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Keywords:

  • person-centered analysis;
  • women's health initiative;
  • fatigue;
  • older adults;
  • longitudinal studies;
  • latent class growth model

Abstract

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. References

Despite the variety of available analytic methods, longitudinal research in nursing has been dominated by use of a variable-centered analytic approach. The purpose of this article is to present the utility of person-centered methodology using a large cohort of American women 65 and older enrolled in the Women's Health Initiative Clinical Trial (N = 19,891). Four distinct trajectories of energy/fatigue scores were identified. Levels of fatigue were closely linked to age, socio-demographic factors, comorbidities, health behaviors, and poor sleep quality. These findings were consistent regardless of the methodological framework. Finally, we demonstrated that energy/fatigue levels predicted future hospitalization in non-disabled elderly. Person-centered methods provide unique opportunities to explore and statistically model the effects of longitudinal heterogeneity within a population. © 2013 Wiley Periodicals, Inc.

The importance of integrating health trajectory modeling into an arsenal of available methods for researchers in nursing has recently been highlighted (Henly, Wyman, & Gaugler, 2011; Wyman & Henly, 2011). Scientists who are interested in modeling longitudinal patterns of change in health to better understand age-related normative dynamics or to study unfolding pathophysiological processes can choose from a number of analytical strategies. These strategies include, among others, variable-centered models (e.g., analysis of variance [ANOVA], hierarchical models, random effect models, growth curve models), person-centered models (e.g., latent class growth modeling [LCGM; Nagin 2005], and growth mixture modeling [GMM; Muthen & Shedden, 1999]).

Despite the variety of available methods, current nursing research has been dominated by use of a variable-centered approach (Henly et al., 2011). Based on the assumption that all individuals in the population follow a similar pattern of change, the variable-centered approach identifies the average longitudinal trajectory, estimates variability about the average, and explains that variability in terms of covariates of interest (Gelman & Hill, 2007; Singer & Willet, 2003). In statistical terms, variable-centered methodologies model the population distribution of trajectories of change over time based on continuous distribution functions (Singer & Willet, 2003). Correlations, regressions, and structural equation models are among the statistical techniques used in a variable-centered approach (Poncheri & Ward, 2008).

However, clinical phenomena with high inter- and intra-individual variability (e.g., depressive symptoms, obesity, disabilities), demonstrate a more multinomial pattern (Ferro, Avison, Campbell, & Speechley, 2011; Gill, Gahbauer, Han, & Allore, 2010; Liang, Bennett, Ye, & Quinones, 2010; Mustillo et al., 2003). In such circumstances, person-centered models will likely provide a better fit to the research question and to the data under investigation than variable centered models (Nagin & Odgers, 2010). Cluster analysis, latent class analysis (LCA), and latent profile analysis are the statistical techniques commonly used to analyze data from a person-centered approach (Poncheri & Ward, 2008). The purpose of this article is to demonstrate the utility of basic person-centered modeling in a real-data application using data from a large cohort of aging American women enrolled in the Women's Health Initiative Clinical Trial (WHI CT; Anderson et al., 2003).

Introduction to Person-Centered Models

Person-centered models belong to the class of finite mixture models, which were designed to analyze data obtained from a mixture of statistically heterogeneous groups (Nagin & Odgers, 2010). These models assume that the population is composed of a mixture of two or more groups whose longitudinal trajectories could be expressed by a distinct number of polynomial and/or non-polynomial nonlinear functions of time. Thus, the estimated group trajectories are used as a convenient statistical device to approximate and summarize an unknown but complex population distribution (Bauer & Curran, 2003). A detailed technical and mathematical overview of person-centered models can be found elsewhere (Muthen & Shedden, 1999; Nagin, 2005).

Two important results of person-centered modeling—estimates of the shape of each class's trajectory and the size of the population belonging to each trajectory—also can be used to identify those factors that predict trajectory group membership or to estimate the effect of longitudinal class membership on proximal or distal outcomes. The association between predictor variables and trajectory group membership is traditionally examined by specifying the probability of trajectory group membership to follow a multinomial logit model (Nagin, 2005). However, as we will further demonstrate, this specification could be easily extended to include ordinal models. The major benefit of using ordinal rather than multinomial models is to minimize the proliferation of regression estimates and instead apply a hierarchical or ordered structure to the estimated longitudinal trajectories.

The person-centered latent class growth model (LCGM) and the growth mixture model (GMM) differ with regard to structural assumptions of a population curve. The former does not make any assumptions about a population's distribution, whereas the latter assumes a heterogenic multimodal distribution. That is, GMM assumes that the population curve consists of a mixture of normally distributed subgroups (Nagin & Odgers, 2010). In applied analysis, among individuals composing a trajectory group, within-class variability is constrained to zero in a LCGM framework and allowed to be freely estimated in GMM analysis. Our discussion will focus on latent class growth models, given that their parsimony allows for the clearest interpretation, but all the models presented could be estimated using the GMM framework.

