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Published in final edited form as: Arch Phys Med Rehabil. 2022 Jan 17;103(8):1607–1614.e1. doi: 10.1016/j.apmr.2021.12.018

Application of Second-Order Growth Mixture Modeling (SO-GMM) to Longitudinal TBI Outcome Research: 15-year Trajectories of Life Satisfaction in Adolescents and Young Adults (AYA) as an Example

Jiabin Shen 1, Yan Wang 1
PMCID: PMC9288558  NIHMSID: NIHMS1772494  PMID: 35051401

Abstract

Objective.

To demonstrate the application of Second-Order Growth Mixture Modeling using life satisfaction among adolescents and young adults with TBI up to 15 years post-injury.

Design.

SO-GMM, a data-driven modeling approach that accounts for measurement errors, was adopted to uncover distinct growth trajectories of life satisfaction over 15 years post-injury. Membership in growth trajectories was then linked with baseline characteristics to understand the contributing factors to distinct growth over time.

Setting.

Traumatic Brain Injury Model System National Database

Participants.

3,756 AYAs with TBI aged 16 - 25 (Mage=20.49, SDage=2.66; 27.24% female)

Interventions.

Not Applicable

Main Outcome Measures.

Satisfaction with Life Scale

Results.

Four quadratic growth trajectories were identified: low-stable (16.6%) that had low initial life satisfaction and remained low over time; high-stable (49.3%) that had high life satisfaction at the baseline and stayed high over time; high-decreasing (15.8%) that started with high life satisfaction but decreased over time; and low-increasing (18.2%) that started with low life satisfaction but increased over time. Sex, race, pre-injury employment status, age, and FIM cognition were associated with group assignment.

Conclusion.

This study applied SO-GMM to a national TBI database and identified four longitudinal trajectories of life satisfaction among AYAs with TBI. Findings provided data-driven evidence for development of future interventions that are tailored at both temporal and personalized levels for improved health outcomes among AYAs with TBI.

Keywords: traumatic brain injury, adolescents, young adults, life satisfaction, growth mixture modeling, trajectory


Traumatic brain injury (TBI) poses a recognized threat to the health of U.S. populations. The Centers for Disease Control and Prevention (CDC) estimated that the TBI-related emergency department visits have increased dramatically in the past decade1. Individuals aged 16 to 25, commonly referred as adolescents and young adults (AYAs), have been recognized as in the “age of transformation” 2. AYAs are particularly vulnerable to TBI, with a total of 55,616 TBI-related deaths estimated by CDC from 2008 to 2014, caused mostly by motor vehicle crashes and falls 3. Increasing research has demonstrated both short-term and long-term impact of TBI on AYAs, including fatigue 4,5, participation 5, substance use 6, risks of attempted suicide 7, and health-related quality of life 5.

Despite the prevalence of TBI and its significant impact on AYAs, limited research has been published on how TBI impacts the long-term trajectories of post-injury outcomes among AYAs1. This is particularly true for life satisfaction – a critical rehabilitation outcome for AYAs with TBI – because individuals who experience TBI at earlier stages of life may experience continuous challenges in cognitive, emotional, and social domains, which would cloud the long-term life satisfaction throughout their life-span development 8. Life satisfaction can be measured by several ways, including self-reported questionnaires as a single construct 911 or multifaceted construct that encompasses self-evaluation of physical, cognitive, and social emotional well-beings 12, interviews 13, or more recently patient-centered dairies supported by the ecological momentary assessment approach for intensive longitudinal measurement 14. Yet few studies address the longitudinal trajectories of life satisfaction among AYAs with TBI. Most research focused on either children or adults15 or a mixed sample with wide age ranges 16,17. Further, most data were analyzed using techniques that often assumed individuals with TBI are a homogenous group; yet this may not be the case especially when the recovery outcomes are examined in the long term, considering the various injury mechanisms, severity, and socio-demographic factors of the patient family 18,19.

