Hypo/HAAF Analysis
Julie Wisch
October 3, 2018
All analysis was completed using the dataset that Aaron processed. It contains 31 individuals, 17 are healthy controls and 14 are type 1 diabetics. Aaron processed all individuals that were scanned on or before 8/15/2018. He rejected any session that had an FD < 0.5 (basically - there was too much movement artifact to have many frames to analyze). I analyzed the rest of the data.
Notes on data-cleaning: I filtered out all measurements that were more than 2 standard deviations away from the mean.
This led to some obviously questionable values being dropped, including negative values . Now the lowest blood flow included in the analysis is 32.34 (in the Thalamus) and the largest blood flow is 124.73 (also in the thalamus). 61 out of 1344 values were dropped (~5%).
After dropping these values, I eliminated any session that had more than 2 rejected measurements. (As an example, BOLD-42 had 4 values that were deemed outliers in the previous step at Glucose Level 65. So I dropped BOLD-42’s measurements at 65 for the analysis. I retained BOLD-42’s measurements at 55 and 45 because they were reasonable.) I had to drop 8 sessions in total, including the baseline for BOLD-05, so that individual will have to be excluded from some of the analysis.
Large Region Analysis
Is there a difference for controls between day 1 and day 2?
Answer: Yes. There is a difference by day in the parietal region, and in the basal ganglia and thalamus by glucose level.
First…model diagnostics.
Now that I’ve removed the crazy values, everything looks pretty good (when outliers were included, this was not the case). Parametric analysis should be appropriate.
for (i in 5:12){
fit = lm(df_practice[,i] ~ Glucose.level*Day, df_practice)
par(mfrow=c(2,2))
plot(fit, main = names(df_practice[i]))}
Here I apply maximum likelihood tests for mixed effect models on a region-by-region basis. I take into account individual variation on day 1 vs. day 2 in this model. The parietal region is significantly affected by day (p = 0.013). The mean CBF is 5.14 +/- 1.69 greater on Day 2 than Day 1. The basal ganglia (p = 7.81e-04) and thalamus (p = 6.97e-9) are significantly affected by glucose level.
library(lme4)
for(i in 5:12){
print(names(df_practice[i]))
df_sub<-as.data.frame(cbind(df_practice[,c("X", "Day", "Glucose.level")], df_practice[,i]))
df_MLT<-df_sub[complete.cases(df_sub),]
mod1.null<-lmer(df_MLT[,4]~Glucose.level+Day+Glucose.level:Day +(1|X), data = df_MLT, REML = FALSE) #accounting for repeated measures in participants with Error term
print(summary(mod1.null))
mod1<-lmer(df_MLT[,4]~Day + (1|X), data = df_MLT, REML = FALSE)
print(anova(mod1.null, mod1))
mod1<-lmer(df_MLT[,4]~Glucose.level + (1|X), data = df_MLT, REML = FALSE)
print(anova(mod1.null, mod1))
mod1<-lmer(df_MLT[,4]~Glucose.level+Day + (1|X), data = df_MLT, REML = FALSE)
print(anova(mod1.null, mod1))}## [1] "Frontal"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 866.3 893.8 -423.1 846.3 106
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.4651 -0.3596 -0.0723 0.4955 2.6578
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 101.8 10.089
## Residual 59.7 7.726
## Number of obs: 116, groups: X, 17
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 78.3951 2.6289 29.821
## Glucose.level.L 2.6545 1.9101 1.390
## Glucose.level.Q -2.5496 1.9235 -1.325
## Glucose.level.C -0.7571 1.9370 -0.391
## Day2 3.4010 1.5185 2.240
## Glucose.level.L:Day2 -0.2901 2.8768 -0.101
## Glucose.level.Q:Day2 1.1752 2.9156 0.403
## Glucose.level.C:Day2 -2.9762 2.9487 -1.009
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Day2 G..L:D G..Q:D
