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Can Change in Prolonged Walking Be Inferred From a Short Test of Gait Speed Among Older Adults Who Are Initially Well-Functioning?

Daniel K. White, Tuhina Neogi, Wendy C. King, Michael P. LaValley, Stephen B. Kritchevsky, Michael C. Nevitt, Tamara B. Harris, Luigi Ferrucci, Eleanor M. Simonsick, Suzanne Satterfield, Elsa S. Strotmeyer, Yuqing Zhang
DOI: 10.2522/ptj.20130628 Published 1 September 2014
Daniel K. White
D.K. White, PT, ScD, MSc, Department of Physical Therapy and Athletic Training, Boston University, 635 Commonwealth Ave, 5th Floor, Boston, MA 02215 (USA).
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Tuhina Neogi
T. Neogi, MD, PhD, Clinical Epidemiology Research and Training Unit, Boston University School of Medicine, Boston, Massachusetts.
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Wendy C. King
W.C. King, PhD, Department of Epidemiology, University of Pittsburgh, Pittsburgh, Pennsylvania.
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Michael P. LaValley
M.P. LaValley, PhD, Department of Biostatistics, School of Public Health, Boston University.
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Stephen B. Kritchevsky
S.B. Kritchevsky, PhD, Sticht Center on Aging, Wake Forest School of Medicine, Winston-Salem, North Carolina.
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Michael C. Nevitt
M.C. Nevitt, PhD, Department of Biostatistics and Epidemiology, University of California–San Francisco, San Francisco, California.
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Tamara B. Harris
T.B. Harris, MD, MS, Geriatric Epidemiology, National Institutes of Health, Bethesda, Maryland.
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Luigi Ferrucci
L. Ferrucci, MD, PhD, Longitudinal Studies Section, National Institutes of Health, Baltimore, Maryland.
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Eleanor M. Simonsick
E.M. Simonsick, PhD, National Institute on Aging, National Institutes of Health, Baltimore, Maryland.
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Suzanne Satterfield
S. Satterfield, MD, DrPH, Preventive Medicine, University of Tennessee, Memphis, Tennessee.
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Elsa S. Strotmeyer
E.S. Strotmeyer, PhD, MPH, Department of Epidemiology, University of Pittsburgh.
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Yuqing Zhang
Y. Zhang, MD, DSc, Clinical Epidemiology Research and Training Unit, Boston University.
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Abstract

Background The ability to walk for short and prolonged periods of time is often measured with separate walking tests. It is unclear whether decline in the 2-minute walk coincides with decline in a shorter 20-m walk among older adults.

Objective The aim of this study was to describe patterns of change in the 20-m walk and 2-minute walk over 8 years among a large cohort of older adults. Should change be similar between tests of walking ability, separate retesting of prolonged walking may need to be reconsidered.

Design A longitudinal, observational cohort study was conducted.

Methods Data were from 1,893 older adults who were well-functioning (≥70 years of age). The 20-m walk and 2-minute walk were repeatedly measured over 8 years to measure change during short and prolonged periods of walking, respectively. Change was examined using a dual group-based trajectory model (dual model), and agreement between walking trajectories was quantified with a weighted kappa statistic.

Results Three trajectory groups for the 20-m walk and 2-minute walk were identified. More than 86% of the participants were in similar trajectory groups for both tests from the dual model. There was high chance-corrected agreement (kappa=.84; 95% confidence interval=.82, .86) between the 20-m walk and 2-minute walk trajectory groups.

Limitations One-third of the original Health, Aging and Body Composition (Health ABC) study cohort was excluded from analysis due to missing clinic visits, followed by being excluded for health reasons for performing the 2-minute walk, limiting generalizability to healthy older adults.

Conclusions Patterns of change in the 2-minute walk are similar to those in the 20-m walk. Thus, separate retesting of the 2-minute walk may need to be reconsidered to gauge change in prolonged walking.

