Last updated: 2020-06-08

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Overview of aims

What is the effect of Prebiotin vs placebo on blood measures (controlling for diet, age, ethnicity, stress?) Did the intervention effect?

Data

blood_data <- read_excel("data/Blood measures data/Copy of Fiber Study Blood Results.xlsx")

meta_data <- microbiome_data$meta.dat

keepVar <- c("SubjectID", "Week", "Intervention", "Stress.Scale", "Ethnicity", "Gender", "Age")
meta_data <- meta_data [, keepVar] %>%
  filter(Week == 1)

mydata <- full_join(blood_data, meta_data)
Joining, by = "SubjectID"
# recoding
mydata <- mydata %>%
  mutate(female = ifelse(Gender == "F", 1, 0),
         c.age = Age - mean(Age),
         IntB = ifelse(Intervention == "B", 1, 0),
         Post = ifelse(time == "Post", 1, 0),
         c.stress = Stress.Scale - mean(Stress.Scale),
         hispanic = ifelse(Ethnicity %in% c("White", "Asian", "Native America"), 1, 0))

# for plotting
plot.data <- mydata[, c(colnames(mydata)[c(1:18,20:24)])]

plot.data <- plot.data %>%
  pivot_longer(cols=colnames(mydata)[3:18],
               names_to = "Variable",
               values_to = "value")

Data summary

Summary Statistics

varNames <- c(colnames(mydata)[c(2:18,20)])

sum.dat <- mydata[,varNames[2:17]] %>%
  summarise_all(list(Mean=mean, SD=sd,
                     min=min, Median=median, Max=max))
sum.dat <- data.frame(matrix(unlist(sum.dat), ncol=5))
colnames(sum.dat) <- c("Mean", "SD", "Min", "Median", "Max")
rownames(sum.dat) <- varNames[2:17]

kable(sum.dat, format="html", digits=3)%>%
  kable_styling(full_width = T)
Mean SD Min Median Max
Glucose 93.591 8.857 84.00 93.500 128.00
BUN 12.636 2.194 7.00 12.500 16.00
Creatinine 0.820 0.088 0.61 0.820 0.99
Sodium 141.682 1.810 138.00 142.000 145.00
Potassium 4.400 0.393 3.70 4.300 5.70
Chloride 102.500 1.871 99.00 102.500 107.00
Carbon_Dioxide 24.955 2.299 21.00 25.500 30.00
Calcium 9.327 0.319 8.70 9.300 9.80
Cholesterol 180.409 39.740 118.00 179.500 261.00
Triglycerides 116.864 90.611 46.00 96.500 415.00
HDL 60.091 14.671 37.00 59.000 96.00
LDL 97.577 33.402 45.00 87.000 171.00
LDL_HDL_Ratio 1.697 0.771 0.63 1.365 3.45
hsCRP 1.973 2.466 0.30 0.900 10.70
Insulin 17.091 27.233 3.00 8.000 101.00
PYY 103.329 175.191 16.56 36.215 742.90

Summary of these data by Intervention Group

varNames <- colnames(mydata)[c(20,3:18)]
sum.dat <- mydata[,varNames] %>%
  group_by(Intervention) %>%
  summarise_all(list(Mean=mean, SD=sd,
                     min=min, Median=median, Max=max))

a <- data.frame(matrix(unlist(sum.dat[1,-1]), ncol=5))
b <- data.frame(matrix(unlist(sum.dat[2,-1]), ncol=5))
a <- cbind(rep("A", 16), a); colnames(a) <- c("Intervention", "Mean", "SD", "Min", "Median", "Max")
b <- cbind(rep("B", 16), b); colnames(b) <- c("Intervention", "Mean", "SD", "Min", "Median", "Max")

sum.dat <- rbind(a,b)
sum.dat <- data.frame(Variable=rep(varNames[-1],2), sum.dat)
 
sum.dat <- arrange(sum.dat, Variable)
kable(sum.dat, format="html", digits=3)%>%
  kable_styling(full_width = T)
Variable Intervention Mean SD Min Median Max
BUN A 12.333 2.674 7.00 12.500 16.00
BUN B 13.000 1.491 11.00 12.500 16.00
Calcium A 9.258 0.401 8.70 9.300 9.80
Calcium B 9.410 0.166 9.20 9.350 9.70
Carbon_Dioxide A 24.833 2.691 21.00 25.500 30.00
Carbon_Dioxide B 25.100 1.853 22.00 25.500 28.00
Chloride A 102.500 1.931 101.00 102.000 107.00
Chloride B 102.500 1.900 99.00 102.500 105.00
Cholesterol A 160.667 25.921 118.00 160.500 198.00
Cholesterol B 204.100 41.479 137.00 203.000 261.00
Creatinine A 0.798 0.086 0.61 0.810 0.92
Creatinine B 0.847 0.087 0.72 0.845 0.99
Glucose A 91.500 4.317 84.00 92.000 97.00
Glucose B 96.100 12.142 84.00 93.500 128.00
HDL A 63.083 13.780 43.00 59.000 96.00
HDL B 56.500 15.615 37.00 55.500 80.00
hsCRP A 2.058 2.863 0.30 0.900 10.70
hsCRP B 1.870 2.037 0.40 1.150 7.00
Insulin A 8.333 5.836 3.00 7.500 26.00
Insulin B 27.600 38.260 7.00 9.000 101.00
LDL A 82.500 23.209 45.00 80.500 117.00
LDL B 115.670 35.750 65.00 114.500 171.00
LDL_HDL_Ratio A 1.383 0.583 0.63 1.255 2.72
LDL_HDL_Ratio B 2.075 0.825 1.27 1.835 3.45
Potassium A 4.442 0.425 4.10 4.300 5.70
Potassium B 4.350 0.366 3.70 4.350 4.90
PYY A 141.648 229.661 22.62 39.075 742.90
PYY B 57.345 53.314 16.56 36.215 161.80
Sodium A 140.917 1.443 138.00 141.000 143.00
Sodium B 142.600 1.838 138.00 143.000 145.00
Triglycerides A 75.250 31.792 46.00 60.000 132.00
Triglycerides B 166.800 113.325 57.00 120.000 415.00