Uses of Person-Centered Analytic Approaches

In health research, and in nursing sciences in particular, LCGM can be used to address many different types of research questions. First, it can identify distinctive and prototypical growth trajectories within target populations with a variety of health conditions. These studies might range from identifying distinct trajectories of disability in the last year of life (Gill et al., 2010) to describing multiple patterns of change in physiological and psycho-emotional indicators (Payette et al., 2011; Smith, Kupper, Jonge, & Denollet, 2010; Smolderen et al., 2008). Second, LCGM provides a convenient framework for estimating the effects of interventions or individual-level characteristics (e.g., ethnicity, education, prior or current health behaviors, cognitive status) on the probability of belonging to a given trajectory. For example, Ferro et al. (2011) found that a child's cognitive function was the strongest predictor of a moderately increasing trajectory of depressive symptoms in mothers of children with newly diagnosed epilepsy. Finally, researchers who are interested in approximating the magnitude of risk carried by members of a group over time can use person-centered models to estimate the effect of membership in a growth trajectory on incidence of clinically relevant health outcomes (e.g., mortality, disability, hospitalization, falls).

Application of LCGM to Analysis of Energy/Fatigue in WHI CT Data

In this article we present the utility and real-data application of basic LCGM and its extensions using a large cohort of American women 65 and older enrolled in the Women's Health Initiative Clinical Trial (WHI CT). The energy/fatigue indicator was selected as a trajectory variable, given that, although its prevalence and incidence appear to increase with advancing age, the patterns of change are not homogeneous. In addition, fatigue is increasingly recognized as a specific geriatric entity (Avlund, Damsgaard, & Schroll, 2001; Moreh, Jacobs, & Stessman, 2010; Vestergaard et al., 2009).

The objectives in using this example are to demonstrate how a LCGM framework can describe longitudinal grouping of self-reported energy/fatigue levels in older women, to relate membership in these longitudinal trajectories to baseline characteristics (e.g., ethnicity, education, health status, behavior), to and estimate the effect of their membership in a particular longitudinal pattern on the first incident hospitalization during 5 years of WHI Extension Study follow-up. We also will compare alternative statistical perspectives on modeling trajectory group assignments as a dependent variable.

Methods

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. References

Design and Data

Data for this analysis came from the large WHI study. Details of the design, recruitment strategies, data collection methods, tabulations of baseline data, and human subject protection protocols are available elsewhere (Anderson et al., 2003). In the present secondary analysis, we focused on data from women ages 65 years and older (at baseline) who enrolled in one or more of the WHI clinical trials and also consented to participate in the 2005–2010 Extension Study that followed participants after study interventions were stopped.

Of note, the number of available observations changed considerably between measurement occasions, mainly due to the protocol-defined data collection schedule that varied by measure. In addition, two other factors had an effect on the availability of a follow-up period: delayed enrollment for a large proportion of women that stretched over 5 years (i.e., 1993–1998), and fixed by design closeout occasions (October 2004–March 2005). In other words, available data collection periods ranged from 7 to 12 years of follow-up. Therefore, among the 19,891 women included in our final sample, 19,645 women had data on energy/fatigue indicators at baseline; 18,750 had non-missing observations in year 1; 1,391 women had non-missing data in year 3; 5,463 participants had non-missing data in year 6; and finally 14,228 participants had non-missing measurements in year 9/closeout (Table 1).

Table 1. Energy/Fatigue Indicators at Five Time Points for the Women's Health Initiative Clinical Trial Cohort (N = 19,891)
 MeanSDn
Note
  1. High scores are more optimal. Original scores were divided by 10 and raised to the second power.

Baseline45.3821.3819,645
Year 145.9322.4018,750
Year 343.9422.171,391
Year 638.9822.255,463
Year 9/closeout37.7421.8614,228

Measures

Energy/fatigue indicator (trajectory variable)

Self-reported energy/fatigue was operationalized using four questions from the Medical Outcomes Study Short Form-36 (SF-36; Ware & Sherbourne, 1992). Participants are asked to consider how much time during the past 4 weeks they: (a) felt full of pep; (b) had a lot of energy; (c) felt worn out; and (d) felt tired. Possible responses ranged from 1 (all the time) to 6 (none of the time). The final index scores are coded on a 0–100 scale with higher values reflecting the more favorable health state. These questions composed the vitality subscale, whose reliability and validity has been provided elsewhere (Ware & Gandek, 1998). In this sample, the vitality subscale also was found to be highly reliable (four items, Cronbach α = 0.86).

Energy/fatigue levels were assessed at baseline, year 1, and closeout in all CT participants, and additionally in years 3, 6, and 9 in roughly 6% of CT cohorts. Of note, closeout and year 9 measurements were merged into a single occasion score to increase power and simplify statistical modeling. Analyses presented here included a combined cohort of individuals who had at least one visit with complete data on energy/fatigue measures.

Baseline predictors

Comprehensive data on demographic, health behavior, health status, personality, and social factors were collected using well-established self-report measures (Matthews et al., 1997) at baseline. Existing literature suggests that these factors are plausible confounders in the relationship between energy/fatigue dynamics and adverse outcomes.

Demographic characteristics included age, education, and ethnicity. Age was treated as a continuous variable in years. Education indicated the highest level of education completed and included three categories: high school, college, and postgraduate education. Ethnicity was coded as a binary variable, with non-white category = 1.