A physical therapist is the most likely member of the health care team to objectively assess walking ability in older adults. This is an important task given that walking plays a central role in the performance of many activities of daily living, the well-known recognition of walking ability as a strong predictor of future limitation in physical functioning and mortality in older adults, and the fact that walking slows with aging.1–4 The 2003 American Physical Therapy Association's Guide to Physical Therapist Practice reinforces this responsibility by adding that measuring walking ability synthesizes the diagnosis, prognosis, and plan of care for patients.5

Because there is no one standard method for measuring walking ability, a physical therapist is left to choose the most appropriate test for a given patient. What specific test of walking ability is ultimately used can be tailored to exploit limitations in specific areas of function. For instance, a short walking test, such as the 20-m walk, can be used to gauge an older adult's gait speed (distance/time) and risk of adverse health outcomes,1,2 whereas a prolonged walking test, such as the 2-minute walk (distance covered), provides insight into restrictions with tasks that require walking for a sustained period of time, such as walking across a large parking lot or grocery shopping.

Small-scale cross-sectional studies have shown moderate to high correlations (r=.69–.80) between short and prolonged walking among people with multiple sclerosis,6 chronic obstructive pulmonary disorder,7 and stroke.8 However, it is not known whether the pattern of decline longitudinally from a short walking test is relatively the same as a prolonged walking test in older adults. For instance, are older adults who are on a trajectory of fast decline as measured by the 20-m walk also on a similar trajectory of fast decline as measured by the 2-minute walk? This is a major gap in physical therapist practice because using multiple tests to quantify different aspects of walking ability is burdensome and time-consuming. Should there be high agreement in changes between both measures over time, then change in the 2-minute walk could be inferred from the quicker-to-test 20-m walk and potentially negate the need to perform both tests in older adults to detect decline in walking ability.

The purpose of this study was to describe patterns of change in the 2-minute walk and 20-m walk within a large cohort of older adults who initially were high functioning. Should change be similar between tests of walking ability, separate retesting of prolonged walking may need to be reconsidered. To determine whether separate retesting is necessary, we examined contemporaneous change over 8 years for the 20-m walk and 2-minute walk using a dual group-based trajectory model, or dual model. The key advantage of the dual model is that it provides conditional proportions linking the 20-m walk and 2-minute walk trajectories.9 This advantage permits a more detailed summary of the connection between the 20-m walk and 2-minute walk trajectories than a single summary statistic.

Method

Study Sample

The Health, Aging and Body Composition (Health ABC) study is a longitudinal study of the association between changes in body composition and functional decline in older adults who initially are well-functioning. Details of the Health ABC study have been described previously.3 In brief, the Health ABC study population consists of 3,075 community-dwelling older adults aged 70 to 79 years at baseline. Participants were recruited from a random sample of Medicare beneficiaries and all community-dwelling black residents in zip codes in and around Memphis, Tennessee, and Pittsburgh, Pennsylvania. Eligibility criteria included no self-reported difficulty walking approximately 400 m (one-quarter mile), climbing 10 steps, or performing basic activities of daily living. People with terminal cancer or plans to move out of the area within 3 years of the baseline examination were excluded. The baseline examinations took place between April 1997 and June 1998. All participants provided informed consent.

Study Subsample

For this study, we used the year 2 visit as our “baseline” because administration of the 20-m walk separately from the 2-minute walk began at this visit. Measurement of the 20-m walk occurred annually for the next 4 years and then biennially, resulting in 7 assessments over 8 years of follow-up (years 2, 3, 4, 5, 6, 8, and 10). Measurement of the 2-minute walk occurred biennially for a total of 5 assessments over 8 years (years 2, 4, 6, 8, and 10). To be included in the trajectory analyses, measurements of the 20-m walk and the 2-minute walk were needed from baseline and from at least 2 follow-up visits.10

Measures of Walking Ability

The 20-m walk and the 2-minute walk were measured over a 20-m course in an unobstructed corridor marked by cones on both ends. For the 20-m walk, participants were instructed to walk one length of the course at their usual pace. Timing started with the first step (footfall) over the starting line and ended with the first step (footfall) over the finishing line. Gait speed was quantified in meters per second (calculated as 20 m divided by seconds needed to complete the 20-m walk). Participants were allowed to use walking aids, such as canes or walkers, during testing, if needed. Gait speed measured over a 20-m walkway has high test-retest reliability in older adults, with intraclass correlation coefficients greater than .9.11,12

To measure the 2-minute walk, participants were first screened in accordance with the American College of Sports Medicine guidelines for exercise testing.13 Participants with electrocardiogram abnormalities, systolic and diastolic blood pressure exceeding 199 mm Hg or 109 mm Hg, respectively, or a heart rate <40 or >110 bpm were excluded. Second, participants reporting heart attack, angioplasty or heart surgery, exacerbation of chest pain, shortness of breath, fainting, or angina within the previous 3 months were excluded. Eligible participants were instructed to “cover as much ground as possible” over a 2-minute walking period on the same course as the 20-m walk. Heart rate was monitored during the 2-minute walk, and participants were stopped if their heart rate exceeded 135 bpm or they experienced debilitating pain, shortness of breath, syncope, or excessive fatigue. The distance walked was recorded in meters. If study participants started the walk, but did not walk for the full 2 minutes, the total distance covered was still recorded.

