Last updated: 2021-02-11

Checks: 6 1

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Question 3

Q3: Is fuso associated with tumor stage (pTNM) in either data set? Does X bacteria predict stage? Multivariable w/ age, sex, BMI, history of Barrett's

Add to this analysis:

  • Fusobacterium nucleatum
  • Streptococcus sanguinis
  • Campylobacter concisus
  • Prevotella spp.

TCGA drop “not reported” from tumor stage.

NCI 16s data

Double Checking Data

# in long format
table(dat.16s$tumor.stage)

    0     1     I    II   III    IV 
11088   264  6336 13464  6072  2640 
# by subject
dat <- dat.16s %>% filter(OTU == "Fusobacterium_nucleatum")
table(dat$tumor.stage)

  0   1   I  II III  IV 
 42   1  24  51  23  10 
sum(table(dat$tumor.stage)) # sample size met
[1] 151
mean.dat <- dat.16s.s %>%
  group_by(tumor.stage, OTU) %>%
  summarize(M = mean(Abundance))
`summarise()` has grouped output by 'tumor.stage'. You can override using the `.groups` argument.
ggplot(dat.16s.s, aes(x=tumor.stage, y=Abundance))+
  geom_violin()+
  geom_jitter(alpha=0.25,width = 0.25)+
  geom_point(data=mean.dat, aes(x=tumor.stage, y = M), size=2, alpha =0.9, color="red")+
  labs(x="Tumor Stage", 
       title="Distribution of abundance across tumor stage",
       subtitle="Red dot is average abundnace")+
  scale_y_continuous(trans="pseudo_log")+
  #  breaks=c(0, 10, 100, 200, 300, 400, 500),
  #  limits = c(0,500),
  #  
  facet_wrap(.~OTU, nrow=1, scales="free")+
  theme_classic()

Stage “1” has only 1 unique sample and will be dropped from subsequent analyses. And remove NA values.

dat.16s.s <- dat.16s.s %>%
  filter(tumor.stage != "1")%>%
  mutate(tumor.stage = droplevels(tumor.stage, exclude=c("1",NA)))

Ordered Logistic Regression

Model 1: TS ~ OTU

## fit ordered logit model and store results 'm'
fit <- MASS::polr(tumor.stage ~ OTU, data = dat.16s.s, Hess=TRUE)

## view a summary of the model
summary(fit)
Call:
MASS::polr(formula = tumor.stage ~ OTU, data = dat.16s.s, Hess = TRUE)

Coefficients:
                                 Value Std. Error   t value
OTUStreptococcus spp.        -6.29e-05      0.207 -0.000303
OTUCampylobacter concisus    -6.28e-05      0.207 -0.000303
OTUPrevotella melaninogenica -6.32e-05      0.207 -0.000305

Intercepts:
       Value  Std. Error t value
0|I    -0.944  0.156     -6.049 
I|II   -0.241  0.151     -1.595 
II|III  1.266  0.161      7.875 
III|IV  2.639  0.207     12.741 

