Using Individual Growth Curve Models to Predict Recovery and Activities of Daily Living After Spinal Cord Injury: An SCIRehab Project Study

Transcription

1 Archives of Physical Medicine and Rehabilitation journal homepage: Archives of Physical Medicine and Rehabilitation 2013;94(4 Suppl 2):S ORIGINAL ARTICLE Using Individual Growth Curve Models to Predict Recovery and Activities of Daily Living After Spinal Cord Injury: An SCIRehab Project Study Allan J. Kozlowski, PhD, a,b Allen W. Heinemann, PhD a,c From the a Center for Rehabilitation Outcomes Research, Rehabilitation Institute of Chicago, Chicago, IL; b Center for Healthcare Studies, Feinberg Medical School, Northwestern University, Chicago, IL; and c Department of Physical Medicine and Rehabilitation, Feinberg Medical School, Northwestern University, Chicago, IL. Abstract Objective: To evaluate change in functional outcomes over 1 year after spinal cord injury (SCI). Design: Observational longitudinal secondary analysis. Setting: Six rehabilitation facilities participating in the SCIRehab project. Participants: Patients (NZ1146) with SCI enrolled from 2007 to Interventions: Not applicable. Main Outcome s: FIM instrument 13-item and 11-item motor, 3-item transfer, 6-item self-care, 3-item self-care upper-extremity, and 3-item self-care lower-extremity subscores modeled as trajectories of change. Results: Patients were on average 37 years old, non-hispanic white, with high school or higher education, a body mass index of 25, and a Comprehensive Severity Index score of 20. Most were men with paraplegia (37%) or high tetraplegia (27%). Median time frames were 22 days from injury to admission, 46 days from admission to discharge, 407 days from admission to follow-up, and 44 days for rehabilitation length of stay. The motor subscores were higher on admission for paraplegia and American Spinal Injury Association (ASIA) Impairment Scale (AIS) grade D groups, and recovered faster for the AIS grade D group. Lower function at admission was associated with older age, higher Comprehensive Severity Index score, longer length of stay, fewer physical therapy and therapeutic recreation hours, and more occupational therapy hours. Slower recovery rates were associated with older age, more days from injury to admission, and fewer physical therapy hours per week. Conclusions: Longitudinal outcomes modeled as individual trajectories of change are clinically meaningful. Individual growth curve models could facilitate recovery prediction and outcome evaluation at individual and group levels. However, assessment of the effects of treatment on outcome trajectories will require the addition of outcome measures at time points during intervention and may require the use of outcome measures specific to aspects of rehabilitation, such as mobility and self-care. Archives of Physical Medicine and Rehabilitation 2013;94(4 Suppl 2):S ª 2013 by the American Congress of Rehabilitation Medicine The SCIRehab Project has established a prospective comprehensive longitudinal database on patients with spinal cord injury (SCI) and the interventions provided during and after inpatient rehabilitation, and reported on outcomes at discharge and 1 year after injury. 1,2 Admission motor FIM score and more physical therapy (PT) treatment time were associated positively with Supported by the National Institute on Disability and Rehabilitation Research (grant no. H133B090024, H133N110014, and H133A060103). No commercial party having a direct financial interest in the results of the research supporting this article has or will confer a benefit on the authors or on any organization with which the authors are associated. discharge and 1-year motor FIM scores. However age, body mass index (BMI), longer length of stay (LOS), longer time from injury to admission, and more occupational therapy (OT) treatment time were negatively associated with motor FIM scores at discharge but not at 1-year anniversary. 2 These results suggest that some associations between relevant characteristics and functional outcomes change over time. Project studies have also examined associations between patient, injury, and treatment characteristics and LOS, 3 treatment time in PT, 4 OT, 5 and therapeutic recreation (TR). 6 Admission FIM scores were variably associated with time spent in all PT 4 and /13/$36 - see front matter ª 2013 by the American Congress of Rehabilitation Medicine

2 FIM individual growth models in SCIRehab some OT activities, 5 but were not associated with activities of daily living or transfer activities for OT 5 or any of the TR activities examined. 5 Similarly, clinician experience was variably associated with time spent in PT and OT activities, 4,5 and was negatively associated with TR activities. 6 However, these studies have not described the patterns of functional recovery after SCI or the patient, injury, or associations between treatment characteristics, such as time in therapy or clinician experience and patterns of recovery. Understanding normative patterns of recovery from SCI is a necessary guide to predicting, monitoring, and evaluating recovery of future patients. Group level outcomes reported at single time points, such as rehabilitation discharge, can neither inform clinicians about the pattern of recovery leading up to that time point nor inform about the recovery for any individual patient. Clinicians would be more able to monitor and evaluate their patients outcomes during rehabilitation if they had access to a predicted recovery curve for each patient adjusted for his or her patient and injury characteristics. Understanding the associations between treatment characteristics and recovery patterns could further facilitate clinical decision-making throughout intervention. The longitudinal nature of the SCIRehab study data provides an opportunity to examine associations between relevant characteristics and functional outcomes as events that evolve over time. A variant of hierarchical linear modeling, 7 known as individual growth curve (IGC) modeling, 7,8 provides a means to examine characteristics associated with the parameters of change, such as the admission levels and recovery rates of FIM subscores, simultaneously for individuals and groups. Rather than predicting the outcome at a single point in time, such as discharge, an IGC model constructs trajectories of change for each individual and for the group average simultaneously, based on the individuals scores at each available time point. Trajectories can be modeled as linear trajectories defined by 2 parameters (intercept and slope), as curvilinear trajectories with the addition of quadratic or cubic parameters, or as more complex, nonlinear models. 