Participant Characteristics

Data for participant characteristics were collected at year 1 of the Health ABC study, except for age and body mass index (BMI), which were collected at our study baseline (ie, year 2 of the Health ABC study).

Data Analysis

We compared the characteristics of Health ABC study participants included and not included (due to insufficient walk test data; Fig. 1) in our sample by performing t tests for continuous variables and chi-square tests for categorical variables. We described trajectories of the 20-m walk and the 2-minute walk over 8 years using group-based trajectory models among participants with both walk tests at baseline and at least 2 follow-up visits. A trajectory group is an assembly of study participants who follow the same pattern of change in an outcome over time. The group-based trajectory model makes no assumptions regarding the pattern or shape of change over time or the distribution of trajectory groups. Rather, the group-based trajectory model is a statistical device that approximates an unknown number and shape of trajectories across a sample.14 This model assumes missing values are missing completely at random.9 We used the SAS (SAS Institute Inc, Cary, North Carolina) macro PROC TRAJ to formulate trajectory groups.15

Figure 1.
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Figure 1.

Flowchart of study participants.

To describe change in walking ability over time, we first identified trajectories for each walking test as a separate outcome using 3 steps. The first step was to determine the number of trajectory groups. We required a minimum of 10% of the sample to be within each group and adjacent trajectory groups to have slopes differing by more than 5%. We chose these restrictions to provide a description of trajectory group that was meaningful and pragmatic from a clinical perspective. Stipulating these differences in trajectory groups enables clinicians to classify patients into one of several broad trajectory groups, rather than an innumerable number of small groups with little difference in change.

The second step was to describe the shape of change over time. We initially added both linear and quadratic terms to test for the presence of a curvilinear pattern of decline. However, none of the quadratic terms attained statistical significance (P>.05); thus, we included only a linear term in the final regression models.

The third step was to evaluate the adequacy of the individual trajectories from each participant fitting the broader trajectory group classification. We calculated the likelihood that an individual's trajectory fit within each of the trajectory groups, which is termed the posterior probability.14 Specifically, higher probability values indicate a higher likelihood that an individual's trajectory pattern fits within the broader trajectory group.

Next, we evaluated contemporaneous change in the 20-m walk and 3-minute walk in 3 steps. As a first step, we used a dual model from the SAS macro PROC TRAJ to identify trajectories for both outcomes at the same time. In particular, we first described the proportion of participants within each 20-m walk trajectory who were in each 2-minute walk trajectory group. Next, we described the proportion of participants within each 2-minute walk trajectory who were in each 20-m walk trajectory. Lastly, we estimated the joint proportion of the trajectories (ie, the cross-tabulation of the proportion in each 20-m walk trajectory by each 2-minute walk trajectory). We required a minimum of 10% of the participants to be in each 20-m walk and 2-minute walk trajectory group and assumed a linear pattern of decline. As a second step, we evaluated the posterior probabilities of group membership. Lastly, we examined the agreement between 20-m walk and 2-minute walk trajectory membership from the dual model by calculating the weighted kappa statistic, an index of chance correct agreement, and 95% confidence interval (95% CI).

Role of the Funding Source

This work was supported, in part, by the Intramural Research Program of the National Institutes of Health (NIH); the National Institute on Aging (NIA) (grants N01-AG-6-2101, N01-AG-6-2103, N01-AG-6-2106, and R01-AG028050); the National Institute of Nursing Research (grant R01-NR0124590); the National Institute of Child Health and Human Development as part of the Medical Rehabilitation Research Infrastructure Network R24HD0065688; the Boston Claude D. Pepper Older Americans Independence Center from the NIA (grant P30-AG031679); the Foundation for Physical Therapy Geriatrics Research Grant; the American College of Rheumatology Research Foundation's Rheumatology Investigator Award; and the National Institute of Arthritis and Musculoskeletal and Skin at NIH (grants AR47785 and R01-AR062506).