## Glucs.lvl.L 0.008
## Glucs.lvl.Q -0.006 0.023
## Glucs.lvl.C 0.003 -0.010 0.008
## Day2 -0.234 -0.017 0.011 -0.008
## Glcs.l.L:D2 -0.006 -0.664 -0.014 0.008 -0.005
## Glcs.l.Q:D2 0.003 -0.016 -0.658 -0.002 -0.019 0.028
## Glcs.l.C:D2 -0.001 0.007 -0.008 -0.661 0.053 -0.018 -0.050
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 862.49 873.51 -427.25 854.49
## mod1.null 10 866.26 893.80 -423.13 846.26 8.2302 6 0.2217
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 864.55 881.07 -426.28 852.55
## mod1.null 10 866.26 893.80 -423.13 846.26 6.2875 4 0.1787
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 861.42 880.69 -423.71 847.42
## mod1.null 10 866.26 893.80 -423.13 846.26 1.1527 3 0.7644
## [1] "OrbitalFrontal"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 847.3 874.6 -413.6 827.3 104
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3893 -0.6047 -0.0516 0.5939 2.6059
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 79.30 8.905
## Residual 59.08 7.686
## Number of obs: 114, groups: X, 17
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 69.6965 2.3657 29.461
## Glucose.level.L 3.1206 1.9042 1.639
## Glucose.level.Q -2.2119 1.9318 -1.145
## Glucose.level.C -0.7549 1.9601 -0.385
## Day2 1.1133 1.5239 0.731
## Glucose.level.L:Day2 -3.5671 2.9026 -1.229
## Glucose.level.Q:Day2 -0.1624 2.9364 -0.055
## Glucose.level.C:Day2 -4.3444 2.9575 -1.469
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Day2 G..L:D G..Q:D
## Glucs.lvl.L 0.006
## Glucs.lvl.Q -0.014 0.031
## Glucs.lvl.C 0.013 -0.022 -0.018
## Day2 -0.261 -0.011 0.024 -0.025
## Glcs.l.L:D2 -0.003 -0.658 -0.023 0.020 0.006
## Glcs.l.Q:D2 0.009 -0.023 -0.658 0.018 -0.017 0.052
## Glcs.l.C:D2 -0.008 0.015 0.009 -0.667 0.068 -0.018 -0.057
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 845.94 856.89 -418.97 837.94
## mod1.null 10 847.28 874.64 -413.64 827.28 10.663 6 0.09936 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 843.64 860.06 -415.82 831.64
## mod1.null 10 847.28 874.64 -413.64 827.28 4.3577 4 0.3598
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 844.95 864.11 -415.48 830.95
## mod1.null 10 847.28 874.64 -413.64 827.28 3.6725 3 0.2991
## [1] "Motor"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 852.1 879.5 -416.0 832.1 104
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8741 -0.5605 -0.0255 0.5958 3.1573
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 76.87 8.768
## Residual 62.50 7.906
## Number of obs: 114, groups: X, 17
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 72.0774 2.3540 30.620
## Glucose.level.L 1.0032 1.9918 0.504
## Glucose.level.Q -3.2520 2.0015 -1.625
## Glucose.level.C -0.1445 2.0328 -0.071
## Day2 3.7010 1.5513 2.386
## Glucose.level.L:Day2 -0.8398 2.9684 -0.283
## Glucose.level.Q:Day2 1.2334 3.0049 0.410
## Glucose.level.C:Day2 -3.9317 3.0506 -1.289
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Day2 G..L:D G..Q:D
## Glucs.lvl.L 0.019
## Glucs.lvl.Q -0.007 0.052
## Glucs.lvl.C 0.023 -0.002 -0.006
## Day2 -0.270 -0.019 0.011 -0.014
## Glcs.l.L:D2 -0.013 -0.671 -0.034 0.003 -0.003
## Glcs.l.Q:D2 0.004 -0.035 -0.664 0.007 -0.019 0.041
## Glcs.l.C:D2 -0.015 0.002 0.002 -0.671 0.057 -0.014 -0.055
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 847.24 858.18 -419.62 839.24
## mod1.null 10 852.10 879.46 -416.05 832.10 7.1377 6 0.3083
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 851.8 868.22 -419.90 839.8
## mod1.null 10 852.1 879.46 -416.05 832.1 7.6998 4 0.1032
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 847.96 867.11 -416.98 833.96
## mod1.null 10 852.10 879.46 -416.05 832.10 1.8602 3 0.6019
## [1] "Parietal"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 866.5 893.8 -423.2 846.5 104
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.1304 -0.5198 -0.0918 0.5498 2.3561