9,10 The motor FIM scores at admission, discharge, and 1-year anniversary permit modeling of trajectories and examination of associations of relevant characteristics with the average trajectories. For a linear trajectory, the intercept parameter could represent the predicted admission level of function, and the rate of change parameter could represent the average recovery of function per week over the time frame for which outcome measures are available. A quadratic curvilinear trajectory requires 2 rate parameters to define an instantaneous rate of change: the first would represent the average change in outcome per week at baseline (eg, admission) and the second would represent the rate of acceleration or deceleration of the rate of change per week. The FIM instrument measures burden of care and provides a proxy for physical and cognitive functioning in rehabilitation List of abbreviations: AIS ASIA Impairment Scale BMI body mass index CSI Comprehensive Severity Index IGC individual growth curve LOS length of stay OT occupational therapy PT physical therapy SCI spinal cord injury TR therapeutic recreation settings, which are often reported as total scores or motor and cognitive subscores. 2,11 Reporting clinically meaningful subsets of FIM items, such as mobility 12,13 and self-care subscores, 13 may provide more information on the effects of interventions provided by specific disciplines. For instance, modeling OT treatment characteristics with FIM self-care subscores may disclose associations that are not apparent on the motor FIM subscore. Little is known about the trajectories of recovery for components of functioning, such as mobility and self-care, or how treatment characteristics, such as hours of PT, OT, or TR per week, are associated with those trajectories. The objectives of this article are to describe the trajectories of functional recovery for 4 SCI level and completeness categories over 1 year on FIM motor subscores and clinically meaningful subsets of mobility and self-care; to examine the associations of patient, injury, and treatment factors with functional status at admission and recovery rate over the first year postinjury; and to develop a model for predicting individual recovery curves. Methods Participants and facilities S155 SCIRehab is a practice-based evidence project implemented at 6 rehabilitation facilities: Craig Hospital (Englewood, CO; the lead site), Shepherd Center (Atlanta, GA), Rehabilitation Institute of Chicago (Chicago, IL), Carolinas Rehabilitation (Charlotte, NC), Mount Sinai Medical Center (New York, NY), and MedStar National Rehabilitation Hospital (Washington, DC). Each facility obtained institutional review board approval for the study and acquired signed consent from their participants, parents, or guardians. Consented patients 12 years of age who were admitted for initial rehabilitation after traumatic SCI from November 2007 through February 2012 were enrolled. Data were collected from 1376 persons with SCI at admission to and discharge from the facility, and at approximately 1 year postinjury. This analysis used a subset of 1146 cases that had complete FIM data for all 3 time points. Patient characteristics included in the analyses were age at time of injury, sex, race/ethnicity, level of education at time of injury, marital status, and BMI at admission. Race/ethnicity was dichotomized as white non-hispanic compared with others because of the small representation of black, Hispanic, Asian, and other groups. Education was categorized as less than high school or greater than high school in comparison with high school or equivalent. Injury was categorized using the International Standards for Neurological Classification of SCI 14 by grouping neurologic level and completeness of SCI into 4 distinct and functionally homogenous categories for analyses, consistent with previous studies. 2,4-6,15 Patients with American Spinal Injury Association (ASIA) Impairment Scale (AIS) grades A, B, and C were grouped by motor level as C1-4 or high tetraplegia, C5-8 or low tetraplegia, and T1 and lower or paraplegia, and all patients with AIS grade D were grouped together. Injury groups were modeled as dummy variables as comparisons of low tetraplegia, paraplegia, and AIS grade D compared with the high tetraplegia group. Comorbidity and complication severity were measured by the Comprehensive Severity Index (CSI). 16 Treatment characteristics included time from injury to rehabilitation admission, LOS (days from admission to discharge less treatment interruptions), treatment hours per week provided by PT, OT, and TR, 4-6 and clinician experience index for PT, OT, and TR. 4-6 The clinician

