American Indian, Asian or Pacific Islander, African American, Hispanic, Caucasian, or Other), gender, age, years of education, and the presence or absence of 24 different physician-diagnosed medical conditions (arthritis, cataracts, fracture, cancer, lung disease, peripheral vascular disease, diabetes, anxiety/depression, outpatient surgery, glaucoma, sleep disorder, osteoporosis, surgery requiring hospitalization, abnormal lipid panel, angina, joint replacement, myocardial infarction, stroke, chronic pain, congestive heart failure, problems with hearing, amputation, fusion, and Parkinson's disease). Weight (kg) and height (m) were recorded at all 3 time points by trained data technicians, and body mass index (BMI) was computed (kg/m2).

Covariates
Covariates were assessed at all 3 measurement points. Depression was evaluated using the Centers for the Epidemiologic Studies of Depression scale (CES-D) (32). Thoracic kyphosis and lumbosacral hypolordosis in the sagittal plane were measured using a kyphometer (33,34). A universal goniometer was used to measure active-assisted dorsiflexion range of motion at the ankle (31). Peripheral sensory impairment was evaluated using standard clinical assessments of joint kinesthesia and vibratory sensation at the toe, ankle, and knee (35). Maximal oxygen uptake (pVO2max) was recorded using a treadmill maximum exercise tolerance test and collection of respired gases (27). Number of self-reported disabilities was recorded as the sum of disabilities present for 13 activities of daily living (bathing, using the phone, traveling, shopping, preparing meals, taking medications, managing money, doing heavy work around the house, walking up/down stairs, walking a half mile, lifting/carrying 10 lb, reaching above shoulder level, and fingering small objects). For each of these tasks, disability was defined as needing assistance, experiencing difficulty, or not being independent.


   ANALYSIS
Top
 Abstract
 Method
 Analysis
Results
 Discussion
 REFERENCES
 
Data analysis was performed using the SAS statistical analysis system. Univariate distributions and missing data were described. Although the amount of missing data was small (less than 5%) and unlikely to influence point estimates, we imputed missing information using SAS multiple imputation procedures (40).

Measure of Lower Extremity Strength
Similar to previous reports (20,21,41,42), strength scores for individual lower extremity muscles were collinear (r = 0.63–0.90), and violated assumptions of independence for linear regression modeling. In addition, Brown and colleagues have shown that summary measures of leg strength are more strongly associated with gait speed than individual muscle strength scores (42). Because of these concerns, we created a summary measure of leg strength by summing 4 individual muscle torques (left and right hip abduction and ankle dorsiflexion) for each individual participant. Similar methods previously have been used by Brown and colleagues (42), Jette and colleagues (41), and by Buchner and colleagues (20,21). The summary measure of leg strength was used in all analyses.

Trajectories of Strength Change
The SAS MIXED procedure was used to generate an empirical Bayes estimate of the rate of strength change for every participant in the study (43,44). In comparison to conventional linear regression methods (e.g., ordinary least squares estimates or change scores), empirical Bayes estimates of individual time slopes have been shown to minimize total estimation error across a distribution of participants (44,45). The result is an optimally precise estimate of the distribution of individual strength trajectories (44,45). In the hierarchical linear model used here,


ß0i and ß1i are individual intercepts and slopes for gait speed change, and eit and µ1i are residual error terms. Baseline covariates included gender, age, race, education, treatment assignment, lower extremity muscle strength, pVO2max, gait speed, BMI, comorbidity, self-reported disability, kyphosis, hypolordosis, ankle dorsiflexion, depression, and presence of a sensory deficit. The within-person residual covariance matrix was evaluated (46) and modeled as compound symmetric. Finally, empirical Bayes estimates of individual-level strength trajectories (44,45) were generated from this model and used as the independent variable in subsequent models evaluating the relationship between strength change and gait speed change.

Relationship Between Strength Change and Gait Speed Change
A second hierarchical linear model (43,44) was used to estimate the association between the previously estimated strength trajectories and change in gait speed:


In this hierarchical linear model of gait speed, ß0i and ß1i represent individual gait speed intercepts and slopes, and µ1i and eit are residual error terms. The effect of strength change on change in gait speed was determined from the magnitude and precision of the {lambda}11 effect shown above. We included baseline gender, age, race, and years of education in all models as well as repeated cross-sectional measures of strength, aerobic capacity (pVO2max), BMI, thoracic kyphosis, lumbosacral hypolordosis, ankle range of motion, and depression.

