ADRC_FC
Julie Wisch
September 26, 2018
All analysis was completed using the dataset that matched Cathy’s that is coming out in Brain in November.
Here are the questions I’m going to answer:
1.1 Is there a relationship between amyloid/tau imaging and CDR status?
1.2 As time passes are there differences in amyloid/tau imaging between converters and non-converters?
2.1 Is there a relationship between BOLD imaging and CDR status?
2.2 As time passes are there differences in network connectivity trajectory between converters and non-converters?
3.1 Are there observable changes to networks over time that increase your risk of CDR conversion?
4.1 Is there are relationship between functional connectivity and amyloid/tau imaging?
1.1- Is there a relationship between amyloid/tau imaging and CDR status? In short: Yes
chisq.test(SUVRandPIB) ##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: SUVRandPIB
## X-squared = 590.63, df = 1, p-value < 2.2e-16chisq.test(CDRandSUVR) ##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: CDRandSUVR
## X-squared = 23.559, df = 1, p-value = 1.211e-06chisq.test(CDRandPIB) ##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: CDRandPIB
## X-squared = 25.63, df = 1, p-value = 4.136e-071.2-As time passes are there differences in amyloid/tau imaging between converters and non-converters?
In short: There are differences of intercept, but not slope. So (in accordance with Cathy’s paper), it seems like these changes must be starting more than 10 years out.
#1 - APOE, 2 - EDUC, 3 - Gender, 4 - CDR, 5 - Time, 6 - CDR*TIME
LikelihoodRatioTests_RandInt(df.pib.demog$PiB_fBP_TOT_CORTMEAN)## [[1]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ cdr05 * years + GENDER + EDUC + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df
## Model.Total 8 -913.91 -877.98 464.96 -929.91
## Model.Total.null 9 -954.80 -914.37 486.40 -972.80 42.887 1
## Pr(>Chisq)
## Model.Total
## Model.Total.null 5.798e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## [[2]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ cdr05 * years + GENDER + APOE + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## Model.Total 8 -956.8 -920.86 486.4 -972.8
## Model.Total.null 9 -954.8 -914.37 486.4 -972.8 5e-04 1 0.9828
##
## [[3]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ cdr05 * years + EDUC + APOE + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df
## Model.Total 8 -954.21 -918.27 485.11 -970.21
## Model.Total.null 9 -954.80 -914.37 486.40 -972.80 2.5878 1
## Pr(>Chisq)
## Model.Total
## Model.Total.null 0.1077
##
## [[4]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ years + GENDER + EDUC + APOE + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df
## Model.Total 7 -935.6 -904.16 474.8 -949.6
## Model.Total.null 9 -954.8 -914.37 486.4 -972.8 23.198 2
## Pr(>Chisq)
## Model.Total
## Model.Total.null 9.173e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## [[5]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ cdr05 + GENDER + EDUC + APOE + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df
## Model.Total 7 -879.54 -848.10 446.77 -893.54
## Model.Total.null 9 -954.80 -914.37 486.40 -972.80 79.259 2
## Pr(>Chisq)
## Model.Total
## Model.Total.null < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## [[6]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ cdr05 + years + GENDER + EDUC + APOE + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df
## Model.Total 8 -953.03 -917.09 484.51 -969.03
## Model.Total.null 9 -954.80 -914.37 486.40 -972.80 3.7722 1
## Pr(>Chisq)
## Model.Total
## Model.Total.null 0.05211 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#APOE status is significant (p = 5.8e-11), CDR status (p = 9.2e-6), Time (p < 2.2e-16)
LikelihoodRatioTests_RandInt(df.pib.demog$PiB_fSUVR_TOT_CORTMEAN)## [[1]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ cdr05 * years + GENDER + EDUC + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df