Residual Deviance: 1781.40 
AIC: 1795.40 
# obtain approximate p-values
ctable <- coef(summary(fit))
p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2
(ctable <- cbind(ctable, "p value" = p))
                                  Value Std. Error    t value   p value
OTUStreptococcus spp.        -6.291e-05     0.2073 -0.0003035 9.998e-01
OTUCampylobacter concisus    -6.281e-05     0.2073 -0.0003030 9.998e-01
OTUPrevotella melaninogenica -6.318e-05     0.2073 -0.0003048 9.998e-01
0|I                          -9.445e-01     0.1562 -6.0485909 1.461e-09
I|II                         -2.412e-01     0.1513 -1.5947287 1.108e-01
II|III                        1.266e+00     0.1607  7.8750312 3.407e-15
III|IV                        2.639e+00     0.2071 12.7409977 3.499e-37
# obtain CIs
(ci <- confint(fit))  # CIs assuming normality
Waiting for profiling to be done...
                               2.5 % 97.5 %
OTUStreptococcus spp.        -0.4065 0.4065
OTUCampylobacter concisus    -0.4065 0.4065
OTUPrevotella melaninogenica -0.4065 0.4065
## OR and CI
exp(cbind(OR = coef(fit), ci))
                                 OR  2.5 % 97.5 %
OTUStreptococcus spp.        0.9999 0.6659  1.502
OTUCampylobacter concisus    0.9999 0.6659  1.502
OTUPrevotella melaninogenica 0.9999 0.6659  1.502
# save fitted logits
pp <- fitted(fit)
# preditive data
dotu <- data.frame(OTU = c("Fusobacterium nucleatum", "Streptococcus spp.", "Campylobacter concisus", "Prevotella melaninogenica"))
predict(fit, newdata = dotu, "probs") # only TINY differences
     0    I   II    III      IV
1 0.28 0.16 0.34 0.1533 0.06667
2 0.28 0.16 0.34 0.1533 0.06667
3 0.28 0.16 0.34 0.1533 0.06667
4 0.28 0.16 0.34 0.1533 0.06667
## store the predicted probabilities for each value of ses
pp.otu <-cbind(dotu, predict(fit, newdata = dotu, "probs", se = TRUE))

## calculate the mean probabilities within each level of OTU
by(pp.otu[, 2:6], pp.otu$OTU, colMeans)
pp.otu$OTU: Campylobacter concisus
      0       I      II     III      IV 
0.28001 0.16000 0.34000 0.15333 0.06667 
------------------------------------------------------------ 
pp.otu$OTU: Fusobacterium nucleatum
      0       I      II     III      IV 
0.27999 0.15999 0.34001 0.15334 0.06667 
------------------------------------------------------------ 
pp.otu$OTU: Prevotella melaninogenica
      0       I      II     III      IV 
0.28001 0.16000 0.34000 0.15333 0.06667 
------------------------------------------------------------ 
pp.otu$OTU: Streptococcus spp.
      0       I      II     III      IV 
0.28001 0.16000 0.34000 0.15333 0.06667 

Model 2: TS ~ Abundance

## fit ordered logit model and store results
fit <- MASS::polr(tumor.stage ~ Abundance, data = dat.16s.s, Hess=TRUE)

## view a summary of the model
summary(fit)
Call:
MASS::polr(formula = tumor.stage ~ Abundance, data = dat.16s.s, 
    Hess = TRUE)

Coefficients:
            Value Std. Error t value
Abundance 0.00203    0.00384   0.529

Intercepts:
       Value  Std. Error t value
0|I    -0.925  0.098     -9.432 
I|II   -0.221  0.091     -2.442 
II|III  1.286  0.106     12.159 
III|IV  2.659  0.168     15.829 

Residual Deviance: 1781.12 
AIC: 1791.12 
# obtain approximate p-values
ctable <- coef(summary(fit))
p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2
(ctable <- cbind(ctable, "p value" = p))
              Value Std. Error t value   p value
Abundance  0.002029   0.003837  0.5286 5.971e-01
0|I       -0.924970   0.098068 -9.4319 4.027e-21
I|II      -0.221123   0.090546 -2.4421 1.460e-02
II|III     1.285730   0.105746 12.1587 5.160e-34
III|IV     2.658753   0.167964 15.8293 1.953e-56
# obtain CIs
(ci <- confint(fit))  # CIs assuming normality
Waiting for profiling to be done...
    2.5 %    97.5 % 
-0.005522  0.009549 
## OR and CI
exp(cbind(OR = coef(fit), ci))
          OR     ci
2.5 %  1.002 0.9945
97.5 % 1.002 1.0096
# save fitted logits
pp <- fitted(fit)
dotu <- data.frame(OTU = c("Fusobacterium nucleatum", "Streptococcus spp.", "Campylobacter concisus", "Prevotella melaninogenica"), Abundance = mean(dat.16s.s$Abundance))
predict(fit, newdata = dotu, "probs") # bigger differences
       0      I     II    III      IV
1 0.2801 0.1602 0.3399 0.1532 0.06662
2 0.2801 0.1602 0.3399 0.1532 0.06662
3 0.2801 0.1602 0.3399 0.1532 0.06662
4 0.2801 0.1602 0.3399 0.1532 0.06662
## look at the averaged predicted probabilities for different values of the continuous predictor variable Abundnace within each level of OTU
dabund <- data.frame(
  OTU = rep(c("Fusobacterium nucleatum", "Streptococcus spp.", "Campylobacter concisus", "Prevotella melaninogenica"), each = 51),
  Abundance = rep(seq(0, 500,10), 4)
)
pp.abund <-cbind(dabund, predict(fit, newdata = dabund, "probs", se = TRUE))