First 3 Months Versus Last 6 Months
We estimated separate strength change-gait speed change associations in the first 3 months of on-site, supervised exercise and in the final 6 months of unsupervised home-based exercise. To accomplish this, a 2-piece linear time spline with a single node at 3 months was included at level 1 of the gait speed model. With only 3 within-person degrees of freedom (i.e., the number of within-person observations for a single individual), we could not estimate a random intercept and 2 time slopes simultaneously for each person without saturating the individual-level model (6). For this reason, we used two separate models to estimate the effect of strength change on gait speed change during the two different periods. In Model 1, gait speed trajectories were allowed to vary across participants during the first 3 months. During the second 6 months, the trajectory was assumed constant. In Model 2, gait speed trajectories were allowed to vary across participants during the second 6 months and assumed to be constant during the first 3 months.

Longitudinal Pattern of Dose Response
The SAS/GRAPH GPLOT procedure (47) was used to model individual empirical Bayes estimates of gait speed change as linear, quadratic, and cubic functions of empirical Bayes strength trajectories. In addition, we reproduced our dose–response curves stratified by treatment assignment to determine whether the overall dose–response association was modified by the underlying exercise regimens experienced by the cohort.

Influence of Baseline Level of Strength
Cross-sectional data suggest that level of lower extremity strength may influence the functional response to strength change experienced by an older adult (9,20,23,25,41). We evaluated the modifying influence of baseline strength on the overall magnitude of the strength–gait speed association by including an interaction between baseline strength score and individual strength change in the gait speed model. Level of strength at the beginning of the last 6 months was used as the potential effect modifier of the 3–9 month strength–gait speed association. Parameter estimates and 95% confidence intervals (CI) are reported.


   RESULTS
Top
 Abstract
 Method
 Analysis
 Results
Discussion
 REFERENCES
 
Participants
A previous publication details recruitment and exclusions (27). Briefly, 486 people were contacted, 286 received telephone screening, 210 were invited for further testing, 24 withdrew before randomization, and 52 did not meet selection criteria. One hundred thirty-four participants were randomized.

Eighty-one percent (108/134) of participants had complete data for all variables at all three waves of measurement. Eighty-five percent (114/134) had complete strength and gait speed data. Sixteen participants (12%) were tested only once. Four participants (3%) were tested only twice.

Among participants tested, the amount of missing data ranged from 0%-1.7% at Wave 1, 0%-3.4% at Wave 2, and 0-4.4% at Wave 3 across all variables, with 3 exceptions. Baseline self-reported disability and depression were missing for 9 participants (6.7%), and pVO2max was missing at the third measurement point for 11 participants (9.6%).

Descriptive Data
Table 1 shows descriptive characteristics of the sample. Most participants (approximately 70%) walked at gait speeds below 1.22 m/s, the norm for the curb-to-curb speed necessary for safely negotiating traffic intersections (5). About 30% had leg muscle force measurements below previously reported age and gender-specific "normal" ranges (48). Less than 1% had normal ankle dorsiflexion motion (20°) (49,50). Approximately 41% of participants were "overweight" (BMI = 25.0–29.9 kg/m2), and another 34% were "obese" (BMI >= 30 kg/m2) (51). Almost 47% of participants had a baseline peak oxygen uptake below 18 ml/kg/min, a cardiopulmonary fitness criterion for disability recognized by the United States Social Security Administration (52). Approximately 35% had more than 45° of thoracic kyphosis, and 27.6% had less than or equal to 27° of lumbar lordosis. Similar levels of spinal configuration have been associated with disability (53), decreased mobility self-confidence (54), and incident vertebral fracture (55). The majority of participants self-reported no difficulty or need for assistance in performing activities of daily living. Of 13 self-reported disabilities possible, the median number was 1.0 (SD [standard deviation] = 1.5).