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 60.02 7.747
## Residual 74.89 8.654
## Number of obs: 114, groups: X, 17
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 73.7770 2.1791 33.856
## Glucose.level.L -1.1766 2.1794 -0.540
## Glucose.level.Q -3.1446 2.1904 -1.436
## Glucose.level.C -0.9867 2.2220 -0.444
## Day2 5.1378 1.6926 3.035
## Glucose.level.L:Day2 1.6596 3.2486 0.511
## Glucose.level.Q:Day2 2.1859 3.2880 0.665
## Glucose.level.C:Day2 -5.8142 3.3357 -1.743
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Day2 G..L:D G..Q:D
## Glucs.lvl.L 0.022
## Glucs.lvl.Q -0.008 0.052
## Glucs.lvl.C 0.026 -0.003 -0.006
## Day2 -0.321 -0.020 0.011 -0.016
## Glcs.l.L:D2 -0.015 -0.671 -0.034 0.003 -0.003
## Glcs.l.Q:D2 0.004 -0.035 -0.664 0.007 -0.019 0.041
## Glcs.l.C:D2 -0.017 0.002 0.002 -0.670 0.058 -0.014 -0.055
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 864.42 875.36 -428.21 856.42
## mod1.null 10 866.47 893.83 -423.24 846.47 9.9474 6 0.1269
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 871.23 887.65 -429.62 859.23
## mod1.null 10 866.47 893.83 -423.24 846.47 12.758 4 0.01252 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 863.99 883.15 -425.00 849.99
## mod1.null 10 866.47 893.83 -423.24 846.47 3.521 3 0.318
## [1] "Temporal"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 836.1 863.4 -408.0 816.1 104
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.92835 -0.55829 -0.01172 0.46647 2.28197
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 53.00 7.280
## Residual 56.07 7.488
## Number of obs: 114, groups: X, 17
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 61.7216 2.0012 30.842
## Glucose.level.L -0.7257 1.8777 -0.386
## Glucose.level.Q -1.9648 1.8760 -1.047
## Glucose.level.C 0.9491 1.8842 0.504
## Day2 1.7121 1.4795 1.157
## Glucose.level.L:Day2 -1.1328 2.8334 -0.400
## Glucose.level.Q:Day2 0.1443 2.8601 0.050
## Glucose.level.C:Day2 -5.5422 2.8719 -1.930
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Day2 G..L:D G..Q:D
## Glucs.lvl.L -0.001
## Glucs.lvl.Q 0.000 0.004
## Glucs.lvl.C -0.003 0.004 -0.002
## Day2 -0.302 -0.001 -0.002 0.002
## Glcs.l.L:D2 0.000 -0.661 0.000 -0.004 -0.029
## Glcs.l.Q:D2 -0.001 -0.001 -0.658 0.009 0.002 -0.001
## Glcs.l.C:D2 0.003 -0.005 0.002 -0.663 0.038 0.001 -0.065
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 831.74 842.68 -411.87 823.74
## mod1.null 10 836.06 863.42 -408.03 816.06 7.6784 6 0.2626
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 833.31 849.73 -410.66 821.31
## mod1.null 10 836.06 863.42 -408.03 816.06 5.2542 4 0.2622
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 833.88 853.03 -409.94 819.88
## mod1.null 10 836.06 863.42 -408.03 816.06 3.8194 3 0.2816
## [1] "Occipital"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 875.9 903.2 -427.9 855.9 104
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.02818 -0.49442 -0.04069 0.58004 2.28901
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 60.21 7.759
## Residual 82.09 9.060
## Number of obs: 114, groups: X, 17
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 63.07955 2.19366 28.755
## Glucose.level.L 0.14710 2.23960 0.066
## Glucose.level.Q -0.59481 2.25560 -0.264
## Glucose.level.C 0.08651 2.27164 0.038
## Day2 2.09950 1.79022 1.173
## Glucose.level.L:Day2 -1.81970 3.46124 -0.526
## Glucose.level.Q:Day2 -1.15587 3.46941 -0.333
## Glucose.level.C:Day2 -6.40132 3.46384 -1.848
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Day2 G..L:D G..Q:D