The self-report health behavior questionnaire included items related to smoking, alcohol consumption, low fat diet, engagement in vigorous exercise at age 50, and leisure walking outside for more than 10 minutes. Smoking was a 3-category variable: never smoker, past smoker, current smoker. Low fat diet and vigorous exercise at age 50 were binary variables (Yes = 1). Alcohol consumption was coded as a continuous score representing the number of servings per week of beer, wine, and/or liquor. Walking outside the home for more than 10 minutes without stopping was coded as an incremental increase in frequency of walking on a categorical ordinal scale with levels starting at 0 (never or rarely walk outside) to 5 (7 or more times each week).

Comorbidities measured included history of coronary heart disease, heart failure, stroke, diabetes mellitus, hypertension, arthritis, cancer, and hip fracture. These variables were collected by self-report and coded as 0 (condition absent) or 1 (condition present). These codes were used to calculate the total number of chronic conditions at baseline.

General symptoms were assessed using a list of 34 symptom items measuring occurrence and severity of symptoms in the last 4 weeks. Scores ranged from 0 to 30, with a higher score indicating more symptoms.

Depression symptoms were assessed using a short form of the Center for Epidemiological Studies Depression scale (CES-D; Burnam, Wells, Leake, & Landsverk, 1988). Scores range from 0 to 10, with a higher score indicating a greater likelihood of depression.

Sleep disturbance was assessed by self-report using the Insomnia Rating Scale (Levine et al., 2003) with a summary score ranging from 0 to 20. A higher score indicates greater sleep disturbance. The scale showed good reliability in this study (five items, Cronbach α = 0.77).

Optimism was measured using the Life Orientation Test-Revised Scale (Scheier & Carver, 1985), with possible scores ranging from 6 to 30, and a higher score indicating greater optimism. The scale found to be acceptably reliable (six items, Cronbach α = 0.73).

Negative life events were assessed using a questionnaire from the Alameda County Study (Berkman & Syme, 1979). Scores ranged from 0 to 11, with a higher score indicating a greater number of negative life events.

Social support was assessed using nine items that asked respondents to indicate how often each of nine different types of support was available to them (Sherbourne & Stewart, 1991). Final scores range from 9 to 45, with a higher score indicating greater support. The instrument showed excellent reliability estimates in present sample (nine items, Cronbach α = 0.92).

Hospitalization (outcome variable)

All 2005–2010 Extension Study participants completed annual medical history update forms in which they indicated the occurrence of any overnight hospitalization. This information was then used to obtain medical records for confirmation. Outcomes information was available for an average length of 13.01 years of follow-up.

Data Analysis

Defining trajectories (Step I)

Analytic strategies began with a calculation of descriptive statistics (Table 2). Skewness and kurtosis were calculated for the energy/fatigue index scores at each measurement occasion in addition to graphical examinations of the data using histograms and normal probability plots (data not shown). Given that non-normally distributed data increase the probability of an over-extraction of spurious classes in the latent class growth framework, division by 10 and raising to the second power transformation was applied to improve normality for the trajectory variable (i.e., energy/fatigue) (Bauer & Curran, 2003). Division by 10 was used simply to facilitate convergence of the iterative maximum likelihood algorithm.

Table 2. Descriptive Statistics of Baseline Predictors of Energy/Fatigue Scores in the Women's Health Initiative Clinical Trial Cohort (N = 19,891)
   MSD
Age  69.53.5
   n%
EthnicityWhite 17,51988.1
EducationHigh school 7,34636.9
 College 7,53837.9
 Postgraduate 4,90724.7
Health behaviorsSmokingNever smoked10,83154.5
  Past smoker7,91639.8
  Current smoker9284.7
 Low fat diet 6,65733.5
 Walking outsideRarely/never3,56717.9
  1–3/month2,99115.0
  1/week2,16910.9
  2–3/week5,54627.9
  4–6/week4,12220.7
  7 or more/week1,4107.1
 Vigorous exercise at 50 7,43537.4
   MSD
 Alcohol serving/week 2.34.5
 No chronic conditions 1.51.3
 Severity of general symptoms 0.40.2
 Severity of sleep disturbances 6.74.4
 Severity of depression symptoms 0.030.1
Psychological, environmental, and social factorsOptimism 23.43.2
 Negative life event 32.9
 Social support 36.17.6

We used the person-centered LCGM framework to identify relatively homogeneous clusters of individuals who followed similar trajectories of change in energy/fatigue index scores (Nagin, 2005; Nagin & Odgers, 2010). Trajectory parameters were estimated using a full information maximum-likelihood method that integrates any available measurements and is robust for missingness with the following specifications:

  • display math(1)

inline image is a latent variable representing the underlying energy/fatigue status of the individual (i) at time (t) given membership in group (g). Time (t) refers to the time interval for data collection from baseline. inline image are the coefficients associated with the intercept, linear, and quadratic rate of change in energy/fatigue scores. ϵit is a time-specific disturbance term assumed to be normally distributed with a zero mean and constant variance.

