Traumatic Brain Injury and Depression: A Survival Analysis Study in R (Part 10)
March 10, 2025
Research
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Introduction
Welcome back to our series exploring the factors that influence survival after a traumatic brain injury (TBI). Previously, we examined our Cox model's assumptions, ensuring its reliability. Now, we're ready for the main event: interpreting the results of our nested Cox regression analysis. We'll dissect what the models tell us about the risk of death within 5 years following an initial interview (Year 1) conducted after a moderate-to-severe TBI. Remember, each model builds upon the last, progressively adding layers of information to refine our understanding of mortality in this population.
Why Nested Models?
Nested models are like a set of Russian dolls. Each doll contains a smaller, simpler version within it. Similarly, each of our models contains the previous one, with additional variables added in each step. This allows us to see how the influence of each factor changes as we account for more information. It's a powerful way to tease apart complex relationships.
The Language of Survival: Hazard Ratios
Before we dive in, let's refresh our memory on the key output of Cox regression: the hazard ratio (HR). It's a measure of how a particular factor affects the hazard, or risk, of death within our 5-year window:
HR > 1: The factor increases the risk of death within 5 years. An HR of 1.50 means a 50% higher risk.
HR < 1: The factor decreases the risk of death within 5 years (making survival beyond 5 years more likely). An HR of 0.75 means a 25% lower risk.
HR = 1: The factor has no effect on the risk of death within 5 years.
We'll also be looking at 95% confidence intervals (CIs) and p-values to gauge the precision and statistical significance of our HRs.
5.10 Interpreting the Nested Cox Regression Models
This section presents a nested Cox regression analysis aimed at identifying key factors influencing 5-year mortality after traumatic brain injury (TBI), providing insights for improving clinical care. The analysis revealed that Major Depression at one year post-injury, after initially appearing non-significant, became a strong predictor of mortality when sociodemographic factors were considered (HR 1.71, p = 0.007). However, this association was reduced when functional status was accounted for, highlighting the interplay between mental health and functional recovery. As expected, older age consistently predicted increased mortality risk (HR 1.06, p < 0.001) across all models. Medicaid status also emerged as a potential marker for increased mortality risk (HR 1.60, p = 0.042 when adjusted for mental health history), although this association was attenuated after accounting for functional status, suggesting that disparities in function may mediate this relationship. Importantly, better functional status at one year post-injury was significantly associated with a reduced risk of death (HR 0.87, p = 0.049). These results highlight the importance of addressing major depression, promoting functional recovery, and considering socioeconomic factors in post-TBI care to improve long-term survival. The nested modeling approach demonstrates the power of iterative analysis in revealing the sophisticated array of factors influencing mortality after TBI.
5.10 Interpreting the Nested Cox Regression Models
Introduction
This study uses a "nested" approach, meaning that we start with a basic model (Model 1) and progressively add more variables to see how they influence the risk and affect the relationships observed in earlier models. Let's examine what each model reveals about the factors influencing death within 5 years post-injury, keeping in mind that our outcome is mortality:
Model 1: The Starting Point - Depression and 5-Year Mortality
Model 1 is our simplest model. It only examines the relationship between depression level at year 1 (categorized as "No Depression," "Minor Depression," or "Major Depression") and the hazard of death within 5 years post-TBI.
Depression's Initial Signal: In this basic model, neither Minor nor Major Depression appear to be significantly associated with an increased risk of death within 5 years (p > 0.05). The HRs are close to 1, and the p-values are not statistically significant. This suggests that, considered on its own, depression level at year 1 might not be a strong predictor of 5-year mortality in this population.
Model 2: Adding Social Context - Sociodemographic Factors
Model 2 adds a layer of complexity by incorporating sociodemographic factors: age at injury, sex, educational attainment, and Medicaid status. These factors can influence access to resources and healthcare, potentially impacting survival.
Major Depression's Emergence as a Risk Factor: Now, the picture changes. Major Depression at year 1 is associated with a significantly increased hazard of death within 5 years (HR = 1.71, p = 0.007). Individuals with Major Depression are estimated to have a 71% higher risk of dying within 5 years compared to those with No Depression, after adjusting for age, sex, education, and Medicaid status. Minor Depression remains non-significant.
Age: A Consistent Predictor of Mortality: Age at injury is a significant predictor of 5-year mortality (HR 1.06, p < 0.001). Each additional year of age increases the hazard of death by 6%. This aligns with the general understanding that older individuals may have a harder time recovering from injuries and are more susceptible to health complications.
Medicaid: A Potential Indicator of Risk: Being on Medicaid shows a trend toward an increased risk of death within 5 years (HR 1.53, p = 0.062), although it's not statistically significant at the conventional 0.05 level in this model. This suggests that factors associated with being on Medicaid (e.g., lower socioeconomic status, limited access to care) might contribute to mortality risk.
Sex and Education: In this model, sex and education level do not appear to be significant predictors of 5-year mortality.
Model 3: Mental Health History
Model 3 expands our investigation by including the individuals' mental health history: mental health treatment, history of suicide attempts, and problematic substance use at the time of injury.
Major Depression: A Consistent Threat: The link between major depression and an increased risk of death within 5 years remains significant (HR 1.62, p = 0.018). This reinforces major depression as a key risk factor for mortality in this population, even after accounting for a more detailed mental health history.
Medicaid: A Significant Risk Factor: Medicaid status is now significantly associated with an increased risk of death within 5 years (HR 1.60, p = 0.042). This suggests that, after accounting for mental health history, those on Medicaid have a 60% higher risk of mortality within the study time frame.
Other Mental Health Factors: The other mental health factors (treatment history, suicide attempt history, and substance use) don't show significant associations with 5-year mortality in this model.