## Model.Total 8 560.53 596.47 -272.27 544.53
## Model.Total.null 9 518.26 558.69 -250.13 500.26 44.269 1
## Pr(>Chisq)
## Model.Total
## Model.Total.null 2.862e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## [[2]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ cdr05 * years + GENDER + APOE + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df
## Model.Total 8 516.28 552.22 -250.14 500.28
## Model.Total.null 9 518.26 558.69 -250.13 500.26 0.0199 1
## Pr(>Chisq)
## Model.Total
## Model.Total.null 0.8877
##
## [[3]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ cdr05 * years + EDUC + APOE + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df
## Model.Total 8 519.93 555.87 -251.97 503.93
## Model.Total.null 9 518.26 558.69 -250.13 500.26 3.6677 1
## Pr(>Chisq)
## Model.Total
## Model.Total.null 0.05548 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## [[4]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ years + GENDER + EDUC + APOE + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df
## Model.Total 7 542.42 573.87 -264.21 528.42
## Model.Total.null 9 518.26 558.69 -250.13 500.26 28.162 2
## Pr(>Chisq)
## Model.Total
## Model.Total.null 7.669e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## [[5]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ cdr05 + GENDER + EDUC + APOE + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df
## Model.Total 7 667.09 698.54 -326.55 653.09
## Model.Total.null 9 518.26 558.69 -250.13 500.26 152.83 2
## Pr(>Chisq)
## Model.Total
## Model.Total.null < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## [[6]]
## Data: df.pib.demog
## Models:
## Model.Total: MEASURE ~ cdr05 + years + GENDER + EDUC + APOE + (1 | ID)
## Model.Total.null: MEASURE ~ cdr05 * years + GENDER + EDUC + APOE + (1 | ID)
## Df AIC BIC logLik deviance Chisq Chi Df
## Model.Total 8 523.88 559.82 -253.94 507.88
## Model.Total.null 9 518.26 558.69 -250.13 500.26 7.6219 1
## Pr(>Chisq)
## Model.Total
## Model.Total.null 0.005766 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#APOE(p = 2.9e-11), CDR Status (p = 7.7e-7), time (p = 2.2e-16), cdr*time (p = 5.8e-3)#Testing for differences of slope
Model.Total.null<-lm(PiB_fBP_TOT_CORTMEAN ~ as.factor(cdr05)*years+as.factor(GENDER)+EDUC+as.factor(APOE), df.pib.demog)
anova(Model.Total.null)## Analysis of Variance Table
##
## Response: PiB_fBP_TOT_CORTMEAN
## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(cdr05) 1 1.5580 1.55796 47.8325 1.11e-11 ***
## years 1 0.1065 0.10653 3.2706 0.07099 .
## as.factor(GENDER) 1 0.1178 0.11784 3.6178 0.05760 .
## EDUC 1 0.0220 0.02200 0.6756 0.41141
## as.factor(APOE) 2 3.1310 1.56551 48.0642 < 2.2e-16 ***
## as.factor(cdr05):years 1 0.0986 0.09858 3.0267 0.08238 .
## Residuals 652 21.2364 0.03257
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Model.Total.null$coefficients## (Intercept) as.factor(cdr05)1 years
## 0.144454386 0.117261239 0.004623222
## as.factor(GENDER)2 EDUC as.factor(APOE)1
## -0.036846301 -0.003075652 0.117406164
## as.factor(APOE)2 as.factor(cdr05)1:years
## 0.269388806 -0.009382740m.lst<-lstrends(Model.Total.null, "cdr05", var = "years")
summary(pairs(m.lst)) #p = 0.08, so no significant difference in slopes## contrast estimate SE df t.ratio p.value
## 0 - 1 0.00938274 0.005393167 652 1.74 0.0824
##
## Results are averaged over the levels of: GENDER, APOEModel.Total.null<-lm(PiB_fSUVR_TOT_CORTMEAN ~ as.factor(cdr05)*years+as.factor(GENDER)+EDUC+as.factor(APOE), df.pib.demog)
anova(Model.Total.null)## Analysis of Variance Table
##
## Response: PiB_fSUVR_TOT_CORTMEAN
## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(cdr05) 1 14.629 14.6288 49.3514 5.399e-12 ***
## years 1 2.884 2.8837 9.7284 0.001894 **
## as.factor(GENDER) 1 1.691 1.6906 5.7034 0.017215 *
## EDUC 1 0.262 0.2622 0.8846 0.347296
## as.factor(APOE) 2 29.004 14.5019 48.9233 < 2.2e-16 ***
## as.factor(cdr05):years 1 0.541 0.5409 1.8249 0.177198
## Residuals 652 193.267 0.2964
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Model.Total.null$coefficients## (Intercept) as.factor(cdr05)1 years
## 1.40930763 0.37395681 0.02080720
## as.factor(GENDER)2 EDUC as.factor(APOE)1
## -0.13378097 -0.01034706 0.36696759
## as.factor(APOE)2 as.factor(cdr05)1:years
## 0.79673876 -0.02197878m.lst<-lstrends(Model.Total.null, "cdr05", var = "years")
summary(pairs(m.lst)) #p = 0.1772, so no significant difference in slopes## contrast estimate SE df t.ratio p.value
## 0 - 1 0.02197878 0.01626979 652 1.351 0.1772
##
## Results are averaged over the levels of: GENDER, APOEggplot(df.pib, aes(x=years, y=PiB_fBP_TOT_CORTMEAN, shape=cdr05, color=cdr05)) +
geom_point()+geom_smooth(method=lm, se=TRUE, fullrange=TRUE)
ggplot(df.pib, aes(x=years, y=PiB_fSUVR_TOT_CORTMEAN, shape=cdr05, color=cdr05)) +
geom_point()+geom_smooth(method=lm, se=TRUE, fullrange=TRUE)
2.1- Is there a relationship between BOLD imaging and CDR status? In short: Yes
PCA shows that a significant relationship exists between cdr status and FC. Although, it’s not super clear exactly which networks correspond to changing cdr status from the PCA.