As the data were collected at up to five time points (i.e., baseline, year 1, 3, 6, and 9/closeout), a quadratic function was fitted to the data. Through a process similar to that of LCA, parameters were estimated to define the shape of the trajectories and the probability of trajectory group membership (Muthen & Shedden, 1999; Nagin, 2005). The number of groups was chosen based on the following selection criteria: (1) interpretability; (2) theoretical justification; (3) parsimony; (4) lowest adjusted Bayesian information criteria (BIC) score; (5) lowest Akaike information criterion (AIC); (6) entropy >0.7; (7) average posterior probability in each class >0.75 and no more than 10% overlap/cross-membership between non-contiguous clusters; and (8) at least 2.5% of total count in each group. In the final selection process (model fit indices and Mplus6 input code are available from authors), we preferred the most parsimonious and interpretable model, provided that the models under consideration were not distinctively different on other formal statistical criteria. Given the continuous nature of the energy/fatigue scores, a normal distribution function was fitted to the data. In order to ensure the most statistically efficient model, non-significant higher-order terms (i.e., quadratic) were removed and the model was re-specified until optimal fit was achieved.

Estimating effects of the predictors on the trajectory group membership (Step II)

To test the effect of predictors on trajectory group membership, individuals were assigned to their highest-probability group, which was initially treated as a nominal dependent variable to be linked to predictors using multinomial logistic specification.

After visual inspection of trajectory group dynamics revealed a clearly ordered structure for the estimated longitudinal patterns without noticeable points of inflection or intersections among trajectories, we coded trajectory group assignment in an incrementally increasing (i.e., ordered) way, so that that the lowest number would represent membership in the most highly functioning trajectory group and the highest number would reflect membership in the most frail trajectory. This modification allowed us to use an ordered logit specification to test the effect of predictors on membership in increasingly more frail trajectories.

It is important to note that the ordered logit model imposes an overly restrictive proportionality assumption that the multiplicative effect of covariates on the odds of being in a category j is the same for all: j = 0,1, … , j−1. This assumption is often violated (Peterson & Harrell, 1990), as was the case here, which is why we proceeded with fitting a less restrictive model, known as a partial proportional-odds model. Conceptually speaking, partial proportional-odds models generate one set of estimates for those variables that do not violate parallel line assumptions, and other category-specific estimates for those covariates that have distinctively different effects across levels of a categorical outcome (Williams, 2006; Stata 11 input code is available from authors).

Estimating the effects of trajectory group membership on hospitalization (Step III)

Finally, the last set of analyses was implemented using Cox proportional hazard models. Membership assignment served as a predictor of the first incident of overnight hospitalization during the WHI Extension Study in sequentially fitted models adjusted for the baseline variables. In the analyses, the days from enrollment to death (or the last contact if no death occurred) were used as the censoring time for those participants without the target event (i.e., overnight hospitalization).

Multinomial and ordered logistic regressions, partial proportional odds modeling, and survival analyses were conducted using Stata 11 Software package (Stata Corp., 2009). LCGM modeling was conducted with MPlus 6 software (Muthén & Muthén, 1998–2011). Full information maximum-likelihood estimation was used to integrate all available information based on missing-at-random (MAR) assumptions for the trajectory variables (i.e., in Step I) and list-wise deletion for the predictors (i.e., in Steps II-III; Muthén & Muthén, 1998–2011). To improve interpretability, all continuous predictors were centered on their means before fitting into regression models.

Results

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. References

Longitudinal Characteristics

Tables 1 and 2 include estimates of the mean, standard deviation, and number of participants at each measurement occasion (baseline, years 1, 3, 6, and 9/closeout) for energy/fatigue scores and baseline distribution of the predictors.

Trajectories of Change

Although model fit scores improved with the addition of groups, we noticed a less dramatic change when going from a four- to five-trajectory model or higher (model fit criteria are available from authors). Also, when models contained five or more trajectories, the average posterior probability of one or more of the trajectory groups reached as low as 68%, in addition to a substantial overlap (i.e., cross-membership) between two or more non-contiguous clusters. Thus, based on an improvement in model selection criteria when comparing two- to three-trajectory models, including an adequate sample size in each of the estimated groups, reasonably good minimum and maximum values of the posterior probabilities (0.81–0.87, mean 0.85), and adequacy of interpretability, we selected a four-trajectory model to represent the data (Table 3).

Table 3. Estimated Group-Specific Trajectory Parameters of Energy/Fatigue Functioning in the Women's Health Initiative Clinical Trial Cohort (N = 19,891)
Trajectory parameterInterceptLinear slopeQuadratic slopeGroup proportion
βSEβSEβSE%N
Note
  • Sigma, M (SE) is 152.12 (2.6)—Baseline, 154.19 (2.8)—Year 1, 161.01 (10.1)—Year 3, 206.58 (6.1)—Year 6, 231.19 (4.4)—Year 9/Closeout. “High Decliner” indicates high baseline and some degree of decline in Energy/Fatigue scores; “Medium Decliner” indicates medium baseline and some degree of decline in Energy/Fatigue scores; “Mid–Low Decliner” indicates mid–low baseline and some degree of decline in Energy/Fatigue scores; “Low Decliner” indicates low baseline and some degree of decline in Energy/Fatigue scores. Data reflect results from fitting 4-group Latent Class Growth Model.

