9 Multivariate distributions

9.1 Overview

9.1.1 Variable correlation

Compute correlations between the independent variables or their suggested transformations.

Show the code

variables <- unique(c(bact_transformed$demog_vars, 
                      bact_transformed$structural_vars,
                      bact_transformed$key_predictors,
                      bact_transformed$leuko_related_vars,
                      bact_transformed$leuko_ratio_vars,
                      bact_transformed$kidney_related_vars,
                      bact_transformed$acute_related_vars,
                      bact_transformed$remaining_vars))

corrp <- c_bact %>%
    dplyr::select(all_of(variables)) %>%
      cor(use="pairwise.complete.obs", method="pearson")

corrs <- c_bact %>%
    dplyr::select(all_of(variables)) %>%
      cor(use="pairwise.complete.obs", method="spearman")

# differences of pearson and spearman correlations to check for outliers
corrd <- corrp-corrs

Next, we depict the correlation coefficient in a quadratic heat map:

Show the code

ggcorrplot(corrp, tl.cex=5, tl.srt=90)

Explore if there are clusters of variables. Such clusters may give rise to define groups of variables for which a summary or only a representative may be considered in modeling:

Show the code

vc_bact<-Hmisc::varclus(as.matrix(c_bact[,variables]))
plot(vc_bact, cex=0.7)

Some of the clusters that pop up here are related to width/volume of blood cells (MPV, PDW), red blood cells (RBC, HGB, HCT; MCV, MCH), and some further ‘known’ associations such as that between CREA and eGFR (which follows from the construction of eGFR), and between ASAT and ALAT, between AMY and PAMY or between TP and ALB).

In the following scatterplots we have a look at those associations:

Show the code

ggplot(c_bact, aes(MPV, PDW))+geom_point(alpha = alpha_value, shape = 20) + geom_smooth()

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1102 rows containing non-finite values (stat_smooth).

Warning: Removed 1102 rows containing missing values (geom_point).

Show the code

ggplot(c_bact, aes(RBC, HGB))+geom_point(alpha = alpha_value, shape = 20) + geom_smooth()

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 461 rows containing non-finite values (stat_smooth).

Warning: Removed 461 rows containing missing values (geom_point).

Show the code

ggplot(c_bact, aes(RBC, HCT))+geom_point(alpha = alpha_value, shape = 20) + geom_smooth()

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 461 rows containing non-finite values (stat_smooth).
Removed 461 rows containing missing values (geom_point).

Show the code

ggplot(c_bact, aes(HGB, HCT))+geom_point(alpha = alpha_value, shape = 20) + geom_smooth()

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 42 rows containing non-finite values (stat_smooth).

Warning: Removed 42 rows containing missing values (geom_point).

Show the code

ggplot(c_bact, aes(MCV, MCH))+geom_point(alpha = alpha_value, shape = 20) + geom_smooth()

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 42 rows containing non-finite values (stat_smooth).
Removed 42 rows containing missing values (geom_point).

Show the code

#ggplot(c_bact, aes(t_KREA, eGFR))+geom_point(alpha = alpha_value, shape = 20) + geom_smooth()


ggplot(c_bact, aes(t_ASAT, t_ALAT))+geom_point(alpha = alpha_value, shape = 20) + geom_smooth()

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1195 rows containing non-finite values (stat_smooth).

Warning: Removed 1195 rows containing missing values (geom_point).

Show the code

ggplot(c_bact, aes(t_AMY, t_PAMY))+geom_point(alpha = alpha_value, shape = 20) + geom_smooth()

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 7182 rows containing non-finite values (stat_smooth).

Warning: Removed 7182 rows containing missing values (geom_point).

Show the code

ggplot(c_bact, aes(t_WBC, t_NEU))+geom_point(alpha = alpha_value, shape = 20) + geom_smooth()

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 728 rows containing non-finite values (stat_smooth).

Warning: Removed 728 rows containing missing values (geom_point).

Create scatterplots for pairs of variables with a large distance between Spearman and Pearson correlations (could be an indication of nonlinear association):

Show the code

for(j in 1:(length(variables)-1)){
  for(jj in (j+1):(length(variables))){
    if(abs(corrd[j, jj])>0.1) print(ggplot(data=c_bact, mapping=aes(x=.data[[variables[j]]],y=.data[[variables[jj]]]))+ geom_point(alpha = alpha_value)+geom_smooth() +
    theme_minimal())
  }
}

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 174 rows containing non-finite values (stat_smooth).