Recent advancements in statistical methodologies such as growth mixture modeling (GMM) have equipped us well to tackle sample heterogeneity by identifying latent classifications of recovery courses among subpopulations20. As a result, GMM has been used in clinical and health research on many topics including health behaviors 20,21, psychopathology disorders 20, and osteoarthritis progression 22. Although few specifically addressed AYAs with TBI, a similar trend was found in applying GMM to TBI outcome research18. However, there are two important limitations in current practices. The first limitation concerns data sources. For example, one study adopted a variant of GMM named group-based trajectory modeling (GBTM) to analyze a population-based national survey dataset (Medical Expenditure Panel Survey) to examine perceived health status among adults with TBI 23. However, population-based databases were not designed for the sole purpose of tracking TBI patients. The rarity of TBIs in the general population often results in relatively moderate sample sizes and shorter follow-up periods (2 years in MEPS) compared to national databases dedicated to track TBI patients 23,24 Prospectively-designed studies targeting the young adult population suffer from similar disadvantages in sample size and many focused on athletes with mild TBI 25 but not moderate to severe TBIs, which constitute a significant long-term rehabilitation burden for both the survivors and their families 26,27.

The second, and perhaps more important limitation in existing literature, is that when applying GMM to TBI outcome research, growth trajectories were usually estimated based on mean or sum composite scores across multiple items that measure a construct, such as sum of items in a life satisfaction scale 28. At issue is the fact that when composite scores are created, it is assumed that all items contribute equally to the measurement of the underlying construct (e.g., life satisfaction) and that there is no measurement error across items of that scale, which may not often be the case. To address this, second-order GMM (SO-GMM, Figure 1 right) has been recommended29,30. SO-GMM incorporates a measurement model for the underlying construct and thus explicitly models the relations of items to the construct in the first order level, allowing for the presence of different weights across items (i.e., factor loadings) and measurement errors. In the second-order level, distinct growth trajectories can then be estimated based on the latent construct which more accurately reflects the longitudinal outcome of interest.

Figure 1.

Figure 1.

Growth Mixture Modeling (GMM; left) and Second-Order Growth Mixture Modeling (SO-GMM; right). C = latent class variable; I = intercept; S = slope (assuming linear growth); T1 – T4 are observed longitudinal outcome variables (squares) in GMM, but latent factors (circles) in SO-GMM. Y11 – Y43 are observed items of latent factors, T1 – T4. Note that Y21 – Y33 are not shown due to space limit. Paths a-c represent measurement invariance over time.

Despite these methodological advantages, we have yet to find any application of SO-GMM in TBI research. To address this important gap, this paper aimed to demonstrate a rigorous application of SO-GMM to TBI outcome research using life satisfaction among 3,756 AYAs with TBI from the Traumatic Brain Injury Model System National Database (TBIMS-NDB) up to 15 years post-admission as an example.

Method

Data Source

This study used the TBIMS-NDB (April 2020)31. TBIMS-NDB is the country’s first and largest prospective, longitudinal multi-center database dedicated to examining the rehabilitation trajectories and follow-up outcomes for individuals at least 16 years old treated for inpatient rehabilitation at one of the participating TBIMS centers and meet one of the following criteria: (1) Glasgow Coma Scale (GCS) score below 13 when assessed at the emergency department, or (2) more than 24 hours of post-traumatic amnesia, or (3) intracranial neuroimaging abnormalities, or (4) loss of consciousness for more than 30 minutes32. The TBIMS-NDB collected data using post-injury repeated surveys at regular intervals, with baseline information (Form I) collected in-person at inpatient rehabilitation discharge and follow-up information (Form II) collected at 1, 2, 5, and every 5 years thereafter up to 30 years post-injury, administered via telephone, in-person or mail questionnaires. Previous research has supported the representativeness of TBIMS-NDB for patients receiving hospitalization and inpatient rehabilitation for TBI in the U.S., especially for patients under 6533. All participants were consented at participating centers according to established standard operating procedures (SOPs) approved by local IRBs and published on TBIMS website (https://www.tbindsc.org/SOP.aspx).