3 S156 A.J. Kozlowski, A.W. Heinemann Table 1 FIM instrument motor items and subscore components FIM Motor-13 Items* 13-Item Motor 11-Item Motor 3-Item Transfer 6-Item Self-Care 3-Item Self-Care Upper Stairs U U Transfer to tub/shower U U U Toileting U U U U Transfer to toilet U U U Walk/wheelchair y U U Dress lower body U U U U Transfer to bed/chair/wheelchair U U U Bathe U U U U Dress upper body U U U U Groom U U U U Eat U U U U Walk/wheelchair y U U Bladder management U Bowel management U 3-Item Self-Care Lower * Items are ordered from more difficult to less difficult, except for bladder and bowel items. y Walk/wheelchair is represented as 1 item on the FIM instrument, but the mobility activities of walking and wheeling represent different measures of motor functioning and therefore were represented separately. experience index is a measure of education and years of experience in SCI rehabilitation. Facilities were coded anonymously as letters A through F. FIM subscores The FIM is a measure of independence with 18 physical and cognitive functioning items rated by trained clinicians 17,18 at admission and discharge and by self-report 19 via telephone or inperson interview at follow-up. The resulting scores are ordinal; thus, scaling was used to estimate item difficulties, person abilities, and the underlying interval-level metric of the constructs of physical and cognitive functioning. The analysis was reported by Whiteneck and Gassaway 20 in this supplement. Outcome measures are the 0 to 100 point -scaled FIM 13-item motor, 11-item motor (without sphincter control items), 3-item transfer, 6-item self-care, 3-item self-care upper-extremity, and 3-item self-care lower-extremity subscores (table 1). We have also included the raw score to measure conversion tables for the 6 FIM subscores as supplemental appendix S1 (available online only at the Archives website: ). We did not model mobility or locomotion subscores, because the walk, wheelchair, and stair items exhibited category inversion in the analysis, which suggests these items did not consistently discriminate person ability for this sample; consequently, the items did not constitute a valid scale for this sample. Analysis We examined the data for differences between included and excluded patients. Patients excluded because of incomplete FIM data differed from those who were included. Excluded patients were on average 3 years older, had lower admission and discharge 11-item motor subscores (15 and 33 points on the transformed scale, respectively), and more often had an unknown education level (22% vs 6%), but they did not differ on other characteristics, including injury group. Descriptive statistics were calculated for patient, injury, and treatment characteristics and FIM subscores at admission, discharge, and 1-year anniversary time points. We examined differences between SCI groups for continuous characteristics with normative distributions using 1-way analysis of variance with Bonferroni post hoc test, and those with skewed distributions were examined using the Kruskal- Wallis test. We examined differences in frequencies of categorical variables using the chi-square test. We used SPSS version 17 statistical software a for all descriptive and inferential statistics and for IGC data preparation. We modeled age, BMI, LOS, treatment hours per week, and the clinician experience ratings as grand-mean-centered characteristics to facilitate interpretation of the admission, rate, and acceleration estimates. The CSI and time from injury to admission were modeled as uncentered characteristics. Uncentered characteristics are interpreted at a value of zero for the reference group, which is not sensible for characteristics, such as age. Grand-meancentering sets the reference value for the characteristic at the mean instead of at zero. We constructed IGC models for each FIM subscore in 6 steps. First we modeled each FIM subscore with each time point as linear group average admission and recovery rate estimates (fixed effects) to determine whether individual patients admission and recovery rate estimates varied from the group averages (random effects). If the individual estimates varied significantly from zero, we added the quadratic parameter, time in weeks squared, to each model in step 2. We retained the quadratic model if it explained more within-person variance than the linear model, which was tested as a significant reduction in the deviance statistic relative to the change in degrees of freedom. 7 We added the injury dummy variables in the third step to examine differences in trajectories for the SCI groups. In the fourth step we generated a set of models for each patient and treatment characteristic to examine their independent associations with the admission, rate, and acceleration estimates, while controlling for injury group. We did not model cubic parameters or examine associations between patient or treatment characteristics and the acceleration parameter to limit the complexity of interpreting the final models. In the fifth step we modeled each subscore with all of the characteristics from step 4 that were significantly associated at

4 FIM individual growth models in SCIRehab alphaz.05 with the admission, rate, or acceleration estimates. In the final step, we revised the multivariate models by excluding characteristics from step 5 that became insignificant in the presence of other characteristics. We used likelihood ratio tests to compare subsequent models for significant differences in explained variance, and retained the most parsimonious model. This model-building approach permits interpretation of the associations of characteristics with admission, rate, and acceleration estimates, and can identify cases where 1 characteristic is modified or suppressed by the presence of other characteristics. We used HLM-7 statistical software b for all IGC analyses with SPSS data files. All models used full maximum likelihood estimation. 