Summary of these data by Pre-Post

varNames <- colnames(mydata)[c(2:18)]

sum.dat <- mydata[,varNames] %>%
  group_by(time) %>%
  summarise_all(list(Mean=mean, SD=sd,
                     min=min, Median=median, Max=max))

a <- data.frame(matrix(unlist(sum.dat[1,-1]), ncol=5))
b <- data.frame(matrix(unlist(sum.dat[2,-1]), ncol=5))
a <- cbind(rep("Post", 16), a); colnames(a) <- c("Pre-Post", "Mean", "SD", "Min", "Median", "Max")
b <- cbind(rep("Pre", 16), b); colnames(b) <- c("Pre-Post", "Mean", "SD", "Min", "Median", "Max")

sum.dat <- rbind(b,a)
sum.dat <- data.frame(Variable=rep(varNames[-1],2), sum.dat)
 
sum.dat <- arrange(sum.dat, Variable)
kable(sum.dat, format="html", digits=3)%>%
  kable_styling(full_width = T)
Variable Pre.Post Mean SD Min Median Max
BUN Pre 12.455 2.734 7.00 13.00 16.00
BUN Post 12.818 1.601 11.00 12.00 16.00
Calcium Pre 9.155 0.327 8.70 9.20 9.80
Calcium Post 9.500 0.205 9.30 9.40 9.80
Carbon_Dioxide Pre 24.182 2.040 21.00 24.00 27.00
Carbon_Dioxide Post 25.727 2.370 21.00 26.00 30.00
Chloride Pre 103.000 1.789 101.00 103.00 107.00
Chloride Post 102.000 1.897 99.00 101.00 105.00
Cholesterol Pre 175.636 42.601 130.00 162.00 253.00
Cholesterol Post 185.182 38.099 118.00 190.00 261.00
Creatinine Pre 0.798 0.097 0.61 0.78 0.94
Creatinine Post 0.842 0.076 0.72 0.82 0.99
Glucose Pre 92.364 4.905 84.00 94.00 100.00
Glucose Post 94.818 11.720 84.00 93.00 128.00
HDL Pre 56.455 12.668 40.00 58.00 75.00
HDL Post 63.727 16.199 37.00 64.00 96.00
hsCRP Pre 2.255 2.935 0.40 1.50 10.70
hsCRP Post 1.691 1.995 0.30 0.80 7.00
Insulin Pre 15.818 27.633 4.00 8.00 99.00
Insulin Post 18.364 28.111 3.00 8.00 101.00
LDL Pre 96.545 38.435 45.00 85.00 171.00
LDL Post 98.609 29.382 52.00 97.70 158.00
LDL_HDL_Ratio Pre 1.838 0.946 0.63 1.39 3.45
LDL_HDL_Ratio Post 1.556 0.555 0.81 1.34 2.67
Potassium Pre 4.482 0.513 3.70 4.40 5.70
Potassium Post 4.318 0.214 3.90 4.30 4.70
PYY Pre 113.258 212.705 17.93 34.24 742.90
PYY Post 93.399 137.814 16.56 38.19 490.10
Sodium Pre 142.091 1.446 140.00 142.00 145.00
Sodium Post 141.273 2.102 138.00 142.00 144.00
Triglycerides Pre 113.636 78.834 48.00 107.00 322.00
Triglycerides Post 120.091 104.900 46.00 86.00 415.00

Summary of these data by Intervention & Pre-Post

varNames <- colnames(mydata)[c(20, 2:18)]

sum.dat <- mydata[,varNames] %>%
  group_by(Intervention, time) %>%
  summarise_all(list(Mean=mean, SD=sd,
                     min=min, Median=median, Max=max))

a2 <- data.frame(matrix(unlist(sum.dat[1,-c(1:2)]), ncol=5))
a1 <- data.frame(matrix(unlist(sum.dat[2,-c(1:2)]), ncol=5))
b1 <- data.frame(matrix(unlist(sum.dat[3,-c(1:2)]), ncol=5))
b2 <- data.frame(matrix(unlist(sum.dat[4,-c(1:2)]), ncol=5))

a2 <- cbind(rep("A", 16), rep("Post", 16), a2); colnames(a2) <- c("Intervention", "Pre-Post", "Mean", "SD", "Min", "Median", "Max")
a1 <- cbind(rep("A", 16), rep("Pre", 16), a1); colnames(a1) <- c("Intervention", "Pre-Post", "Mean", "SD", "Min", "Median", "Max")

b1 <- cbind(rep("B", 16), rep("Pre", 16), b1); colnames(b1) <- c("Intervention", "Pre-Post", "Mean", "SD", "Min", "Median", "Max")

b2 <- cbind(rep("B", 16), rep("Post", 16), b2); colnames(b2) <- c("Intervention", "Pre-Post", "Mean", "SD", "Min", "Median", "Max")

sum.dat <- rbind(a1,a2, b1, b2)
sum.dat <- data.frame(Variable=rep(varNames[-c(1:2)],4), sum.dat)
 