  • ***

    p < .001.

High Decliner80.661.08***1.050.39***−0.210.04***5985
Medium Decliner61.320.53***0.130.19−0.150.02***367,205
Mid–Low Decliner41.720.83***−1.160.06***NSNS356,976
Low Decliner20.670.45***−1.090.17***0.090.02***244,725

Parameter estimates for the four-trajectory model showed significant variation in the intercepts. Three groups were best modeled with inclusion of a quadratic term to capture the slightly concave (i.e., decelerated) shape of the trajectory groups. One group (Mid–Low Decliner) required the inclusion of simple linear terms only.

Figure 1 illustrates estimated longitudinal dynamics in the energy/fatigue index scores. We assigned labels to each of the derived trajectory groups such that the first word of a label represented an ordinal ranking of that trajectory's intercept relative to other groups (i.e., High, Medium, Low), and the second word (Decliner) indicated the direction of change over time.

image

Figure 1. Estimated Four trajectories of energy/fatigue index scores during 9 years of follow-up in older Women's Health Initiative Clinical Trial Participants (N = 19,891). Results are from regression via Latent Class Growth Models. Estimated groups are depicted as: Low Decliner (24%)a = dashed dotted; Mid Low Decliner (35%)a = dotted; Medium Decliner (36%)a = dashed; High Decliner (5%)a = dashed dotted dotted.

a(%)—percentage from total sample in a given group.

Download figure to PowerPoint

Almost a quarter of the sample (n = 4,725, 24%) fell into the lowest-intercept declining trajectory (Low Decliner). The trajectory with the second-lowest intercept included 35% (n = 6,976) of the sample and is described as Mid–Low Decliner. These women had a relatively steep rate of decline [Slope = −1.16, 95% CI = (−1.04, −1.26)]. The third and the largest trajectory (n = 7,205, 36%) described women who had a Medium-intercept Declining trajectory. The last trajectory included women with a High-intercept Declining trajectory (n = 985, 5%); these participants had relatively high and stable energy/fatigue levels during the first 9 years of follow-up, with only a slight degree of annual decline.

Predictors of Trajectory Group Membership

Predictors of membership in the energy/fatigue trajectories were initially examined with multinomial logistic regression. Odds ratios (OR) using the High Decliner group as the reference category are summarized in Table 4. Briefly, in comparison to women with the highest baseline and least decline in energy over time, the Medium Decliner group was more educated; had a higher number of chronic conditions, general symptoms, and sleep disturbances; had lower levels of optimism; and was less engaged in vigorous exercise at age 50 or leisure walking at WHI baseline. The Mid–Low Decliner group was older and predominantly white; had more education; had a higher number of chronic conditions and general/depression symptoms; had a higher prevalence of sleep disturbances; had lower levels of optimism; was less engaged in vigorous exercise at age 50 or leisure walking; had lower alcohol consumption; and also had less social support. Finally, the Low Decliner group was older and predominantly white; had more education; had a higher number of chronic conditions and general and depression symptoms; had a higher prevalence of sleep disturbances; had lower levels of optimism; was less engaged in vigorous exercise at age 50 or leisure walking; had lower alcohol consumption; and also had less social support than the least-fatigued reference group (i.e., High Decliner).

Table 4. Estimated Odd Ratios (OR) and 95% Confidence Intervals (CI) From a Multinomial Logistic Regression of Energy/Fatigue Trajectory Groups on Baseline Characteristics in a WHI CT Cohort (n = 15,811)
Baseline characteristicsHigh Decliner vs. Medium DeclinerHigh Decliner vs. Mid–Low DeclinerHigh Decliner vs. Low Decliner
OR(95% CI)OR(95% CI)OR(95% CI)
Note
  • WHI CT = Women's Health Initiative Clinical Trial. The model estimates the effect of predictors on a likelihood of being in High Decliner versus Moderate Decliner, Mid–Low Decliner, and Low Decliner Trajectory Groups. All variables were entered simultaneously into the multinomial logistic model. ORs <1 denotes benefit for continuous and categorical variables. Reference category: High Decliner. Model fit statistic: likelihood ratio chi-square statistic—LR inline image = 7308.51, p < .001.

  • a

    Reference category: high school.

  • *

    p < .05.

  • **

    p < .01.

  • ***

    p < .001.