## calculate the mean probabilities within each level of OTU
by(pp.abund[, 3:7], pp.abund$OTU, colMeans)
pp.abund$OTU: Campylobacter concisus
     0      I     II    III     IV 
0.1970 0.1319 0.3530 0.2106 0.1075 
------------------------------------------------------------ 
pp.abund$OTU: Fusobacterium nucleatum
     0      I     II    III     IV 
0.1970 0.1319 0.3530 0.2106 0.1075 
------------------------------------------------------------ 
pp.abund$OTU: Prevotella melaninogenica
     0      I     II    III     IV 
0.1970 0.1319 0.3530 0.2106 0.1075 
------------------------------------------------------------ 
pp.abund$OTU: Streptococcus spp.
     0      I     II    III     IV 
0.1970 0.1319 0.3530 0.2106 0.1075 
## melt data set to long for ggplot2
lpp <- melt(pp.abund, id.vars = c("OTU", "Abundance"), value.name = "probability")

## plot predicted probabilities across Abundance values for each level of OTU
## facetted by tumor.stage
ggplot(lpp, aes(x = Abundance, y = probability)) +
  geom_line() + 
  facet_grid(variable ~., scales="free")+
  labs(y="Probability of Tumor Stage",
       title="Tumor stage likelihood with bacteria abundance")+
  theme(
    panel.grid = element_blank()
  )

Model 3: TS ~ OTU + Abundance

## fit ordered logit model and store results
fit <- MASS::polr(tumor.stage ~ OTU + Abundance, data = dat.16s.s, Hess=TRUE)

## view a summary of the model
summary(fit)
Call:
MASS::polr(formula = tumor.stage ~ OTU + Abundance, data = dat.16s.s, 
    Hess = TRUE)

Coefficients:
                                Value Std. Error t value
OTUStreptococcus spp.        -0.07580    0.23782 -0.3187
OTUCampylobacter concisus     0.01201    0.20806  0.0577
OTUPrevotella melaninogenica -0.00282    0.20726 -0.0136
Abundance                     0.00309    0.00474  0.6527

Intercepts:
       Value  Std. Error t value
0|I    -0.931  0.157     -5.921 
I|II   -0.227  0.153     -1.489 
II|III  1.280  0.162      7.895 
III|IV  2.653  0.208     12.744 