#Manova analysis
dependent.vars <- as.matrix(pcaOutput2[,1:8])
summary(manova(dependent.vars~df$cdr05))## Df Pillai approx F num Df den Df Pr(>F)
## df$cdr05 1 0.05373 5.4936 8 774 9.131e-07 ***
## Residuals 781
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1logit.cdr <- glm(pcaOutput2$groups ~pcaOutput2$PC1 +pcaOutput2$PC2+
pcaOutput2$PC3+pcaOutput2$PC4+pcaOutput2$PC5+pcaOutput2$PC6+
pcaOutput2$PC7+pcaOutput2$PC8, family = "binomial")
summary(logit.cdr)##
## Call:
## glm(formula = pcaOutput2$groups ~ pcaOutput2$PC1 + pcaOutput2$PC2 +
## pcaOutput2$PC3 + pcaOutput2$PC4 + pcaOutput2$PC5 + pcaOutput2$PC6 +
## pcaOutput2$PC7 + pcaOutput2$PC8, family = "binomial")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.2977 -0.6111 -0.4934 -0.3577 2.6802
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.86552 0.11252 -16.579 < 2e-16 ***
## pcaOutput2$PC1 -0.06644 0.02810 -2.364 0.01807 *
## pcaOutput2$PC2 0.11961 0.03744 3.194 0.00140 **
## pcaOutput2$PC3 -0.10728 0.04721 -2.272 0.02306 *
## pcaOutput2$PC4 -0.12821 0.04723 -2.715 0.00664 **
## pcaOutput2$PC5 -0.10817 0.05535 -1.954 0.05067 .
## pcaOutput2$PC6 -0.12611 0.05637 -2.237 0.02527 *
## pcaOutput2$PC7 -0.06821 0.06110 -1.116 0.26427
## pcaOutput2$PC8 0.12022 0.06630 1.813 0.06978 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 670.74 on 782 degrees of freedom
## Residual deviance: 627.01 on 774 degrees of freedom
## AIC: 645.01
##
## Number of Fisher Scoring iterations: 5The networks that comprise each of the significant components are shown in the figures below.
2.2 - As time passes are there differences in network connectivity trajectory between converters and non-converters?
In short: Yes
## Region pValue
## 14 zSM_lat_x_SM_lat 0.006247446
## 23 zSM_lat_x_VAN 0.006019155
## 26 zCO_x_CO 0.022418205
## 82 zSUBCort_x_SUBCort 0.033604233Slope varies over time for four networks: SMlatxSMlat, SMlatxVAN, COxCO, and SUBCortxSUBCort.
