inst/extdata/analysis_reply_to_comment.R
In courtiol/twinR: A Supporting R Package for the Paper "Mothers with higher twinning propensity had lower fertility in pre-industrial Europe" (Rickard et al., Nature Communications 2002)
## Analysis for reply to comment in NatCom
library(twinR)
library(spaMM)
library(doSNOW)
library(dplyr)
library(ggplot2)
library(cowplot)
nb_cores <- min(c(50L, parallel::detectCores() - 1))
spaMM.options(nb_cores = nb_cores)
# Functions definition -----------------------------------------------------
create_data_plots <- function(data, nb_boot){
## original data
data_births_monthly <- data
data_mothers_monthly <- aggregate_data(data_births_monthly)
## original data after dropping last births
data |>
mutate(last_birth = row_number() == n(), .by = "maternal_id") |>
filter(!last_birth) -> data_births_all_noLB
data_mothers_monthly_noLB <- aggregate_data(data_births_all_noLB)
## data without mothers born before 1850
data_births_all_post1850 <- data[data$maternal_birthyear >= 1850, ]
data_mothers_monthly_post1850 <- aggregate_data(data_births_all_post1850)
## data without LB and mothers born before 1850
data_births_all_noLB_post1850 <- data_births_all_noLB[data_births_all_noLB$maternal_birthyear >= 1850, ]
data_mothers_monthly_noLB_post1850 <- aggregate_data(data_births_all_noLB_post1850)
## original fit
fit <- fit_twinning.binomial(data_mothers_monthly)
## original fit without last birth
fit_noLB <- fit_twinning.binomial(data_mothers_monthly_noLB)
## original fit without data from mothers born before 1850
fit_post1850 <- fit_twinning.binomial(data_mothers_monthly_post1850)
## original fit without last births and without data from mothers born before 1850
fit_noLB_post1850 <- fit_twinning.binomial(data_mothers_monthly_noLB_post1850)
## original plot
min_births <- min(data_mothers_monthly$births_total)
max_births <- max(data_mothers_monthly$births_total)
data_fig_2 <- compute_predictions(fit,
newdata = data.frame(births_total = min_births:max_births),
nb_boot = nb_boot,
random = length(unique(data$pop)) > 1)
## predictions without last births
min_births_noLB <- min(data_mothers_monthly_noLB$births_total)
max_births_noLB <- max(data_mothers_monthly_noLB$births_total)
data_fig_2_noLB <- compute_predictions(fit_noLB,
newdata = data.frame(births_total = min_births_noLB:max_births_noLB),
nb_boot = nb_boot,
random = length(unique(data$pop)) > 1)
## predictions without mothers born before 1850
min_births_post1850 <- min(data_mothers_monthly_post1850$births_total)
max_births_post1850 <- max(data_mothers_monthly_post1850$births_total)
data_fig_2_post1850 <- compute_predictions(fit_post1850,
newdata = data.frame(births_total = min_births_post1850:max_births_post1850),
nb_boot = nb_boot,
random = length(unique(data$pop)) > 1)
## predictions without LB and without mothers born before 1850
min_births_noLB_post1850 <- min(data_mothers_monthly_noLB_post1850$births_total)
max_births_noLB_post1850 <- max(data_mothers_monthly_noLB_post1850$births_total)
data_fig_2_noLB_post1850 <- compute_predictions(fit_noLB_post1850,
newdata = data.frame(births_total = min_births_noLB_post1850:max_births_noLB_post1850),
nb_boot = nb_boot,
random = length(unique(data$pop)) > 1)
## return
list(data_fig_2 = data_fig_2,
data_fig_2_noLB = data_fig_2_noLB,
data_fig_2_post1850 = data_fig_2_post1850,
data_fig_2_noLB_post1850 = data_fig_2_noLB_post1850,
fits = list(fit = fit,
fit_noLB = fit_noLB,
fit_post1850 = fit_post1850,
fit_noLB_post1850 = fit_noLB_post1850))
}