7,21 Results Patient, injury, treatment, and outcome characteristics Of the patients with complete FIM data at all time points, 81% were men, 67% were non-hispanic white, 38% were married, and 79% had high school or greater education. The sample had a mean age SD of 3716 years at injury and a mean BMI SD of 256 on admission to rehabilitation (table 2). Patients with paraplegia and low tetraplegia were younger; the low tetraplegia group had more white/non-hispanic persons; the low tetraplegia and paraplegia groups had less education; and CSI score at admission was greatest for the high tetraplegia group. The individual variability in recovery on 11-item motor FIM scores is demonstrated by a 5% random sample of patient response patterns (fig 1). Median milestone times were 22 days from injury to admission, 46 days from admission to discharge, and 407 days from admission to follow-up interview. Times from injury to admission and admission to discharge were shortest for participants in the AIS grade D group and longest for the high tetraplegia group. Substantial variation existed in time from admission to 1-year anniversary; thus, we refer to this time point as follow-up rather than anniversary. Treatment hours per week for PT were lowest for the high tetraplegia group; treatment hours per week for both OT and TR were highest for the low tetraplegia group. The distributions of the PT and OT clinician experience index scores were positively skewed, and the TR distribution was bimodal. The PT experience and OT scores were lowest for the AIS grade D group, and TR scores did not differ by SCI category. Except for the 13- and 11-item FIM subscores for the paraplegia and AIS grade D groups, outcome data distributions at most time points were skewed (table 3). IGC models Missing data for predictor characteristics reduced the number to 1142 cases in the final models (table 4). Quadratic trajectories fit better than linear trajectories for all models, providing 3 curve parameters: the predicted admission FIM subscore (admission estimate), the instantaneous rate of change at admission (rate estimate), and the acceleration of the instantaneous rate of change per week (acceleration estimate). Trajectories differed for SCI groups for all models. No associations were found between the curve parameters and the patient characteristics of sex, race/ ethnicity, education, or marital status. Age at injury was associated with either the admission or rate estimates for the transfer and self-care models and with both estimates for the 13- and 11-item S157 motor subscore models. BMI was negatively associated only with the admission estimate for the transfer subscore model. Injury to admission time frame was consistently associated with the recovery rate estimates and variably with the admission estimates. Facility associations varied across all models. Treatment hours per week were consistent for most of the models; PT hours were positively associated with admission and rate estimates, OT hours were negatively associated with admission estimates, and TR hours per week were positively associated with admission estimates. Only TR clinical experience was associated with the admission estimates for the 13- and 11-item motor subscores, but the magnitude was small. The curve parameter estimates are interpreted from the reference groups, which are defined by the characteristics that were included in each model when set to a value of zero. For example, the reference group for the 11-item motor subscore model describes persons with high tetraplegia, an age of 37 years, a CSI score of zero, zero days from injury to rehabilitation admission, an LOS of 55 days, who received treatment at facility A, which was comprised of 7 PT and 7 OT treatment hours per week, and 3 treatment hours per week from a TR with a clinician experience index of 8. The reference group for the transfer subscore model also has a BMI of 25 but excludes the TR clinician experience index. The interpretation of the additional contributions of each patient or treatment characteristic to the curve parameters depends on whether the characteristic is continuous or categorical, and if continuous, if it was grand-mean centered. For example, on the 11-item motor subscore, persons with paraplegia would have an admission estimate 18 points higher than the reference group s estimate of 13 points. Age at injury was grand-mean centered, and therefore each additional year of age more than the average represents a decrease of the admission estimate by.04. A person of 62 years of age would have a 1-point lower admission estimate. The CSI was not grand-mean centered, and therefore each 1-point increase represents a decrease of.09 points. A person with an average CSI of 20 would have a 2-point lower admission estimate. On the transfer subscore model only, each additional 3 units above the average BMI of 25 represents a decrease of 1 point in transfer ability. The rate and acceleration estimates for the SCI groups are interpreted together as an instantaneous rate of change in subscore per week from admission. For example, the high tetraplegia group will on average gain item motor subscore points in the week after admission, but this rate will decelerate by.02 points for each successive week. The paraplegia group would gain 1.6 points in the first week of treatment but decelerate at a rate of.022 points per week. Patient and treatment characteristics are interpreted as a change in the rate at admission only, because we did not test associations with the acceleration parameter. An individual s functional status can be estimated for any point in time by substituting the values of their patient, injury, and treatment characteristics and adjusting the curve parameters for the desired time frame (supplemental appendix 2). Trajectories can also be represented graphically for individuals or subgroups. We provide depictions of the trajectories for the SCI groups who received 6 or 8 hours of PT per week during intervention on the 11-item motor subscore (fig 2), and for SCI groups with a BMI of 20 and 30 on the transfer model, with all other characteristics equivalent to the reference group (fig 3). We also provide a tool to estimate predicted recovery curves for new patients in the online supplement, for demonstration purposes.

