Last updated: 2021-02-11
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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:
TCGA drop “not reported” from tumor stage.
# 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)))
## 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
## 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()
)
## 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()
)
## 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