sum.dat <- arrange(sum.dat, Variable)
kable(sum.dat, format="html", digits=3)%>%
  kable_styling(full_width = T)
Variable Intervention Pre.Post Mean SD Min Median Max
BUN A Pre 11.333 3.141 7.00 11.500 16.00
BUN A Post 13.333 1.862 11.00 13.000 16.00
BUN B Pre 12.200 1.095 11.00 12.000 14.00
BUN B Post 13.800 1.483 12.00 14.000 16.00
Calcium A Pre 9.017 0.397 8.70 8.900 9.80
Calcium A Post 9.500 0.237 9.30 9.400 9.80
Calcium B Pre 9.500 0.187 9.30 9.600 9.70
Calcium B Post 9.320 0.084 9.20 9.300 9.40
Carbon_Dioxide A Pre 23.833 2.229 21.00 23.000 27.00
Carbon_Dioxide A Post 25.833 2.927 21.00 26.000 30.00
Carbon_Dioxide B Pre 25.600 1.817 23.00 26.000 28.00
Carbon_Dioxide B Post 24.600 1.949 22.00 24.000 27.00
Chloride A Pre 103.333 2.338 101.00 103.000 107.00
Chloride A Post 101.667 1.033 101.00 101.000 103.00
Chloride B Pre 102.400 2.702 99.00 104.000 105.00
Chloride B Post 102.600 0.894 102.00 102.000 104.00
Cholesterol A Pre 155.333 21.332 130.00 151.000 185.00
Cholesterol A Post 166.000 30.900 118.00 173.000 198.00
Cholesterol B Pre 208.200 34.946 165.00 205.000 261.00
Cholesterol B Post 200.000 51.069 137.00 201.000 253.00
Creatinine A Pre 0.760 0.100 0.61 0.770 0.89
Creatinine A Post 0.835 0.055 0.77 0.820 0.92
Creatinine B Pre 0.850 0.103 0.72 0.850 0.99
Creatinine B Post 0.844 0.081 0.76 0.840 0.94
Glucose A Pre 93.333 3.983 87.00 95.000 97.00
Glucose A Post 89.667 4.131 84.00 88.500 95.00
Glucose B Pre 101.000 15.313 91.00 95.000 128.00
Glucose B Post 91.200 6.099 84.00 90.000 100.00
HDL A Pre 60.000 11.730 43.00 59.000 75.00
HDL A Post 66.167 16.043 52.00 62.000 96.00
HDL B Pre 60.800 17.740 37.00 64.000 80.00
HDL B Post 52.200 13.700 40.00 47.000 71.00
hsCRP A Pre 3.000 3.873 0.50 1.850 10.70
hsCRP A Post 1.117 0.952 0.30 0.800 3.00
hsCRP B Pre 2.380 2.781 0.50 0.800 7.00
hsCRP B Post 1.360 0.976 0.40 1.500 2.80
Insulin A Pre 7.000 1.789 4.00 7.500 9.00
Insulin A Post 9.667 8.214 3.00 7.500 26.00
Insulin B Pre 28.800 40.518 7.00 12.000 101.00
Insulin B Post 26.400 40.599 7.00 8.000 99.00
LDL A Pre 79.167 24.203 45.00 78.500 117.00
LDL A Post 85.833 23.928 52.00 80.500 114.00
LDL B Pre 113.940 30.065 84.00 99.000 158.00
LDL B Post 117.400 44.320 65.00 130.000 171.00
LDL_HDL_Ratio A Pre 1.410 0.697 0.63 1.255 2.72
LDL_HDL_Ratio A Post 1.355 0.510 0.81 1.290 2.20
LDL_HDL_Ratio B Pre 1.798 0.558 1.31 1.700 2.67
LDL_HDL_Ratio B Post 2.352 1.014 1.27 2.400 3.45
Potassium A Pre 4.550 0.589 4.10 4.350 5.70
Potassium A Post 4.333 0.151 4.10 4.300 4.50
Potassium B Pre 4.300 0.292 3.90 4.300 4.70
Potassium B Post 4.400 0.458 3.70 4.400 4.90
PYY A Pre 157.692 287.213 23.44 38.995 742.90
PYY A Post 125.605 181.461 22.62 54.815 490.10
PYY B Pre 54.752 53.844 16.56 38.190 149.00
PYY B Post 59.938 58.985 17.93 34.240 161.80
Sodium A Pre 141.167 0.983 140.00 141.500 142.00
Sodium A Post 140.667 1.862 138.00 141.000 143.00
Sodium B Pre 142.000 2.345 138.00 143.000 144.00
Sodium B Post 143.200 1.095 142.00 143.000 145.00
Triglycerides A Pre 80.833 37.965 48.00 64.000 132.00
Triglycerides A Post 69.667 26.598 46.00 59.500 118.00
Triglycerides B Pre 180.600 135.038 86.00 116.000 415.00
Triglycerides B Post 153.000 100.918 57.00 124.000 322.00

Analysis

Next, the aim is to more formally test for differences between intervention groups.