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  		Table 1. Univariate Descriptive Statistics for Participants in the Axial Aerobic Randomized Trial (Claude D. Pepper Older American's Independence Center, 1993–97).

 
Trajectories of Individual Strength Change
Figure 1 shows the empirical Bayes distribution of the rate of individual strength change. On average, the rate of strength change in this cohort was positive (median strength change = +0.26 ft-lb/mo). Strength increased over the 9 months for 74 people (55%) and decreased for 60 people (45%). The monthly rate of strength change ranged from a maximum loss of 7.23 ft-lb/mo to a maximum gain of 7.69 ft-lb/mo. Total torque change during the study is computed by multiplying the monthly rate of strength change by the total months in the study. The average amount of torque change in the cohort was small (median change = 0.26 ft-lb/mo x 9 months = 2.34 ft-lb), but large strength losses (-7.23 ft-lb/mo x 9 months = -65 ft-lb) as well as large strength gains (7.69 ft-lb/mo x 9 months = +69 ft-lb) were also observed.



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  		Figure 1. An empirical Bayes distribution of individual strength change. IQR = interquartile range

 
Gait Speed Trajectories
Figure 2 shows individual-level observations of gait velocity for the entire cohort, along with the average gait speed values and 95% CI at each time point. Although the average gait speed values shown appear to remain stable over time, considerable between-person variability in gait speed was present at each cross-sectional measurement point as well as in the rates of gait speed change.



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  		Figure 2. Observed individual trajectories of gait speed in the cohort, and average predicted value of gait speed at each measurement point (predicted values were obtained by regressing repeated measures of gait speed on time (0, 3, and 9 months), then plotting the average value of gait speed at each time point along with its 95% confidence interval)

 
Initial parameter estimates from the linear mixed model of gait speed change suggested that, on average, gait speed changed at a rate of 0.0011 m/s/mo (0.07 m/min/mo, 95% CI = -0.08, 0.22). However, this initial model assumes a constant rate of change over 9 months. When we accounted for the 2 different time periods of the study by including a time spline, average gait speed change in the cohort during the first 3 months was 0.0173 m/s/mo (1.04 m/min/mo, 95% CI = 0.58–1.49), compared with 0.0031 m/s/mo during the second 6-month period (0.19 m/min/mo, 95% CI = -0.04, 0.41). Because the average rate of gait speed change was different in the 2 different time periods, a 2-piece linear time spline was used in all subsequent models.

Relationship Between Change in Strength and Change in Gait Speed
Table 3 shows parameter estimates and standard errors from an empirical Bayes analysis of individual gait speed trajectories. In Model 1, gait speed slopes are allowed to vary across participants during the first 3 months. Results of this model suggest that, for each additional unit difference in the rate of strength change during this interval, the rate of change in gait speed increased by a corresponding 0.0048 m/s per month (0.29 m/min/mo; 95% CI = 0.03, 0.55).


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  		Table 3. Estimated Absolute Change in Gait Speed* Due to Strength Change at the End of the Study.

 
In the second model, gait speed slopes vary randomly across participants during the last 6 months of the study. This model suggests that, for each additional unit difference in the rate of strength change per month during the second 6 months, the rate of change in gait speed increased by a corresponding 0.0024 m/s per month (0.14 m/min/mo; 95% CI = -0.006, 0.29).

The absolute difference between the adjusted and unadjusted strength effect estimates was extremely small for all time-dependent covariates evaluated (table available from author upon request). However, removing covariates from the model of gait speed did not substantially improve precision of the strength change effects compared with a fully adjusted model, so all time-dependent covariates were retained. Finally, when we controlled for the effects of baseline gait speed, baseline strength, and treatment assignment on individual gait speed trajectories, the effects of individual strength change on gait speed change did not substantially differ. Table 2 shows fully adjusted estimates.


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  		Table 2. Association Between Empirical Bayes Strength Trajectories and Change in Usual Walking Velocity Among Older Sedentary Adult Participants of the Axial Aerobic Randomized Trial (Claude D. Pepper Older American's Independence Center, 1993–1997).