Residual Deviance: 1780.97 
AIC: 1796.97 
# obtain approximate p-values
ctable <- coef(summary(fit))
p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2
(ctable <- cbind(ctable, "p value" = p))
                                 Value Std. Error  t value   p value
OTUStreptococcus spp.        -0.075802   0.237819 -0.31874 7.499e-01
OTUCampylobacter concisus     0.012013   0.208062  0.05774 9.540e-01
OTUPrevotella melaninogenica -0.002818   0.207263 -0.01360 9.892e-01
Abundance                     0.003091   0.004736  0.65267 5.140e-01
0|I                          -0.931388   0.157314 -5.92055 3.209e-09
I|II                         -0.227249   0.152659 -1.48861 1.366e-01
II|III                        1.279684   0.162094  7.89470 2.910e-15
III|IV                        2.652544   0.208139 12.74410 3.363e-37
# obtain CIs
(ci <- confint(fit))  # CIs assuming normality
Waiting for profiling to be done...
                                 2.5 %  97.5 %
OTUStreptococcus spp.        -0.542806 0.39021
OTUCampylobacter concisus    -0.396086 0.41996
OTUPrevotella melaninogenica -0.409287 0.40363
Abundance                    -0.006224 0.01237
## OR and CI
exp(cbind(OR = coef(fit), ci))
                                 OR  2.5 % 97.5 %
OTUStreptococcus spp.        0.9270 0.5811  1.477
OTUCampylobacter concisus    1.0121 0.6729  1.522
OTUPrevotella melaninogenica 0.9972 0.6641  1.497
Abundance                    1.0031 0.9938  1.012
# save fitted logits
pp <- fitted(fit)
# predit data
dotu <- data.frame(OTU = c("Fusobacterium nucleatum", "Streptococcus spp.", "Campylobacter concisus", "Prevotella melaninogenica"), Abundance = mean(dat.16s.s$Abundance))
predict(fit, newdata = dotu, "probs") # bigger differences
       0      I     II    III      IV
1 0.2768 0.1595 0.3411 0.1549 0.06763
2 0.2922 0.1628 0.3352 0.1467 0.06301
3 0.2744 0.1589 0.3420 0.1563 0.06840
4 0.2774 0.1596 0.3409 0.1546 0.06746
## look at the averaged predicted probabilities for different values of the continuous predictor variable Abundnace within each level of OTU
dabund <- data.frame(
  OTU = rep(c("Fusobacterium nucleatum", "Streptococcus spp.", "Campylobacter concisus", "Prevotella melaninogenica"), each = 51),
  Abundance = rep(seq(0, 500,10), 4)
)
pp.abund <-cbind(dabund, predict(fit, newdata = dabund, "probs", se = TRUE))

## calculate the mean probabilities within each level of OTU
by(pp.abund[, 3:7], pp.abund$OTU, colMeans)
pp.abund$OTU: Campylobacter concisus
     0      I     II    III     IV 
0.1615 0.1142 0.3400 0.2418 0.1425 
------------------------------------------------------------ 
pp.abund$OTU: Fusobacterium nucleatum
     0      I     II    III     IV 
0.1631 0.1149 0.3404 0.2406 0.1410 
------------------------------------------------------------ 
pp.abund$OTU: Prevotella melaninogenica
     0      I     II    III     IV 
0.1635 0.1150 0.3405 0.2403 0.1407 
------------------------------------------------------------ 
pp.abund$OTU: Streptococcus spp.
     0      I     II    III     IV 
0.1734 0.1194 0.3425 0.2324 0.1323 
## melt data set to long for ggplot2
lpp <- melt(pp.abund, id.vars = c("OTU", "Abundance"), value.name = "probability")

## plot predicted probabilities across Abundance values for each level of OTU
## facetted by tumor.stage
ggplot(lpp, aes(x = Abundance, y = probability, colour = OTU)) +
  geom_line() + 
  facet_grid(variable ~., scales="free", labeller="label_both")+
  labs(y="Probability of Tumor Stage",
       title="Tumor stage likelihood with bacteria abundance and OTU")+
  theme(
    panel.grid = element_blank()
  )

Model 4: TS ~ OTU + Abundance + OTU:Abundnace

## fit ordered logit model and store results
fit <- MASS::polr(tumor.stage ~ OTU + Abundance+ OTU:Abundance, data = dat.16s.s, Hess=TRUE)

## view a summary of the model
summary(fit)
Call:
MASS::polr(formula = tumor.stage ~ OTU + Abundance + OTU:Abundance, 
    data = dat.16s.s, Hess = TRUE)

Coefficients:
                                          Value Std. Error t value
OTUStreptococcus spp.                   0.11164     0.2670   0.418
OTUCampylobacter concisus               0.07891     0.2167   0.364
OTUPrevotella melaninogenica           -0.02403     0.2284  -0.105
Abundance                               0.01545     0.0118   1.306
OTUStreptococcus spp.:Abundance        -0.01691     0.0131  -1.294
OTUCampylobacter concisus:Abundance    -0.03294     0.0639  -0.516
OTUPrevotella melaninogenica:Abundance  0.00191     0.0188   0.102

