Lower Extremity Function Trajectories in the African American Health Cohort

Abstract

Background.

We addressed two understudied issues in estimating lower extremity functional trajectories in older adults—incorporating the effect of mortality and evaluating heterogeneity among African Americans.

Methods.

Data were taken from the 998 participants in the African American Health cohort. A highly reliable and valid 8-item lower extremity function scale was used at baseline and at the 1-, 2-, 3-, 4-, 7-, and 9-year follow-up interviews. Semiparametric (ie, discrete) group-based mixture modeling identified the trajectories, and multinomial logistic regression identified risk factors for differential trajectory groups.

Results.

When treating mortality as informative censoring, six discrete trajectories were observed with 45% of the participants belonging to three stable trajectories (good, fair, or poor function), and the remainder belonging to three declining trajectories (very high function with minimal improvement then minimal decline, very good function with a slow and modest decline, and very good function with a large and quick decline).

Conclusion.

Substantial heterogeneity in lower extremity function trajectories exists in the African American Health cohort, after appropriately treating mortality as informative censoring.

Functional trajectories are keenly important and often frame discussions of successful versus pathological aging (1). Recent studies have focused on mobility activities affected by the lower extremities, included data at several proximal measurement points, and used sophisticated methods for identifying multiple common group trajectories (2–22). These trajectories are differentiated by starting points (ie, intercepts), stable versus changing patterns (ie, slopes), and rates of change (4). For example, Gill and coworkers (7) used the number of difficulties with activities of daily living from brief monthly telephone interviews in the last year of life to identify five disability trajectories. Of these, two reflected no change prior to death (ie, intercept only trajectories for no vs persistently severe disability), whereas the other three reflected differences in the rate of disability onset (ie, intercept and slope trajectories for progressive [linear], accelerated [exponential], or catastrophic [sudden onset]).

The advances of recent studies notwithstanding, several issues remain. This article addresses two issues. The first issue involves exploring potential mortality bias in estimating lower extremity function, which may result in trajectories that understate true change by either excluding or alternatively noninformatively censoring decedents, resulting in survivor bias (4–7,16). The second issue is that when race or ethnic differentials have been studied, it has been assumed that a single trajectory fits all members (15,18) of individual race or ethnic groups. To address these issues, we used data on the African American Health (AAH) cohort, demonstrating first the reliability and validity of an 8-item measure of lower extremity function. We then used a semiparametric (ie, discrete) group-based mixture modeling strategy (23–26) to simultaneously estimate person-centered, multiple common (or group) trajectories employing four approaches for addressing mortality bias. Finally, we used multinomial logistic regression to identify factors predicting trajectory group membership (27).

Based on previous studies (2–22), two hypotheses framed our approach. The first was that several qualitatively distinct intraindividual lower extremity function trajectories would be identified involving different intercepts, slopes, and/or onsets of change. Because of the excessive disease, functional, and mortality burdens in the AAH cohort (28,29), we did not expect trajectories reflecting recovery. The second hypothesis was that these qualitatively distinct trajectories would be associated with characteristics of the participants and the neighborhoods in which they lived (30).

Methods

Sample

The AAH cohort included 998 self-identified African American men and women 49–65 years old at the time of their baseline interviews in 2000–2001 (28,29). By design, participants lived in two areas: a generally poor inner-city area of St. Louis, Missouri, or its near northwest suburbs with higher but variable socioeconomic status. Because equal numbers of participants randomly recruited from each area resulted in a higher probability of selection in the inner city, we used sampling weights to adjust for unequal selection probabilities, the multistage cluster sampling design, and baseline nonresponse. The only inclusion criterion other than race was a Mini-Mental Status Examination (31) score ≥ 16. A 76% response rate was obtained for the baseline in-home evaluations. Follow-up interviews occurred at 1, 2, 3, 4, 7, and 9 years postbaseline. All predictor variables were taken from the baseline in-home evaluations, whereas lower extremity function was taken from the baseline and follow-up interviews. Of the 998 original participants, 582 (58%) were reinterviewed at the final follow-up for a 9-year retention rate of 67.8% among known survivors. Multivariable logistic regression analysis (not shown) using 24 baseline characteristics indicated that the survivors lost to follow-up were less likely to be married and to think about their race frequently, and more likely to have asthma, lower self-rated health, and poorer hearing.

