Measures

DTI

FA Trajectory

Model

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts. We find that model with random slope leads to a boundary singular fit. Therefore, we go with the intercept model only (i.e., 1 | Tract)

 

mixed.model_linear <- lmer(FA ~ WeeksSinceTBI_z + HeadMotion_z + (1 | Tract), data = df)

 

mixed.model_quadratic <- lmer(FA ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (1 | Tract), data = df)

 

Which model is better?

Model Comparison Metric Linear Model Quadratic Model Interpretation
AIC (BIC) -1569.0 (-1551.8) -157 1.7 (-1550.9) Change i n AIC_Q is only marginally better (less than 3 units relative to AIC_L), suggesting only marginal support.
Anova p-value=0.03155* Anova model comparison => quadratic model significantly different from linear model at alpha=0.05

Note however that when we try to generate confidence intervals with mixed.model_quadratic, we get a model convergence error. Reverting to a mixed.model_linear also does not help-same model convergence error. Therefore, the simplest model appears to be a simple multiple linear regression model. ))

Confidence Intervals of Multiple Linear Regression Model Generated by Bootstrapping (n=1000)

2.5 % 97.5 %
(Intercept) 0.4782230 0.4870496
WeeksSinceTBI_z -0.0074849 0.0041866
HeadMotion_z -0.0075645 0.0045093

Plot

FA across Tracts

  • This plot illustrates the predicted FA across different values of time since TBI, accounting for both linear and quadratic effects and adjusting for random effects of Tract (i.e., holding random effects constant, focusing on the relationship between weeks since TBI with FA, in isolation).
FA across Specific Tracts
Forceps Major

AD Trajectory

Model

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts. We find that model with random slope leads to a boundary singular fit. Therefore, we go with the intercept model only (i.e., 1 | Tract)

 

mixed.model_linear <- lmer(AD ~ WeeksSinceTBI_z + HeadMotion_z + (1 | Tract), data = df)

 

mixed.model_quadratic <- lmer(AD ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (1 | Tract), data = df)

 

Which model is better?

Model Comparison Metric Linear Model Quadratic Model Interpretation
AIC (BIC) -4799.6 (-4782.4) - 4799.8 (-4779.0) Negligible change in AIC_Q. Keep linear model.
Anova p-value=0.1425 N o significant different between linear and quadratic models. Keep linear model.

Confidence Intervals of Mixed Linear Model Generated by Bootstrapping (n=1000)

2.5 % 97.5 %
.sig01 0.0000421 0.0000854
.sigma 0.0000057 0.0000070
(Intercept) 0.0007466 0.0008033
WeeksSinceTBI_z -0.0000016 0.0000006
HeadMotion_z -0.0000001 0.0000022

Plot

AD across Tracts

This plot illustrates the predicted AD across different values of time since TBI, adjusting for head motion as well as the variance attributed to different tract intercepts (i.e., holding effects due to head motion and random tract intercepts constant, and focusing on the relationship between weeks since TBI with AD, in isolation).

AD across Specific Tracts
Forceps Major

RD Trajectory

Model

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts. We find that model with random slope leads to a boundary singular fit. Therefore, we go with the intercept model only (i.e., 1 | Tract)

 

mixed.model_linear <- lmer(RD ~ WeeksSinceTBI_z + HeadMotion_z + (1 | Tract), data = df)

 

mixed.model_quadratic <- lmer(RD ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (1 | Tract), data = df)

 

Which model is better?

Model Comparison Metric Linear Model Quadratic Model Interpretation
AIC (BIC) -5014.5 (-4997.3) - 5017.8 (-4997.1) AIC_Q is only marginally better than AIC_L (3 units). Quadratic model has weak support.
Anova p-value=0.02198 * Quadratic fit is significantly different from linear fit.
conf_int(nsim=1000) Model convergences. Convergence Error Only linear model is stable.

Confidence Intervals of Mixed Linear Model Generated by Bootstrapping (n=1000)

2.5 % 97.5 %
.sig01 0.0000202 0.0000405
.sigma 0.0000037 0.0000045
(Intercept) 0.0003315 0.0003583
WeeksSinceTBI_z 0.0000003 0.0000018
HeadMotion_z 0.0000007 0.0000021

Plot

RD across Tracts

This plot illustrates the predicted RD across different values of time since TBI, adjusting for head motion as well as the variance attributed to different tract intercepts (i.e., holding effects due to head motion and random tract intercepts constant, and focusing on the relationship between weeks since TBI with RD, in isolation).

RD across Specific Tracts
Forceps Major

MD Trajectory

Model

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts. We find that model with random slope leads to a boundary singular fit. Therefore, we go with the intercept model only (i.e., 1 | Tract)

 

mixed.model_linear <- lmer(MD ~ WeeksSinceTBI_z + HeadMotion_z + (1 | Tract), data = df)

 

mixed.model_quadratic <- lmer(MD ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (1 | Tract), data = df)

 

Which model is better?

Model Comparison Metric Linear Model Quadratic Model Interpretation
AIC (BIC) -5124 (-5106.7) -5123 (-5102.3) Quadratic model has very weak support (AIC difference is less than 3 units). Keep linear model.
Anova p-value=0.3177. Keep linear model.
conf_int M odel is stable. Not considered.

Confidence Intervals of Mixed Linear Model Generated by Bootstrapping (n=1000)

2.5 % 97.5 %
.sig01 0.0000244 0.0000482
.sigma 0.0000028 0.0000034
(Intercept) 0.0004723 0.0005044
WeeksSinceTBI_z 0.0000000 0.0000010
HeadMotion_z 0.0000007 0.0000019

Plot

MD across Tracts

This plot illustrates the predicted MD across different values of time since TBI, adjusting for head motion as well as the variance attributed to different tract intercepts (i.e., holding effects due to head motion and random tract intercepts constant, and focusing on the relationship between weeks since TBI with MD, in isolation).

MD across Specific Tracts
Forceps Major

Cognitive

Trajectory

Antisaccade

Linear

Quadratic

Go-No-Go

Linear

Quadratic

Number-Symbol

Linear

Quadratic

Mediation Models

Mediation model with linear effects of Weeks Since Injury on RT is NOT significant.

Emotion

Trajectory

Depression

Model Comparison Metric Linear Model Quadratic Model Interpretation
AIC 650.9361 642.2746 Moderate support for Quadratic model (AIC_Q is about 9 units less than AIC_L).
Anova p-value=0.001185 ** Anova model comparison => quadratic model significantly different from linear model at alpha=0.05

 

We consider a quadratic effect to better model the relationship between depression and Weeks Since Injury following TBI.

Linear

Quadratic

Anxiety

Model Comparison Metric Linear Model Quadratic Model Interpretation
AIC 641.7314 524.4498 Strong support for Quadratic model (AIC_Q >> AIC_L, more than 10 units).
Anova p-value< 2.2e-16 *** Anova model comparison => quadratic model significantly different from linear model at alpha=0.05

 

We consider a quadratic effect to better model the relationship between anxiety and Weeks Since Injury following TBI.

Linear

Quadratic

Mediation Models

Depression

FA and RD do not mediate the relationship between Weeks Since Injury and Depression for any tract.

Anxiety

FA and RD do not mediate the relationship between Weeks Since Injury and Anxiety for any tract.