Intercepts:
       Value  Std. Error t value
0|I    -0.880  0.164     -5.363 
I|II   -0.173  0.160     -1.080 
II|III  1.340  0.170      7.863 
III|IV  2.715  0.215     12.642 

Residual Deviance: 1778.15 
AIC: 1800.15 
# obtain approximate p-values
ctable <- coef(summary(fit))
p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2
(ctable <- cbind(ctable, "p value" = p))
                                           Value Std. Error t value   p value
OTUStreptococcus spp.                   0.111638    0.26698  0.4181 6.758e-01
OTUCampylobacter concisus               0.078914    0.21672  0.3641 7.158e-01
OTUPrevotella melaninogenica           -0.024033    0.22839 -0.1052 9.162e-01
Abundance                               0.015445    0.01183  1.3061 1.915e-01
OTUStreptococcus spp.:Abundance        -0.016909    0.01306 -1.2943 1.956e-01
OTUCampylobacter concisus:Abundance    -0.032940    0.06388 -0.5156 6.061e-01
OTUPrevotella melaninogenica:Abundance  0.001913    0.01884  0.1016 9.191e-01
0|I                                    -0.879584    0.16400 -5.3633 8.174e-08
I|II                                   -0.172875    0.16011 -1.0797 2.803e-01
II|III                                  1.340472    0.17047  7.8633 3.740e-15
III|IV                                  2.715144    0.21478 12.6417 1.244e-36
# obtain CIs
(ci <- confint(fit))  # CIs assuming normality
Waiting for profiling to be done...
                                           2.5 %   97.5 %
OTUStreptococcus spp.                  -0.412893 0.634477
OTUCampylobacter concisus              -0.345946 0.504079
OTUPrevotella melaninogenica           -0.472057 0.423783
Abundance                              -0.007727 0.039526
OTUStreptococcus spp.:Abundance        -0.043247 0.008643
OTUCampylobacter concisus:Abundance    -0.169623 0.092063
OTUPrevotella melaninogenica:Abundance -0.035537 0.038820
## OR and CI
exp(cbind(OR = coef(fit), ci))
                                           OR  2.5 % 97.5 %
OTUStreptococcus spp.                  1.1181 0.6617  1.886
OTUCampylobacter concisus              1.0821 0.7076  1.655
OTUPrevotella melaninogenica           0.9763 0.6237  1.528
Abundance                              1.0156 0.9923  1.040
OTUStreptococcus spp.:Abundance        0.9832 0.9577  1.009
OTUCampylobacter concisus:Abundance    0.9676 0.8440  1.096
OTUPrevotella melaninogenica:Abundance 1.0019 0.9651  1.040
# save fitted logits
pp <- fitted(fit)
# predit data
gmeans <- dat.16s.s %>% group_by(OTU) %>% summarise(M = mean(Abundance))
dotu <- data.frame(OTU = c("Fusobacterium nucleatum", "Streptococcus spp.", "Campylobacter concisus", "Prevotella melaninogenica"), Abundance = gmeans$M)
predict(fit, newdata = dotu, "probs") # bigger differences
       0      I     II    III      IV
1 0.2815 0.1612 0.3403 0.1515 0.06552
2 0.2788 0.1606 0.3413 0.1530 0.06633
3 0.2788 0.1606 0.3413 0.1530 0.06635
4 0.2793 0.1607 0.3411 0.1527 0.06618
## look at the averaged predicted probabilities for different values of the continuous predictor variable Abundnace within each level of OTU
dabund <- data.frame(
  OTU = rep(c("Fusobacterium nucleatum", "Streptococcus spp.", "Campylobacter concisus", "Prevotella melaninogenica"), each = 51),
  Abundance = rep(seq(0, 500,10), 4)
)
pp.abund <-cbind(dabund, predict(fit, newdata = dabund, "probs", se = TRUE))