5 Table 2 Characteristic Patient and treatment characteristics by SCI group C1-4 AIS Grades AeC (nz314; 27%) C5-8 AIS Grades AeC (nz229; 20%) Paraplegia AIS Grades AeC (nz422; 37%) All AIS Grade D (nz181; 16%) Total (NZ1146*) Significance Test y P Age (y), mean SD F 3,1142 Z47.3 <.001 Sex, % male c 2 3Z Race/ethnicity, % White non-hispanic Black Hispanic c 2 3Z Asian Other BMI z, mean SD F 3,1142 Z CSI x 26.0, 21.0 (28.0) 20.0, 16.0 (17.0) 18.0, 16.0 (17.0) 14.0, 9.0 (16.0) 20.0, 16.0 (18.0) F 3,1142 Z22.2 <.001 Education, % <High school High school or c 2 6Z equivalent >High school Marital status, % married c 2 3Z13.1 <.001 Injury to admission x 38.0, 29.0 (30.0) 32.0, 25.0 (28.0) 30.0, 20.0 (24.0) 18.0, 13.0 (12.0) 30.0, 22.0 (26.0) c 2 3Z114.1 <.001 Rehabilitation LOS x 73.0, 64.0 (57.0) 67.0, 56.0 (41.0) 44.0, 38.0 (26.0) 33.0, 28.0 (23.0) 55.0, 44.0 (42.0) c 2 3Z262.1 <.001 Admission to discharge x 76.0, 70.0 (58.0) 69.0, 58.0 (44.0) 47.0, 40.0 (29.0) 34.0, 29.0 (24.0) 57.0, 46.0 (44.0) c 2 3Z262.9 <.001 Admission to follow-up x 435.0, 4120 (128.0) 440.0, (113.0) 440.0, (140.0) 452.0, (160.0) 444.0, (134.0) c 2 3Z Treatment hours per week, mean (SD) PT 6.7 (1.8) 7.4 (1.7) 7.8 (2.4) 8.0 (2.0) 7.4 (2.1) F 3,1142 Z23.3 <.001 OT 7.1 (1.6) 7.8 (1.7) 6.3 (2.0) 7.0 (2.0) 6.9 (1.9) F 3,1142 Z35.9 <.001 TR x 2.8, 2.2 (3) 2.5, 2.1 (2.4) 3.3, 2.9 (3.1) 1.9, 1.4 (2.8) 2.8, 2.3 (3.0) c 2 3Z55.6 <.001 Clinician experience index x PT 6.1, 4.0 (6.0) 5.5, 4.0 (5.0) 5.7, 3.9 (7.0) 4.8, 2.9 (5.0) 5.6, 3.8 (6.0) c 2 3Z OT 5.6, 4.4 (4.0) 6.5, 4.6 (4.0) 4.6, 3.2 (3.0) 4.3, 3.1 (4.0) 5.2, 3.9 (4.0) c 2 3Z50.7 <.001 TR 7.9, 2.8 (16.0) 9.2, 3.0 (9.0) 7.2, 2.8 (5.0) 7.2, 2.5 (5.0) 7.8, 2.8 (8.0) c 2 3Z * Marital status (nz1144), race/ethnicity (nz1131), and education (nz1063). y Analysis of variance used for normally distributed continuous data, Kruskal-Wallis used for skewed continuous variables, and chi-square used for categorical variables. z d on admission to rehabilitation. x Skewed distributions reported as mean, median (SD). S158 A.J. Kozlowski, A.W. Heinemann

6 FIM individual growth models in SCIRehab 11-Item Motor FIM Discussion Time from Rehabilitation Admission (weeks) Fig 1 Five percent random sample of SCIRehab project motor FIM individual responses. This study describes improvement in physical functioning over the year after admission to rehabilitation for persons with SCI on 6 FIM subscores using IGC models. Models revealed different average admission, recovery rate, and acceleration estimates for SCI injury groups on the 13- and 11-item motor subscores and on transfer and self-care subscores. Patient characteristics of sex, race/ethnicity, education level, and marital status were not S159 associated with curve parameters. Treatment hours per week were associated with the admission and rate estimates for PT and the admission estimate for OT and TR. These models provide a basis for evaluating change in function over time for individuals and groups of patients represented in the SCIRehab project, and a basis from which individual prediction models could be developed. The 13- and 11-item motor subscores provide trajectories of recovery of physical functioning for 4 injury groups during the year after admission to rehabilitation, controlling for patient and treatment characteristics. These models relate to clinical practice in 2 ways that standard regression models often do not. First, aggregate scores are often reported for the FIM motor and cognitive subscores for system- and facility-level interpretation Such models represent outcomes at a specific point in time, which do not represent individual-level variability. Indices such as FIM gain scores do not account for the within-person correlations between admission and discharge time points, and indices such as the FIM efficiency scores reduce change over time to a linear slope estimate. The IGC models explicitly account for time, providing a more precise estimate for an individual at any point along the trajectory by adjusting the growth parameters (eg, admission, rate, and acceleration estimates) for the associated characteristics at the individual level, and by accounting for correlations within individuals between time points 7 and individual differences in distributions of time points. Consequently, an individual trajectory will more adequately represent an individual patient s outcome than a group-averaged estimate, and the group-average trajectories will more adequately represent change over time for the group. Second, individual predictions for new patients can be generated Table 3 FIM FIM subscores* by SCI group C1-4 AIS Grades AeC (nz314) C5-8 AIS Grades AeC (nz229) Paraplegia AIS Grades AeC (nz422) All AIS Grade D (nz181) Total (NZ1146) 13-item motor Admission y 5, 0 (14) 13, 16 (20) 27, 27 (5) 25, 27 (11) 18, 21 (28) Discharge 25, 23 (11) 33, 32 (11) 44, 44 (8) 47, 47 (11) 37, 39 (19) Follow-up 29, 23 (17) 41, 37 (22) 54, 53 (12) 70, 66 (32) 47, 47 (29) 11-item motor Admission y 10, 0 (9) 12, 15 (19) 27, 27 (6) 23, 25 (12) 17, 20 (27) Discharge 24, 22 (10) 32, 31 (12) 45, 45 (9) 47, 48 (13) 37, 39 (20) Follow-up 28, 21 (18) 41, 37 (24) 54, 55 (9) 71, 69 (32) 47, 49 (28) 3-item transfer Admission y 1, 0 (0) 1, 0 (0) 9, 0 (15) 17, 15 (26) 6, 0 (9) Discharge 11, 0 (19) 20, 19 (34) 47, 45 (32) 58, 66 (21) 34, 34 (55) Follow-up 22, 0 (34) 42, 34 (73) 76, 80 (34) 84, 100 (34) 56, 66 (100) 6-item self-care Admission y 6, 0 (12) 18, 20 (31) 44, 44 (9) 31, 36 (29) 26, 32 (44) Discharge 27, 30 (43) 48, 48 (14) 65, 65 (13) 62, 61 (13) 51, 56 (24) Follow-up 33, 30 (51) 59, 52 (28) 84, 100 (32) 84, 100 (32) 65, 68 (55) 3-item self-care upper Admission y 8, 0 (15) 22, 24 (38) 59, 59 (16) 37, 41 (41) 34, 38 (56) Discharge 34, 36 (53) 60, 59 (20) 89, 100 (24) 72, 70 (26) 65, 70 (39) Follow-up 39, 38 (66) 72, 70 (44) 95, 100 (0) 89, 100 (24) 74, 100 (47) 3-item self-care lower Admission y 1, 0 (0) 3, 0 (0) 18, 14 (29) 20, 23 (34) 11, 0 (23) Discharge 15, 0 (25) 34, 34 (24) 58, 56 (17) 59, 60 (15) 42, 47 (37) Follow-up 23, 0 (40) 46, 40 (64) 81, 100 (34) 84, 100 (34) 59, 66 (77) * All FIM scores are for 0 to 100 point -scaled data and are reported as mean, median (SD). y Admission represents day 0 for all IGC models