## $Region
## [1] "zSM_lat_x_SM_lat"
##
## $p.value
## [1] 0.006247446
##
## $plot
##
## Call:
## lm(formula = zSM_lat_x_SM_lat ~ as.factor(cdr05) * years + GENDER +
## EDUC + APOE, data = df, REML = FALSE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1732 -0.6463 0.0493 0.6756 2.7544
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.002525 0.268361 0.009 0.99250
## as.factor(cdr05)1 -0.463977 0.104776 -4.428 1.09e-05 ***
## years -0.016861 0.011393 -1.480 0.13928
## GENDER -0.130627 0.073426 -1.779 0.07563 .
## EDUC 0.013053 0.013631 0.958 0.33855
## APOE 0.105246 0.063438 1.659 0.09751 .
## as.factor(cdr05)1:years -0.077253 0.029568 -2.613 0.00916 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9834 on 776 degrees of freedom
## Multiple R-squared: 0.04043, Adjusted R-squared: 0.03301
## F-statistic: 5.449 on 6 and 776 DF, p-value: 1.555e-05## (Intercept) as.factor(cdr05)1 years
## 0.002525081 -0.463976913 -0.016861007
## GENDER EDUC APOE
## -0.130627106 0.013053162 0.105245548
## as.factor(cdr05)1:years
## -0.077252687## cdr05 years.trend SE df lower.CL upper.CL
## 0 -0.01686101 0.01139250 776 -0.03922479 0.005502773
## 1 -0.09411369 0.02730456 776 -0.14771326 -0.040514131
##
## Confidence level used: 0.95## contrast estimate SE df t.ratio p.value
## 0 - 1 0.07725269 0.02956816 776 2.613 0.0092## $Region
## [1] "zSM_lat_x_VAN"
##
## $p.value
## [1] 0.006019155
##
## $plot
##
## Call:
## lm(formula = zSM_lat_x_VAN ~ as.factor(cdr05) * years + GENDER +
## EDUC + APOE, data = df, REML = FALSE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9629 -0.6352 0.0167 0.6829 4.3382
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.244437 0.272299 0.898 0.36964
## as.factor(cdr05)1 -0.135299 0.106314 -1.273 0.20353
## years 0.021784 0.011560 1.884 0.05987 .
## GENDER -0.075908 0.074503 -1.019 0.30859
## EDUC -0.006301 0.013831 -0.456 0.64884
## APOE 0.018281 0.064369 0.284 0.77648
## as.factor(cdr05)1:years -0.081605 0.030002 -2.720 0.00667 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9978 on 776 degrees of freedom
## Multiple R-squared: 0.01206, Adjusted R-squared: 0.004423
## F-statistic: 1.579 on 6 and 776 DF, p-value: 0.1502## (Intercept) as.factor(cdr05)1 years
## 0.244436843 -0.135298629 0.021783931
## GENDER EDUC APOE
## -0.075907706 -0.006300739 0.018281451
## as.factor(cdr05)1:years
## -0.081605486## cdr05 years.trend SE df lower.CL upper.CL
## 0 0.02178393 0.01155968 776 -0.0009080262 0.044475889
## 1 -0.05982156 0.02770525 776 -0.1142076657 -0.005435444
##
## Confidence level used: 0.95## contrast estimate SE df t.ratio p.value
## 0 - 1 0.08160549 0.03000206 776 2.72 0.0067## $Region
## [1] "zCO_x_CO"
##
## $p.value
## [1] 0.02241821
##
## $plot
##
## Call:
## lm(formula = zCO_x_CO ~ as.factor(cdr05) * years + GENDER + EDUC +
## APOE, data = df, REML = FALSE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3187 -0.7047 -0.0609 0.6235 4.1690
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.3536189 0.2679347 -1.320 0.1873