## Glucs.lvl.L 0.011
## Glucs.lvl.Q -0.009 0.023
## Glucs.lvl.C 0.004 -0.011 0.008
## Day2 -0.324 -0.017 0.007 -0.009
## Glcs.l.L:D2 -0.010 -0.647 -0.008 0.009 -0.039
## Glcs.l.Q:D2 0.007 -0.016 -0.652 -0.002 0.007 -0.012
## Glcs.l.C:D2 -0.002 0.008 -0.006 -0.660 0.043 -0.003 -0.060
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 870.89 881.84 -431.45 862.89
## mod1.null 10 875.88 903.25 -427.94 855.88 7.0102 6 0.3199
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 873.19 889.60 -430.59 861.19
## mod1.null 10 875.88 903.25 -427.94 855.88 5.3028 4 0.2576
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 873.71 892.87 -429.86 859.71
## mod1.null 10 875.88 903.25 -427.94 855.88 3.8288 3 0.2806
## [1] "BasalGanglia"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 856.9 884.2 -418.4 836.9 103
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1357 -0.5441 -0.1253 0.5716 2.4889
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 50.82 7.129
## Residual 74.80 8.648
## Number of obs: 113, groups: X, 17
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 56.7624 2.0418 27.801
## Glucose.level.L 7.0551 2.1759 3.242
## Glucose.level.Q -3.1093 2.1744 -1.430
## Glucose.level.C -1.1529 2.1713 -0.531
## Day2 -2.2027 1.7175 -1.283
## Glucose.level.L:Day2 1.7010 3.2783 0.519
## Glucose.level.Q:Day2 4.3005 3.3167 1.297
## Glucose.level.C:Day2 -0.6698 3.3278 -0.201
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Day2 G..L:D G..Q:D
## Glucs.lvl.L 0.025
## Glucs.lvl.Q 0.002 0.049
## Glucs.lvl.C 0.008 0.002 0.017
## Day2 -0.337 -0.027 0.003 -0.011
## Glcs.l.L:D2 -0.016 -0.660 -0.028 0.002 0.026
## Glcs.l.Q:D2 -0.003 -0.036 -0.656 -0.009 -0.015 0.046
## Glcs.l.C:D2 -0.004 0.001 -0.012 -0.656 0.047 -0.011 -0.026
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 867.94 878.85 -429.97 859.94
## mod1.null 10 856.90 884.17 -418.45 836.90 23.048 6 0.0007806 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 852.37 868.74 -420.19 840.37
## mod1.null 10 856.90 884.17 -418.45 836.90 3.4776 4 0.4813
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 852.8 871.89 -419.40 838.8
## mod1.null 10 856.9 884.17 -418.45 836.9 1.9029 3 0.5928
## [1] "Thalamus"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 886.0 913.2 -433.0 866.0 102
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6692 -0.6141 0.0602 0.6466 2.0118
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 85.83 9.265
## Residual 100.71 10.035
## Number of obs: 112, groups: X, 17
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 52.0495 2.5849 20.136
## Glucose.level.L 14.1457 2.5379 5.574
## Glucose.level.Q -5.4052 2.5402 -2.128
## Glucose.level.C -2.1376 2.5612 -0.835
## Day2 2.1235 1.9981 1.063
## Glucose.level.L:Day2 0.9259 3.8132 0.243
## Glucose.level.Q:Day2 5.2085 3.8497 1.353
## Glucose.level.C:Day2 0.1351 3.8969 0.035
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Day2 G..L:D G..Q:D
## Glucs.lvl.L 0.031
## Glucs.lvl.Q -0.008 0.037
## Glucs.lvl.C -0.007 -0.016 0.037
## Day2 -0.314 -0.034 0.011 0.001
## Glcs.l.L:D2 -0.019 -0.662 -0.024 0.010 -0.004
## Glcs.l.Q:D2 0.008 -0.018 -0.658 -0.025 -0.019 0.009
## Glcs.l.C:D2 0.001 0.002 -0.027 -0.657 0.025 -0.012 -0.030
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 923.19 934.06 -457.59 915.19
## mod1.null 10 886.04 913.23 -433.02 866.04 49.147 6 6.968e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 881.07 897.38 -434.54 869.07
## mod1.null 10 886.04 913.23 -433.02 866.04 3.0312 4 0.5526
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Day + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Day + Glucose.level:Day + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 881.91 900.94 -433.96 867.91
## mod1.null 10 886.04 913.23 -433.02 866.04 1.8729 3 0.5992We can visualize the differences between Day 1 and Day 2 with a collection of boxplots. Day 1 is navy blue, Day 2 is light blue.