Results

Of the 3,075 Health ABC study participants at baseline, 1,182 were excluded for the reasons detailed in Figure 1, leaving 1,893 participants eligible for the trajectory analysis. No statistically significant differences in sex or study site distribution existed between groups. However, compared with participants included in the trajectory analysis, those not included were more likely to be older and black; have a higher BMI, lower strength, and a slower 20-m walk speed; and cover less distance in the 2-minute walk at baseline (Tab. 1).

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Table 1.

Baseline Characteristics of Health ABC Study Participants Included and Not Included in the Trajectory Analysis

20-m Walk Trajectories Over 8 Years

We identified three 20-m walk trajectories. Figure 2 (panel A) shows the superimposed mean decline of each trajectory along with a random sample of 100 individual 20-m walk values within each trajectory group. The posterior probability of allocating study participants to trajectory groups was greater than .94, indicating a good fit of the model of group trajectories to individual patterns of change. As shown in Figure 2 (panel A), participants in the group with the greatest decline in 20-m walk (n=518 [22%]) had a mean baseline gait speed of 0.90 m/s (SD=0.15) and slowed 0.030 m/s per year on average (95% CI=−0.033, −0.028). Participants in the group with the least decline in 20-m walk (n=637 [27%]) had a mean baseline gait speed of 1.37 m/s (SD=0.13) and slowed 0.020 m/s per year on average (95% CI=−0.022, −0.019).

Figure 2.
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Figure 2.

Modeled mean decrease (95% confidence interval) in the separate trajectories for (A) 20-m walk (n=2,364) and (B) 2-minute walk (n=1,922) over 8 years. Tables underneath graphs show the number of observations at each follow-up visit. A random sample of 100 individual trajectories were included within each trajectory group. Group membership of individual trajectories is indicated by color. 95% CI=95% confidence interval.

Two-Minute Walk Trajectories Over 8 Years

We identified three 2-minute walk trajectories (Fig. 2, panel B). The posterior probability of group membership was greater than .89. Participants in the group with the greatest decline (n=398 [21%]) walked a mean of 127.2 m (SD=22.3) over 2 minutes at baseline and on average changed −3.3 meters per year (95% CI=−3.8, −2.8). The mean distance walked over 2 minutes for participants in the group with the least decline (n=450 [23%]) was 196.2 m (SD=21.5) at baseline, and on average these participants changed −2.3 meters per year (95% CI=−2.6, −1.9).

Dual Trajectory Model

There were 3 trajectory groups for both the 20-m walk and the 2-minute walk using the dual model. Among those participants who experienced fast decline in the 20-m walk, 85.4% also had fast decline in the 2-minute walk, and none had slow decline in the 2-minute walk (Tab. 2, panel A). Similarly, among those participants with moderate decline in the 20-m walk, 87.8% had moderate decline in the 2-minute walk. Lastly, among those participants with slow decline in the 20-m walk, 91.9% had slow decline in the 2-minute walk, and 0.4% had fast decline in the 2-minute walk. We observed similar proportions in participants with fast, moderate, and slow decline in the 20-m walk among those in the same respective 2-minute walk trajectories (Tab. 2, panel B). The posterior probability of group membership was greater than .92. The joint proportion of membership in trajectories along the diagonal summed to 86.9%, and there was high chance-corrected agreement (weighted kappa=.84; 95% CI=.82, .86) between the 20-m walk and 2-minute walk trajectory groups (Tab. 2, panel C).

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Table 2.

Proportions (%) of Trajectory Group Membership for the 20-m Walk and 2-Minute Walk From the Dual Model

Discussion

The majority of Health ABC study participants experienced a similar trajectory pattern for the 2-minute walk as for the 20-m walk over 8 years. In particular, 86.9% of participants with a pattern of slow, moderate, or fast decline for the 2-minute walk had the same respective pattern for the 20-m walk. We also found high chance-corrected agreement (weighted kappa=.84) with patterns of decline in the 20-m walk and 2-minute walk over this period despite representing different components of walking ability in older adults. Hence, older adults with the fastest decline for walking a short distance are unlikely to sustain the ability to walk for prolonged distances. Our findings are consistent with previous cross-sectional studies of people with neurological6,8 and cardiorespiratory pathology7 and add that there is high correlation with patterns of decline in short and prolonged walking among older adults who initially are well-functioning. These findings suggest that patterns of change in the 2-minute walk can be reasonably measured from the 20-m walk, and separate retesting of the 2-minute walk may not be necessary in healthy older adults to detect decline in walking ability.