Study Population

The study population was adolescents and young adults aged 16-25 in the TBIMS-NDB. The sample consisted of 3,756 individuals (Age: M = 20.49, SD = 2.66). Most of the sample (72.76%) were males, white (65.41%), employed at baseline (63%).

Outcome variable

Life satisfaction.

Life satisfaction is derived from five items of Satisfaction with Life Scale (SWLS) in the TBIMS-NDB: “In most ways my life is close to my ideal” , “The conditions of my life are excellent”, “I am satisfied with my life” , “So far I have gotten the important things I want in life” , and “If I could live my life over, I would change almost nothing” in Form 2. Item scores ranged from 1 to 79,34. Higher values indicated greater life satisfaction. Given that SO-GMM can directly incorporate the measurement model, all five items were used in the analysis without averaging or summing.

Covariates

Functional Independence Measure (FIM) Cognitive on Admission: sum of five FIM cognitive items with each item ranging from 1 (total assist) to 7 (complete independence) Therefore, higher values of this variable indicated greater cognitive independence35.

Pre-injury disability:blindness, deafness, or a severe vision or hearing impairment” and “a condition that substantially limited one or more basic physical activities such as walking, climbing stairs, reaching, lifting, or carrying” in Form 1. All pre-injury disability covariates were scored as “Yes[1]” or “No[2]”36

TBI severity: TBI severity was a categorical variable in Form 1 with three categories used in this study: mild[3], moderate[2], or severe[1] based on patients’ total GCS scores37.

Demographics: age at injury (AGENoPHI), sex (SEX), race (RACE), pre-injury employment status (EMPLOYMENT) in Form 1.

Statistical Analyses

First, descriptive analyses were conducted for the outcome and all covariates. Second, longitudinal measurement invariance (MI) was tested to ensure that changes in outcomes over time originated from changes in the construct, rather than measurement properties. Three levels of invariance were tested sequentially: configural, metric and scalar invariance that imposes constraints on equal factor structure, equal factor loadings, and equal intercepts over time, respectively. The fit of invariance models was compared: a non-significant Satorra-Bentler scaled chi-square difference test, change in comparative fit index (CFI) less than .0138, and change in root mean square error of approximation (RMSEA) less than .01539 indicated that imposing constraints on the measurement parameters did not deteriorate fit significantly and thus the tested level of invariance was established.

Next, the optimal growth function (linear or quadratic) was determined using second-order latent growth models (SO-LGM) which is identical to SO-GMM with one class. The fit of SO-LGMs with linear or quadratic growth was compared with Akaike’s information criterion (AIC)40, Bayesian information criterion (BIC)41, and sample-size-adjusted BIC (saBIC)42. Growth function that had smaller values of these criteria was supported. We also performed visual inspection of the growth trajectories to determine growth function. Then, SO-GMM was conducted by fitting models with varying numbers of latent classes using Mplus 8.443. To decide the optimal number of latent classes, model fit was compared based on AIC, BIC, saBIC, the Lo-Mendell-Rubin (LMR) likelihood ratio test44, adjusted LMR, and the bootstrap likelihood ratio test (BLRT)45,46. The latter three tests compared the fit of a k-class model versus a (k-1)-class model and p-values less than .05 indicate that the k-class model had significantly better fit to the data. Substantive interpretability was also examined in model selection to ensure that the best-fitting model provided theoretically sound solutions.

Finally, subsequent analyses were conducted using SAS software to examine the relationships between latent class membership and covariates. Specifically, chi-square tests of independence were performed for categorical covariates, i.e., pre-injury conditions, TBI severity, sex, race, and employment status. Depending on the number of latent classes, t-tests (two classes) or ANOVAs (three or more classes) were conducted for continuous covariates, including age and FIM cognition.

An in-depth version of the statistical analysis plan can be found in Supplementary Materials.