Warning: Removed 174 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1279 rows containing non-finite values (stat_smooth).

Warning: Removed 1279 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

Warning: Removed 732 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).
Removed 732 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).
Removed 732 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).
Removed 732 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).
Removed 732 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).
Removed 732 rows containing missing values (geom_point).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1580 rows containing non-finite values (stat_smooth).

Warning: Removed 1580 rows containing missing values (geom_point).

9.1.2 Distribution of age by sex

Distribution of age by sex

9.1.3 Distribution of leukocytes by age, coloured by sex

Show the code

c_bact$gender=factor(c_bact$SEX, levels=c(1,2), labels=c("male","female"))


#c_bact %>% ggplot(data=c_bact, mapping=aes(x=Alter, y=t_WBC, color=gender)) + geom_point(shape = 20) + geom_smooth()

9.1.4 Plot all variables vs. WBC in age/sex groups

Show the code

c_bact$Agegroup <- factor(cut(c_bact$AGE, c(min(c_bact$AGE), 50, 65, max(c_bact$AGE))))
table(c_bact$gender,c_bact$Agegroup)

        
         (16,50] (50,65] (65,101]
  male      2900    2671     2962
  female    2460    1579     2114

Show the code

for(j in 4:length(variables)){
    p1 <- 
      c_bact %>% 
      filter(!is.na(Agegroup)) %>% 
      ggplot(c_bact, mapping=aes(x=t_WBC,y=.data[[variables[j]]])) + 
      geom_point(alpha = alpha_value, shape = 20) + 
      geom_smooth() +  
      geom_rug(alpha = alpha_value) +
      facet_grid(gender ~ Agegroup)
    print(p1)
}

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 634 rows containing non-finite values (stat_smooth).

Warning: Removed 634 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 620 rows containing non-finite values (stat_smooth).

Warning: Removed 620 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 728 rows containing non-finite values (stat_smooth).

Warning: Removed 728 rows containing missing values (geom_point).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 462 rows containing non-finite values (stat_smooth).

Warning: Removed 462 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 552 rows containing non-finite values (stat_smooth).

Warning: Removed 552 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 557 rows containing non-finite values (stat_smooth).

Warning: Removed 557 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 666 rows containing non-finite values (stat_smooth).

Warning: Removed 666 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 648 rows containing non-finite values (stat_smooth).

Warning: Removed 648 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

Warning: Removed 732 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).
Removed 732 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).
Removed 732 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).
Removed 732 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).
Removed 732 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2428 rows containing non-finite values (stat_smooth).

Warning: Removed 2428 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 620 rows containing non-finite values (stat_smooth).

Warning: Removed 620 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 635 rows containing non-finite values (stat_smooth).

Warning: Removed 635 rows containing missing values (geom_point).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2990 rows containing non-finite values (stat_smooth).

Warning: Removed 2990 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 614 rows containing non-finite values (stat_smooth).

Warning: Removed 614 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1610 rows containing non-finite values (stat_smooth).

Warning: Removed 1610 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1446 rows containing non-finite values (stat_smooth).

Warning: Removed 1446 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1718 rows containing non-finite values (stat_smooth).

Warning: Removed 1718 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

Warning: Removed 463 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 462 rows containing non-finite values (stat_smooth).

Warning: Removed 462 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

Warning: Removed 463 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).
Removed 463 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).
Removed 463 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 476 rows containing non-finite values (stat_smooth).

Warning: Removed 476 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1104 rows containing non-finite values (stat_smooth).

Warning: Removed 1104 rows containing missing values (geom_point).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2887 rows containing non-finite values (stat_smooth).

Warning: Removed 2887 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2955 rows containing non-finite values (stat_smooth).

Warning: Removed 2955 rows containing missing values (geom_point).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1724 rows containing non-finite values (stat_smooth).

Warning: Removed 1724 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1733 rows containing non-finite values (stat_smooth).

Warning: Removed 1733 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1696 rows containing non-finite values (stat_smooth).

Warning: Removed 1696 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2313 rows containing non-finite values (stat_smooth).

Warning: Removed 2313 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 3476 rows containing non-finite values (stat_smooth).