Model 4: The Role of Function - Physical Ability and its Impact on Survival
Model 4 introduces a critical element: functional status at year 1, measured by the Function Factor Score quintiles. This tells us how well someone is functioning in their daily life after the injury, reflecting their physical and cognitive abilities.
Depression, Function, and Mortality: The association between Major Depression and the hazard of death weakens slightly and loses statistical significance (HR 1.43, p = 0.094) after accounting for functional status. This suggests that an individual's functional ability might partially explain the link between Major Depression and the risk of death. Those with Major Depression who maintain higher function might have a lower mortality risk.
Age: A Consistent Predictor: Age remains a highly significant predictor of 5-year mortality (HR 1.06, p < 0.001).
Medicaid and Function: Similar to Major Depression, Medicaid status is no longer statistically significant (p = 0.068) when functional status is included in the model. This further supports the idea that functional status might be a key factor underlying the increased mortality risks associated with both Major Depression and Medicaid status.
The Protective Power of Function: Higher functional status (better functioning) is significantly associated with a lower hazard of death within 5 years (HR 0.87, p = 0.049). This underscores the crucial role of rehabilitation and interventions that help people regain function after an injury, as it can be a strong protective factor against mortality.
Key Takeaways: Implications for Survival
Major Depression: A Serious Concern: Major Depression at year 1 is consistently associated with an increased risk of death within 5 years, especially when we consider social factors and mental health history. However, functional ability might partially mitigate this risk.
Age: A Dominant Factor in Mortality: Age is a strong and consistent predictor of 5-year mortality across all models, highlighting the increased vulnerability of older individuals after TBI.
Function: A Protective Force: Functional status is a critical factor. Better functioning is protective against death within 5 years, and it might explain some of the mortality risks associated with Major Depression and Medicaid status.
Medicaid: A Marker of Potential Disparities: While its effect is attenuated in Model 4, Medicaid status is associated with increased mortality in earlier models. This highlights potential socioeconomic disparities in survival after injury and warrants further investigation.
Holistic Care is Crucial: These findings underscore the need for a comprehensive approach to care after TBI. Addressing mental health (particularly major depression), promoting functional recovery through rehabilitation, and considering social factors are all essential for improving survival rates.
Thresholds:
1-5: Generally considered acceptable.
>5: Suggests multicollinearity that warrants attention.
>10: Indicates severe multicollinearity requiring corrective action (e.g., removing or transforming variables).
The Power of Nested Models
Our journey through these nested models has allowed us to peel back the layers of complexity, revealing how different factors interact to influence the risk of death within 5 years after an injury. This step-by-step approach provides a more nuanced understanding of mortality risks and highlights the value of considering a wide range of factors when designing interventions and providing care.
Moving Forward
This analysis provides valuable insights into the factors that contribute to mortality after injury. These findings can inform targeted interventions, such as early screening and treatment for major depression, comprehensive rehabilitation programs to enhance functional recovery, and policies to address socioeconomic disparities in healthcare access. By continuing to investigate these complex relationships, we can work towards improving long-term outcomes and enhancing the quality of life for individuals recovering from TBIs.
Conclusion
In this final installment of our series exploring survival after TBI, we dove into the intricate web of factors influencing 5-year mortality using a powerful tool: nested Cox regression models. By progressively adding layers of information—from sociodemographic factors to mental health history and functional status—we've gained a more nuanced understanding of the risks and protective factors at play. Let's recap the key insights that have emerged from this journey:
The Intertwined Fates of Depression, Function, and Survival: Our analysis revealed a compelling narrative about the role of major depression in post-TBI mortality. While initially appearing insignificant, major depression at year 1 emerged as a potent risk factor once we accounted for social context. However, the story didn't end there. When we factored in functional status, the impact of major depression diminished, suggesting that the ability to function in daily life may partially offset the risks associated with depression. This highlights the crucial interplay between mental and physical health in shaping long-term survival.
Age and the Inescapable March of Time: As expected, age proved to be a steadfast predictor of mortality across all models. Each additional year of age at the time of injury conferred a 6% increase in the hazard of death within 5 years. This underscores the heightened vulnerability of older individuals after TBI and the need for age-appropriate interventions.
Function as a Beacon of Hope: Perhaps the most encouraging finding was the strong protective effect of functional status. Higher functional ability at year 1 was significantly associated with a reduced risk of death, highlighting the power of rehabilitation and interventions aimed at restoring physical and cognitive function. This provides a clear mandate for prioritizing functional recovery in post-TBI care.
Socioeconomic Disparities: A Call to Action: The association between Medicaid status and increased mortality in earlier models—although weakened after adjusting for function—hints at the potential impact of socioeconomic disparities on survival. This finding warrants further investigation and underscores the need to address systemic barriers to care that may disadvantage vulnerable populations.
The Power of Holistic Care: Taken together, these findings paint a clear picture: a holistic approach to post-TBI care is paramount. Early identification and treatment of major depression, aggressive rehabilitation programs to maximize functional recovery, and proactive measures to mitigate the impact of social determinants of health are all essential components of a strategy to improve long-term survival.
The Value of the Nested Approach: The nested modeling approach proved invaluable in this analysis, allowing us to disentangle the intricate relationships between our predictors and mortality. By progressively building upon each model, we were able to identify how the influence of certain factors shifted as new information was introduced.
Looking Ahead
This study provides a roadmap for targeted interventions and future research. By focusing on the modifiable risk factors identified here—particularly depression and functional limitations—and addressing the potential influence of socioeconomic disparities, we can strive to improve not only survival rates but also the quality of life for individuals living with the long-term consequences of TBI. The journey toward better outcomes after TBI is complex, but with continued research and a commitment to comprehensive care, we can make significant strides in improving the lives of those affected by this challenging condition.
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