Lower Extremity Function

Eight questions targeting bathing, bed or chair transfers, getting to places outside of walking distance, walking a quarter mile, climbing up and down a flight of steps, standing for 2 hours or more, stooping or crouching or kneeling, and lifting and carrying 10 pounds were asked at each interview. Two statements focused participants on the ability to do these activities themselves without using special equipment, and that the difficulties should last 3 months or more. If the participant reported not doing the activity for a nonhealth reason, they were asked if they would have any difficulty if they tried. The sum of “yes” responses is the scale score (range = 0–8).

Trajectory Predictors

Age in years, sex (women as referent), and a set of dummy variables for marital status (married as the referent) captured demographic variations. Education in years, Medicaid status, annual household income less than $20,000, and inability to afford health care when needed captured socioeconomic status variations. Geographic area (suburbs as referent), a 4-item scale of self-reported neighborhood conditions (alpha = 0.78), a 5-item scale of interviewer-assessed housing conditions (alpha = 0.96), and a 5-item scale of housing enumerator-evaluated block faces (alpha = 0.92) captured variations in neighborhood context. Body mass index, the Yale Physical Activity Scale (YPAS; test–retest = 0.65; 32), a set of dummy variables for cigarette smoking (never smoked as referent), and alcohol dependency (CAGE; 33) captured variations in healthy lifestyles. A 5-item religiosity scale (alpha = 0.66) and thinking about one’s race constantly captured variations in specific attitudes and beliefs. Indicators for having hypertension, diabetes, cancer, chronic obstructive pulmonary disease, congestive heart failure, angina, asthma, arthritis, stroke, kidney disease, or a recent sentinel health event (hospitalization) captured variations in morbidity. A 3-item visual acuity scale (alpha = 0.75), self-rated hearing acuity, depressive symptoms (CESD-11; 34), self-rated health, and the lower body extremity scale captured variations in physical and mental function.

Analytic Approach

We tested for factorial validity with exploratory factor analysis and internal consistency with coefficient alpha (35). Trajectories were identified using a semiparametric mixture model (23–26) with the optimal number of trajectory groups and their specifications selected by comparing the Bayesian Information Criterion associated with each model, beginning with a one-group model and then serially increasing the number of groups (26). This approach identified distinct intraindividual trajectories first and then grouped them into common patterns. The probability that each individual belonged to each group pattern was estimated using likelihood functions, with each individual assigned to the group representing their predominant probability. Four models treated deaths in distinctly different ways. The first assigned decedents a 9 on the lower extremity function measure, the second omitted persons who had died at any point during the study, the third incorporated the probability of dropout due to death (informative censoring), and the fourth treated dropout due to death as noninformative censoring (missing at random). All models included a floor effect term for having no lower extremity limitations (coded 0) and a ceiling effect term for having the maximum number of lower extremity limitations (coded 8). All other unobserved data points were treated as missing at random. Selection of the best method for treating death was based on mean assignment probabilities and substantive interpretation. Multivariable multinomial logistic regression characterized the identified trajectory groups (27). Given the number of covariates and the absence of multicollinearity (minimum tolerance = 0.49, maximum VIF = 2.0), backwards elimination (with p ≤ .05 for retention or re-entry) achieved the most parsimonious final model and minimized overfitting. Model fit was determined by pseudo r ² statistics (27).

Results

Sample Characteristics at Baseline

Median age was 57, 42% were men, and 47% were married. Median education was 12 years, and 28% had incomes of $20,000 or less. The median YPAS score was 57, 30% were current and 37% were former smokers, and 20% had positive screens for alcoholism. The most common morbidities were hypertension (63%), arthritis (45%), and diabetes (26%), with 18% having had a sentinel health event requiring hospitalization in the past year. The median score on the depressive symptoms scale was 4. Scores on the lower extremity function scale ranged from 0 to 8, with a mean of 2.1 (median = 1; SD = 2.5).