# plot
p1 <- ggplot(plot.data,
             aes(x=time, y=value, group=time, color=time))+
  geom_boxplot(outlier.shape = NA)+
  geom_jitter(width = 0.25)+
  facet_wrap(.~Variable, scales = "free") +
  labs(x=NULL, title="Pre and Post Blood Measures")+
  theme(panel.grid = element_blank(),
        axis.text = element_text(size=10))
p1

p2 <- ggplot(plot.data,
             aes(x=time, y=value, group=time, color=time))+
  geom_boxplot(outlier.shape = NA)+
  geom_jitter(width = 0.25, size=2)+
  labs(x=NULL,y=NULL, title="Blood Measures by Time & Intervention Group")+
  facet_grid(Variable~Intervention, scale="free", labeller = labeller(Intervention = c(A = "Group A", B = "Group B")))+
  theme(panel.grid = element_blank(),
        axis.text = element_text(size=10),
        strip.text = element_text(size=10))
p2

Run Analyses

This is simply to double check that no differences occured at baseline.

results.out <- list()

i <- 1
varNames <- colnames(mydata)[3:18]

for(i in 1:length(varNames)){
  cat("\n\n=======================")
  cat("\n=======================")
  cat("\nOutcome:\t",varNames[i])
  cat("\n")
  form <- as.formula(paste0(varNames[i], "~ IntB + Post + IntB:Post + c.age"))
  fit <- lm(form, mydata)
  anova(fit)
  
  results.out[[varNames[i]]] <- summary(fit)[["coefficients"]]
  
  
  # diagnostic plots
  layout(matrix(c(1,2,3,4),2,2)) # optional layout
  plot(fit) # diagnostic plots
  
  # normality again
  shapiro.test(residuals(fit))
  
  # independence
  durbinWatsonTest(fit)
  layout(matrix(c(1),1,1))
  acf(residuals(fit))
  
  # nice wrapper function to generally test a lot of stuff
  gvmodel <- gvlma(fit)
  summary(gvmodel)

}


=======================
=======================
Outcome:     Glucose


Call:
lm(formula = form, data = mydata)

Residuals:
   Min     1Q Median     3Q    Max 
-8.113 -5.496 -1.866  3.483 25.742 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  93.0792     3.5046  26.559 2.78e-15 ***
IntB         -1.5742     5.2540  -0.300    0.768    
Post         -3.6667     4.9115  -0.747    0.466    
c.age        -0.5242     0.9690  -0.541    0.596    
IntB:Post    13.4667     7.2850   1.849    0.082 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 8.507 on 17 degrees of freedom
Multiple R-squared:  0.2532,    Adjusted R-squared:  0.07743 
F-statistic: 1.441 on 4 and 17 DF,  p-value: 0.2636


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                     Value   p-value                   Decision
Global Stat        32.4590 1.541e-06 Assumptions NOT satisfied!
Skewness           11.5465 6.788e-04 Assumptions NOT satisfied!
Kurtosis           13.4942 2.393e-04 Assumptions NOT satisfied!
Link Function       7.1556 7.473e-03 Assumptions NOT satisfied!
Heteroscedasticity  0.2628 6.082e-01    Assumptions acceptable.


=======================
=======================
Outcome:     BUN


Call:
lm(formula = form, data = mydata)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.3997 -0.6578 -0.3396  1.2209  4.7993 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  11.2369     0.8780  12.798 3.73e-10 ***
IntB          2.6789     1.3162   2.035   0.0577 .  
Post          2.0000     1.2305   1.625   0.1225    
c.age        -0.1990     0.2428  -0.820   0.4238    
IntB:Post    -3.6000     1.8251  -1.973   0.0650 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.131 on 17 degrees of freedom
Multiple R-squared:  0.2362,    Adjusted R-squared:  0.05645 
F-statistic: 1.314 on 4 and 17 DF,  p-value: 0.3045


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                    Value p-value                   Decision
Global Stat        6.1746 0.18648    Assumptions acceptable.
Skewness           0.2160 0.64214    Assumptions acceptable.
Kurtosis           0.6861 0.40748    Assumptions acceptable.
Link Function      0.2798 0.59686    Assumptions acceptable.
Heteroscedasticity 4.9928 0.02545 Assumptions NOT satisfied!


=======================
=======================
Outcome:     Creatinine


Call:
lm(formula = form, data = mydata)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.150164 -0.064169 -0.001211  0.062296  0.138817 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.7597609  0.0365006  20.815 1.56e-13 ***
IntB         0.0845260  0.0547198   1.545    0.141    
Post         0.0750000  0.0511536   1.466    0.161    
c.age       -0.0004931  0.0100926  -0.049    0.962    
IntB:Post   -0.0690000  0.0758731  -0.909    0.376    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.0886 on 17 degrees of freedom
Multiple R-squared:  0.1853,    Adjusted R-squared:  -0.00642 
F-statistic: 0.9665 on 4 and 17 DF,  p-value: 0.4512


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                      Value p-value                Decision
Global Stat        0.786360  0.9403 Assumptions acceptable.
Skewness           0.001561  0.9685 Assumptions acceptable.
Kurtosis           0.595412  0.4403 Assumptions acceptable.
Link Function      0.163503  0.6860 Assumptions acceptable.
Heteroscedasticity 0.025885  0.8722 Assumptions acceptable.


=======================
=======================
Outcome:     Sodium


Call:
lm(formula = form, data = mydata)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.9986 -0.9253  0.1651  0.9587  2.3356 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.412e+02  6.992e-01 201.903   <2e-16 ***
IntB         2.034e+00  1.048e+00   1.941   0.0691 .  
Post        -5.000e-01  9.799e-01  -0.510   0.6164    
c.age       -8.651e-04  1.933e-01  -0.004   0.9965    
IntB:Post   -7.000e-01  1.453e+00  -0.482   0.6362    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.697 on 17 degrees of freedom
Multiple R-squared:  0.288, Adjusted R-squared:  0.1205 
F-statistic: 1.719 on 4 and 17 DF,  p-value: 0.1922


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                    Value p-value                Decision
Global Stat        7.8333 0.09788 Assumptions acceptable.
Skewness           2.4541 0.11722 Assumptions acceptable.
Kurtosis           0.2386 0.62523 Assumptions acceptable.
Link Function      1.8066 0.17891 Assumptions acceptable.
Heteroscedasticity 3.3340 0.06786 Assumptions acceptable.