What about our healthy controls vs. Diabetics. Are they different?
Yes. There are differences as a function of glucose level for the frontal, parietal, basal ganglia, and thalamus. There are differences as a function of group for the frontal and thalamus regions. There is also a significant interactive effect (Glucose x Group) in the frontal and thalamus regions.
The model diagnostics look fine.
The analysis process is the same. I used a maximum likelihood test for mixed effect models, and I found significant effects by group in the Frontal (being diabetic resulted in 3.57+/- 4.8 lower CBF than the controls, p = 0.014) and Thalamus ( p = 3.3e-03) regions. The frontal (p = 3.12e-03), parietal (p = 0.03), basal ganglia (p = 6.51e-04), and thalamus (p = 3.3e-03) regions were all significantly affected by glucose level. There was also an interactive effect of glucose*group in the frontal (p = 6.38e-03) and thalamus (p = 1.8e-03) regions.
for(i in 5:12){
print(names(df_compare[i]))
df_sub<-as.data.frame(cbind(df_compare[,c("X", "Group", "Glucose.level")], df_compare[,i]))
df_MLT<-df_sub[complete.cases(df_sub),]
mod1.null<-lmer(df_MLT[,4]~Glucose.level+Group+Glucose.level:Group +(1|X), data = df_MLT, REML = FALSE) #accounting for repeated measures in participants with Error term
print(summary(mod1.null))
mod1<-lmer(df_MLT[,4]~Group + (1|X), data = df_MLT, REML = FALSE)
print(anova(mod1.null, mod1))
mod1<-lmer(df_MLT[,4]~Glucose.level + (1|X), data = df_MLT, REML = FALSE)
print(anova(mod1.null, mod1))
mod1<-lmer(df_MLT[,4]~Glucose.level+Group + (1|X), data = df_MLT, REML = FALSE)
print(anova(mod1.null, mod1))}## [1] "Frontal"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 817.1 844.1 -398.5 797.1 100
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.10262 -0.51307 -0.09124 0.64743 2.19355
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 130.14 11.408
## Residual 45.03 6.711
## Number of obs: 110, groups: X, 28
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 80.1253 2.8958 27.670
## Glucose.level.L 0.3981 1.6091 0.247
## Glucose.level.Q -4.7914 1.5704 -3.051
## Glucose.level.C -2.3220 1.4828 -1.566
## Group -3.5680 4.7779 -0.747
## Glucose.level.L:Group 7.8909 3.3563 2.351
## Glucose.level.Q:Group 10.7192 3.2858 3.262
## Glucose.level.C:Group 1.5528 3.1174 0.498
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Group G..L:G G..Q:G
## Glucs.lvl.L -0.010
## Glucs.lvl.Q -0.023 0.221
## Glucs.lvl.C 0.007 0.027 0.012
## Group -0.606 0.006 0.014 -0.004
## Glcs.lv.L:G 0.005 -0.479 -0.106 -0.013 -0.103
## Glcs.lv.Q:G 0.011 -0.105 -0.478 -0.006 -0.069 0.133
## Glcs.lv.C:G -0.004 -0.013 -0.006 -0.476 -0.017 0.075 -0.015
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 824.77 835.57 -408.39 816.77
## mod1.null 10 817.07 844.07 -398.53 797.07 19.707 6 0.003123 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 821.51 837.72 -404.76 809.51
## mod1.null 10 817.07 844.07 -398.53 797.07 12.448 4 0.01432 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 823.38 842.28 -404.69 809.38
## mod1.null 10 817.07 844.07 -398.53 797.07 12.315 3 0.006377 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "OrbitalFrontal"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 802.7 829.5 -391.3 782.7 98
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1911 -0.5689 -0.0254 0.5280 2.5334
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 69.65 8.346
## Residual 53.26 7.298
## Number of obs: 108, groups: X, 28
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 71.1369 2.2189 32.060
## Glucose.level.L 0.8507 1.7340 0.491
## Glucose.level.Q -3.2584 1.7066 -1.909
## Glucose.level.C -1.6600 1.6331 -1.016
## Group -1.2252 3.7785 -0.324
## Glucose.level.L:Group 4.1175 3.5858 1.148
## Glucose.level.Q:Group 6.8610 3.6060 1.903
## Glucose.level.C:Group 1.1518 3.4134 0.337
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Group G..L:G G..Q:G
