HIV Resting State Graph Theory

Demographics

##                              Stratified by status
##                               HIVneg         Pos_UnCon       
##   n                             227               81         
##   participant_age (mean (sd)) 40.59 (18.91)    37.74 (16.81) 
##   gender_check = 1 (%)          122 ( 53.7)       14 ( 17.3) 
##   bmi (mean (sd))             26.73 (5.93)     25.70 (6.29)  
##   nadir_cd4 (mean (sd))         NaN (NA)      248.39 (203.47)
##   recent_cd4 (mean (sd))        NaN (NA)      420.69 (311.15)
##   recent_cd8 (mean (sd))        NaN (NA)     1034.83 (377.48)
##   status (%)                                                 
##      HIVneg                     227 (100.0)        0 (  0.0) 
##      Pos_UnCon                    0 (  0.0)       81 (100.0) 
##      Pos_Con                      0 (  0.0)        0 (  0.0) 
##                              Stratified by status
##                               Pos_Con         p      test
##   n                              202                     
##   participant_age (mean (sd))  46.95 (15.45)  <0.001     
##   gender_check = 1 (%)            47 ( 23.3)  <0.001     
##   bmi (mean (sd))              26.35 (5.65)    0.415     
##   nadir_cd4 (mean (sd))       234.15 (191.38)  0.624     
##   recent_cd4 (mean (sd))      638.58 (287.27) <0.001     
##   recent_cd8 (mean (sd))      909.09 (420.46)  0.481     
##   status (%)                                  <0.001     
##      HIVneg                        0 (  0.0)             
##      Pos_UnCon                     0 (  0.0)             
##      Pos_Con                     202 (100.0)

As in the other analysis, I first regressed out the effects of age and sex since our cohorts are so poorly matched. Then I Z-transformed the Pearson correlation coefficients.

#Regress out age and sex effect
 coef.fcn = function(REGION) {
   coeffs = coef(lm(REGION ~ participant_age + gender_check, data=df))
   return(data.frame(Intercept=coeffs[1], Slope=coeffs[2], Gender=coeffs[3]))
 }
 
 AdjustForAge<-function(REGION){
   Slope<-coef.fcn(REGION)
   AdjustedREGION<-REGION-df$participant_age*Slope[,2]
   AdjustedREGION<-AdjustedREGION-as.numeric(as.character(df$gender_check))*Slope[,3]
   return(AdjustedREGION)}
 
df[,9:99]<-data.frame(apply(df[,9:99], 2, AdjustForAge))
df[9:99]<-apply(df[,9:99], 2, function(x) scale(x, center = TRUE, scale = TRUE))

I pretty much copied the analysis laid out in Anderson & Cohen, 2013 (https://www.frontiersin.org/articles/10.3389/fnhum.2013.00520/full).

After I obtained the graph theory metrics following their methods, I compared these metrics by HIV status using anova followed by Tukey HSD tests. I did not correct for any covariates since I performed that correction earlier. You can see that there’s not much going on here, although it does appear that there may be some distinction made by Edge Connectivity.

##                 Metric   Overallp      LevelComp      p_adj
## 1    AveragePathLength 0.93546809 Pos_Con-HIVneg 0.93087867
## 2    AveragePathLength 0.93546809 Pos_Con-HIVneg 0.99716413
## 3    AveragePathLength 0.93546809 Pos_Con-HIVneg 0.97935821
## 4         CliqueNumber 0.57030917 Pos_Con-HIVneg 0.63676862
## 5         CliqueNumber 0.57030917 Pos_Con-HIVneg 0.68170949
## 6         CliqueNumber 0.57030917 Pos_Con-HIVneg 0.98684449
## 7         GraphDensity 0.76508522 Pos_Con-HIVneg 0.89271542
## 8         GraphDensity 0.76508522 Pos_Con-HIVneg 0.76517692
## 9         GraphDensity 0.76508522 Pos_Con-HIVneg 0.93384203
## 10    EdgeConnectivity 0.03581061 Pos_Con-HIVneg 0.04801043
## 11    EdgeConnectivity 0.03581061 Pos_Con-HIVneg 0.16559702
## 12    EdgeConnectivity 0.03581061 Pos_Con-HIVneg 0.99884839
## 13     MedianCloseness 0.76853568 Pos_Con-HIVneg 0.84309809
## 14     MedianCloseness 0.76853568 Pos_Con-HIVneg 0.96872519
## 15     MedianCloseness 0.76853568 Pos_Con-HIVneg 0.79489428
## 16 MedianGraphCoreness 0.74019221 Pos_Con-HIVneg 0.85557153
## 17 MedianGraphCoreness 0.74019221 Pos_Con-HIVneg 0.75424180
## 18 MedianGraphCoreness 0.74019221 Pos_Con-HIVneg 0.94741180
## 19           MaxDegree 0.75251106 Pos_Con-HIVneg 0.99733041
## 20           MaxDegree 0.75251106 Pos_Con-HIVneg 0.77609610
## 21           MaxDegree 0.75251106 Pos_Con-HIVneg 0.75236396
## 22        MedianDegree 0.26337800 Pos_Con-HIVneg 0.93237032
## 23        MedianDegree 0.26337800 Pos_Con-HIVneg 0.23823046
## 24        MedianDegree 0.26337800 Pos_Con-HIVneg 0.37817249
## 25           MinDegree 0.03581061 Pos_Con-HIVneg 0.04801043
## 26           MinDegree 0.03581061 Pos_Con-HIVneg 0.16559702
## 27           MinDegree 0.03581061 Pos_Con-HIVneg 0.99884839
## 28         VertexCount 0.46823337 Pos_Con-HIVneg 0.56963711
## 29         VertexCount 0.46823337 Pos_Con-HIVneg 1.00000000
## 30         VertexCount 0.46823337 Pos_Con-HIVneg 0.73722905
## 31           EdgeCount 0.76508522 Pos_Con-HIVneg 0.89271542
## 32           EdgeCount 0.76508522 Pos_Con-HIVneg 0.76517692
## 33           EdgeCount 0.76508522 Pos_Con-HIVneg 0.93384203
## 34        Transitivity 0.97345866 Pos_Con-HIVneg 0.97081257
## 35        Transitivity 0.97345866 Pos_Con-HIVneg 0.99562897
## 36        Transitivity 0.97345866 Pos_Con-HIVneg 0.99623022

Normality is not an appropriate assumption for edge connectivity, though. You can see that by looking at its density plot. A chi-square test shows a trend to suggest that HIV+ individuals have more edge connectivity than controls. This suggests that they have slightly less specific connectivity; however, this is all pretty weak.

## 
##  Pearson's Chi-squared test
## 
## data:  table(df.results$EdgeConnectivity, df.results$status)
## X-squared = 8.457, df = 4, p-value = 0.0762

HIV Resting State Graph Theory

Julie Wisch

February 21, 2019

Demographics