=======================
=======================
Outcome:     Potassium


Call:
lm(formula = form, data = mydata)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.47235 -0.26090 -0.02216  0.14516  1.06061 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.51750    0.16363  27.608 1.46e-15 ***
IntB        -0.07849    0.24531  -0.320    0.753    
Post        -0.21667    0.22932  -0.945    0.358    
c.age       -0.06704    0.04524  -1.482    0.157    
IntB:Post    0.11667    0.34014   0.343    0.736    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3972 on 17 degrees of freedom
Multiple R-squared:  0.1722,    Adjusted R-squared:  -0.02253 
F-statistic: 0.8843 on 4 and 17 DF,  p-value: 0.4941


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                     Value p-value                   Decision
Global Stat        7.43923 0.11442    Assumptions acceptable.
Skewness           4.45281 0.03484 Assumptions NOT satisfied!
Kurtosis           2.33163 0.12677    Assumptions acceptable.
Link Function      0.00619 0.93729    Assumptions acceptable.
Heteroscedasticity 0.64861 0.42061    Assumptions acceptable.


=======================
=======================
Outcome:     Chloride


Call:
lm(formula = form, data = mydata)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.3170 -0.7144 -0.3819  1.3634  3.5975 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 103.3082     0.8047 128.384   <2e-16 ***
IntB         -0.6780     1.2063  -0.562    0.581    
Post         -1.6667     1.1277  -1.478    0.158    
c.age        -0.0519     0.2225  -0.233    0.818    
IntB:Post     1.4667     1.6727   0.877    0.393    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.953 on 17 degrees of freedom
Multiple R-squared:  0.1176,    Adjusted R-squared:  -0.09007 
F-statistic: 0.5662 on 4 and 17 DF,  p-value: 0.6905


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                      Value p-value                Decision
Global Stat        0.497308  0.9738 Assumptions acceptable.
Skewness           0.007587  0.9306 Assumptions acceptable.
Kurtosis           0.266516  0.6057 Assumptions acceptable.
Link Function      0.207461  0.6488 Assumptions acceptable.
Heteroscedasticity 0.015744  0.9001 Assumptions acceptable.


=======================
=======================
Outcome:     Carbon_Dioxide


Call:
lm(formula = form, data = mydata)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.7933 -0.9730 -0.0523  1.4779  4.0865 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  23.8916     0.9736  24.539 1.03e-14 ***
IntB          0.6384     1.4596   0.437    0.667    
Post          2.0000     1.3645   1.466    0.161    
c.age         0.1202     0.2692   0.447    0.661    
IntB:Post    -1.0000     2.0239  -0.494    0.628    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.363 on 17 degrees of freedom
Multiple R-squared:  0.1442,    Adjusted R-squared:  -0.05714 
F-statistic: 0.7162 on 4 and 17 DF,  p-value: 0.5923


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                     Value p-value                Decision
Global Stat        2.14800  0.7086 Assumptions acceptable.
Skewness           0.13256  0.7158 Assumptions acceptable.
Kurtosis           0.04022  0.8410 Assumptions acceptable.
Link Function      1.49279  0.2218 Assumptions acceptable.
Heteroscedasticity 0.48243  0.4873 Assumptions acceptable.


=======================
=======================
Outcome:     Calcium


Call:
lm(formula = form, data = mydata)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.31482 -0.17012 -0.06351  0.08168  0.79072 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  9.019351   0.110992  81.261   <2e-16 ***
IntB         0.297428   0.166393   1.788   0.0917 .  
Post         0.483333   0.155549   3.107   0.0064 ** 
c.age        0.005536   0.030690   0.180   0.8590    
IntB:Post   -0.303333   0.230717  -1.315   0.2061    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2694 on 17 degrees of freedom
Multiple R-squared:  0.4244,    Adjusted R-squared:  0.2889 
F-statistic: 3.133 on 4 and 17 DF,  p-value: 0.04214


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                     Value   p-value                   Decision
Global Stat        23.1065 0.0001206 Assumptions NOT satisfied!
Skewness            9.8606 0.0016885 Assumptions NOT satisfied!
Kurtosis            9.2705 0.0023288 Assumptions NOT satisfied!
Link Function       3.6266 0.0568615    Assumptions acceptable.
Heteroscedasticity  0.3488 0.5547935    Assumptions acceptable.


=======================
=======================
Outcome:     Cholesterol


Call:
lm(formula = form, data = mydata)

Residuals:
    Min      1Q  Median      3Q     Max 
-60.985 -20.503  -3.721  24.219  51.534 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  154.723     14.902  10.383  8.9e-09 ***
IntB          46.010     22.340   2.060   0.0551 .  
Post          10.667     20.884   0.511   0.6161    
c.age         -1.260      4.120  -0.306   0.7636    
IntB:Post     -2.467     30.976  -0.080   0.9375    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 36.17 on 17 degrees of freedom
Multiple R-squared:  0.3293,    Adjusted R-squared:  0.1715 
F-statistic: 2.087 on 4 and 17 DF,  p-value: 0.1274


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                     Value p-value                Decision
Global Stat        2.70701  0.6080 Assumptions acceptable.
Skewness           0.01125  0.9155 Assumptions acceptable.
Kurtosis           0.70279  0.4018 Assumptions acceptable.
Link Function      1.33685  0.2476 Assumptions acceptable.
Heteroscedasticity 0.65612  0.4179 Assumptions acceptable.