Age1.00(0.98,1.03)1.03(1.01,1.06)**1.05(1.02,1.07)**
Non-white0.77(0.59,1.01)0.66(0.49,0.87)**0.44(0.33,0.60)***
Collegea1.24(1.03,1.49)*1.28(1.05,1.56)*1.39(1.13,1.72)**
Postgraduatea1.44(1.17,1.77)***1.43(1.16,1.78)**1.47(1.17,1.86)**
Number of chronic conditions1.10(1.02,1.18)*1.32(1.23,1.42)***1.61(1.48,1.74)***
General symptoms1.85(1.73,1.99)***2.55(2.37,2.75)***3.36(3.10,3.59)***
Depression symptoms1.42(0.89,2.26)1.60(1.01,2.55)*1.88(1.18,2.99)**
Sleep disturbances1.05(1.02,1.07)***1.09(1.07,1.12)***1.12(1.09,1.15)***
Smoking0.93(0.81,1.07)0.98(0.85,1.13)0.97(0.83,1.13)
Alcohol consumption0.99(0.97,1.00)0.97(0.95,0.99)***0.96(0.95,0.98)***
Low fat diet0.99(0.83,1.17)0.94(0.79,1.13)0.89(0.74,1.08)
Walking outside0.92(0.87,0.97)**0.82(0.77,0.86)***0.70(0.66,0.74)***
Exercise at age 500.74(0.63,0.87)***0.59(0.50,0.69)***0.49(0.41,0.58)***
Negative life events1.01(0.97,1.04)1.02(0.98,1.05)0.99(0.95,1.03)
Optimism0.90(0.88,0.93)***0.84(0.82,0.87)***0.79(0.76,0.81)***
Social support0.99(0.98,1.01)0.98(0.97,0.99)***0.95(0.94,0.97)***

Table 5 presents the results of the fitted ordered logit regression, explaining the effect of predictors on orderly, structured trajectories of the energy/fatigue index scores. The effects are presented as odds ratios (ORs). This means that we compared the women who were in trajectory groups greater than j to those who were in groups less than or equal to j, where j is the level of the outcome variable. ORs greater than 1 reflected increased odds of being in the frailer trajectories of the energy/fatigue index scores than the comparison category, and ORs less than 1 reflected decreased odds. For example, for a 1-unit increase in the general symptoms score, the odds of being in the Low Decliner trajectory rather than the combined High, Medium, and Mid–Low Decliner trajectories were 1.51 greater (95% CI = 1.48, 1.53) than in those who did not exhibit such a trait, when all other variables were held constant. Given the proportionality assumption, a similar interpretation is valid regardless of the selected reference category.

Table 5. Estimated Odds Ratios (OR) and 95% Confidence Intervals (CI) From an Ordered Logistic Regression of Energy/Fatigue Trajectory Groups on Baseline Characteristics in a WHI CT cohort (n = 15,811)
Baseline characteristicsOR95% CI
Note
  • WHI CT-Women's Health Initiative Clinical Trial. The model estimates the effect of predictors on ordered trajectories of energy/fatigue index scores. All variables were entered simultaneously into the ordered logistic model. ORs <1 denotes benefit for continuous and categorical variables. Model fit statistic: likelihood ratio chi-square statistic—LR inline image = 7074.69, p < .001.

  • a

    Reference category: high school.

  • *

    p < .05.

  • **

    p < .01.

  • ***

    p < .001.

Age1.03(1.02,1.04)***
Non-white0.71(0.64,0.79)***
Collegea1.10(1.02,1.18)*
Postgraduatea1.07(0.99,1.16)
Number of chronic
Conditions1.28(1.25,1.32)***
General symptoms1.51(1.48,1.53)***
Depression symptoms1.18(1.13,1.24)***
Sleep disturbances1.05(1.04,1.06)***
Smoking1.03(0.97,1.08)
Alcohol consumption0.98(0.98,0.99)***
Low fat diet0.93(0.88,0.99)*
Walking outside0.84(0.82,0.86)***
Exercise at age 500.74(0.69,0.79)***
Negative life events0.99(0.98,1.01)
Optimism0.91(0.89,0.92)***
Social support0.98(0.97,0.98)***
Threshold (1)−4.38(−4.50,−4.26)
Threshold (2)−1.20(−1.29,−1.11)
Threshold (3)0.94(0.85,1.03)

Multinomial and order logit outputs were consistent in estimates of directionality of the effects. For instance, having a college degree, a higher number of chronic conditions and general symptoms, presence of sleep disturbances, engagement in leisure walking and exercise at age 50, and higher optimism scores were consistent and significant predictors of membership in longitudinal trajectories in both models. Of note, the magnitude of the effects tended to be higher in the multinomial model than in the proportional odds model, presumably due to a more granular interpretation of the estimates.

A partial proportional odds model, shown in Table 6, provided additional details about the specified model, revealing clinically meaningful information that was obscured in the proportional odds model. For example, higher general symptom scores were consistently associated with membership in frailer trajectories of the energy/fatigue index score, but the greatest effect was in differentiating between the most functionally vigorous trajectory (i.e., High Decliner) and the combination of all other more frail trajectories (OR = 2.05; 95% CI = 1.92, 2.19).

Table 6. Estimated Odd Ratios (OR) and 95% Confidence Intervals (CI) From a Partial Proportional Odds Model of Energy/Fatigue Trajectory Groups on Baseline Characteristics in a WHI CT Cohort (n = 15,811)
Baseline characteristicsConstant components of odds ratio across trajectoriesHigh Decliner vs. Medium, Mid–Low, Low DeclinerHigh, Medium Decliner vs. Mid–Low, Low DeclinerHigh, Medium, Mid–Low Decliner vs. Low Decliner
OR(95% CI)OR(95% CI)OR(95% CI)OR(95% CI)
Note
  • WHI CT-Women's Health Initiative Clinical Trial. The model estimates the effects of predictors on ordered trajectories of energy/fatigue index scores.