Results

Descriptive Statistics

Table 1 presents descriptive statistics for all the five items of life satisfaction across the 15 years of follow-up. Among the five items, slightly higher responses were observed for “I am satisfied with my life” and lower response were observed for “If I could live my life over, I would change almost nothing”. Inspection of skewness and kurtosis showed that all item responses were approximately normally distributed. Table 2 presents descriptive statistics for all the baseline covariates. Most participants (97.14% and 97.28% respectively) did not have pre-injury impairment and physical limitations. About half (49.85%) had mild TBI, followed by 30.25% severe and 19.90% moderate TBI.

Table 1.

Descriptive Statistics for Life Satisfaction Across the 15-Year Follow-up Period

Variable Year N Mean SD Skewness Kurtosis
In most ways my life is close to my ideal 1 2988 4.29 1.99 −.32 −1.27
2 2686 4.41 2.00 −.40 −1.23
5 2121 4.52 2.00 −.47 −1.17
10 1338 4.47 2.06 −.41 −1.25
15 625 4.35 2.09 −.30 −1.30

The conditions of my life are excellent 1 2992 4.37 2.03 −.30 −1.30
2 2688 4.56 1.98 −.46 −1.15
5 2122 4.59 1.97 −.48 −1.15
10 1339 4.56 1.99 −.44 −1.15
15 626 4.46 2.04 −.40 −1.25

I am satisfied with my life 1 2992 4.90 1.96 −.75 −.79
2 2687 5.03 1.87 −.86 −.53
5 2122 5.02 1.90 −.83 −.62
10 1339 5.00 1.92 −.83 −.60
15 625 4.88 1.99 −.70 −.89

So far I have gotten the important things I want in life 1 2990 4.64 1.98 −.52 −1.10
2 2685 4.64 1.97 −.54 −1.08
5 2120 4.77 1.97 −.65 −.96
10 1339 4.81 1.91 −.68 −.84
15 626 4.75 2.04 −.58 −1.08

If I could live my life over, I would change almost nothing 1 2986 3.82 2.26 .10 −1.59
2 2683 3.92 2.25 .03 −1.60
5 2118 4.03 2.26 −.05 −1.61
10 1338 4.06 2.27 −.06 −1.60
15 626 3.87 2.23 .11 −1.57

Table 2.

Descriptive Statistics for Baseline Covariates

Continuous Covariates N Mean SD
Age 3701 20.49 2.66
FIM Cognition 3731 15.53 7.77
Categorical Covariates Level N %

Gender
Females 1023 27.24
Males 2733 72.67
Race
White 2455 65.41
Black 676 18.01
Hispanic 418 11.13
Others 204 5.44
TBI Severity
Mild 824 49.85
Moderate 329 19.90
Severe 500 30.25
Pre-Injury Employment Status
Employed 2358 63.34
Student 783 21.03
Unemployed 582 15.63
Pre-Injury Impairment
No 2141 97.14
Yes 63 2.86
Pre-Injury Physical Limitation
No 2144 97.28
Yes 60 2.72

Longitudinal Measurement Invariance

Table 3 presents the longitudinal measurement invariance testing results. Comparing the fit of configural and metric invariance models supported the establishment of metric invariance, ΔCFI < .01 and ΔRMSEA < .015. Similarly, scalar invariance was supported based on ΔCFI and ΔRMSEA, despite that the Satorra-Bentler chi-square difference test was significant.

Table 3.

Testing Results for Longitudinal Measurement Invariance

Model # of Free Parameters χ2(df) Scaling Correction Factor RMSEA CFI SRMR§ Δχ2(Δdf) ΔCFI ΔRMSEA
Configural invariance 88 1029(262)* 1.193 .028 .962 .046
Metric invariance 72 1074(278)* 1.174 .028 .961 .047 39(16)* −.001 .001
Scalar invariance 56 1118(294)* 1.162 .027 .960 .047 40(16)* −.001 .000

Note.

*

p<0.05;

RMSEA = root mean square error of approximation;

CFI = comparative fit index;

§

SRMR = standardized root mean square residual.