=======================
=======================
Outcome:     Triglycerides


Call:
lm(formula = form, data = mydata)

Residuals:
    Min      1Q  Median      3Q     Max 
-105.12  -37.94  -19.27   19.52  250.18 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)   84.022     34.769   2.417   0.0272 *
IntB          65.152     52.124   1.250   0.2283  
Post         -11.167     48.727  -0.229   0.8215  
c.age          6.576      9.614   0.684   0.5032  
IntB:Post     38.767     72.274   0.536   0.5986  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 84.4 on 17 degrees of freedom
Multiple R-squared:  0.2977,    Adjusted R-squared:  0.1324 
F-statistic: 1.801 on 4 and 17 DF,  p-value: 0.1751


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                     Value   p-value                   Decision
Global Stat        26.8974 2.085e-05 Assumptions NOT satisfied!
Skewness           12.4843 4.104e-04 Assumptions NOT satisfied!
Kurtosis           13.6347 2.220e-04 Assumptions NOT satisfied!
Link Function       0.5387 4.630e-01    Assumptions acceptable.
Heteroscedasticity  0.2397 6.244e-01    Assumptions acceptable.


=======================
=======================
Outcome:     HDL


Call:
lm(formula = form, data = mydata)

Residuals:
     Min       1Q   Median       3Q      Max 
-23.6547 -11.1001  -0.9495  10.5849  29.6719 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 60.02936    6.30676   9.518 3.18e-08 ***
IntB        -7.86459    9.45477  -0.832    0.417    
Post         6.16667    8.83859   0.698    0.495    
c.age        0.06055    1.74385   0.035    0.973    
IntB:Post    2.43333   13.10974   0.186    0.855    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 15.31 on 17 degrees of freedom
Multiple R-squared:  0.1185,    Adjusted R-squared:  -0.08889 
F-statistic: 0.5714 on 4 and 17 DF,  p-value: 0.687


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                    Value p-value                Decision
Global Stat        4.3646  0.3589 Assumptions acceptable.
Skewness           0.5017  0.4788 Assumptions acceptable.
Kurtosis           0.4370  0.5086 Assumptions acceptable.
Link Function      2.9838  0.0841 Assumptions acceptable.
Heteroscedasticity 0.4422  0.5061 Assumptions acceptable.


=======================
=======================
Outcome:     LDL


Call:
lm(formula = form, data = mydata)

Residuals:
    Min      1Q  Median      3Q     Max 
-47.561 -21.674  -1.805  26.744  46.341 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   77.700     12.858   6.043 1.32e-05 ***
IntB          41.459     19.276   2.151   0.0462 *  
Post           6.667     18.019   0.370   0.7160    
c.age         -3.024      3.555  -0.851   0.4068    
IntB:Post    -10.127     26.727  -0.379   0.7095    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 31.21 on 17 degrees of freedom
Multiple R-squared:  0.2932,    Adjusted R-squared:  0.1269 
F-statistic: 1.763 on 4 and 17 DF,  p-value: 0.1829


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                      Value p-value                Decision
Global Stat        1.447064  0.8360 Assumptions acceptable.
Skewness           0.026420  0.8709 Assumptions acceptable.
Kurtosis           1.180484  0.2773 Assumptions acceptable.
Link Function      0.236073  0.6271 Assumptions acceptable.
Heteroscedasticity 0.004087  0.9490 Assumptions acceptable.


=======================
=======================
Outcome:     LDL_HDL_Ratio


Call:
lm(formula = form, data = mydata)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.07463 -0.44308 -0.08132  0.27873  1.29772 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.41893    0.30068   4.719 0.000198 ***
IntB         0.92235    0.45076   2.046 0.056528 .  
Post        -0.05500    0.42139  -0.131 0.897686    
c.age        0.01843    0.08314   0.222 0.827249    
IntB:Post   -0.49900    0.62502  -0.798 0.435664    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.7299 on 17 degrees of freedom
Multiple R-squared:  0.274, Adjusted R-squared:  0.1032 
F-statistic: 1.604 on 4 and 17 DF,  p-value: 0.2189


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                    Value p-value                Decision
Global Stat        3.5627  0.4684 Assumptions acceptable.
Skewness           0.4087  0.5226 Assumptions acceptable.
Kurtosis           0.4020  0.5260 Assumptions acceptable.
Link Function      0.2042  0.6514 Assumptions acceptable.
Heteroscedasticity 2.5478  0.1104 Assumptions acceptable.


=======================
=======================
Outcome:     hsCRP


Call:
lm(formula = form, data = mydata)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.5433 -1.2468 -0.4666  0.5678  7.5268 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)   2.9370     1.0620   2.766   0.0132 *
IntB         -1.5014     1.5921  -0.943   0.3589  
Post         -1.8833     1.4883  -1.265   0.2228  
c.age        -0.1299     0.2936  -0.442   0.6637  
IntB:Post     2.9033     2.2075   1.315   0.2059  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.578 on 17 degrees of freedom
Multiple R-squared:  0.1154,    Adjusted R-squared:  -0.09275 
F-statistic: 0.5544 on 4 and 17 DF,  p-value: 0.6986


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                     Value   p-value                   Decision
Global Stat        26.2310 2.843e-05 Assumptions NOT satisfied!
Skewness           12.6428 3.770e-04 Assumptions NOT satisfied!
Kurtosis           11.3214 7.662e-04 Assumptions NOT satisfied!
Link Function       1.2733 2.591e-01    Assumptions acceptable.
Heteroscedasticity  0.9934 3.189e-01    Assumptions acceptable.