Our study showed a slightly stronger correlation between the 20-m walk and 2-minute walk trajectories for participants with slow rather than fast decline. Specifically, the proportion of fast decline in the 20-m walk among people with fast decline in the 2-minute walk (84.2%) was similar to the opposite comparison (ie, the proportion of fast decline in the 2-minute walk among those with fast decline in the 20-m walk [85.4%]). However, for slow decline, the proportion was 91.9% for the 20-m walk among participants with slow decline in the 2-minute walk and 86.8% for the opposite comparison. These findings suggest that although both tests similarly predict fast decline in the other over time, prolonged walking is slightly more predictive of slow decline in short walking than vice versa. This conclusion suggests that if clinicians have flexibility to perform either test, the 2-minute walk is marginally better at capturing slow decline than the 20-m walk, although each test appears to equally predict fast decline. These findings are important for physical therapists' understanding of how both tests of walking ability change together over time and help set uncertainty for inferring change in one test from another.

The rates of decline we found within trajectory groups were small relative to known clinically meaningful thresholds. For instance, we found yearly decline to occur at a rate of −0.03 m/s in the fastest decline 20-m walk trajectory, which is well below a known clinically meaningful threshold of about −0.1 m/s for older adults.16 However, over time, health will be affected sooner in the fastest decline trajectory compared with slowest decline trajectory. For example, walking less than 1.0 m/s is a known risk factor for poor health outcomes in older adults.1 Given our sample's average starting speed of 1.18 m/s, those individuals within the fastest decline trajectory would reach the 1.0 m/s threshold in about 6 years compared with 9 years for the slowest decline trajectory, which slowed −0.02 m/s per year.

Limitations of our study should be acknowledged. More than a third of the Health ABC study cohort (1,182 of 3,075), which already was limited to older adults who were well-functioning, was excluded for our analyses. Study participants most commonly were excluded for not attending the baseline visit (29% [343/1,182]), for not attending at least 2 follow-up visits (27% [319/1.182]), and for attempting the baseline 2-minute walk due to health reasons (38% [445/1,182]). These excluded study participants had poorer health status, characterized by higher BMI, less strength, a slower gait speed, and less distance covered during the 2-minute walk.

Consequently, reported rates of decline in gait speed or prolonged walking may be underestimated by our sample. Although the exclusion of participants with worse health limits the generalizability of findings to all older adults, it focuses this study to specifically evaluate whether different walk tests are needed among older adults who are well-functioning and have low cardiovascular disease risk, given the strict exclusion criteria for attempting the 2-minute walk test. Interestingly, the strict stopping criteria for participants attempting the 2-minute walk was not a major reason for exclusion. Among those excluded from our sample, only 15 study participants were stopped during the 2-minute walk due to having a heart rate >135 bpm or painful symptoms. Our study did not investigate the causal relationship between the 20-m walk and 2-minute walk but rather described the contemporaneous change between these tests over time. Thus, no inference can be made regarding whether treatment targeting improved gait speed translates to improvement in prolonged walking, and vice versa. Lastly, the ability of trajectories of the 20-m walk and 2-minute walk to predict future adverse health outcomes, such as mortality or functional limitation, was not examined, as it was beyond the scope of our present study. Before a firm conclusion can be made regarding the necessity of both measures, future studies should evaluate whether each test provides unique information about the development of adverse health outcomes.

Despite these limitations, there are several strengths to this study. First, Health ABC is a well-described cohort of older adults who had systematic 20-m walk and 2-minute walk assessments over 8 years. Second, to our knowledge, this is the first study to use a dual model to describe contemporaneous change in measures of walking ability. This approach provides a more detailed description of the linkages of contemporaneous change between measures of walking ability than a single summary estimate of agreement.9 Third, given the mean posterior probabilities were higher than 89% for all group classifications, we believe there were few instances of misclassification of individual trajectories into their respective trajectory group.