SO-GMM

Prior to examining the number of optimal classes in SO-GMM, growth function was first examined by comparing the fit of a linear and quadratic SO-LGM. The quadratic growth model was chosen supported by smaller AIC, BIC, and saBIC (Table 4). Subsequently, a series of quadratic SO-GMMs with varying numbers of classes (K = 1 to 7) were fitted. We did not examine SO-GMM with 8 or more classes because one class of the seven-class SO-GMM had a small proportion of the sample (below 5%). Inconsistency among approaches to model fit comparisons was observed that the seven-class model was supported by AIC, saBIC, and BLRT whereas BIC showed the six-class had the best fit. However, the decrease in ICs was more substantial as K increased from 1 to 4 but leveled off with 5 or more classes. LMR and aLMR also favored four-class over five-class model. Therefore, we concluded that the four-class quadratic SO-GMM was the best-fitting model.

Table 4.

Second-Order Latent Growth Modeling (SO-LGM) and Second-Order Growth Mixture Modeling (SO-GMM) for Life Satisfaction

Modela AIC BIC saBIC LMR aLMR BLRT
Linear SO-LGM 183333 183620 183474
Quadratic SO-LGM (K = 1) 183301 183613 183454
Quadratic SO-GMM (K = 2) 183029 183334 183178 .0004 .0005 < .0001
Quadratic SO-GMM (K = 3) 182800 183129 182961 .0002 .0003 < .0001
Quadratic SO-GMM (K = 4) 182571 182927 182746 .0121 .0134 < .0001
Quadratic SO-GMM (K = 5) 182503 182883 182689 .0888 .0936 < .0001
Quadratic SO-GMM (K = 6) 182427 182832 182625 .0083 .0092 < .0001
Quadratic SO-GMM (K = 7) 182406 182836 182617 .2596 .2684 < .0001

Note. K = the number of classes; AIC = Akaike’s information criterion; BIC = Bayesian information criterion; saBIC = sample-size-adjusted BIC; LMR = the Lo-Mendell-Rubin test; aLMR = adjusted LMR test; BLRT = the bootstrap likelihood ratio test. Values for the LMR, aLMR, and BLRT columns are the p-values of the test. “—” indicates that the test was not applicable for LGM because technically there was one class or one homogeneous sample with LGM and we could not compare the fit of 1-class and 0-class model. Variances of linear and quadratic slopes were constrained to be zero in SO-GMMs with K=2 or more.

We further checked the interpretability of the four-class solution by examining the estimated growth trajectories across classes (Figure 2). Specifically, we extracted the estimated factor scores of life satisfaction at each time point and standardized the factor scores by creating Z-scores. The high-stable class (55%) had very high intercept and individuals’ life satisfaction remained high over time. Both the linear and quadratic slopes (.78 and −.84, respectively) were statistically significant. The low-stable class (17%) was characterized by a low intercept at baseline and life satisfaction remained low over time. The high-decreasing class (11%) had high intercept, decrease in life satisfaction until the 10-year follow-up, and then increase from the 10-year to 15-year follow-up. By contrast, the low-increasing class (17%) had low intercept, increase until the 10-year follow-up, and then decrease afterwards. Linear and quadratic slopes were both significant, −6.77 and 5.19 for the high-decreasing class and 8.13 and −6.65 for the low-increasing class, respectively.

Figure 2.

Figure 2.

Growth Trajectories of Satisfaction with Life

Latent Class Membership and Covariates

Age, sex, race, employment status, and FIM cognition showed significant relationships with latent class membership (Table 5). That is, a higher proportion of females (19.55%) were assigned to the low-increasing class than males (15.81%). Among racial groups, a smaller proportion of Black individuals (39.50%) belonged to the high-stable class as compared with White (59.59%) – Blacks were more likely to be in any of the other three classes instead. No significant relationships were found for Hispanic and other racial groups when using White as the reference group. Individuals that were unemployed at baseline were less likely to be in the high-stable class (41.92%) than those that were employed (56.96%). Particularly, the unemployed tended to be in the low-stable class. By contrast, more people who identified themselves as students (60.92%) were in the high-stable class than the employed. Individuals in the high-stable class tended to be younger and have higher FIM cognition scores than those in the low-stable and low-increasing classes.