Warning: Removed 3476 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1892 rows containing non-finite values (stat_smooth).

Warning: Removed 1892 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2008 rows containing non-finite values (stat_smooth).

Warning: Removed 2008 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2108 rows containing non-finite values (stat_smooth).

Warning: Removed 2108 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 4323 rows containing non-finite values (stat_smooth).

Warning: Removed 4323 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 7410 rows containing non-finite values (stat_smooth).

Warning: Removed 7410 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 4108 rows containing non-finite values (stat_smooth).

Warning: Removed 4108 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2865 rows containing non-finite values (stat_smooth).

Warning: Removed 2865 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1851 rows containing non-finite values (stat_smooth).

Warning: Removed 1851 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2149 rows containing non-finite values (stat_smooth).

Warning: Removed 2149 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2514 rows containing non-finite values (stat_smooth).

Warning: Removed 2514 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 4572 rows containing non-finite values (stat_smooth).

Warning: Removed 4572 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 5440 rows containing non-finite values (stat_smooth).

Warning: Removed 5440 rows containing missing values (geom_point).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 5417 rows containing non-finite values (stat_smooth).

Warning: Removed 5417 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1104 rows containing non-finite values (stat_smooth).

Warning: Removed 1104 rows containing missing values (geom_point).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

Warning: Removed 463 rows containing missing values (geom_point).

Show the code

#+
#  theme_minimal()

9.1.5 Plot all variables vs. WBC in age/sex groups: loess curves only

Show the code

for(j in 4:length(variables)){
    p1 <- 
      c_bact %>% 
      filter(!is.na(Agegroup)) %>% 
      ggplot(c_bact, mapping=aes(x=t_WBC,y=.data[[variables[j]]])) + 
     # geom_point(alpha = alpha_value) + 
      geom_smooth() +  
     # geom_rug() +
      facet_grid(gender ~ Agegroup)
    print(p1)
}

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 634 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 620 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 728 rows containing non-finite values (stat_smooth).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 462 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 552 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 557 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 666 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 648 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2428 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 620 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 635 rows containing non-finite values (stat_smooth).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2990 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 614 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1610 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1446 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1718 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 462 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 476 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1104 rows containing non-finite values (stat_smooth).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2887 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2955 rows containing non-finite values (stat_smooth).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1724 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1733 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1696 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2313 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 3476 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1892 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2008 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2108 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 4323 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 7410 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 4108 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2865 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1851 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2149 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2514 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 4572 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 5440 rows containing non-finite values (stat_smooth).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 5417 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1104 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

9.1.6 Plot all variables vs. WBC in age/sex groups: loess curves only

Show the code

for(j in 4:length(variables)){
    p1 <- 
      c_bact %>% 
      filter(!is.na(Agegroup)) %>% 
      ggplot(c_bact, mapping=aes(x=t_WBC,y=.data[[variables[j]]])) + 
     # geom_point(alpha = alpha_value) + 
      geom_smooth() +  
     # geom_rug() +
      facet_grid(gender ~ Agegroup, labeller=label_both)
    print(p1) +
    theme_minimal()
}

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 634 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 620 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 728 rows containing non-finite values (stat_smooth).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 462 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 552 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 557 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 666 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 648 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 732 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2428 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 620 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 635 rows containing non-finite values (stat_smooth).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2990 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 614 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1610 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1446 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1718 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 462 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 476 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1104 rows containing non-finite values (stat_smooth).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2887 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2955 rows containing non-finite values (stat_smooth).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1724 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1733 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1696 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2313 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 3476 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1892 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2008 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2108 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 4323 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 7410 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 4108 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2865 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1851 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2149 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 2514 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 4572 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 5440 rows containing non-finite values (stat_smooth).

Don't know how to automatically pick scale for object of type labelled/integer. Defaulting to continuous.
`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 5417 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 1104 rows containing non-finite values (stat_smooth).

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 463 rows containing non-finite values (stat_smooth).

9.2 Variable redundancy

9.2.1 Redundancy among key predictors

First we start with a redundancy analysis with the predictors deemed important by preceding studies.

