SAR-2023-016-BH

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Time-adjusted effect of socioeconomic status in mortality rates after brain injury: cohort study

Document version

Version Alterations
01 Initial version

Abbreviations

Context

This analysis expands on a previous analysis with a similar objective (SAR-2023-004-BH-v02), by employing more flexible modeling strategies to include time-dependent covariates that were dropped from the previous analysis. In the process the raw FIM scores were substituted by their quartiles.

Objectives

To determine the effect of socioeconomic status of the neighborhood on mortality of patients with brain injury, accounting for time-dependent covariates.

Methods

The data procedures, design and analysis methods used in this report are fully described in the annex document SAP-2023-016-BH-v01.

This analysis was performed using statistical software R version 4.3.0.

Results

Study population and follow up

There initially were 76,665 observations on 19,303 study participants considered for inclusion. After excluding follow up measurements during the COVID-19 pandemic to mitigate confounding on mortality causes there were 69,440 observations left in the study sample. After applying the inclusion criteria for the study period between 2010-01-01 and 2018-12-31 and considering the status at the last available follow up time for each individual a total of 7,414 participants were included in the analysis.

The epidemiological profile of the participant included in the study was a male participant (417 (74%)) with an average (SD) age of 43 (20) years.

Races were not homogeneously available in the study population with 315 (56%) individuals being white; 288 (52%) were single (never married) at the time of injury, and most participants were well educated with 208 (38%) at greater than high school level. A total of 334 (60%) were employed and 287 (53%) participants lived in an urban area.

Table: Table 1 Epidemiological, demographic and clinical characteristics of study participants at the time of discharge.

Characteristic N = 564
SES quintiles, n (%)  
Prosperous 69 (15%)
Comfortable 88 (19%)
Mid-Tier 97 (21%)
At-Risk 119 (26%)
Distressed 91 (20%)
Missing 100
Sex:, n (%)  
Male 417 (74%)
Female 146 (26%)
Missing 1
What is your race?, n (%)  
White 315 (56%)
Black 97 (17%)
Hispanic 120 (21%)
Other 30 (5.3%)
Missing 2
What is your marital status?, n (%)  
Single (Never Married) 288 (52%)
Married 153 (27%)
Divorced 65 (12%)
Separated 20 (3.6%)
Widowed 31 (5.5%)
Other 2 (0.4%)
Missing 5
Age at Injury, Mean (SD) 43 (20)
Missing 2
Substance Problem Use, n (%) 228 (43%)
Missing 33
Education, n (%)  
Greater Than High School 208 (38%)
Less Than High School 142 (26%)
High School/GED 204 (37%)
Missing 10
At time of injury, what was your employment status?, n (%)  
Employed 334 (60%)
Unemployed 76 (14%)
Other 146 (26%)
Missing 8
Urbanization based on zip code of address at discharge., n (%)  
Suburban 145 (27%)
Rural 107 (20%)
Urban 287 (53%)
Missing 25
Prior to this injury, has a physician ever told you that you have a seizure disorder?, n (%) 7 (6.0%)
Missing 447
Spinal cord injury:, n (%) 22 (3.9%)
Missing 4
Cause of injury:, n (%)  
Vehicular 266 (48%)
Violence 59 (11%)
Falls 171 (31%)
Other 64 (11%)
Missing 4
Primary rehabilitation payor:, n (%)  
Private Insurance 237 (42%)
Public Insurance 235 (42%)
Other 90 (16%)
Missing 2
Residence after rehab discharge:, n (%)  
Private Residence 441 (80%)
Other 112 (20%)
Missing 11
Days From Injury to Rehab Discharge, Mean (SD) 41 (28)
FIM Motor at Discharge quartiles, n (%)  
Q1 110 (20%)
Q2 150 (27%)
Q3 139 (25%)
Q4 150 (27%)
Missing 15
FIM Cognitive at Discharge quartiles, n (%)  
Q1 143 (26%)
Q2 143 (26%)
Q3 120 (22%)
Q4 149 (27%)
Missing 9

The observed overall mortality was 13.5% in the study period. The distribution of cases appear homogeneous across SES quintiles (Figure 1), ranging from 10.6% to 13.5%. We will test the effect of SES quintiles on the hazard rate in the next section. See also Figure A2 in the appendix for the distribution of sexes in each SES quintile in the study population.

**Figure 1** Proportion of cases per SES quintiles.

**Figure 1** Proportion of cases per SES quintiles.

Time-adjusted effect of SES on mortality

Following the findings of SAR-2023-017-BH-v01 the multiple observations per individual should be favored where the time-varying SES exposure allows the full model specification in this analytical plan to be used. This analysis, however includes an additional model with interactions between the two FIM scores and the exposure that renders those findings obsolete, given that with this new specification all terms satisfy the proportional hazards assumption. This is the model that will be described in this section.