## as.factor(cdr05)1 -0.5753132 0.1046098 -5.500 5.17e-08 ***
## years -0.0007509 0.0113744 -0.066 0.9474
## GENDER 0.0920354 0.0733091 1.255 0.2097
## EDUC 0.0178908 0.0136092 1.315 0.1890
## APOE -0.0296437 0.0633371 -0.468 0.6399
## as.factor(cdr05)1:years -0.0725581 0.0295212 -2.458 0.0142 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9818 on 776 degrees of freedom
## Multiple R-squared: 0.04348, Adjusted R-squared: 0.03608
## F-statistic: 5.879 on 6 and 776 DF, p-value: 5.186e-06## (Intercept) as.factor(cdr05)1 years
## -0.3536189376 -0.5753132386 -0.0007508814
## GENDER EDUC APOE
## 0.0920354253 0.0178907816 -0.0296437305
## as.factor(cdr05)1:years
## -0.0725580842## cdr05 years.trend SE df lower.CL upper.CL
## 0 -0.0007508814 0.01137439 776 -0.0230791 0.02157734
## 1 -0.0733089656 0.02726115 776 -0.1268233 -0.01979463
##
## Confidence level used: 0.95## contrast estimate SE df t.ratio p.value
## 0 - 1 0.07255808 0.02952115 776 2.458 0.0142## $Region
## [1] "zSUBCort_x_SUBCort"
##
## $p.value
## [1] 0.03360423
##
## $plot
##
## Call:
## lm(formula = zSUBCort_x_SUBCort ~ as.factor(cdr05) * years +
## GENDER + EDUC + APOE, data = df, REML = FALSE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.2256 -0.7275 -0.0757 0.5776 3.3774
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.17300 0.26995 -0.641 0.52181
## as.factor(cdr05)1 -0.29845 0.10540 -2.832 0.00475 **
## years -0.01869 0.01146 -1.630 0.10341
## GENDER -0.08852 0.07386 -1.199 0.23108
## EDUC 0.01727 0.01371 1.259 0.20836
## APOE 0.14842 0.06381 2.326 0.02029 *
## as.factor(cdr05)1:years -0.06244 0.02974 -2.099 0.03612 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9892 on 776 degrees of freedom
## Multiple R-squared: 0.02902, Adjusted R-squared: 0.02151
## F-statistic: 3.866 on 6 and 776 DF, p-value: 0.0008262## (Intercept) as.factor(cdr05)1 years
## -0.17299744 -0.29845103 -0.01868520
## GENDER EDUC APOE
## -0.08852318 0.01726503 0.14841917
## as.factor(cdr05)1:years
## -0.06243799## cdr05 years.trend SE df lower.CL upper.CL
## 0 -0.01868520 0.01146003 776 -0.04118155 0.003811139
## 1 -0.08112319 0.02746641 776 -0.13504047 -0.027205912
##
## Confidence level used: 0.95## contrast estimate SE df t.ratio p.value
## 0 - 1 0.06243799 0.02974343 776 2.099 0.0361As a sanity check, I tested the correlation between each of those networks and time for both converters and nonconverters.
The good news is, there was a weak to non-existant correlation with time for the nonconverters, and there was a significant correlation with time for the converters. Since the assignment of time for nonconverters was totally arbitrary, any observed correlation would be a result of this random assignment.
FisherRtoZ(df$zSM_lat_x_SM_lat) #The correlation for nonconverters (r = -0.053) was significantly weaker than converters (r = -.295) (p = 0.01)
FisherRtoZ(df$zSM_lat_x_VAN)#The correlation for nonconverters (r = 0.07) was significantly weaker than converters (r = -0.20) (p = 0.01)
FisherRtoZ(df$zCO_x_CO) #The correlation for nonconverters (r = -0.003) was significantly weaker than converters (r = -0.24) (p = 0.01)
FisherRtoZ(df$zSUBCort_x_SUBCort) #there was no difference in pearson correlation between the nonconverters (r = -0.05) and converters (r = -.24) (p = 0.06)3- Are there observable changes to networks over time that increase your risk of CDR conversion?
In short: yes
91 Cox proportional hazards mixed effect models tested associations of each z-transformed functional connectivity network with conversion to CDR > 0. I controlled for demographic covariates of age, education, gender, race, and number of APOE4 genes. Because this dataset contained longitudinal measurements for many participants, subject ID was treated as a random effect.
