The TBIMS NDB is a multicenter prospective longitudinal study of TBI outcomes funded by the National Institute on Disability, Independent Living, and Rehabilitation Research (NIDILRR, formerly NIDRR) within the Agency on Community Living in Health and Human Services. Further information about the database, measures, and study protocols can be found at www.tbindsc.org. Individuals are enrolled in the TBIMS NDB if they have sustained a TBI as defined by at least 1 of the following characteristics: Glasgow Coma Scale score <13 on emergency admission (not because of intubation, sedation, or intoxication), loss of consciousness >30 minutes (not because of sedation or intoxication), posttraumatic amnesia >24 hours, or trauma-related intracranial abnormality on neuroimaging. All TBIMS NDB participants are age 16 or older at the time of injury, receive medical care in a TBIMS-affiliated trauma center within 72 hours of injury, are transferred to an affiliated inpatient TBI rehabilitation program, and provide informed consent or consent by legal proxy to participate. Participants or their proxies complete a brief assessment protocol during inpatient rehabilitation and are followed prospectively (1, 2, and 5 years post-injury and every 5 years thereafter) with a standardized follow-up assessment protocol.

The first part of the current study uses a cross sectional cohort design to describe the rates and most common reasons for rehospitalization among TBI survivors at four different points in time: 1, 2, 5, and 10 years post-injury. The second part of this study uses a longitudinal cohort design to describe the probability of rehospitalization over time using GLMM and IGC analysis (further discussion of these methods can be found in Kozlowski et al, 2013¹⁹ and Pretz et al, 2014²⁰). The use of both cross-sectional and longitudinal approaches in this project allows us to evaluate rehospitalization after TBI in complementary ways: we first characterize the rates and reasons for rehospitalization at four distinct time points, and then evaluate the factors that explain variability in risk for rehospitalization at the individual level over time.

All data analyses were performed using SAS 9.4 or SPSS 19.0.^22,23 First, we used descriptive statistics (percentages) to characterize the most common reasons for rehospitalization among TBI survivors at 1, 2, 5 and 10 years post-injury, and by calendar year between 2004–2014. Next, we employed a two-step process to illustrate the risk of being rehospitalized (for any reason, dichotomized as yes/no) longitudinally over time. The first step involved fitting a random intercept logistic generalized linear mixed model to generate logit based individual level temporal profiles. Only covariates that demonstrated a relationship with the outcome (p-value level of less than 0.05) were retained in the reduced model. A logit based profile was created for each individual in the database, and these profiles essentially serve as the data which are subsequently fit by way of random effects modeling i.e. IGC analysis in the second step. In the second step, we considered various unconditional models (models free of covariates) to determine which model optimally associates outcome (estimated logits) with time;²⁴ we used AIC values to determine the best-fitting model which we then used to fit the data. We describe this longitudinal model by calculating estimates for the intercept, linear term, and quadratic term (i.e. growth parameters), and we explain variability across individuals by introducing covariates in a conditioned model and associations between the covariates and growth parameters were estimated. To enhance interpretably of the conditional model, all continuous covariates were centered about their respective means.¹⁹ The growth parameter estimates were transformed from logits to probabilities to enhance interpretability. To illustrate the complex relationships between growth parameters and covariates presented, we posted an interactive tool that encapsulates this information and reconfigures it into a user friendly visual format on the NDSC website (https://www.tbindsc.org/Researchers.aspx).

The cross-sectional analyses reported below include all participants who were interviewed at each time point (1 year (n=7503), 2 years (n=6656), 5 years (n=5443), or 10 years (n=2598) post-injury) between 1/1/2004 and 10/1/2015). As seen in Table 1, individuals who are rehospitalized are more likely to be unemployed, on Medicare/Medicaid, and have lower education. Longitudinal analyses require at least three (not necessarily consecutive) three temporal measures to fit a model which, in combination with missing covariate values, reduces the number of participants in the longitudinal analyses to 2377. Accordingly, the samples included in the cross sectional and longitudinal analyses differ slightly in their composition. Participants included in the longitudinal models were younger (mean (standard deviation) 37.7 (17.0) versus 42.9 (20.1) years of age), performed higher on the FIM^™ (67.6 (18.3) versus 65.3 (18.1)), and had longer duration of post-traumatic amnesia (PTA; 24.8 (23.0) versus 22.8 (21.3) days) compared to individuals who were included in cross-sectional analyses. The results of the longitudinal analyses are likely not representative of individuals who die soon after injury or who were recently added to the database.