## Glucs.lvl.L -0.005
## Glucs.lvl.Q -0.028 0.212
## Glucs.lvl.C 0.020 0.015 -0.010
## Group -0.587 0.003 0.017 -0.012
## Glcs.lv.L:G 0.002 -0.484 -0.102 -0.007 -0.094
## Glcs.lv.Q:G 0.013 -0.100 -0.473 0.005 -0.098 0.060
## Glcs.lv.C:G -0.010 -0.007 0.005 -0.478 -0.027 0.030 0.002
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 798.97 809.70 -395.49 790.97
## mod1.null 10 802.66 829.48 -391.33 782.66 8.3173 6 0.2158
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 798.87 814.97 -393.44 786.87
## mod1.null 10 802.66 829.48 -391.33 782.66 4.2174 4 0.3774
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 800.87 819.65 -393.44 786.87
## mod1.null 10 802.66 829.48 -391.33 782.66 4.2168 3 0.239
## [1] "Motor"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 797.9 824.8 -389.0 777.9 98
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.89586 -0.72767 -0.06142 0.59716 2.50015
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 68.31 8.265
## Residual 51.09 7.148
## Number of obs: 108, groups: X, 27
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 75.3129 2.2378 33.655
## Glucose.level.L -0.3816 1.7093 -0.223
## Glucose.level.Q -4.6768 1.6682 -2.803
## Glucose.level.C -2.8289 1.5788 -1.792
## Group -1.3409 3.7583 -0.357
## Glucose.level.L:Group 3.2325 3.5206 0.918
## Glucose.level.Q:Group 8.0730 3.5326 2.285
## Glucose.level.C:Group 3.1250 3.3338 0.937
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Group G..L:G G..Q:G
## Glucs.lvl.L 0.021
## Glucs.lvl.Q -0.004 0.217
## Glucs.lvl.C 0.021 0.029 0.013
## Group -0.595 -0.013 0.003 -0.013
## Glcs.lv.L:G -0.010 -0.486 -0.105 -0.014 -0.086
## Glcs.lv.Q:G 0.002 -0.102 -0.472 -0.006 -0.091 0.062
## Glcs.lv.C:G -0.010 -0.014 -0.006 -0.474 -0.026 0.034 0.007
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 797.58 808.31 -394.79 789.58
## mod1.null 10 797.94 824.77 -388.97 777.94 11.638 6 0.07055 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 795.66 811.75 -391.83 783.66
## mod1.null 10 797.94 824.77 -388.97 777.94 5.7164 4 0.2214
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 797.66 816.44 -391.83 783.66
## mod1.null 10 797.94 824.77 -388.97 777.94 5.7164 3 0.1263
## [1] "Parietal"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 829.1 856.0 -404.6 809.1 99
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.00864 -0.64881 -0.08742 0.71003 2.17926
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 63.13 7.945
## Residual 68.29 8.264
## Number of obs: 109, groups: X, 27
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 76.685 2.217 34.588
## Glucose.level.L -2.759 1.967 -1.402
## Glucose.level.Q -4.492 1.922 -2.337
## Glucose.level.C -4.608 1.824 -2.526
## Group -1.744 3.755 -0.464
## Glucose.level.L:Group 6.326 3.971 1.593
## Glucose.level.Q:Group 8.343 3.928 2.124
## Glucose.level.C:Group 1.893 3.799 0.498
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Group G..L:G G..Q:G
## Glucs.lvl.L 0.029
## Glucs.lvl.Q -0.002 0.211
## Glucs.lvl.C 0.026 0.028 0.013
## Group -0.590 -0.017 0.001 -0.015
## Glcs.lv.L:G -0.014 -0.495 -0.105 -0.014 -0.104
## Glcs.lv.Q:G 0.001 -0.103 -0.489 -0.006 -0.062 0.081
## Glcs.lv.C:G -0.013 -0.013 -0.006 -0.480 -0.005 0.046 -0.035
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 830.83 841.59 -411.41 822.83
## mod1.null 10 829.13 856.04 -404.56 809.13 13.703 6 0.03313 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 827.31 843.46 -407.65 815.31
## mod1.null 10 829.13 856.04 -404.56 809.13 6.1831 4 0.1859
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 829.28 848.12 -407.64 815.28
## mod1.null 10 829.13 856.04 -404.56 809.13 6.1544 3 0.1043
## [1] "Temporal"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 798.0 824.8 -389.0 778.0 98
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8557 -0.6006 -0.0328 0.5555 2.2328
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 51.11 7.149
## Residual 54.26 7.366
## Number of obs: 108, groups: X, 28
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 63.2271 1.9577 32.297
## Glucose.level.L -2.0885 1.7757 -1.176
## Glucose.level.Q -2.6806 1.7146 -1.563
## Glucose.level.C -1.2736 1.6280 -0.782
## Group -0.4119 3.3505 -0.123
## Glucose.level.L:Group 4.5694 3.5532 1.286
## Glucose.level.Q:Group 6.7484 3.5039 1.926
## Glucose.level.C:Group 2.3877 3.3883 0.705
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Group G..L:G G..Q:G