## calculate the mean probabilities within each level of OTU
by(pp.abund[, 3:7], pp.abund$OTU, colMeans)
pp.abund$OTU: Campylobacter concisus
       0        I       II      III       IV 
0.849088 0.052662 0.068093 0.021732 0.008426 
------------------------------------------------------------ 
pp.abund$OTU: Fusobacterium nucleatum
      0       I      II     III      IV 
0.04697 0.03502 0.12530 0.15395 0.63875 
------------------------------------------------------------ 
pp.abund$OTU: Prevotella melaninogenica
      0       I      II     III      IV 
0.04299 0.03181 0.11282 0.13782 0.67457 
------------------------------------------------------------ 
pp.abund$OTU: Streptococcus spp.
      0       I      II     III      IV 
0.35013 0.16995 0.30904 0.12107 0.04981 
## melt data set to long for ggplot2
lpp <- melt(pp.abund, id.vars = c("OTU", "Abundance"), value.name = "probability") %>%
  mutate(Tumor_Stage = variable)

## plot predicted probabilities across Abundance values for each level of OTU
## facetted by tumor.stage
ggplot(lpp, aes(x = Abundance, y = probability, colour = OTU)) +
  geom_line() + 
  facet_grid(Tumor_Stage ~., scales="free", labeller="label_both")+
  labs(y="Probability of Tumor Stage",
       title="Tumor stage likelihood with bacteria abundance and OTU")+
  theme(
    panel.grid = element_blank()
  )

# proportional odds assumption
glm(I(as.numeric(tumor.stage) >= 2) ~ OTU, family="binomial", data = dat.16s.s)

Call:  glm(formula = I(as.numeric(tumor.stage) >= 2) ~ OTU, family = "binomial", 
    data = dat.16s.s)

Coefficients:
                 (Intercept)         OTUStreptococcus spp.  
                    9.44e-01                     -1.38e-15  
   OTUCampylobacter concisus  OTUPrevotella melaninogenica  
                   -5.28e-16                     -3.14e-16  

Degrees of Freedom: 599 Total (i.e. Null);  596 Residual
Null Deviance:      712 
Residual Deviance: 712  AIC: 720
glm(I(as.numeric(tumor.stage) >= 3) ~ OTU, family="binomial", data = dat.16s.s)

Call:  glm(formula = I(as.numeric(tumor.stage) >= 3) ~ OTU, family = "binomial", 
    data = dat.16s.s)

Coefficients:
                 (Intercept)         OTUStreptococcus spp.  
                    2.41e-01                     -1.88e-15  
   OTUCampylobacter concisus  OTUPrevotella melaninogenica  
                   -2.70e-15                     -1.73e-15  

Degrees of Freedom: 599 Total (i.e. Null);  596 Residual
Null Deviance:      823 
Residual Deviance: 823  AIC: 831
glm(I(as.numeric(tumor.stage) >= 4) ~ OTU, family="binomial", data = dat.16s.s)

Call:  glm(formula = I(as.numeric(tumor.stage) >= 4) ~ OTU, family = "binomial", 
    data = dat.16s.s)

Coefficients:
                 (Intercept)         OTUStreptococcus spp.  
                   -1.27e+00                     -5.08e-15  
   OTUCampylobacter concisus  OTUPrevotella melaninogenica  
                   -7.88e-16                     -3.16e-15  

Degrees of Freedom: 599 Total (i.e. Null);  596 Residual
Null Deviance:      632 
Residual Deviance: 632  AIC: 640
glm(I(as.numeric(tumor.stage) >= 5) ~ OTU, family="binomial", data = dat.16s.s)

Call:  glm(formula = I(as.numeric(tumor.stage) >= 5) ~ OTU, family = "binomial", 
    data = dat.16s.s)

Coefficients:
                 (Intercept)         OTUStreptococcus spp.  
                   -2.64e+00                      8.92e-16  
   OTUCampylobacter concisus  OTUPrevotella melaninogenica  
                    2.04e-15                      3.21e-16  