7 S160 A.J. Kozlowski, A.W. Heinemann Table 4 IGC models FIM Estimates (NZ1142) Predictor 13-Item Motor 11-Item Motor 3-Item Transfer 6-Item Self-Care 3-Item Self-Care Upper 3-Item Self-Care Lower C1-4 AIS grades AeC (reference) Admission * * 6.500* * * * Rate at admission 1.400* 1.400* 0.900* 1.200* 1.200* 1.000* Acceleration of rate 0.020* 0.020* 0.008* 0.010* 0.009* 0.009* C5-8 AIS grades AeC Admission y 7.300* 6.900* NA * * 6.500* Rate at admission z NA NA 0.500* 0.400* 0.500* 0.800* Acceleration of rate x NA NA jj { { 0.008* Paraplegia AIS grades AeC Admission y * * * * * * Rate at admission z NA jj 2.000* 0.400* NA 1.700* Acceleration of rate x NA jj 0.020* { NA 0.020* All levels AIS grade D Admission y * * * * * * Rate at admission z NA 1.000* 2.400* 1.100* 0.700* 1.900* Acceleration of rate x NA 0.010* 0.030* 0.010* 0.009* 0.020* Age at injury (per year) Admission y jj { NA NA jj NA Rate at admission z jj jj 0.004* jj NA 0.004* CSI at admission (per point) Admission y 0.090* 0.090* 0.090* 0.100* 0.100* 0.100* Rate at admission z NA NA BMI (per point) Admission y NA NA 0.300* NA NA NA Rate at admission z NA NA NA NA NA NA Injury to admission (per day) Admission y NA NA { NA jj NA Rate at admission z 0.003* 0.003* 0.005* 0.003* 0.002* 0.005* LOS (per day) Admission y 0.100* 0.100* 0.060* { 0.100* 0.100* Rate at admission z NA NA NA NA NA NA Facility B Admission y NA NA NA 7.600* * { Rate at admission z NA jj NA NA NA NA C Admission y NA NA NA NA NA NA Rate at admission z NA NA jj NA NA jj D Admission y NA NA NA { { jj Rate at admission z jj { NA NA NA jj E Admission y NA NA NA jj 7.800* NA Rate at admission z NA NA NA NA 0.200* NA F Admission y NA NA NA 5.000* NA 7.000* Rate at admission z 0.100* 0.090* 0.300* 0.200* NA 0.300* Treatment (h/wk) PT Admission y 0.500* 0.440* 1.200* 0.800* 0.800* 0.700* Rate at admission jj jj 0.040* { jj 0.030* OT Admission y 0.600* 0.700* 1.200* 0.900* 0.900* 1.100* Rate at admission z NA NA NA NA NA NA (continued on next page)

8 FIM individual growth models in SCIRehab S161 Table 4 (continued) FIM Estimates (NZ1142) Predictor 13-Item Motor 11-Item Motor 3-Item Transfer 6-Item Self-Care 3-Item Self-Care Upper 3-Item Self-Care Lower TR Admission y { { NA { { jj Rate at admission z NA NA NA NA NA NA Clinical experience (per point) TR Admission y { 0.100* NA NA NA NA Rate at admission z NA NA NA NA NA NA Abbreviation: NA, not applicable. * P<.001. y Additional contribution to the reference group intercept parameter estimate of FIM subscore at rehabilitation admission. z Additional contribution to the reference group instantaneous rate of change at admission parameter estimate of change in FIM subscore per week. x Additional contribution to the reference group acceleration of the instantaneous rate of change parameter estimate in FIM subscore per week. jj P<.05. { P<.01. by substituting the values of an individual s characteristics into the IGC model equations to estimate the new patient s trajectory. Predicting aspects of recovery can assist in decision-making on nature and duration of intervention and on discharge disposition. Prediction models in SCI rehabilitation focus on point in time outcomes of discharge or follow-up at times up to 1 year postinjury. A clinical prediction rule for early prognosis of ambulation outcomes uses age, 2 motor scores, and 2 sensory scores to predict independent, dependent, and nonwalkers at 1 year postinjury. 25 A recent systematic review found age, admission FIM scores, and a host of other factors to be predictive of FIM scores at follow-up times ranging from 4 months to 1 year. 26 However, these forms of prediction may be of limited utility to clinicians. Clinical prediction rules can facilitate initial treatment planning by predicting a distal outcome; however, they may not be sensitive to change over time. Systematic reviews enhance evidence for group level outcomes but do not represent any individual level outcomes, and neither form of prediction can provide clinicians with estimates of individual level function for any point in time during intervention. IGC models can be used to generate predicted recovery curves for new patients, because the individual trajectories represent the average for all patients with that specific set of characteristics. While predicted curves will not describe the actual path of recovery for any patient, IGC model-based predictions offer clinicians more precise estimates than those available from research studies that examine group differences for 2 reasons. First, a predicted score can be estimated for any specific time point on the trajectory, whereas group estimates are typically defined as occurring at a specific time point, such as discharge. Second, IGC models retain the individual differences of all characteristics of the patients included in the model rather than reducing these differences to group averages. Consequently, predictions would improve as more patient data become available and by comparing actual outcomes with the predicted curves. Supplemental appendix S2 (available online only at the Archives website: ) provides an example of how to estimate a recovery in functional status at a point on a curve. Constructing separate subscores for clinically meaningful components of functioning could yield more informative associations between functional outcome trajectories and treatment characteristics. However, this