 
Longitudinal Pattern of Dose Response
Figure 3 shows point estimates of individual strength change and gait speed change, along with the predicted linear dose–response curve and 95% CI for the strength change–gait speed change association during the two different time periods of this study. Alternative nonlinear prediction models (using quadratic and cubic functions of strength change) did not provide strong evidence of a nonlinear pattern of dose response, and are not shown here. The underlying treatment assignment also did not appear to modify the dose–response association between strength change and gait speed change (nonlinear dose–response curves and stratified dose–response curves available upon request).



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  		Figure 3. Linear dose–response relationship characterizing the association between change in strength and change in gait speed. A, 0–3 months, ß = 0.0048 m/s per month (0.29 m/min per month; 95% CI [confidence interval] = 0.03, 0.55); B, 3–9 months, ß = 0.0024 m/s per month (0.14 m/min per month; 95% CI = -0.006, 0.29)

 
Influence of Baseline Strength on the Magnitude of Dose Response
During the first 3 months, each additional foot/pound of baseline leg strength decreased the effect of strength change on gait speed change by only -0.00002 m/s (-0.001 m/min; 95% CI = -0.006, 0.004). The baseline summary score for lower extremity muscle strength ranged from approximately 41 to 232 ft-lb across individuals in this study. Two people who differed in their baseline strength by even the maximal amount possible in this study (approximately 190 ft-lb) differed by only 0.01 m/s (0.60 m/min) in their absolute 3-month change in gait speed (0.00002 m/s/mo x 190 ft-lb x 3 mo). The direction of this effect is consistent with predictions from previous studies based on cross-sectional data; however, the magnitude of the effect was extremely small and of questionable clinical importance. Compared with the first 3 months, the modifying effect of baseline strength during the second 6 months was smaller, and likely to have an even smaller clinical impact. During this second time period, each additional foot/pound of leg strength present at baseline decreased the effect of strength change on gait speed change by only 0.00001 m/s (-0.0006 m/min; 95% CI = -0.002, 0.003). In summary, changes in functional walking speed depended more on the magnitude of strength changes observed during this study than on the amount of muscle weakness present at baseline.


   DISCUSSION
Top
 Abstract
 Method
 Analysis
 Results
 Discussion
REFERENCES
 
This study had several important results. First, for the sedentary older participants we studied, we observed a clinically meaningful positive association between strength change and gait speed change. Second, the basic pattern of longitudinal dose response was linear, a finding that conflicts with previous assumptions of nonlinear dose response. Finally, baseline level of lower extremity muscle strength was not a strong predictor of the magnitude of association between strength change and gait speed change.

Trajectories of Strength and Gait Speed
The fact that many participants declined in strength and gait speed is not an unusual finding in a cohort participating in an intervention that is not designed to alter leg strength or gait speed. Cohort studies of the natural history of strength change, for example, demonstrate average declines in strength over time among healthy older adults (56). Recent work also suggests that aerobic exercise intervention without resistance training may not be enough to prevent the losses in muscle mass and strength that occur with aging (57). Thus, we believe it would be unusual if we did not observe individuals in the cohort whose strength was declining. We do not believe these declines indicate that the cohort responded in an unusual way to the underlying exercise programs. For example, peak oxygen uptake differed between the two underlying exercise groups at the end of the first 3 months, with the group that exercised aerobically for 40 minutes demonstrating twice the effect of those exercising for 20 minutes (27). Thus, the outcomes targeted in the underlying intervention changed as expected. On the other hand, the distribution of strength change in this sample (Figure 1) appears almost as it would in a stable cohort, with the number of people improving in strength approximating the number of people declining.

We would expect that, even in an intervention specifically designed to alter strength, we would observe individuals whose strength and function would decline. For example, causal theory posits at least four causal subtypes of individuals who should be considered in any test of causation: (a) people who will improve regardless of the intervention, (b) people who improve due to the intervention, (c) people who decline in spite of the intervention, perhaps because of decline in areas not intervened upon, and (d) people who may be susceptible to some aspect of the intervention causing them to decline, for example, those susceptible to accident or injury during the intervention (58). Even in a randomly sampled cohort, these four causal subtypes of people could be equally or unequally distributed. Depending on the population sampled in an observational study, this fact alone might preclude expectations that all individuals in the sample will experience positive change as a result of the intervention.