Degrees of Freedom: 599 Total (i.e. Null);  596 Residual
Null Deviance:      294 
Residual Deviance: 294  AIC: 302

sessionInfo()
R version 4.0.3 (2020-10-10)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19042)

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_1.1.1     dendextend_1.14.0 ggdendro_0.1.22   reshape2_1.4.4   
 [5] car_3.0-10        carData_3.0-4     gvlma_1.0.0.3     patchwork_1.1.1  
 [9] viridis_0.5.1     viridisLite_0.3.0 gridExtra_2.3     xtable_1.8-4     
[13] kableExtra_1.3.1  MASS_7.3-53       data.table_1.13.6 readxl_1.3.1     
[17] forcats_0.5.1     stringr_1.4.0     dplyr_1.0.3       purrr_0.3.4      
[21] readr_1.4.0       tidyr_1.1.2       tibble_3.0.6      ggplot2_3.3.3    
[25] tidyverse_1.3.0   lmerTest_3.1-3    lme4_1.1-26       Matrix_1.2-18    
[29] vegan_2.5-7       lattice_0.20-41   permute_0.9-5     phyloseq_1.34.0  
[33] workflowr_1.6.2  

loaded via a namespace (and not attached):
 [1] minqa_1.2.4         colorspace_2.0-0    rio_0.5.16         
 [4] ellipsis_0.3.1      rprojroot_2.0.2     XVector_0.30.0     
 [7] fs_1.5.0            rstudioapi_0.13     farver_2.0.3       
[10] lubridate_1.7.9.2   xml2_1.3.2          codetools_0.2-16   
[13] splines_4.0.3       knitr_1.31          ade4_1.7-16        
[16] jsonlite_1.7.2      nloptr_1.2.2.2      broom_0.7.4        
[19] cluster_2.1.0       dbplyr_2.1.0        BiocManager_1.30.10
[22] compiler_4.0.3      httr_1.4.2          backports_1.2.1    
[25] assertthat_0.2.1    cli_2.3.0           later_1.1.0.1      
[28] htmltools_0.5.1.1   prettyunits_1.1.1   tools_4.0.3        
[31] igraph_1.2.6        gtable_0.3.0        glue_1.4.2         
[34] Rcpp_1.0.6          Biobase_2.50.0      cellranger_1.1.0   
[37] vctrs_0.3.6         Biostrings_2.58.0   rhdf5filters_1.2.0 
[40] multtest_2.46.0     ape_5.4-1           nlme_3.1-149       
[43] iterators_1.0.13    xfun_0.20           ps_1.5.0           
[46] openxlsx_4.2.3      rvest_0.3.6         lifecycle_0.2.0    
[49] statmod_1.4.35      zlibbioc_1.36.0     scales_1.1.1       
[52] hms_1.0.0           promises_1.1.1      parallel_4.0.3     
[55] biomformat_1.18.0   rhdf5_2.34.0        curl_4.3           
[58] yaml_2.2.1          stringi_1.5.3       highr_0.8          
[61] S4Vectors_0.28.1    foreach_1.5.1       BiocGenerics_0.36.0
[64] zip_2.1.1           boot_1.3-25         rlang_0.4.10       
[67] pkgconfig_2.0.3     evaluate_0.14       Rhdf5lib_1.12.1    
[70] labeling_0.4.2      tidyselect_1.1.0    plyr_1.8.6         
[73] magrittr_2.0.1      R6_2.5.0            IRanges_2.24.1     
[76] generics_0.1.0      DBI_1.1.1           foreign_0.8-80     
[79] pillar_1.4.7        haven_2.3.1         withr_2.4.1        
[82] mgcv_1.8-33         abind_1.4-5         survival_3.2-7     
[85] modelr_0.1.8        crayon_1.4.1        rmarkdown_2.6      
[88] progress_1.2.2      grid_4.0.3          git2r_0.28.0       
[91] reprex_1.0.0        digest_0.6.27       webshot_0.5.2      
[94] httpuv_1.5.5        numDeriv_2016.8-1.1 stats4_4.0.3       
[97] munsell_0.5.0