=======================
=======================
Outcome:     Insulin


Call:
lm(formula = form, data = mydata)

Residuals:
    Min      1Q  Median      3Q     Max 
-23.965 -15.153  -1.912  -0.034  75.447 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   7.6560    11.5542   0.663    0.516
IntB         17.9569    17.3215   1.037    0.314
Post          2.6667    16.1926   0.165    0.871
c.age         1.3529     3.1948   0.423    0.677
IntB:Post    -0.2667    24.0176  -0.011    0.991

Residual standard error: 28.05 on 17 degrees of freedom
Multiple R-squared:  0.1414,    Adjusted R-squared:  -0.06067 
F-statistic: 0.6997 on 4 and 17 DF,  p-value: 0.6027


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                    Value   p-value                   Decision
Global Stat        30.834 3.310e-06 Assumptions NOT satisfied!
Skewness           16.186 5.741e-05 Assumptions NOT satisfied!
Kurtosis           12.626 3.803e-04 Assumptions NOT satisfied!
Link Function       0.112 7.378e-01    Assumptions acceptable.
Heteroscedasticity  1.909 1.671e-01    Assumptions acceptable.


=======================
=======================
Outcome:     PYY


Call:
lm(formula = form, data = mydata)

Residuals:
    Min      1Q  Median      3Q     Max 
-142.85  -89.12  -41.44  -14.65  581.35 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)  160.501     77.397   2.074   0.0536 .
IntB        -103.935    116.029  -0.896   0.3829  
Post         -32.087    108.467  -0.296   0.7710  
c.age          5.795     21.401   0.271   0.7898  
IntB:Post     26.901    160.883   0.167   0.8692  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 187.9 on 17 degrees of freedom
Multiple R-squared:  0.06906,   Adjusted R-squared:  -0.15 
F-statistic: 0.3153 on 4 and 17 DF,  p-value: 0.8638


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = fit) 

                    Value   p-value                   Decision
Global Stat        63.837 4.522e-13 Assumptions NOT satisfied!
Skewness           20.571 5.747e-06 Assumptions NOT satisfied!
Kurtosis           23.973 9.772e-07 Assumptions NOT satisfied!
Link Function       1.146 2.845e-01    Assumptions acceptable.
Heteroscedasticity 18.148 2.043e-05 Assumptions NOT satisfied!

Results Adjusted for Multiple Comparisons

all_results <- unlist.res(results.out)
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
Joining, by = c("Estimate", "Std. Error", "t value", "Pr(>|t|)", "Outcome", "Parameter")
all_results <- filter(all_results, Parameter %in% c("IntB", "Post", "IntB:Post"))
all_results$p.adj <- p.adjust(all_results$`Pr(>|t|)`, "fdr") 
all_results$sigflag <- ifelse(all_results$p.adj < 0.05, "*", " ")
all_results$`Pr(>|t|)` <- round(all_results$`Pr(>|t|)`, 3)
all_results$p.adj.fdr <- round(all_results$p.adj, 3)
all_results <- all_results[, c(5:6, 1:4, 7:8)]

kable(all_results, format="html", digits=3) %>%
  kable_styling(full_width = T)
Outcome Parameter Estimate Std. Error t value Pr(>|t|) p.adj sigflag
Glucose IntB -1.574 5.254 -0.300 0.768 0.903
Glucose Post -3.667 4.912 -0.747 0.466 0.828
Glucose IntB:Post 13.467 7.285 1.849 0.082 0.489
BUN IntB 2.679 1.316 2.035 0.058 0.474
BUN Post 2.000 1.230 1.625 0.122 0.552
BUN IntB:Post -3.600 1.825 -1.973 0.065 0.474
Creatinine IntB 0.085 0.055 1.545 0.141 0.552
Creatinine Post 0.075 0.051 1.466 0.161 0.552
Creatinine IntB:Post -0.069 0.076 -0.909 0.376 0.786
Sodium IntB 2.034 1.048 1.941 0.069 0.474
Sodium Post -0.500 0.980 -0.510 0.616 0.898
Sodium IntB:Post -0.700 1.453 -0.482 0.636 0.898
Potassium IntB -0.078 0.245 -0.320 0.753 0.903
Potassium Post -0.217 0.229 -0.945 0.358 0.786
Potassium IntB:Post 0.117 0.340 0.343 0.736 0.903
Chloride IntB -0.678 1.206 -0.562 0.581 0.898
Chloride Post -1.667 1.128 -1.478 0.158 0.552
Chloride IntB:Post 1.467 1.673 0.877 0.393 0.786
Carbon_Dioxide IntB 0.638 1.460 0.437 0.667 0.903
Carbon_Dioxide Post 2.000 1.364 1.466 0.161 0.552
Carbon_Dioxide IntB:Post -1.000 2.024 -0.494 0.628 0.898
Calcium IntB 0.297 0.166 1.788 0.092 0.489
Calcium Post 0.483 0.156 3.107 0.006 0.307
Calcium IntB:Post -0.303 0.231 -1.315 0.206 0.609
Cholesterol IntB 46.010 22.340 2.060 0.055 0.474
Cholesterol Post 10.667 20.884 0.511 0.616 0.898
Cholesterol IntB:Post -2.467 30.976 -0.080 0.937 0.957
Triglycerides IntB 65.152 52.124 1.250 0.228 0.609
Triglycerides Post -11.167 48.727 -0.229 0.821 0.929
Triglycerides IntB:Post 38.767 72.274 0.536 0.599 0.898
HDL IntB -7.865 9.455 -0.832 0.417 0.801
HDL Post 6.167 8.839 0.698 0.495 0.848
HDL IntB:Post 2.433 13.110 0.186 0.855 0.929
LDL IntB 41.459 19.276 2.151 0.046 0.474
LDL Post 6.667 18.019 0.370 0.716 0.903
LDL IntB:Post -10.127 26.727 -0.379 0.709 0.903
LDL_HDL_Ratio IntB 0.922 0.451 2.046 0.057 0.474
LDL_HDL_Ratio Post -0.055 0.421 -0.131 0.898 0.937
LDL_HDL_Ratio IntB:Post -0.499 0.625 -0.798 0.436 0.804
hsCRP IntB -1.501 1.592 -0.943 0.359 0.786
hsCRP Post -1.883 1.488 -1.265 0.223 0.609
hsCRP IntB:Post 2.903 2.208 1.315 0.206 0.609
Insulin IntB 17.957 17.322 1.037 0.314 0.786
Insulin Post 2.667 16.193 0.165 0.871 0.929
Insulin IntB:Post -0.267 24.018 -0.011 0.991 0.991
PYY IntB -103.935 116.029 -0.896 0.383 0.786
PYY Post -32.087 108.467 -0.296 0.771 0.903
PYY IntB:Post 26.901 160.883 0.167 0.869 0.929
#readr::write_csv(all_results, "tab/results_blood_data.csv")