#http://www.sthda.com/english/wiki/cox-proportional-hazards-model
regions<- c("zSM_x_SM","zSM_x_SM_lat","zSM_x_CO","zSM_x_AUD","zSM_x_DMN",
"zSM_x_MEM","zSM_x_VIS","zSM_x_FP","zSM_x_SAL","zSM_x_SUBCort","zSM_x_VAN",
"zSM_x_DAN","zSM_x_CEREB","zSM_lat_x_SM_lat","zSM_lat_x_CO","zSM_lat_x_AUD","zSM_lat_x_DMN",
"zSM_lat_x_MEM","zSM_lat_x_VIS","zSM_lat_x_FP","zSM_lat_x_SAL","zSM_lat_x_SUBCort","zSM_lat_x_VAN",
"zSM_lat_x_DAN","zSM_lat_x_CEREB","zCO_x_CO","zCO_x_AUD","zCO_x_DMN","zCO_x_MEM",
"zCO_x_VIS","zCO_x_FP","zCO_x_SAL","zCO_x_SUBCort","zCO_x_VAN","zCO_x_DAN",
"zCO_x_CEREB","zAUD_x_AUD","zAUD_x_DMN","zAUD_x_MEM","zAUD_x_VIS","zAUD_x_FP",
"zAUD_x_SAL","zAUD_x_SUBCort","zAUD_x_VAN","zAUD_x_DAN","zAUD_x_CEREB","zDMN_x_DMN",
"zDMN_x_MEM","zDMN_x_VIS","zDMN_x_FP","zDMN_x_SAL","zDMN_x_SUBCort","zDMN_x_VAN",
"zDMN_x_DAN","zDMN_x_CEREB","zMEM_x_MEM","zMEM_x_VIS","zMEM_x_FP","zMEM_x_SAL",
"zMEM_x_SUBCort","zMEM_x_VAN","zMEM_x_DAN","zMEM_x_CEREB","zVIS_x_VIS","zVIS_x_FP",
"zVIS_x_SAL","zVIS_x_SUBCort","zVIS_x_VAN","zVIS_x_DAN","zVIS_x_CEREB","zFP_x_FP",
"zFP_x_SAL","zFP_x_SUBCort","zFP_x_VAN","zFP_x_DAN","zFP_x_CEREB","zSAL_x_SAL" ,
"zSAL_x_SUBCort","zSAL_x_VAN","zSAL_x_DAN","zSAL_x_CEREB","zSUBCort_x_SUBCort","zSUBCort_x_VAN",
"zSUBCort_x_DAN","zSUBCort_x_CEREB","zVAN_x_VAN","zVAN_x_DAN","zVAN_x_CEREB","zDAN_x_DAN",
"zDAN_x_CEREB","zCEREB_x_CEREB" )
univ_formulas <- sapply(regions,
function(x) as.formula(paste('Surv(years, cdr05)~GENDER + EDUC+APOE + (1|ID)+', x)))
univ_models2 <- lapply( univ_formulas, function(x){coxme(x, data = df)})
extract_coxme_table <- univ_results_quick<-lapply(univ_models2, function (x){
beta <- x$coefficients
nvar <- length(beta)
nfrail <- nrow(x$var) - nvar
se <- sqrt(diag(x$var)[nfrail + 1:nvar])
z<- round(beta/se, 2)
p<- signif(1 - pchisq((beta/se)^2, 1), 2)
table=data.frame(cbind(beta,se,z,p))
return(table)
})After correcting for repeated measures (Bonferroni, p = 5.5e-04), 4 regions were found to be affiliated with time to CDR > 0.
univ_models2$zSM_x_VIS## Cox mixed-effects model fit by maximum likelihood
## Data: df
## events, n = 120, 783
## Iterations= 43 186
## NULL Integrated Fitted
## Log-likelihood -689.4148 -618.7076 -412.426
##
## Chisq df p AIC BIC
## Integrated loglik 141.41 5.00 0 131.41 117.48
## Penalized loglik 553.98 171.74 0 210.50 -268.23
##
## Model: x
## Fixed coefficients
## coef exp(coef) se(coef) z p
## GENDER -0.17084765 0.8429500 0.48769041 -0.35 0.73000
## EDUC -0.04406304 0.9568936 0.08553961 -0.52 0.61000
## APOE -0.04198539 0.9588838 0.45125551 -0.09 0.93000
## zSM_x_VIS 0.60580118 1.8327200 0.15945910 3.80 0.00015
##
## Random effects
## Group Variable Std Dev Variance
## ID Intercept 2.929402 8.581399univ_models2$zVIS_x_SAL## Cox mixed-effects model fit by maximum likelihood
## Data: df
## events, n = 120, 783
## Iterations= 19 90
## NULL Integrated Fitted
## Log-likelihood -689.4148 -613.9053 -411.3322
##
## Chisq df p AIC BIC
## Integrated loglik 151.02 5.00 0 141.02 127.08
## Penalized loglik 556.17 167.72 0 220.73 -246.77
##
## Model: x
## Fixed coefficients
## coef exp(coef) se(coef) z p
## GENDER -0.17985125 0.8353945 