Table 5.

Characterization of Latent Classes with Covariates

Covariates Low-Stable High-Stable High-Decreasing Low-Increasing Test Statistic
Age 20.75a 20.34b 20.39ab 20.80a 7.14(3,3697)**
Sex
 Male 17.34% 55.54% 11.31% 15.81%
 Female 16.13% 54.64% 9.68% 19.55% 8.77(3)*
Race
 White 14.75% 59.59% 9.98% 15.68%
 Black 25.44% 39.50% 14.94% 20.12% 89.60(3)**
 Hispanic 17.70% 55.26% 9.33% 17.70% 1.37(3)
 Other 14.71% 55.88% 11.27% 18.14% .93(3)
Employment Status
 Employed 15.90% 56.96% 10.05% 17.09%
 Unemployed 25.60% 41.92% 12.71% 19.76% 59.79(3)**
 Student 13.15% 60.92% 12.01% 13.92% 19.55(3)**
Pre-Injury Impairment
 No 15.23% 58.24% 9.39% 17.14%
 Yes 6.35% 71.43% 6.35% 15.87% .0002c
Pre-Injury Physical Limitation
 No 15.07% 58.54% 9.38% 17.02%
 Yes 11.67% 61.67% 6.67% 20.00% .0022c
TBI Severity
 Mild 19.90% 49.88% 11.53% 18.69%
 Moderate 19.45% 53.80% 10.64% 16.11% .94(3)
 Severe 16.80% 55.40% 10.40% 17.40% 3.23(3)
FIM Cognition 14.95a 16.04b 15.05ab 14.76a 6.78(3,3727)**

Note. Parentheses are the degrees of freedom associated with the test. For age and FIM cognition, numbers with different subscripts are statistically significant at alpha = .05. For all categorical variables, the first category served as the reference group.

c

Fisher’s Exact test was conducted as an alternative to chi-square test of independence, due to less than five counts in one cell.

*

p < .05;

**

p < .0001.

Discussion

This study demonstrated the use of SO-GMM to analyze longitudinal health outcomes (e.g., life satisfaction) in a large sample of AYAs with TBIs. After testing the longitudinal measurement invariance for the five-item life satisfaction scale, the study found four distinct longitudinal trajectories developed over 15 years after admission: low-stable, high-stable, high-decreasing, and low-increasing. Age, sex, race, employment status, and FIM cognition were found to be significantly associated with trajectory membership. Several contributions of this study are worth noting.

First, this study is the first to apply a rigorous SO-GMM methodology to TBI outcome research. Existing research examining longitudinal TBI outcomes using sophisticated statical modeling techniques such as HLM 47 or GMM 28 have often treated a measurement scale for a latent construct as a single averaged/summed score across all items. Such an approach, despite its commonality, not only resulted in potential loss of information when creating a single composite score out of multiple scale items, but more importantly assumed (without testing) that all items in the Satisfaction with Life Scale contributed equally to the underlying latent construct - life satisfaction - without any measurement error. The SO-GMM approach addressed this critical limitation by rigorously testing the longitudinal measurement invariance and using all measured items directly in the modeling process. Therefore, all growth curve modeling and analyses of covariates were conducted under a statistical framework that satisfied its original assumptions.

Second, this study focused on the long-term life satisfaction among a unique group – AYAs with TBI. As a patient population in a critical transitional period physically and psychologically, AYAs experience rapid changes in personal life and career development hence are particularly vulnerable to the long-term detrimental effects of TBI. For example, research suggested that AYAs with TBI are more likely to report more fatigue and fewer physical activities 48, reduced reading ability 49, and more suicidal attempts7. Moreover, post-TBI rehabilitation may add significant economic and psychological burdens to families and society24,50. However, prior to the present study, long-term life satisfaction research has not sufficiently attended the AYA population with TBI, although existing research in the adult TBI population did suggest patients with various characteristics may develop differentiated trajectories over time, consistent with the current findings 28,47