sessionInfo()
R version 3.6.3 (2020-02-29)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 18362)

Matrix products: default

locale:
[1] LC_COLLATE=English_United States.1252 
[2] LC_CTYPE=English_United States.1252   
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] cowplot_1.0.0     microbiome_1.8.0  car_3.0-8         carData_3.0-4    
 [5] gvlma_1.0.0.3     patchwork_1.0.0   viridis_0.5.1     viridisLite_0.3.0
 [9] gridExtra_2.3     xtable_1.8-4      kableExtra_1.1.0  plyr_1.8.6       
[13] data.table_1.12.8 readxl_1.3.1      forcats_0.5.0     stringr_1.4.0    
[17] dplyr_0.8.5       purrr_0.3.4       readr_1.3.1       tidyr_1.1.0      
[21] tibble_3.0.1      ggplot2_3.3.0     tidyverse_1.3.0   lmerTest_3.1-2   
[25] lme4_1.1-23       Matrix_1.2-18     vegan_2.5-6       lattice_0.20-38  
[29] permute_0.9-5     phyloseq_1.30.0  

loaded via a namespace (and not attached):
  [1] Rtsne_0.15          minqa_1.2.4         colorspace_1.4-1   
  [4] rio_0.5.16          ellipsis_0.3.1      rprojroot_1.3-2    
  [7] XVector_0.26.0      fs_1.4.1            rstudioapi_0.11    
 [10] farver_2.0.3        fansi_0.4.1         lubridate_1.7.8    
 [13] xml2_1.3.2          codetools_0.2-16    splines_3.6.3      
 [16] knitr_1.28          ade4_1.7-15         jsonlite_1.6.1     
 [19] workflowr_1.6.2     nloptr_1.2.2.1      broom_0.5.6        
 [22] cluster_2.1.0       dbplyr_1.4.4        BiocManager_1.30.10
 [25] compiler_3.6.3      httr_1.4.1          backports_1.1.7    
 [28] assertthat_0.2.1    cli_2.0.2           later_1.0.0        
 [31] htmltools_0.4.0     tools_3.6.3         igraph_1.2.5       
 [34] gtable_0.3.0        glue_1.4.1          reshape2_1.4.4     
 [37] Rcpp_1.0.4.6        Biobase_2.46.0      cellranger_1.1.0   
 [40] vctrs_0.3.0         Biostrings_2.54.0   multtest_2.42.0    
 [43] ape_5.3             nlme_3.1-144        iterators_1.0.12   
 [46] xfun_0.14           openxlsx_4.1.5      rvest_0.3.5        
 [49] lifecycle_0.2.0     statmod_1.4.34      zlibbioc_1.32.0    
 [52] MASS_7.3-51.5       scales_1.1.1        hms_0.5.3          
 [55] promises_1.1.0      parallel_3.6.3      biomformat_1.14.0  
 [58] rhdf5_2.30.1        RColorBrewer_1.1-2  curl_4.3           
 [61] yaml_2.2.1          stringi_1.4.6       highr_0.8          
 [64] S4Vectors_0.24.4    foreach_1.5.0       BiocGenerics_0.32.0
 [67] zip_2.0.4           boot_1.3-24         rlang_0.4.6        
 [70] pkgconfig_2.0.3     evaluate_0.14       Rhdf5lib_1.8.0     
 [73] labeling_0.3        tidyselect_1.1.0    magrittr_1.5       
 [76] R6_2.4.1            IRanges_2.20.2      generics_0.0.2     
 [79] DBI_1.1.0           foreign_0.8-75      pillar_1.4.4       
 [82] haven_2.3.0         whisker_0.4         withr_2.2.0        
 [85] mgcv_1.8-31         abind_1.4-5         survival_3.1-8     
 [88] modelr_0.1.8        crayon_1.3.4        rmarkdown_2.1      
 [91] grid_3.6.3          blob_1.2.1          git2r_0.27.1       
 [94] reprex_0.3.0        digest_0.6.25       webshot_0.5.2      
 [97] httpuv_1.5.2        numDeriv_2016.8-1.1 stats4_3.6.3       
[100] munsell_0.5.0