Clinical Impact of Lower Extremity Strength Change
In this study, we found that the rate of lower extremity strength change ranged from approximately -7.0 to +8.0 ft-lb/mo across individuals. Average gait speed change in response to each unit difference in the rate of strength change was 0.0048 m/s/mo (or 0.29 m/min/mo) during the first 3-month period of active intervention, and 0.0024 m/s/mo (or 0.14 m/min/mo) during the second time interval. This means that, across the first 3-month period, the absolute change in walking velocity resulting from strength changes ranged from a loss of about 6 m/min (0.29 m/min/mo x -7 ft-lb/mo x 3 mo) to a gain of an additional 7 m/min in walking speed (0.29 m/min/mo x 8 ft-lb/mo x 3 mo). During the second 6 months, the absolute change in gait speed with respect to strength change was similar, but occurred over a longer period of time (6 months versus 3 months). Taking both time intervals into account, the total absolute change in walking velocity due to strength changes observed in this 9-month study ranged from a loss of about 13 m/min to a gain of an additional 15 m/min (Table 3).

Relative to an individual with a baseline "safe" walking velocity of 1.2 m/s (72 m/min) (5), these absolute changes in walking speed represent percentage changes ranging from -18% to +20%. Gait speed changes of this magnitude may represent clinically important effects, especially considering that they reflect the impact of change in a single impairment-level variable, adjusted for changes caused by other individual covariates. In addition, these potentially clinically relevant changes in gait speed correspond to relatively slow rates of strength change that occurred in this study. Larger absolute changes in walking velocity due to strength change might be possible when lower extremity strength changes at a faster rate, such as what might occur during a progressive muscle strengthening intervention.

Longitudinal Pattern of Dose Response
We do not dispute that a "nonlinear" association may be present in cross-sectional data. Rather, we would like to challenge some of the inferences about longitudinal change that frequently are based on cross-sectional data, rather than longitudinal data. Our results do not provide strong support for a nonlinear longitudinal relationship between individual strength change and gait speed change. Neither of the 2 nonlinear dose–response curves we investigated (quadratic and cubic functions of strength change) suggested a pattern of longitudinal dose response substantially different from the basic linear model. This finding is important, for several reasons. First, a quadratic pattern of dose response like that observed in cross-sectional studies may not provide an adequate model for longitudinal effects. A quadratic pattern observed in the longitudinal setting would imply that large changes in strength have less of an impact on gait speed change than small changes in strength, regardless of whether one is weak or strong to begin with. More importantly, nonlinear cross-sectional patterns of dose response frequently have been used to suggest that people who are weak might experience a larger functional response to strength change compared with people who are strong (9,20,23,25,41,59–61). One potentially incorrect inference based on this theory is that even very large changes in leg strength will not have a substantial functional impact on healthy older adults. Until now, however, these assumptions have not been evaluated using longitudinal data.

In our study, the association between strength change and gait speed change was linear, and changes in functional walking speed depended more on the magnitude of strength changes observed during the study than on the amount of muscle weakness present at baseline. We do not believe that this finding is explained by the fact that we sampled mostly nondisabled people. The range of our baseline strength data, for example, is comparable to that in previous reports of a nonlinear cross-sectional association (20,21). In addition, while most individuals in our study were independent in instrumental and basic activities of daily living, a substantial number of people in our study were weak at baseline, had multiple prevalent impairments, and walked at speeds below those considered normal. As previously reported in the text, about one third of the sample had leg muscle force measurements below previously reported age- and gender-specific "normal" ranges. High levels of baseline strength were also well represented in this particular cohort. Finally, while we are unable to directly compare our summary measure of lower extremity strength to that used in previous studies due to slight differences in the four muscle groups summed, we were able to compare our data for ankle dorsiflexion strength to that observed in several previous studies:

We believe that we have adequately explored the potential for effect modification by baseline strength, and that a wide range of leg strength including both strong and weak individuals was present in this cohort. Thus, our longitudinal results challenge previous clinical assumptions about the relationship between strength change and gait speed change which, to date, have been supported only by cross-sectional patterns of dose response (9,20,23,25,41,56–58).