Show the code

formula <- as.formula(
              paste("~AGE+",
                    paste(unique(c(bact_transformed$structural_vars,
                                   bact_transformed$key_predictors)),
                          collapse="+")))


Hmisc::redun(formula, data=c_bact)


Redundancy Analysis

Hmisc::redun(formula = formula, data = c_bact)

n: 13793    p: 7    nk: 3 

Number of NAs:   898 
Frequencies of Missing Values Due to Each Variable
   AGE  t_WBC    SEX  t_BUN t_CREA  t_NEU    PLT 
     0    462      0    172    159    728     42 


Transformation of target variables forced to be linear

R-squared cutoff: 0.9   Type: ordinary 

R^2 with which each variable can be predicted from all other variables:

   AGE  t_WBC    SEX  t_BUN t_CREA  t_NEU    PLT 
 0.198  0.934  0.112  0.610  0.587  0.933  0.164 

Rendundant variables:

t_WBC

Predicted from variables:

AGE SEX t_BUN t_CREA t_NEU PLT 

  Variable Deleted   R^2 R^2 after later deletions
1            t_WBC 0.934

This analysis suggests redundancy of WBC after NEU is in the predictor set. We investigate this further by looking only at leukocyte-related variables.

9.2.2 Redundancy among leukocyte-related variables

In redundancy analysis of all predictor variables, the large number of non-complete cases is an issue. First we start with the leukocyte ratios - there should be large redundancy issues. This is even the case if no nonlinear modeling is applied.

Show the code

Hmisc::redun(~I(EOSR)+I(BASOR)+I(NEUR)+I(LYMR)+I(MONOR), data=c_bact)


Redundancy Analysis

Hmisc::redun(formula = ~I(EOSR) + I(BASOR) + I(NEUR) + I(LYMR) + 
    I(MONOR), data = c_bact)

n: 13959    p: 5    nk: 3 

Number of NAs:   732 
Frequencies of Missing Values Due to Each Variable
 I(EOSR) I(BASOR)  I(NEUR)  I(LYMR) I(MONOR) 
     732      732      732      732      732 


Transformation of target variables forced to be linear

R-squared cutoff: 0.9   Type: ordinary 

R^2 with which each variable can be predicted from all other variables:

 I(EOSR) I(BASOR)  I(NEUR)  I(LYMR) I(MONOR) 
       1        1        1        1        1 

Rendundant variables:

I(EOSR)

Predicted from variables:

I(BASOR) I(NEUR) I(LYMR) I(MONOR) 

  Variable Deleted R^2 R^2 after later deletions
1          I(EOSR)   1

Now we use the absolute concentrations. BASO is modeled as linear because it has very few distinct values:

Show the code

Hmisc::redun(~t_EOS+I(t_BASO)+t_NEU+t_LYM+MONO, data=c_bact)


Redundancy Analysis

Hmisc::redun(formula = ~t_EOS + I(t_BASO) + t_NEU + t_LYM + MONO, 
    data = c_bact)

n: 13963    p: 5    nk: 3 

Number of NAs:   728 
Frequencies of Missing Values Due to Each Variable
    t_EOS I(t_BASO)     t_NEU     t_LYM      MONO 
      135       146       728       262       246 


Transformation of target variables forced to be linear

R-squared cutoff: 0.9   Type: ordinary 

R^2 with which each variable can be predicted from all other variables:

    t_EOS I(t_BASO)     t_NEU     t_LYM      MONO 
    0.144     0.171     0.312     0.266     0.348 

No redundant variables

Now we add WBC:

Show the code

Hmisc::redun(~t_EOS+I(t_BASO)+t_NEU+t_LYM+MONO+t_WBC, data=c_bact)


Redundancy Analysis

Hmisc::redun(formula = ~t_EOS + I(t_BASO) + t_NEU + t_LYM + MONO + 
    t_WBC, data = c_bact)

n: 13963    p: 6    nk: 3 

Number of NAs:   728 
Frequencies of Missing Values Due to Each Variable
    t_EOS I(t_BASO)     t_NEU     t_LYM      MONO     t_WBC 
      135       146       728       262       246       462 


Transformation of target variables forced to be linear

R-squared cutoff: 0.9   Type: ordinary 

R^2 with which each variable can be predicted from all other variables:

    t_EOS I(t_BASO)     t_NEU     t_LYM      MONO     t_WBC 
    0.176     0.179     0.982     0.658     0.500     0.984 

Rendundant variables:

t_WBC

Predicted from variables:

t_EOS I(t_BASO) t_NEU t_LYM MONO 

  Variable Deleted   R^2 R^2 after later deletions
1            t_WBC 0.984

This indicates very large \(R^2\) values for NEU and WBC, meaning that probably because of their large correlation, the variables are nearly redundant. (This also becomes clear from the histogram of NEUR, which shows the ratios of NEU to WBC.) When including both covariates in a model, it may happen that standard errors are inflated such that an association cannot be statistically proven; nevertheless, according to the preceding studies both variables could be important! One way to circumvent the problem is to generate a complementary variable that is defined as the difference of WBC and NEU and use this variable instead of WBC.