Psychometric Analyses

Table 1 contains the exploratory factor analysis results at each wave of data collection. The minimum Kaiser–Meyer–Olkin sampling adequacy coefficient was 0.909, and the minimum p value for Bartlett’s sphericity test was < .001, indicating excellent factorability. Only one factor had an eigenvalue ≥ 1.0, indicating stable unidimensionality over time, with a minimum explanation of 53% of the item variance. The minimum factor loading was 0.622, reflecting substantial primary loadings. The minimum coefficient alpha was 0.869, reflecting high reliability.

Table 1.

Factor Loadings, Cronbach’s Alpha, Proportion of Total Variance Explained by the Single Factor Solution, Kaiser–Meyer–Olkin Sampling Adequacy, and Bartlett’s Sphericity Tests for the 8-Item Lower Extremity Function Scale, by Year of Administration in the African American Health Cohort

Difficulty in Performing Unassisted or Inability to Perform at All	Factor Loadings
	2000	2001	2002	2003	2004	2008	2010
Bathing or showering	0.637	0.622	0.648	0.702	0.724	0.683	0.696
Getting in and out of beds or chairs	0.683	0.719	0.709	0.739	0.745	0.739	0.743
Walking across a room	0.734	0.732	0.759	0.746	0.751	0.755	0.711
Standing or being on your feet for 2 h	0.765	0.789	0.797	0.775	0.813	0.816	0.814
Stooping, crouching, or kneeling	0.694	0.771	0.815	0.669	0.808	0.744	0.777
Lifting or carrying something as heavy as 10 pounds	0.725	0.750	0.793	0.752	0.793	0.773	0.728
Walking a quarter of a mile without resting	0.811	0.692	0.728	0.824	0.732	0.679	0.665
Walking up 10 steps without resting	0.767	0.730	0.762	0.799	0.789	0.732	0.737
Cronbach’s coefficient alpha	0.872	0.869	0.889	0.887	0.900	0.883	0.875
Proportion of variance explained	0.533	0.529	0.567	0.566	0.593	0.555	0.541
Kaiser–Meyer–Olkin sampling adequacy	0.909	0.910	0.925	0.918	0.928	0.919	0.914
Bartlett’s sphericity test (p value)	.001	.001	.001	.001	.001	.001	.001

Trajectory Analyses

The four sets of estimated trajectories are shown in Figure 1. Because comparable overall mean assignment probabilities were obtained across models (0.80–0.85), selection of the best approach was based on substantive interpretation. Imputing a 9 at death essentially yielded a mortality model, with the three steeply declining trajectories (Groups 3, 4, and 8) consisting of 87%, 97%, and 100% decedents, respectively. Moreover, this approach resulted in a trajectory (Group 8) with a mean assignment probability of .01 and required the strong assumption that at the time of death, participants had the worst possible lower extremity function. In contrast, informative censoring for death yielded trajectories driven by declining function (Groups 2 and 4) rather than by death, having only 16% and 6% decedents, respectively. Furthermore, the informative censoring approach revealed that the intercept-only trajectories for Groups 3, 5, and 6 had 16%, 29%, and 22% decedents, indicating that these groups had stable trajectories up to their deaths. Although omitting decedents altogether identified trajectories somewhat similar to those for informative censoring, it resulted in a thinly populated trajectory (n = 14), did not provide the same clarity of substantive interpretation, and by ignoring data from 17% of the AAH participants severely constrained generalizability. Finally, although treating deaths as missing at random (noninformative censoring) also identified trajectories somewhat similar to those for informative censoring, it also included a very thinly populated (n = 23) group trajectory, and the notion of death as noninformative censoring in the context of lower extremity function trajectories is counterintuitive. Therefore, the informative censoring approach was chosen, and its trajectory parameter estimates are shown in Table 2.

Figure 1.

The discrete 8-item lower extremity function trajectories estimated using four different approaches for treating death.

Table 2.