## Glucs.lvl.L -0.009
## Glucs.lvl.Q -0.016 0.174
## Glucs.lvl.C 0.014 0.034 0.003
## Group -0.584 0.005 0.010 -0.008
## Glcs.lv.L:G 0.005 -0.500 -0.087 -0.017 -0.116
## Glcs.lv.Q:G 0.008 -0.085 -0.489 -0.001 -0.067 0.073
## Glcs.lv.C:G -0.007 -0.016 -0.001 -0.480 -0.008 0.048 -0.037
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 791.72 802.45 -391.86 783.72
## mod1.null 10 797.97 824.79 -388.98 777.97 5.756 6 0.4511
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 794.94 811.03 -391.47 782.94
## mod1.null 10 797.97 824.79 -388.98 777.97 4.973 4 0.2901
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 796.91 815.69 -391.46 782.91
## mod1.null 10 797.97 824.79 -388.98 777.97 4.9456 3 0.1758
## [1] "Occipital"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 831.1 857.9 -405.6 811.1 98
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.53030 -0.58171 0.01995 0.59079 2.69192
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 53.58 7.320
## Residual 78.16 8.841
## Number of obs: 108, groups: X, 28
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 64.076 2.076 30.859
## Glucose.level.L -1.545 2.118 -0.729
## Glucose.level.Q -2.635 2.050 -1.286
## Glucose.level.C -2.928 1.953 -1.499
## Group 4.584 3.602 1.273
## Glucose.level.L:Group 4.676 4.212 1.110
## Glucose.level.Q:Group 7.392 4.167 1.774
## Glucose.level.C:Group 3.798 4.053 0.937
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Group G..L:G G..Q:G
## Glucs.lvl.L -0.004
## Glucs.lvl.Q -0.013 0.166
## Glucs.lvl.C 0.018 0.033 0.002
## Group -0.576 0.002 0.008 -0.011
## Glcs.lv.L:G 0.002 -0.503 -0.084 -0.016 -0.114
## Glcs.lv.Q:G 0.006 -0.082 -0.492 -0.001 -0.062 0.057
## Glcs.lv.C:G -0.009 -0.016 -0.001 -0.482 -0.004 0.039 -0.042
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 825.31 836.04 -408.65 817.31
## mod1.null 10 831.13 857.95 -405.56 811.13 6.1841 6 0.4029
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 830.23 846.32 -409.11 818.23
## mod1.null 10 831.13 857.95 -405.56 811.13 7.1037 4 0.1305
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 829.89 848.66 -407.94 815.89
## mod1.null 10 831.13 857.95 -405.56 811.13 4.7608 3 0.1902
## [1] "BasalGanglia"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 795.6 822.4 -387.8 775.6 97
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.74032 -0.54531 -0.01745 0.40407 3.04600
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 52.25 7.228
## Residual 57.26 7.567
## Number of obs: 107, groups: X, 28
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 54.7765 2.0072 27.290
## Glucose.level.L 5.7810 1.8460 3.132
## Glucose.level.Q -2.3412 1.7909 -1.307
## Glucose.level.C -1.0816 1.6936 -0.639
## Group -2.9646 3.4154 -0.868
## Glucose.level.L:Group 5.7781 3.6570 1.580
## Glucose.level.Q:Group 4.6107 3.6109 1.277
## Glucose.level.C:Group 0.0922 3.4897 0.026
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Group G..L:G G..Q:G
## Glucs.lvl.L 0.038
## Glucs.lvl.Q -0.017 0.222
## Glucs.lvl.C 0.021 0.047 0.044
## Group -0.588 -0.022 0.010 -0.012
## Glcs.lv.L:G -0.019 -0.505 -0.112 -0.024 -0.101
## Glcs.lv.Q:G 0.009 -0.110 -0.496 -0.022 -0.066 0.084
## Glcs.lv.C:G -0.010 -0.023 -0.021 -0.485 -0.006 0.050 -0.027
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 807.13 817.82 -399.56 799.13
## mod1.null 10 795.65 822.38 -387.82 775.65 23.479 6 0.000651 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 791.65 807.69 -389.82 779.65
## mod1.null 10 795.65 822.38 -387.82 775.65 4.0008 4 0.4059
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 793.23 811.94 -389.62 779.23
## mod1.null 10 795.65 822.38 -387.82 775.65 3.5821 3 0.3103
## [1] "Thalamus"
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## X)
## Data: df_MLT
##
## AIC BIC logLik deviance df.resid
## 844.9 871.7 -412.4 824.9 98
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.53954 -0.56550 -0.00481 0.74704 1.84312