In summary, decline in the ability to walk for a prolonged period of time is likely to coincide with decline in the ability to walk for a short period of time in adults who are initially well-functioning as they transition from their eighth to ninth decade of life. The separate testing of gait speed and prolonged walking should continue when physical therapists believe both tests are necessary. However, our study results indicate that physical therapists may reconsider the need to separately retest both in follow-up visits for healthy older adults and instead retest the less burdensome 20-m walk to detect decline in walking ability.

The Bottom Line

What do we already know about this topic?

Walking speed and prolonged walking measure different aspects of walking ability.

What new information does this study offer?

Changes in prolonged walking from the 2-minute walk can be inferred from changes in gait speed measured from the 20-m walk in older adults.

If you're a patient or a caregiver, what might these findings mean for you?

Slowing of walking is likely accompanied by limitation with walking long distances in older adults.

Footnotes

  • Dr White, Dr Neogi, Dr King, Dr LaValley, Dr Kritchevsky, Dr Nevitt, Dr Ferrucci, and Dr Zhang provided concept/idea/research design. Dr White, Dr Neogi, Dr King, Dr Nevitt, Dr Harris, Dr Simonsick, Dr Satterfield, Dr Strotmeyer, and Dr Zhang provided writing. Dr Neogi, Dr Nevitt, Dr Harris, and Dr Simonsick provided data collection. Dr White, Dr Neogi, Dr LaValley, and Dr Zhang provided data analysis. Dr Satterfield, Dr Simonsick, Dr Strotmeyer, and Dr Harris provided project management and study participants. Dr White, Dr Neogi, Dr Nevitt, and Dr Harris provided fund procurement. Dr Nevitt, Dr Ferrucci, Dr Satterfield, and Dr Simonsick provided institutional liaisons. Dr Neogi, Dr King, Dr LaValley, Dr Ferrucci, Dr Satterfield, Dr Strotmeyer, and Dr Simonsick provided consultation (including review of manuscript before submission).

  • The study protocol was approved by the institutional review boards of the University of Tennessee–Memphis, the University of California–San Francisco, and the University of Pittsburgh. The present analysis was approved by the Institutional Review Board at Boston University.

  • This work was supported, in part, by the Intramural Research Program of the National Institutes of Health (NIH); the National Institute on Aging (NIA) (grants N01-AG-6-2101, N01-AG-6-2103, N01-AG-6-2106, and R01-AG028050); the National Institute of Nursing Research (grant R01-NR0124590); the National Institute of Child Health and Human Development as part of the Medical Rehabilitation Research Infrastructure Network R24HD0065688; the Boston Claude D. Pepper Older Americans Independence Center from the NIA (grant P30-AG031679); the Foundation for Physical Therapy Geriatrics Research Grant; the American College of Rheumatology Research Foundation's Rheumatology Investigator Award; and the National Institute of Arthritis and Musculoskeletal and Skin at NIH (grants AR47785 and R01-AR062506).

  • Received January 13, 2014.
  • Accepted April 20, 2014.
  • © 2014 American Physical Therapy Association

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Vol 94 Issue 9 Table of Contents
Physical Therapy: 94 (9)

Issue highlights

  • Early Intervention Post-Hospital Discharge for Infants Born Preterm
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Can Change in Prolonged Walking Be Inferred From a Short Test of Gait Speed Among Older Adults Who Are Initially Well-Functioning?
Daniel K. White, Tuhina Neogi, Wendy C. King, Michael P. LaValley, Stephen B. Kritchevsky, Michael C. Nevitt, Tamara B. Harris, Luigi Ferrucci, Eleanor M. Simonsick, Suzanne Satterfield, Elsa S. Strotmeyer, Yuqing Zhang
Physical Therapy Sep 2014, 94 (9) 1285-1293; DOI: 10.2522/ptj.20130628

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Can Change in Prolonged Walking Be Inferred From a Short Test of Gait Speed Among Older Adults Who Are Initially Well-Functioning?
Daniel K. White, Tuhina Neogi, Wendy C. King, Michael P. LaValley, Stephen B. Kritchevsky, Michael C. Nevitt, Tamara B. Harris, Luigi Ferrucci, Eleanor M. Simonsick, Suzanne Satterfield, Elsa S. Strotmeyer, Yuqing Zhang
Physical Therapy Sep 2014, 94 (9) 1285-1293; DOI: 10.2522/ptj.20130628
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