The previous seizure disorder diagnosis was missing for most of the study population and was not included in the model as a covariate to preserve study power. After excluding participants with missing data from other variables a total of 5,754 complete cases were available for analysis. The cause of injury was removed from the model due to violations of the proportional hazards assumption (see section 8.2.1.1.3 in the appendix).

The survival curves of both sexes by SES quintiles can be seen in Figure 2. Overall, the distressed neighborhoods appear to have a lower survival probability then other neighborhoods. This appears to be true for both sexes, and males had a higher risk of dying than females in all neighborhoods. This plot was cropped at 50% survival for presentation purposes, see Figure A3 in the appendix for an uncropped version.

**Figure 2** Survival of participants, by sex and by SES quintiles.

**Figure 2** Survival of participants, by sex and by SES quintiles.

The effect of SES of the neighborhood to which the individuals were discharged was associated with mortality and it was modified by the FIM Motor at Discharge quartiles (Table 2). No level of FIM motor function appears to be protective, but participants with the highest functional scores (within the fourth quartile) had a significant increased risk of dying in all neighborhoods, compared to the prosperous neighborhoods.

Table: Table 2 Effect of SES on mortality; HR estimates were adjusted for sex, race, age, education, employment status, residence after rehab discharge, urbanization, rehabilitation payer, spinal cord injury, substance abuse, days from injury to rehab, FIM scores quartiles and interactions between FIM scores and the exposure.

Characteristic HR 95% CI p-value
SES quintiles      
Prosperous — —  
Comfortable 0.81 0.53 to 1.24 0.328
Mid-Tier 0.69 0.43 to 1.11 0.125
At-Risk 0.84 0.54 to 1.31 0.440
Distressed 1.07 0.71 to 1.62 0.742
SES quintiles * FIM Motor at Discharge quartiles      
Comfortable * Q2 1.56 0.86 to 2.83 0.147
Mid-Tier * Q2 1.41 0.74 to 2.71 0.296
At-Risk * Q2 1.22 0.68 to 2.21 0.504
Distressed * Q2 1.00 0.55 to 1.82 0.998
Comfortable * Q3 1.06 0.52 to 2.17 0.880
Mid-Tier * Q3 1.15 0.56 to 2.39 0.702
At-Risk * Q3 1.09 0.54 to 2.21 0.802
Distressed * Q3 1.05 0.54 to 2.04 0.880
Comfortable * Q4 5.22 2.09 to 13.0 <0.001
Mid-Tier * Q4 3.60 1.38 to 9.43 0.009
At-Risk * Q4 3.43 1.35 to 8.71 0.009
Distressed * Q4 5.14 2.07 to 12.7 <0.001
SES quintiles * FIM Cognitive at Discharge quartiles      
Comfortable * Q2 0.93 0.49 to 1.76 0.826
Mid-Tier * Q2 1.19 0.60 to 2.33 0.617
At-Risk * Q2 0.82 0.44 to 1.56 0.549
Distressed * Q2 0.76 0.41 to 1.41 0.379
Comfortable * Q3 0.78 0.38 to 1.59 0.497
Mid-Tier * Q3 2.04 0.98 to 4.25 0.056
At-Risk * Q3 1.25 0.64 to 2.45 0.516
Distressed * Q3 1.01 0.51 to 1.98 0.979
Comfortable * Q4 0.73 0.34 to 1.54 0.406
Mid-Tier * Q4 0.87 0.38 to 2.01 0.742
At-Risk * Q4 1.81 0.85 to 3.84 0.125
Distressed * Q4 0.89 0.42 to 1.91 0.773

Additionally it appears that the risk of dying associated with the DCI in neighborhoods has a “U-shape”, where “comfortable” and “distressed” locations show a higher incidence than both “mid-tier” and “at-risk” locations. This might indicate a more complex non-linear relationship between SES and FIM scores that could be evaluated in future studies.

Observations and Limitations

Recommended reporting guideline

The adoption of the EQUATOR network (http://www.equator-network.org/) reporting guidelines have seen increasing adoption by scientific journals. All observational studies are recommended to be reported following the STROBE guideline (von Elm et al, 2014).

Conclusions

The epidemiological profile of the study participant is a 31 years old white male, that has greater than high school level of education, is actively employed and lives in an urban setting.

After controlling for demographic, geographical, clinical variables and FIM scores SES is associated with an increased incidence of mortality when participants also have higher levels of motor function. This association holds regardless of what neighborhood participants were discharged to.