0.47667262 -0.38 7.1e-01
## EDUC -0.05121482 0.9500745 0.08363327 -0.61 5.4e-01
## APOE -0.09829976 0.9063772 0.45044427 -0.22 8.3e-01
## zVIS_x_SAL -0.72408703 0.4847669 0.16141653 -4.49 7.3e-06
##
## Random effects
## Group Variable Std Dev Variance
## ID Intercept 2.865598 8.211654univ_models2$zVIS_x_CEREB## Cox mixed-effects model fit by maximum likelihood
## Data: df
## events, n = 120, 783
## Iterations= 29 159
## NULL Integrated Fitted
## Log-likelihood -689.4148 -616.9011 -411.8704
##
## Chisq df p AIC BIC
## Integrated loglik 145.03 5.00 0 135.03 121.09
## Penalized loglik 555.09 171.24 0 212.61 -264.73
##
## Model: x
## Fixed coefficients
## coef exp(coef) se(coef) z p
## GENDER -0.12764217 0.8801683 0.49267477 -0.26 8.0e-01
## EDUC -0.04776733 0.9533556 0.08594206 -0.56 5.8e-01
## APOE -0.07460559 0.9281095 0.45887984 -0.16 8.7e-01
## zVIS_x_CEREB -0.63628843 0.5292531 0.15401042 -4.13 3.6e-05
##
## Random effects
## Group Variable Std Dev Variance
## ID Intercept 2.947939 8.690346univ_models2$zDAN_x_CEREB## Cox mixed-effects model fit by maximum likelihood
## Data: df
## events, n = 120, 783
## Iterations= 13 81
## NULL Integrated Fitted
## Log-likelihood -689.4148 -615.7156 -408.5079
##
## Chisq df p AIC BIC
## Integrated loglik 147.40 5.00 0 137.40 123.46
## Penalized loglik 561.81 172.64 0 216.53 -264.71
##
## Model: x
## Fixed coefficients
## coef exp(coef) se(coef) z p
## GENDER -4.594241e-05 0.9999541 0.53563965 0.00 1.0e+00
## EDUC -4.001822e-02 0.9607719 0.09352115 -0.43 6.7e-01
## APOE -1.347507e-01 0.8739338 0.51014855 -0.26 7.9e-01
## zDAN_x_CEREB -7.205045e-01 0.4865068 0.17678299 -4.08 4.6e-05
##
## Random effects
## Group Variable Std Dev Variance
## ID Intercept 3.177633 10.0973544 - Is there are relationship between functional connectivity and amyloid/tau imaging?
In short: Yes.
Just like in 2, I used PCA to compare the functional connectivity matrices with either PIB positivity or abnormal SUVR levels.
summary(manova(dependent.vars~df.pib.FC$SUVRabnormal)) ## Df Pillai approx F num Df den Df Pr(>F)
## df.pib.FC$SUVRabnormal 1 0.017956 3.3529 8 1467 0.0008171 ***
## Residuals 1474
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1logit.SUVR <- glm(df.pib.FC$SUVRabnormal ~pcaOutput2$PC1 +pcaOutput2$PC2+
pcaOutput2$PC3+pcaOutput2$PC4+pcaOutput2$PC5+pcaOutput2$PC6+
pcaOutput2$PC7+pcaOutput2$PC8, family = "binomial")
summary(manova(dependent.vars~df.pib.FC$PIBpos))## Df Pillai approx F num Df den Df Pr(>F)
## df.pib.FC$PIBpos 1 0.01345 2.5 8 1467 0.0107 *
## Residuals 1474
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1logit.PIB <- glm(df.pib.FC$PIBpos ~pcaOutput2$PC1 +pcaOutput2$PC2+
pcaOutput2$PC3+pcaOutput2$PC4+pcaOutput2$PC5+pcaOutput2$PC6+
pcaOutput2$PC7+pcaOutput2$PC8, family = "binomial")Again I generated visualizations of the significant components and which networks comprised them.
MakeBarPlots(subset(var.contrib[,4], var.contrib[,4] > 0.028), "Principal Component 4")
MakeBarPlots(subset(var.contrib[,7], var.contrib[,7] > 0.0266), "Principal Component 7")
MakeBarPlots(subset(var.contrib[,8], var.contrib[,8] > 0.0266), "Principal Component 8")