Third, findings of four distinct long-term trajectories and their associated covariates among AYAs with TBI were consistent with previous research examining life satisfaction among general population with TBI. For example, one recent study examined life satisfaction among 3012 patients with TBI over a five-year follow-up period revealed similar four-group trajectories as the best fitting model 28. It was also consistent with existing literature that certain demographic and baseline clinical characteristics were significantly associated with trajectory membership, such as age, sex, race, and employment status. For instance, previous research has indicated that Black children were less likely to receive medical treatment than those of other racial groups, even after controlling for other socio-demographic characteristics such as age, sex, family income, parental education, and health insurance status 24. Consistent with current findings, such lags in receiving medical care from TBI could lead to negative impact on longterm health outcomes 51. Such findings reinforce the call for more health disparity research among disadvantaged populations. Interestingly though, the present study did not find TBI severity or pre-injury condition (impairment or limitation) as significant predictors of long-term life satisfaction trajectories. Although this finding appears in contrast with existing data from the general TBI population, 52,53 it is not surprising considering this study sample were AYAs who may have greater developmental plasticity (and generally longer time to recover after injury) than those injured at a later developmental stage 54.

Study Limitations

Several important limitations of the present study should also be noted. First, despite the benefits of SO-GMM in considering measurement errors while identifying heterogeneous trajectories, there are unresolved methodological issues in measurement invariance testing that warrant future investigations. In SO-GMM, measurement invariance across classes is needed for valid comparison of growth factors between trajectories; however, it remains unclear how to test invariance across classes when the tasks of testing longitudinal measurement invariance and identifying heterogeneous growth patterns are both present in TBI outcome research. Accordingly, measurement invariance across classes was assumed in this study but future research is needed to identify an optimal approach to testing invariance across classes in conjunction of other tasks in SO-GMM. Second, due to the nature of the TBIMS-NDB database, all patients included in this study sample must be treated at one of the sixteen participating centers, limiting the generalizability of the findings. Third, because the primary goal of this paper is to introduce SO-GMM to the TBI research community, only one outcome and a selection of covariates were analyzed. This by no means a comprehensive or even representative selection. We look forward to hearing from fellow TBI researchers to explore the utility of SO-GMM in other domains in future studies.

Conclusions

This is the first study applying SO-GMM to examine longitudinal rehabilitation outcomes among AYAs with TBI, enabling researchers to utilize all measurement information. Findings of the study could also inform evidence-based design of future rehabilitation programs based on the temporal and individualized characteristics to improve long-term outcomes for this vulnerable population.

Supplementary Material

1

Acknowledgements:

This material has not been presented anywhere at the time of the submission. The Traumatic Brain Injury (TBI) Model Systems National Database is a multicenter study of the TBI Model Systems Centers Program, and is supported by the National Institute on Disability, Independent Living and Rehabilitation Research (NIDILRR), a center within the Administration for Community Living (ACL), Department of Health and Human Services (HHS). However, these contents do not necessarily reflect the opinions or views of the TBI Model Systems Centers, NIDILRR, ACL or HHS. Research reported in this publication was supported by the Eunice Kennedy Shriver National Institute of Child Health and Human Development of the National Institutes of Health under award number R00HD093814. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Abbreviations:

AIC

Akaike’s information criterion

AYA

adolescent and young adult

BIC

Bayesian information criterion

CDC

Centers for Disease Control and Prevention

CFI

comparative fit index

GBTM

group-based trajectory modeling

GCS

Glasgow Coma Scale

GMM

growth mixture modeling

MI

measurement invariance

saBIC

sample-size-adjusted BIC

SO-GMM

second-order growth mixture modeling

SO-LGM

second-order latent growth models

SRMR

standardized root mean square residual

RMSEA

root mean square error of approximation

TBI

traumatic brain injury

TBIMS-NDB

Traumatic Brain Injury Model System National Database

Footnotes

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Conflicts of interest: none

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