##
## Random effects:
## Groups Name Variance Std.Dev.
## X (Intercept) 72.37 8.507
## Residual 85.61 9.252
## Number of obs: 108, groups: X, 28
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 52.552 2.361 22.261
## Glucose.level.L 12.626 2.195 5.752
## Glucose.level.Q -4.733 2.154 -2.197
## Glucose.level.C -2.480 2.077 -1.194
## Group -5.384 4.053 -1.329
## Glucose.level.L:Group 14.685 4.429 3.316
## Glucose.level.Q:Group 11.428 4.389 2.604
## Glucose.level.C:Group -1.698 4.267 -0.398
##
## Correlation of Fixed Effects:
## (Intr) Glc..L Glc..Q Glc..C Group G..L:G G..Q:G
## Glucs.lvl.L 0.005
## Glucs.lvl.Q -0.019 0.181
## Glucs.lvl.C 0.005 0.008 0.016
## Group -0.583 -0.003 0.011 -0.003
## Glcs.lv.L:G -0.003 -0.496 -0.090 -0.004 -0.112
## Glcs.lv.Q:G 0.009 -0.089 -0.491 -0.008 -0.066 0.070
## Glcs.lv.C:G -0.002 -0.004 -0.008 -0.487 -0.010 0.038 -0.035
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 4 898.26 908.99 -445.13 890.26
## mod1.null 10 844.89 871.71 -412.44 824.89 65.371 6 3.623e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 6 852.68 868.78 -420.34 840.68
## mod1.null 10 844.89 871.71 -412.44 824.89 15.795 4 0.003307 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: df_MLT
## Models:
## mod1: df_MLT[, 4] ~ Glucose.level + Group + (1 | X)
## mod1.null: df_MLT[, 4] ~ Glucose.level + Group + Glucose.level:Group + (1 |
## mod1.null: X)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mod1 7 853.89 872.67 -419.95 839.89
## mod1.null 10 844.89 871.71 -412.44 824.89 15.005 3 0.001812 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1These data are visualized in the same way. Healthy controls are navy blue, diabetics are light blue.
The most interesting thing that I see is the control vs. diabetic response in the thalamus and frontal regions at 65. Controls are already beginning to increase their blood flow, but diabetics are not physiologically compensating in the same fashion. This is the interactive effect that I described earlier.
Here I compare all 3 groups. Controls are group 0, Diabetics are group 1. Clusters are formatted as “Group, Day”, thus healthy controls on day 1 are red, healthy controls on day 2 are green, and diabetics are blue.
I also created boxplots relative to baseline. The groupings are as before. I added a dashed line at y = 0 to denote “No difference from baseline scan”. For this analysis I had to drop 1 individual who did not have a baseline. Observe that response in the thalamus is not different from baseline at 65 for either the Day 2 controls or the diabetics. In the frontal region, there is a change in response at 45 for diabetics, but not for healthy controls. This is another good visualization of that interactive effect I talked about earlier.
Hormone Analysis
At this point, I’ve only created a bunch of visualizations for the hormone results. I think there is probably some interesting stuff in it, but I need someone with some knowledge of how the human body works to give me a direction to go. Then I can do some statistical testing and provide quantitative results.