  • All variables were entered simultaneously into the partial proportional odds model. Model fit statistic: likelihood ratio chi-square statistic—LR inline image = 7210.87, p < .001. ORs <1 denote benefit for continuous and categorical variables. Reference category: High Decliner.

  • a

    Reference category: high school.

  • *

    p < .05.

  • **

    p < .01.

  • ***

    p < .001.

Age1.03(1.02,1.04)***      
Non-white0.72(0.65,0.80)***      
Collegea1.09(1.02,1.18)**      
Postgraduatea  1.31(1.10,1.55)**1.05(0.96,1.15)1.03(0.93,1.15)
Number of chronic conditions1.28(1.25,1.31)***      
General symptoms  2.05(1.92,2.19)***1.52(1.48,1.55)***1.45(1.42,1.49)***
Depression symptoms1.20(1.15,1.25)***      
Sleep disturbances1.05(1.04,1.06)***      
Smoking1.02(0.97,1.08)      
Alcohol consumption0.98(0.97,0.99)***      
Low fat diet0.93(0.87,1.00)      
Walking outside0.84(0.82,0.86)***      
Exercise at age 500.74(0.70,0.79)***      
Negative life events  1.00(0.97,1.05)1.00(0.99,1.01)0.98(0.97,0.99)*
Optimism0.91(0.90,0.92)***      
Social support0.98(0.97,0.99)***      

Outcomes of Trajectory Group Membership

As of March 31, 2011, 5,547 out of 19,891 (28%) women ages 65 and older at baseline who were enrolled in the CT had reported at least one overnight hospitalization during the 2005–2010 WHI Extension Study follow-up. Of the 5,547 women with at least one incident of hospitalization, 17.9% were in the High Decliner trajectory, 23.0% in the Medium Decliner trajectory group, 29.1% in the Mid–Low Declining trajectory cluster, and 35.5% in the Low Declining trajectory (Table 7). In the partially adjusted model, those who were in the Low Declining trajectory were approximately twice as likely as the High Decliner group members to report a first incident hospitalization (HR = 2.25; 95% CI = 1.92, 2.63). Final multivariate adjustment slightly attenuated these results. The fully adjusted model showed that membership in the Medium, Mid–Low, and Low Declining trajectories carried a statistically significant additional risk of hospitalization (28%, 50%, and 66%, respectively) compared with the High Decliner reference group.

Table 7. Relative Hazard of First Incidence of Hospitalization by Membership in Longitudinal Trajectory Groups of Energy/Fatigue Index Scores in a WHI CT cohort
Trajectory groupHospitalization n (%)Hazard ratio (95% CI)
Model 1a (n = 19,891)Model 2b (n = 15,811)
Note
  • WHI CT, Women's Health Initiative Clinical Trial. CI, confidence interval. Follow-up averaged 13.01 years.

  • a

    Adjusted for age and years of follow-up in WHI at the start of extension study.

  • b

    Adjusted for age, years of follow-up in WHI at the start of Extension study, ethnicity, education, health behaviors (i.e., smoking, alcohol consumption, low fat diet, recreational walking and vigorous exercise at age 50), number of chronic comorbidities, depression symptoms, sleep disturbances, general symptoms, optimism, negative life events, social support, and number of hospitalization prior to start of extension study.

  • **

    p < .01.

  • ***

    p < .001.

High Decliner177 (17.99)1.00 (reference)1.00 (reference)
Medium Decliner1,658 (23.02)1.31 (1.12,1.53)**1.28 (1.07,1.53)**
Mid–Low Decliner2,031 (29.13)1.73 (1.49,2.02)***1.50 (1.25,1.80)***
Low Decliner1,675 (35.48)2.25 (1.92,2.63)***1.66 (1.37,2.01)***

Discussion

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. References

The purpose of this article was to provide a step-by-step example of the utility of the LCGM framework and its extensions. In this demonstration, we calculated descriptive statistics and performing normalizing data transformations; ran a LCGM-driven model selection process using a battery of indicators including, but not limited to, theoretical justifications and information criteria; linked predictor variables with trajectory group memberships using multinomial, ordered, or partial proportional logistic regression models; and used a Cox proportional hazard framework to estimate the effects of membership assignments on distal outcomes.

Four distinct trajectories of energy/fatigue scores were identified during the first 9 years of follow-up of women 65 years and older in the WHI. The number of trajectories in this sample was similar to several longitudinal patterns identified in other studies (Gill et al., 2010; Liang et al., 2010) using similar methodology. It is important to acknowledge the prospective nature of these findings, indicating, for example, that the most vigorous individuals (those in High Decliner trajectory) did not merely have elevated energy levels at baseline but sustained fairly high vitality for up to 9 years of follow-up.