Parameter Estimates Obtained From the Trajectory Model for the Lower Extremity Functioning Scale Treating Death as Informative Censoring

Trajectory Group Number and Name	Parameter Estimates for the Terms in the Trajectory Models
	Intercept	Linear	Quadratic	Cubic	Dropout
Group 1: Stable high functioning	−2.11***	−0.98***	0.25**	−0.01**	−1.13***
Group 2: High functioning with a slow and modest decline	−0.24	−0.51**	0.17***	−0.01**	−1.21***
Group 3: Stable very good functioning	1.91***				−1.15***
Group 4: High functioning with a large but gradual decline	0.64	−0.02	0.28**	−0.02***	−1.25***
Group 5: Good functioning with a large and quick decline	4.30***				−1.18***
Group 6: Stable fair functioning	6.55***				−1.17***

Notes: **p < .01. ***p < .001. BIC = −9,634 (N = 5,753); BIC = −9,611 (N = 998); AIC = −9,545; L = −9,518.

Three stable trajectories reflected stable very good function (Group 3; 17.4%), stable fair function (Group 5; 14.1%), and stable poor function (Group 6; 13.5%). Thus, 45% of the AAH participants experienced no change in lower extremity function over 9 years, and the only significant parameters for Groups 3, 5, and 6 were the intercepts and informative censoring dropout functions for death. Group 1 (24.0%) had significant intercept, linear, quadratic, cubic, and dropout function parameters, which reflected very high function with minimal recovery then minimal decline over 9 years. These groups contrasted with the two declining trajectories for very good function with a slow and modest decline (Group 2; 23.5%) or very good function with a large and quick decline (Group 4; 7.5%).

Multinomial Modeling

Table 3 contains the results from the multinomial logistic regression analysis with backwards elimination using the very high function with minimal improvement followed by minimal decline trajectory (Group 1) as the reference. The model fit the data well with a mean assignment probability of .82, a χ² reduction of 1,421 at 90 df with p < .001, and pseudo R ² ranging from .439 to .798. The consistent effect of baseline lower extremity function reflected group starting values, with the largest effects for Groups 3, 5, and 6 that started with good, fair, and poor function and remained that way. Widowed participants were more likely to end up with very good health. Angina increased the likelihood of being in Groups 4, 5, or 6 which either began or ended in fair or poor health. Arthritic participants were more likely to be in Groups 2, 3, or 4. Participants with kidney disease were more likely to be in Group 2 and least likely to be in Group 4. Obese participants were less likely to be in the reference group. Current smokers were more likely to be in Group 5, with former smokers least likely to be in Group 6. Participants with lesser religiosity scores were more likely to be in Group 5. Greater CAGE scores increased the likelihood of being in Group 4. Poorer vision reduced the likelihood of being in the reference group, whereas poorer hearing decreased the likelihood of being in Groups 2 or 4. Depressive symptoms and prior hospitalization increased the likelihood of being in Groups 5 and 6. Low income increased the likelihood of being in Group 3. Worse neighborhood ratings reduced the likelihood of being in the reference group.

Table 3.

Adjusted Odds Ratios From the Multinomial Logistic Regression Model for the Six Lower Extremity Trajectories Estimated Treating Death as Informative Censoring, With the Very High Function With Minimal Improvement and Then Minimal Decline Trajectory (Group 1; N = 239) as the Reference Group

	Group 2 (N = 235)	Group 3 (N = 174)	Group 4 (N = 75)	Group 5 (N = 141)	Group 6 (N = 134)	Likelihood Ratio Test p Value
Demographics
Widowed	2.06*	4.07***	2.06	1.79	2.67	.015
Disease history
Angina	5.31**	7.31***	13.22***	26.64***	31.06***	.001
Arthritis	2.64***	1.97*	3.63***	1.99	2.76	.001
Kidney	1.65	6.53*	0.01***	3.26	1.71	.025
Healthy lifestyle
Obesity	2.33***	2.72***	1.26	2.94**	3.17*	.010
Smoking status
Former smoker	0.89	0.63	0.53	0.96	0.24*	.040
Current smoker	1.10	1.05	1.37	4.00**	0.63	.001
CAGE alcoholism score†	1.14	0.91	1.38*	1.07	1.35	.033
Attitudes and beliefs
Religiosity†	1.00	0.98	0.96	0.92**	0.97	.028
Functional health
Lower extremity function score	6.46***	19.75***	10.45***	40.75***	117.50***	.001
Visual acuity†	1.14*	1.04	1.31***	1.28**	1.25*	.001
Hearing acuity†	0.76*	0.99	0.68*	0.88	1.06	.039
CESD-11 depressive symptoms†	1.05	1.08	0.98	1.15**	1.23***	.007
Hospitalized in the past year	1.06	1.78	1.82	4.42**	5.60**	.032
Socioeconomic status
Income under $20K	1.04	2.49*	1.16	1.04	0.66	.005
Neighborhood context
City	0.66	0.27**	0.86	0.81	0.36	.006
Interviewer’s rating†	1.03	1.18**	1.08	1.11	1.51***	.001
Respondent’s rating†	1.11**	1.15**	1.12*	1.08	1.04	.015
Mean assignment probability (Group 1 = .87)	.78	.75	.82	.81	.92	.82, overall