References

Appendix

Exploratory data analysis

**Figure A1** Distribution of age in the study population.

**Figure A1** Distribution of age in the study population.

**Figure A2** Distribution of SES in the study population.

**Figure A2** Distribution of SES in the study population.

**Figure A3** Alternative version of figure 2.

**Figure A3** Alternative version of figure 2.

Modeling strategy

Approaches to control for time-dependent covariates

Before location/SES imputation

Imputation was done in a separate analysis and is described in the report SAR-2023-017-v01.

Schoenfeld and Martingale residuals
**Figure A4** caption

**Figure A4** caption

**Figure A5** caption

**Figure A5** caption

Notes:

Martingale residuals of covariates against the null model
**Figure A6** caption

**Figure A6** caption

**Figure A7** caption

**Figure A7** caption

Notes:

Stratification by cause of injury
**Figure A8** caption

**Figure A8** caption

**Figure A9** caption

**Figure A9** caption

Notes:

Time split
**Figure A10** caption

**Figure A10** caption

Notes:

Non-linear fitting
**Figure A11** caption

**Figure A11** caption

**Figure A12** caption

**Figure A12** caption

Notes:

Interaction with time
**Figure A13** caption

**Figure A13** caption

Notes:

FIM scores quartiles
**Figure A14** caption

**Figure A14** caption

Notes:

Best model specification

**Figure A15** caption

**Figure A15** caption

Notes:

After location/SES imputation

Schoenfeld test

Table: Table A1 P-values of the Schoenfeld test for all 6 models.

term model1 model2 model3 model4 model5 model6
exposure 0.069 0.7 0.7 0.6 0.5 0.6
GLOBAL 0.069 0.3 0.4 0.7 0.3 0.3
SexF NA 0.048 0.11 0.2 0.2 0.12
Race NA 0.12 0.13 0.2 0.3 0.3
AGE NA 0.14 0.3 0.5 0.8 0.9
EDUCATION NA >0.9 >0.9 0.9 >0.9 >0.9
EMPLOYMENT NA 0.067 0.095 0.2 0.3 0.3
ResDis NA NA 0.2 0.3 0.4 0.5
RURALdc NA NA 0.2 0.3 0.4 0.3
RehabPay1 NA NA NA 0.5 0.6 0.6
SCI NA NA NA 0.4 0.2 0.14
PROBLEMUse NA NA NA 0.4 0.4 0.4
DAYStoREHABdc NA NA NA 0.2 0.055 0.077
FIMMOTD4 NA NA NA NA 0.047 0.12
FIMCOGD4 NA NA NA NA 0.2 0.2
exposure:FIMMOTD4 NA NA NA NA NA 0.091
exposure:FIMCOGD4 NA NA NA NA NA 0.3

Final model specification

Table: Table A2 Alternative version of Table 2, showing the coefficients from all covariates included in all 6 models.