Show the code

WBC_NEU <- c_bact$WBC - c_bact$NEU
sum_noNEU <- apply(c_bact[,c("EOS","BASO","LYM","MONO")],1,sum)

ggplot(c_bact, aes(NEU, WBC_NEU)) + geom_point(alpha = alpha_value) + geom_smooth() + scale_x_continuous(trans="pseudo_log") + scale_y_continuous(trans="pseudo_log")

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 728 rows containing non-finite values (stat_smooth).

Warning: Removed 728 rows containing missing values (geom_point).

This variable is expected to be highly correlated with the sum of MONO, LYM, BASO and EOS:

Show the code

ggplot(c_bact, aes(sum_noNEU, WBC_NEU)) + geom_point(alpha = alpha_value) + geom_smooth() + scale_x_continuous(trans="pseudo_log") + scale_y_continuous(trans="pseudo_log")

`geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Warning: Removed 728 rows containing non-finite values (stat_smooth).

Warning: Removed 728 rows containing missing values (geom_point).

9.2.3 Redundancy among all potential predictors

Now we perform a full redundancy analysis, but omitting WBC, the leukocyte ratio variables, and BUN and KREA (for their use in constructing BUN_CREA and eGFR).

Show the code

formula <- as.formula(
              paste("~I(t_EOS)+I(t_BASO)+t_LYM+MONO+t_NEU+",
                    paste(unique(c(bact_transformed$demog_vars,
                                   c("t_BUN_CREA","eGFR","POTASS"),
                                   bact_transformed$acute_related_vars,
                                   bact_transformed$remaining_vars)),collapse="+")))


Hmisc::redun(formula, data=c_bact)


Redundancy Analysis

Hmisc::redun(formula = formula, data = c_bact)

n: 3980     p: 44   nk: 3 

Number of NAs:   10711 
Frequencies of Missing Values Due to Each Variable
  I(t_EOS)  I(t_BASO)      t_LYM       MONO      t_NEU        AGE        SEX 
       135        146        262        246        728          0          0 
t_BUN_CREA       eGFR     POTASS        FIB        CRP     t_ASAT     t_ALAT 
       174        159       2008       2567        155       1154        987 
     t_GGT        MCV        HGB        HCT        MCH       MCHC        RDW 
      1262         42         41         42         42         42         56 
       MPV         NT     t_APTT     SODIUM         CA     t_PHOS         MG 
       702       2467       2549       1282       1276       1242       1869 
        HS     t_GBIL         TP        ALB      t_AMY     t_PAMY      t_LIP 
      3061       1441       1583       1676       3913       7114       3699 
       CHE       t_AP      t_LDH       t_CK      t_GLU     t_TRIG       CHOL 
      2447       1400       1714       2080       4192       5061       5045 
       PDW        RBC 
      1102        461 


Transformation of target variables forced to be linear

R-squared cutoff: 0.9   Type: ordinary 

R^2 with which each variable can be predicted from all other variables:

  I(t_EOS)  I(t_BASO)      t_LYM       MONO      t_NEU        AGE        SEX 
     0.251      0.244      0.390      0.426      0.425      0.612      0.321 
t_BUN_CREA       eGFR     POTASS        FIB        CRP     t_ASAT     t_ALAT 
     0.376      0.637      0.300      0.670      0.659      0.874      0.760 
     t_GGT        MCV        HGB        HCT        MCH       MCHC        RDW 
     0.643      0.993      0.996      0.996      0.995      0.984      0.530 
       MPV         NT     t_APTT     SODIUM         CA     t_PHOS         MG 
     0.905      0.340      0.257      0.335      0.530      0.316      0.244 
        HS     t_GBIL         TP        ALB      t_AMY     t_PAMY      t_LIP 
     0.482      0.393      0.787      0.855      0.667      0.720      0.580 
       CHE       t_AP      t_LDH       t_CK      t_GLU     t_TRIG       CHOL 
     0.658      0.615      0.588      0.585      0.263      0.384      0.498 
       PDW        RBC 
     0.899      0.977 