Notes: χ² Reduction from an intercept-only model = 1,422 at 90 df for a p value < .001; pseudo R ²: Cox and Snell = 0.770; Nagelkerke = 0.798; McFadden = 0.439; Group 2 = very good function with a slow and modest decline; Group 3 = stable very good function; Group 4 = very good function with a large but gradual decline; Group 5 = stable good function; Group 6 = stable poor function. *p < .05. **p < .01. ***p < .001.

^†Higher values reflect greater alcohol consumption, lower religiosity scores, poorer vision and hearing, worse scores on the CESD-11, and living in less desirable neighborhoods.

Discussion

This article makes three contributions. First, the psychometric properties of the 8-item lower extremity function scale were robust. Psychometric analysis revealed a stable, simple unidimensional factor structure with strong factor loadings and high reliability at each wave of data collection. These properties engender confidence that our trajectory findings were not measurement artifacts.

The second contribution stems from the four methods used to estimate the lower extremity function trajectories. Because all four approaches achieved comparable mean assignment probabilities (.80–.85), three were not chosen based on substantive interpretation. The first assigned a score of 9 on the 8-item scale at the point of death and essentially resulted in a mortality rather than a functional model and required the rather strong assumption that at the time of their deaths decedents had the worst possible lower extremity function. The second and third approaches not chosen either restricted the analyses to survivors or assumed that censoring due to death was noninformative. Both of these models resulted in very thinly populated trajectories and were based on strong assumptions (deaths are either irrelevant or reflect noninformative censoring) that are at best counterintuitive, even though they have been used in many previous studies. In contrast, the informative censoring approach for treating death yielded trajectories that were driven by declining function (Groups 2 and 4) rather than by death. Moreover, the informative censoring approach revealed that the intercept-only trajectories for Groups 3, 5, and 6 had 16%, 29%, and 22% decedents, indicating that these groups had stable trajectories up to their deaths.

The third contribution involves the demonstration of the considerable heterogeneity of lower extremity function in the AAH cohort. Specifically, the trajectory analysis identified six discrete trajectory groups. Three of these reflected stable function over 9 years, albeit from different starting points (intercepts) at baseline—good, fair, or poor function—and accounted for about half of the AAH participants. The three remaining trajectory groups reflected minimal recovery from very high function followed by a minimal decline, very good function with a large but gradual decline, and very good function with a large and quick decline. These trajectories demonstrate the considerable variability in lower extremity function among African Americans that may have been masked by previous studies assuming homogeneity.

In conclusion, using a highly reliable and valid measure in a large, probability-based sample of older African Americans we demonstrated substantial heterogeneity in lower extremity function trajectories after treating mortality as informative censoring. Our work, however, has three limitations. One is the loss to follow-up among survivors over 9 years. Another is the age-, time- and geographically bound nature of the AAH cohort. A third is the absence of other racial groups in the AAH for trajectory comparisons. Therefore, further research is needed that investigates heterogeneity similarly and separately among European Americans and among Hispanic Americans, preferably within the same context. Only then can it be known whether there is differential within-race heterogeneity in lower extremity function trajectories.

Funding

Supported by the National Institute on Aging (AG 010436).