Based on the longitudinal data in this study, we suggest that screening programs targeting lower extremity muscle weakness in isolation may not efficiently identify those who will attain the most functional benefit from increases in lower extremity strength. From one cross-sectional assessment of muscle strength, it may be difficult to predict how much functional benefit an individual will gain when strength changes. Sarcopenia interventions and screening programs that select participants based on prevalent muscle weakness may exclude many people likely to benefit functionally from sarcopenia interventions.

Limitations and Strengths of the Study
Our study had several limitations. First, the underlying interventions experienced by participants in our cohort were designed to improve aerobic capacity through progressive walking or biking exercise. Because change in strength was not randomized, the association between strength change and gait speed change we observed might not be causal, and/or the direction of causation could be opposite from that inferred in this investigation. Changes in gait speed occurring through pathways other than strength change may have actually caused the changes in gait speed. We attempted to control for the effects of measured confounders potentially threatening the validity of estimated strength–gait speed associations. When we controlled for the effects of underlying interventions, baseline gait speed, and individual impairments on gait speed change, our estimates of the relationship between strength change and gait speed change were relatively unaltered.

Nevertheless, our analyses did not examine the effects of several potentially important covariates pointed out by our reviewers, namely exercise history and compliance to exercise. While we controlled for aerobic capacity, we did not have a measure of exercise history, which could potentially confound the association of interest. We were able to conduct follow-up analyses with a crude indicator of exercise compliance, identifying individuals who completed at least 78 20-minute (or longer) exercise sessions during the home-based portion of the study (compliers, 54%) versus those who were less compliant (46%). We subsequently reanalyzed our data using this variable as a potential confounder. The association between strength change and gait speed change during the last 6 months did not appear to be confounded by level of exercise compliance (parameter estimate = 0.0024 before adjustment; 0.0026 after adjustment).

An additional limitation of the current study is that the strength measurements utilized in the original randomized clinical trial were not selected a priori to be those most closely related to gait speed. While our data suggest that changes in hip abduction and ankle dorsiflexion strength are associated with trajectories of walking speed, in this study, we are unable to compare the relative importance of hip abductors and ankle dorsiflexors to changes that might occur over time in other lower extremity muscles.

Several strengths of this study deserve mention. Notably, this is one of a very small number of studies that have used longitudinal data to investigate the association between strength change and gait speed change (21,26). This study is the first to document a potentially clinically meaningful longitudinal pattern of dose response, adjusted for important confounders. In addition, we used empirical Bayes methodology to maximize precision when estimating individual trajectories of strength change and gait speed change over time. One advantage of using empirical Bayes estimates of change instead of the more familiar change score methodology is that we obtain a net "shrinkage" in random error across a distribution of individual estimates. Our application of the method allows us to obtain a net "shrinkage" in random error for the independent as well as the dependent variable. Finally, this work is novel because it begins to explore contextual factors that potentially influence the association between strength change and gait speed change over time.

Conclusion
We conclude that longitudinal change in lower extremity muscle strength was associated with potentially clinically meaningful change in gait speed among the sedentary older adults we studied. The basic longitudinal pattern of association was linear, not nonlinear as had previously been assumed. Baseline level of lower extremity strength did not strongly influence the magnitude of the association between strength change and gait speed change.


   Acknowledgments
 
This analysis was pursuant to National Institute on Aging funding (Claude D. Pepper Older Americans Independence Center, 5P60AG-11268), and to funding by the National Center for Research Resources, General Clinical Research Centers Program (MO1-RR-30). Partial support was provided by the Foundation for Physical Therapy, Inc., and by the Research Training Program in Duke's Center for Aging and Human Development (5T32-AG00029-26). The manuscript was completed in partial fulfillment of requirements for a PhD in Epidemiology, Department of Epidemiology, University of North Carolina School of Public Health. We acknowledge the contributions of Drs. June Stevens, Wayne Rosamond, and Larry Branch, who reviewed earlier versions of the manuscript and made helpful comments.

Address correspondence to Jama L. Purser, PT, PhD, Box 3003, Duke University Medical Center, Durham, NC, 27710. E-mail: jlp{at}geri.duke.edu

Received July 29, 2002

Accepted January 17, 2003


   REFERENCES
Top
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 Method
 Analysis
 Results
 Discussion
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