clinical utility comes at a cost. We found evidence of a ceiling effect for the AIS grade D group on the transfer subscore, whose average level of function reached 100 points at about 35 weeks (see fig 3). The 13- and 11-item motor subscores are more suitable for modeling AIS grade D recovery, because they include the more difficult items of walking and stairs. We found few notable differences in the patterns of associations of the treatment characteristics for the transfer and selfcare subscore models. The unique association between BMI and 11-Item Motor FIM score Time from Rehabilitation Admisson (Weeks) High Tetraplegia, 6 PT Hrs/Wk High Tetraplegia, 8 PT Hrs/Wk LowTetraplegia, 6 PT Hrs/Wk LowTetraplegia, 8 PT Hrs/Wk Paraplegia, 6 PT Hrs/Wk Paraplegia, 8 PT Hrs/Wk AIS-D, 6 PT Hrs/Wk AIS-D, 8 PT Hrs/Wk Transfer FIM Time from Rehabilitation Admission (Weeks) High Tetraplegia, BMI = 20 High Tetraplegia, BMI = 30 LowTetraplegia, BMI = 20 LowTetraplegia, BMI = 30 Paraplegia, BMI = 20 Paraplegia, BMI = 30 AIS-D, BMI = 20 AIS-D, BMI = 30 Fig 2 Average trajectories for SCI groups by PT hours per week. Fig 3 Average trajectories for SCI groups by BMI.

9 S162 the admission estimate for the transfer subscore model may reflect the upper body function required to move one s body mass with little or no contribution from the lower extremities. The unique positive association between TR clinician experience and the admission estimates for the 13- and 11-item motor subscore models may reflect differences in TR decision-making related to higher levels of activity such as ability to walk or manage stairs, because these items are not represented in the other subscores. However, the magnitude of this association was small and may represent an artifact of the bimodal distribution or a chance finding. TR intervention tends to relate more to participation, 6 and the clinician experience index may not be an indicator of skill or decision-making. The transfer and self-care subscores may not be good measures of specific professional interventions. The lack of unique associations between OT hours of treatment per week and the self-care subscore model estimates may indicate a lack of sensitivity of FIM items to detect, or lack of specificity of the OT hours per week variable to depict, the OT-specific contributions to recovery of self-care functioning. Specific measures of upper- and lower-extremity functioning that are more directly related to PT, TR, and OT interventions may yield better models of disciplinary contributions to recovery of functioning. The associations between treatment hours per week and the admission and rate estimates were consistent across the models. PT hours per week were associated with the higher functioning at admission and with faster recovery, while OT hours were associated only with lower scores at admission. Patients who begin rehabilitation with higher levels of functioning may tolerate higher intensity or longer duration of strengthening and endurance exercise and mobility-specific activities provided by PT, and consequently exhibit faster recovery rates. Conversely, persons with tetraplegia will spend more time in OT activities, and will on average regain less function at slower rates than persons in the paraplegia or AIS grade D groups. For stroke rehabilitation inpatients, therapy hours did not differ by level of impairment on admission or between OT and PT disciplines but did vary by type of activity, 27 and earlier initiation and higher intensity activities were associated with better discharge outcomes. 28 While average outcome trajectories may well vary between conditions, such as SCI and stroke, individual trajectories within a diagnostic group probably vary based on complex interactions of the patient and injury characteristics with the nature and timing of treatment characteristics. While IGC models can accommodate time-varying characteristics, our models are not sufficiently sophisticated to examine such variations in treatment characteristics because of the lack of time points between admission and discharge and the lack of specificity of the variation of treatment hours by discipline across the intervention. Our results were consistent with associations reported in other SCIRehab studies for PTand OT total treatment hours and discharge motor FIM scores 2 and with admission motor FIM scores and hours of OT therapeutic activities per week. 5 Although our results appear contrary to the association between admission motor FIM scores and hours of PT transfer training per week, 4 our models included PT hours per week for all activities, which may be distributed according to patient need and ability. For example, persons with lower levels of functioning are likely to spend more time in transfer and self-care training than persons with higher levels of functioning. Differences between SCIRehab study results and prior publications may indicate that relations among treatment characteristics are more complex than were modeled here. Treatment characteristics could exhibit mediation and suppression effects, which would require analytic methods, such as structural equation modeling, to assess, and other evidence-based practice projects to validate. Of the subscores modeled, the 13- and 11-item motor subscore results compare with a previous IGC study of data from the SCI Model Systems National Database. Warschausky et al 15 fit a nonlinear model estimating recovery rate on the 13-item motor FIM subscore to a plateau, but did not estimate admission scores because of collinearity between the admission and plateau estimates. Their models, which extended 10 years postinjury, included sex, age, LOS, education, and injury group characteristics for 142 cases. Sex and LOS were associated with the recovery rate, and age, injury group, and LOS were associated with the plateau in their pooled sample model. Higher education was also associated with faster recovery rate for the high tetraplegia group. 