Although taken together these findings suggest that there is substantial heterogeneity of indicators of functional and energy levels among aging individuals, a number of major categories of indicators could be distinguished that were in concordance with related discussions of variability in normal aging, successful aging, and pathological aging (Fried et al., 2001; Rowe & Kahn, 1997; Woods et al., 2012). In line with other studies (Avlund et al., 2001; Moreh et al., 2010; Vestergaard et al., 2009), this analysis showed that fatigue was closely linked to age, socio-demographic factors, comorbidities, health behaviors, and poor sleep quality. However, contrary to previous published work, we demonstrated that, in fully adjusted models, additional factors such as optimism and social support had significant positive and independent effects on the likelihood of membership in vigorous trajectories of energy/fatigue index scores. These findings were consistent regardless of the methodological framework used, and they hold promise for developing behavioral interventions to help the elderly maintain optimal levels of energy throughout the aging process.

Another interesting finding pertains to the negative effect of education on trajectory group assignment. One plausible explanation of this conundrum is that higher education influences an individual's sensitivity to fatigue, making these persons more likely to perceive and report lower energy scores. This assertion deserves further examination in other longitudinal studies. Worth noting is that the WHI-CT sample is in no sense a nationally representative selection of elderly women, and a quarter of the sample used here reported postgraduate education. Another important caveat is that in large cohort studies, the balances between statistical and clinical significance may be disproportional. In other words, even though the WHI cohort provided an excellent opportunity to examine the effects of intervening factors on age-sensitive indicators, the clinical significance of the results cannot be assumed.

As found in other studies (Avlund et al., 2001), we demonstrated that energy/fatigue levels predicted future hospitalization in non-disabled elderly. However, in contrast to other prospective studies in which the association between such distal outcomes (e.g., hospitalization, mortality) and cross-sectional distribution of predictors was measured, the LCGM framework enabled us to capture subtle longitudinal dynamics in energy/fatigue scores over a relatively long follow-up and relate these levels to a clinically relevant outcome. In this way, consideration of trajectory groups can be a tool for empirical partitioning of a population curve into clinically and statistically distinct longitudinal clusters. This application is especially useful, given that investigators frequently use less precise categorization criteria such as tertiles and quintiles, as well as other a priori assumptions, to assign individuals to different clinical categories. Although such a subjective categorization is methodologically reasonable, it has one major weakness, in that it provides no basis for calibrating the precision of an individual's classification into a particular category. In other words, when using traditional (i.e., variable-centered) methodology, we cannot quantify the probability of a category assignment. The LCGM-based analysis presented here supports an empirical statement that there is a 24% chance that randomly selected women age 65 years old and older who participated in the WHI CT will demonstrate an energy/fatigue-related longitudinal trend similar to that found in the Low Decliner group, a claim that would be challenging to make using a traditional variable-centered framework.

As always there are certain caveats to any analysis. Measurement error in LCGM and general models can create problems, and these issues have been thoroughly discussed in the literature (see Muthen & Shedden, 1999; Nagin, 2005). While not eliminating the problem, our use of established scales for our measures helped to minimize this issue.

Second, the pros and cons of a multi-step (used here) versus single-step approach have been recently debated in biomedical literature (Asparouhov & Muthen, ; Clark & Muthen, ). In some simulation studies it was demonstrated that multi-step analysis might result in biased standard error estimates (Clark & Muthen, ). Careful considerations using the latest development in the field are warranted in future research.

A third issue in the analysis deserves brief discussion. Women with low energy/fatigue levels presumably were less likely than less fatigued women to complete all occasions of follow-up. If that is the case, then the proportion of older women at risk of being in low-energy/fatigue-level trajectories may be misrepresented. However, the main aim of the analyses presented here was to describe the heterogeneity in energy/fatigue scores, rather than to estimate their prevalence. The LCGM framework can serve as a convenient analytic approach for outlining longitudinal patterns occurring in the population. In addition, LCGM successfully integrates full information maximum-likelihood techniques that generate consistent estimates when MAR assumptions hold (Muthén & Muthén, 1998–2011). In the analyses presented here, delayed enrollment, a flexible data collection protocol, and sparsely scheduled measurement occasions resulted in a large proportion of missing observations, supporting a MAR assumption. That is, a large proportion of missing observations were attributable to protocol-defined features of the study rather than to other confounding events.

Conclusion

Researchers in nursing and health can benefit from using person-centered methodologies. The estimates (i.e., trajectory functions and membership probabilities) from these basic analytic techniques could be easily used to identify factors that predict trajectory group membership and to approximate the magnitude of risk carried by membership in certain longitudinal clusters. The association between predictors and trajectory group membership could be specified using either a traditional multinomial framework or an alternative categorically ordered specification, provided that the estimated longitudinal patterns show a clear ordered structure. Sensible application of either model generates comparable estimates. However, to ensure the most parsimonious and statistically justifiable model (i.e., the model that does not violate parallel-line assumptions), a partial proportional odds model should be used. The latter provides a detailed output that is easily interpreted. Finally, either discrete- or continuous-time survival analyses can be readily fit to the data to approximate the magnitude of risk that is carried by membership in particular longitudinal clusters. In summary, person-centered methods provide unique opportunities to explore and statistically model the effects of longitudinal heterogeneity within a population and can be more fully integrated into nursing research analyses.

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  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. References
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