Rendundant variables:

HCT MCH HGB MPV

Predicted from variables:

I(t_EOS) I(t_BASO) t_LYM MONO t_NEU AGE SEX t_BUN_CREA eGFR POTASS FIB CRP t_ASAT t_ALAT t_GGT MCV MCHC RDW NT t_APTT SODIUM CA t_PHOS MG HS t_GBIL TP ALB t_AMY t_PAMY t_LIP CHE t_AP t_LDH t_CK t_GLU t_TRIG CHOL PDW RBC 

  Variable Deleted   R^2 R^2 after later deletions
1              HCT 0.996         0.996 0.975 0.975
2              MCH 0.994               0.994 0.994
3              HGB 0.975                     0.975
4              MPV 0.904

This analysis suggests that HCT, MCH, HGB and MPV may be redundant on top of the other variables. Note that BUN, CREA and WBC were already omitted from this redundancy analysis.

9.3 Section session info

R version 4.1.2 (2021-11-01)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur 10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

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

other attached packages:
 [1] mice_3.14.0      ggcorrplot_0.1.3 gtsummary_1.6.1  Hmisc_4.6-0     
 [5] Formula_1.2-4    survival_3.2-13  lattice_0.20-45  plotly_4.10.0   
 [9] forcats_0.5.1    stringr_1.4.0    dplyr_1.0.9      purrr_0.3.4     
[13] readr_2.1.1      tidyr_1.2.0      tibble_3.1.7     ggplot2_3.3.6   
[17] tidyverse_1.3.1  here_1.0.1      

loaded via a namespace (and not attached):
 [1] nlme_3.1-153        fs_1.5.2            lubridate_1.8.0    
 [4] RColorBrewer_1.1-3  httr_1.4.2          rprojroot_2.0.2    
 [7] tools_4.1.2         backports_1.4.1     utf8_1.2.2         
[10] R6_2.5.1            rpart_4.1-15        mgcv_1.8-38        
[13] DBI_1.1.2           lazyeval_0.2.2      colorspace_2.0-3   
[16] nnet_7.3-16         withr_2.5.0         tidyselect_1.1.2   
[19] gridExtra_2.3       compiler_4.1.2      cli_3.3.0          
[22] rvest_1.0.2         gt_0.6.0            htmlTable_2.3.0    
[25] xml2_1.3.3          labeling_0.4.2      scales_1.2.0       
[28] checkmate_2.1.0     digest_0.6.29       foreign_0.8-81     
[31] rmarkdown_2.11      base64enc_0.1-3     jpeg_0.1-9         
[34] pkgconfig_2.0.3     htmltools_0.5.2     dbplyr_2.1.1       
[37] fastmap_1.1.0       htmlwidgets_1.5.4   rlang_1.0.3        
[40] readxl_1.3.1        rstudioapi_0.13     farver_2.1.0       
[43] generics_0.1.2      jsonlite_1.7.2      crosstalk_1.2.0    
[46] magrittr_2.0.3      Matrix_1.3-4        Rcpp_1.0.8.3       
[49] munsell_0.5.0       fansi_1.0.3         lifecycle_1.0.1    
[52] yaml_2.2.1          stringi_1.7.6       plyr_1.8.6         
[55] grid_4.1.2          crayon_1.5.1        haven_2.4.3        
[58] splines_4.1.2       hms_1.1.1           knitr_1.37         
[61] pillar_1.7.0        reshape2_1.4.4      reprex_2.0.1       
[64] glue_1.6.2          evaluate_0.14       latticeExtra_0.6-29
[67] data.table_1.14.2   broom.helpers_1.7.0 renv_0.15.5        
[70] modelr_0.1.8        png_0.1-7           vctrs_0.4.1        
[73] tzdb_0.2.0          cellranger_1.1.0    gtable_0.3.0       
[76] assertthat_0.2.1    xfun_0.31           broom_0.8.0        
[79] viridisLite_0.4.0   cluster_2.1.2       ellipsis_0.3.2