Characteristic HR (SE) HR (SE) HR (SE) HR (SE) HR (SE) HR (SE)
SES quintiles            
Prosperous — — — — — —
Comfortable 1.18 (0.118) 1.07 (0.118) 0.98 (0.121) 0.98 (0.121) 0.98 (0.121) 0.81 (0.218)
Mid-Tier 1.00 (0.125) 1.17 (0.127) 1.14 (0.130) 1.13 (0.130) 1.09 (0.130) 0.69 (0.244)
At-Risk 1.29* (0.120) 1.31* (0.122) 1.20 (0.125) 1.18 (0.126) 1.12 (0.126) 0.84 (0.226)
Distressed 1.35** (0.116) 1.38** (0.124) 1.33* (0.127) 1.31* (0.127) 1.21 (0.128) 1.07 (0.211)
Sex:            
Male   — — — — —
Female   0.64*** (0.088) 0.65*** (0.088) 0.68*** (0.089) 0.70*** (0.089) 0.70*** (0.090)
What is your race?            
White   — — — — —
Black   0.83 (0.117) 0.81 (0.119) 0.81 (0.119) 0.81 (0.120) 0.81 (0.120)
Hispanic   0.64** (0.162) 0.61** (0.167) 0.61** (0.168) 0.59** (0.168) 0.56*** (0.169)
Other   0.73 (0.206) 0.73 (0.207) 0.72 (0.207) 0.71 (0.208) 0.68 (0.210)
Age at Injury   1.04*** (0.002) 1.04*** (0.002) 1.04*** (0.003) 1.04*** (0.003) 1.04*** (0.003)
Education            
Greater Than High School   — — — — —
Less Than High School   1.21 (0.114) 1.25 (0.114) 1.23 (0.115) 1.17 (0.116) 1.21 (0.117)
High School/GED   1.39*** (0.087) 1.39*** (0.088) 1.36*** (0.088) 1.36*** (0.088) 1.34*** (0.089)
At time of injury, what was your employment status?            
Employed   — — — — —
Unemployed   2.23*** (0.136) 2.13*** (0.137) 1.82*** (0.142) 1.76*** (0.142) 1.79*** (0.143)
Other   2.22*** (0.100) 2.18*** (0.100) 2.03*** (0.105) 1.83*** (0.106) 1.85*** (0.107)
Residence after rehab discharge:            
Private Residence     — — — —
Other     1.77*** (0.083) 1.70*** (0.085) 1.44*** (0.089) 1.41*** (0.089)
Urbanization based on zip code of address at discharge.            
Suburban     — — — —
Rural     1.00 (0.115) 1.01 (0.116) 1.04 (0.116) 1.02 (0.117)
Urban     1.14 (0.096) 1.09 (0.096) 1.14 (0.096) 1.16 (0.097)
Primary rehabilitation payor:            
Private Insurance       — — —
Public Insurance       1.40*** (0.095) 1.37*** (0.095) 1.38*** (0.095)
Other       1.16 (0.185) 1.10 (0.185) 1.09 (0.186)
Spinal cord injury:       1.22 (0.175) 1.30 (0.176) 1.27 (0.178)
Substance Problem Use       1.23* (0.093) 1.28** (0.094) 1.30** (0.095)
Days From Injury to Rehab Discharge       1.00* (0.001) 1.00 (0.001) 1.00 (0.001)
FIM Motor at Discharge quartiles            
Q1         — —
Q2         0.67*** (0.102) 0.55** (0.217)
Q3         0.65*** (0.122) 0.60* (0.248)
Q4         0.55*** (0.144) 0.17*** (0.379)
FIM Cognitive at Discharge quartiles            
Q1         — —
Q2         0.84 (0.105) 0.92 (0.221)
Q3         0.82 (0.111) 0.73 (0.255)
Q4         0.65*** (0.128) 0.67 (0.275)
SES quintiles * FIM Motor at Discharge quartiles            
Comfortable * Q2           1.56 (0.305)
Mid-Tier * Q2           1.41 (0.332)
At-Risk * Q2           1.22 (0.302)
Distressed * Q2           1.00 (0.305)
Comfortable * Q3           1.06 (0.367)
Mid-Tier * Q3           1.15 (0.372)
At-Risk * Q3           1.09 (0.359)
Distressed * Q3           1.05 (0.339)
Comfortable * Q4           5.22*** (0.467)
Mid-Tier * Q4           3.60** (0.491)
At-Risk * Q4           3.43** (0.475)
Distressed * Q4           5.14*** (0.463)
SES quintiles * FIM Cognitive at Discharge quartiles            
Comfortable * Q2           0.93 (0.324)
Mid-Tier * Q2           1.19 (0.344)
At-Risk * Q2           0.82 (0.324)
Distressed * Q2           0.76 (0.315)
Comfortable * Q3           0.78 (0.363)
Mid-Tier * Q3           2.04 (0.374)
At-Risk * Q3           1.25 (0.343)
Distressed * Q3           1.01 (0.343)
Comfortable * Q4           0.73 (0.383)
Mid-Tier * Q4           0.87 (0.428)
At-Risk * Q4           1.81 (0.385)
Distressed * Q4           0.89 (0.386)

Availability

All documents from this consultation were included in the consultant’s Portfolio.

The portfolio is available at:

https://philsf-biostat.github.io/SAR-2023-016-BH/

Associated analyses

This analysis is part of a larger project and is supported by other analyses, linked below.

Effect of socioeconomic status in mortality rates after brain injury: cohort study

https://philsf-biostat.github.io/SAR-2023-004-BH/

Sensitivity of mortality rates to the imputation of missing socioeconomic data: cohort study

https://philsf-biostat.github.io/SAR-2023-017-BH/

Analytical dataset

Table A3 shows the structure of the analytical dataset.

id exposure outcome Time SexF Race Mar AGE PROBLEMUse EDUCATION EMPLOYMENT RURALdc PriorSeiz SCI Cause RehabPay1 ResDis DAYStoREHABdc FIMMOTD FIMCOGD FollowUpPeriod FIMMOTD4 FIMCOGD4
1                                            
2                                            
3                                            
…                                            
N                                            

Table: Table A3 Analytical dataset structure

Due to confidentiality the data-set used in this analysis cannot be shared online in the public version of this report.