We calculated the proportion of the sample that reported having been rehospitalized at each follow-up and found that 27.8% of participants were rehospitalized at year 1, 23.0% at year 2, 22.1% at year 5 and 23.4% at year 10.

Reasons for rehospitalization change slightly over time since injury. The data presented in Table 2 reflect the proportion of total rehospitalizations attributable to each reason category, not proportion of people rehospitalized; a single individual may have been rehospitalized more than once. Orthopedic and reconstructive surgeries account for the majority of (17.1%) of rehospitalizations in Year 1, which is unsurprising given that this category includes cranioplasty and other follow-up procedures to address concomitant injuries that are commonly addressed after acute and postacute TBI care needs have been addressed. The General Health category accounts for the largest proportion of rehospitalizations by Year 2 (18.7%) and this proportion increases in the later years post-injury (21.9% at Year 5 and 23.7% at Year 10). Seizures continue to be the 4^th or 5^th most common reason for rehospitalization in Years 2, 5, and 10. Psychiatric conditions are the only reason for rehospitalization that increases in absolute numbers after Year 1 and also accounts for a greater proportion of total rehospitalizations in Years 2, 5, and 10 compared to Year 1.

We also examined rates of rehospitalization by calendar year. Figure 1 displays rates of rehospitalization reported at follow-up between the years 2004–2014 by follow-up time point (1, 2, 5 and 10 years post-injury). Rates of rehospitalization have remained rather stable over this 10 year period.

The first step in evaluating rehospitalization risk over time was to generate logit based individual level temporal profiles using a random intercept generalized linear mixed model. These profiles were estimated using a reduced model (presented in Table 3) which we built by removing covariates in which type III sums of squares analysis indicates a p-value level of less than 0.05.. As seen in Table 3, we adopted the customary approach of retaining the main effects in the model when the main effect was included in a significant interaction term.

The logit based individual profiles are represented by black lines in Figure 2.

In the next step, we used the individual profiles generated in the first step to fit a random effects (i.e., IGC) model. To do this we evaluated various unconditional models and determined that a quadrating model best fit the data, as indicated by AIC value.²⁴ The estimates for the growth parameters for the quadratic model (intercept, linear term, and quadratic term) are reported in Table 4.

To illustrate the group mean trajectory, in Figure 2 we have overlaid upon the individual profiles (black dashed-lines) a white curve which represents the trajectory associated with these growth. It is clear that considerable variability exists around that group mean trajectory, and to explain some of this variability across individuals we built a conditioned model (see Table 5) which included the covariates listed above. We estimated the associations between the covariates and growth parameters; covariates covariates that demonstrated significant relationships with the growth parameters and that had significant interactions with time are displayed in Table 5.

The estimates in Table 5 are given in terms of logits, though these were subsequently transformed into probabilities to enhance interpretability. The growth parameters and covariate associations were able to be estimated with considerable accuracy, as reflected by the narrow width of the 95% confidence intervals.

Due to the complex system of relationships between growth parameters and covariates presented in Table 5, we created an interactive tool that encapsulates this information and reconfigures it into a user friendly visual format. The interactive tool generates individual-level trajectories based on both logits and probability of re-hospitalization for specified covariate values. The interactive tool is provided on the NDSC website (https://www.tbindsc.org/Researchers.aspx).

To illustrate the impact of demographic and injury information on risk (probability) for rehospitalization over time, a case example is provided. In Figure 3, the average trajectory of risk for the longitudinal sample is contrasted with the risk trajectory for individuals who were Black Hispanic female, aged 70 years, unemployed prior to injury, received insurance coverage through Medicare or Medicaid, were discharged to an institutional setting (as opposed to home) after inpatient rehabilitation, had a Cognitive FIM score of 16 and Motor FIM score of 35 at rehabilitation discharge, and whose rehabilitation length of stay lasted 40 days. As seen in Figure 3, individuals with this combination of characteristics differ markedly in rehospitalization risk from the group mean. Their risk for rehospitalization is higher at the intercept, and risk increases over time with most marked increase in risk starting at around 5 years post-injury. This example illustrates only one of countless trajectories of individual level change with regard to probability of re-hospitalization. We encourage readers to enter any plausible combination of covariate values into the interactive tool to investigate how individual and injury characteristics produce different trajectories of risk over time.