15 The comparable associations in our models are age and LOS with the admission estimate, given collinearity of their admission and plateau estimates. The differences in characteristic associations are likely because of the differences in model specification; they were able to model more sophisticated trajectories because of the availability of 4 time points over longer postrehabilitation time frames, while we were able to model more patient and treatment characteristics for more cases over a shorter time frame, and we did not model the SCI groups independent of one another. Study limitations A.J. Kozlowski, A.W. Heinemann Only cases with scores and dates for all 3 time points were included, and included cases differed from the excluded cases on some characteristics. Three time point data permitted fitting of quadratic curvilinear trajectories; however, functional recovery for SCIRehab participants may be better characterized as a nonlinear rapid rise to plateau sometime between discharge and followup. 10,15 Additional time points between rehabilitation admission and discharge are required to construct more informative models. Characteristics, such as age, CSI, and treatment hours per week, which can change over time, were modeled as constant at the time of injury or admission. Modeling these as time-varying characteristics may provide more accurate results. The FIM instrument is a measure of burden of care and serves as a proxy for physical and cognitive functioning, but may lack the sensitivity and specificity needed to detect profession-specific contributions or other treatment effects to components of functioning, such as mobility or self-care. The FIM instrument was administered at follow-up by self-report, which may have contributed error to the results. 19 The extent to which the admission and recovery rate estimates might be biased by floor and ceiling effects is unknown. SCIRehab data are not representative of the nation; thus, results are not generalizable beyond the participating facilities. Although we reported facility differences, these represent either individual- or facilitylevel characteristics that have not been modeled, rather than true differences in facility outcomes. Facility was included as a between-person characteristic but would be more suitably modeled as a set of relevant facility-level characteristic variables in a 3-level hierarchical model of change over time within patients and patients nested within facilities. Our variable definitions or the FIM instrument may not be sufficiently sensitive to changes associated with the unique contributions of PT, OT, TR, and other disciplines to recovery from SCI. We may not have outcome data corresponding to the specific time frames in which OT intervention has its greatest effect, and a measure of participation may be more suited to examining the effect of TR intervention. Our prediction models have not been validated.

10 FIM individual growth models in SCIRehab Conclusions This study helps open the black box of SCI rehabilitation by examining treatment characteristics. Modeling recovery as individual and average group trajectories permits the interpretation of outcome as an evolving event rather than the state at a single time point. While we found associations between PT, OT, and TR treatment hours per week and the trajectories of recovery of groups of persons with SCI, our models are not sufficiently sophisticated to parse out the unique professional contributions to specific components of functioning, such as ability to transfer or manage self-care. Modeling individual trajectories will facilitate the development of prognostic tools to support clinical and administrative planning, and may provide a basis to examine disparities, effectiveness of clinical interventions, and other aspects of rehabilitation. However, these advances will require measures that are more sensitive to change associated with specific intervention strategies and data collected at multiple time points where most of the change occurs. Future studies should accommodate IGC methods where change over time within individuals is a factor of importance, specifically by gathering data at additional time points and by modeling facility-level characteristics. Suppliers a. IBM Corp, 1 New Orchard Rd, Armonk, New York, NY b. Scientific Software International Inc, 7383 N Lincoln Ave, Ste 100, Lincolnwood, IL c. Excel 2007 Spread-sheet software; Microsoft, One Microsoft Way, Redmond WA Keywords Longitudinal studies; Rehabilitation; Spinal cord injuries; Treatment outcome Corresponding author Allan J. Kozlowski, PhD, Rehabilitation Institute of Chicago, 345 E Ontario St, Chicago, IL address: akozlowski@ric.org. Acknowledgments We thank Gale G. Whiteneck, PhD, FACRM and Marcel P. Dijkers, PhD, FACRM, for their contributions to the revisions of this article, Christopher R. Pretz, PhD for revisions to the individual growth models, and Rita K. Bode, PhD for providing the FIM conversion tables. References 1. Whiteneck G, Gassaway J, Dijkers M, Jha A. New approach to study the contents and outcomes of spinal cord injury rehabilitation: the SCIRehab Project. J Spinal Cord Med 2009;32: Backus D, Gassaway J, Smout RJ, et al. Relation between inpatient and postdischarge services and outcomes 1 year postinjury in people with traumatic spinal cord injury. Arch Phys Med Rehabil 2013; 94(4 Suppl 2):S S Whiteneck G, Gassaway J, Dijkers M, et al. The SCIRehab project: treatment time spent in SCI rehabilitation. Inpatient treatment time across disciplines in spinal cord injury rehabilitation. J Spinal Cord Med 2011;34: Taylor-Schroeder S, LaBarbera J, McDowell S, et al. The SCIRehab project: treatment time spent in SCI rehabilitation. 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