draw_plot <- function(data, title = "") {
ggplot(data) +
aes(x = births_total, y = estimate, colour = pop) +
geom_ribbon(aes(ymin = lwr, ymax = upr, fill = pop), alpha = 0.3) +
geom_line(linewidth = 1) +
labs(title = title) +
scale_x_continuous(breaks = seq(1, 20, 2)) +
scale_y_continuous(trans = "logit",
breaks = seq(0.005, 0.03, by = 0.005)) +
scale_color_manual(values = c("purple4", "azure3")) +
scale_fill_manual(values = c("purple4", "azure3")) +
theme_twin(larger = 0.8) +
coord_cartesian(xlim = c(1, 18), ylim = c(0.008, 0.03)) +
labs(y = "Per-birth twin. prob.",
x = "Maternal total births",
colour = "Populations",
fill = "Populations") +
theme(legend.direction = "vertical", legend.title.align = 0.5)
}
# Fitting the models --------------------------------------------------------
data_births_all_EE <- readRDS(paste0(system.file(package = "twinR"), "/extdata/data_births_all_EE.rds"))
data_births_all_EE$monthly <- TRUE
data_births_all_EE$pop <- "EE"
data_births_all |>
count(maternal_id, maternal_birthyear) |>
count(maternal_id) |>
filter(n > 1) |>
pull(maternal_id) -> ID_wrong_maternal_year ## a few data preparation error exist for Norway
## this applies to maternal birth years which we did not use before
data_births_all |>
filter(!maternal_id %in% ID_wrong_maternal_year) -> data_births_all2
nb_boot <- 5000 ## use > 1000 for plots
result_estonian_study <- create_data_plots(data = data_births_all_EE, nb_boot = nb_boot)
result_original_study <- create_data_plots(data = data_births_all2, nb_boot = nb_boot)
# Extracting info on datasets ---------------------------------------------
## Estonia all data
length(unique(result_estonian_study$fits$fit$data$maternal_id)) # 125575 mothers
sum(result_estonian_study$fits$fit$data$births_total) # 417418 birth events
## Estonia without last births
length(unique(result_estonian_study$fits$fit_noLB$data$maternal_id)) # 98183 mothers
sum(result_estonian_study$fits$fit_noLB$data$births_total) # 291843 birth events
## Original all data
length(unique(result_original_study$fits$fit$data$maternal_id)) # 23267 mothers
sum(result_original_study$fits$fit$data$births_total) # 115963 birth events
## Original without last births
length(unique(result_original_study$fits$fit_noLB$data$maternal_id)) # 20309 mothers
sum(result_original_study$fits$fit_noLB$data$births_total) # 92696 birth events
## Original no pre 1850
length(unique(result_original_study$fits$fit_post1850$data$maternal_id)) # 5410 mothers
sum(result_original_study$fits$fit_post1850$data$births_total) # 24735 birth events
## Original no pre 1850 without last births
length(unique(result_original_study$fits$fit_noLB_post1850$data$maternal_id)) # 4549 mothers
sum(result_original_study$fits$fit_noLB_post1850$data$births_total) # 19325 birth events
## Mothers born before 1850 in original data:
data_births_all2 |>
select(-maternal_age) |>
mutate(post_1850 = maternal_birthyear >= 1850) |>
summarise(n = length(unique(maternal_id)), .by = c("post_1850")) |>
mutate(pct = 100 * n / sum(n))
# A tibble: 2 × 3
# post_1850 n pct
# <lgl> <int> <dbl>
# 1 FALSE 17857 76.7
# 2 TRUE 5410 23.3
# Compare datasets using models with last births -------------------------------
data_all_post1850 <- bind_rows(result_original_study$fits$fit_post1850$data,
result_estonian_study$fits$fit_post1850$data) |>
mutate(dataset = ifelse(pop == "EE", "EE", "original"))
fit_all_post1850 <- fitme(cbind(twin_total, singleton_total) ~ 1 + births_total*dataset + (1 | pop),
family = binomial(link = "logit"),
data = data_all_post1850)
fit_all_post1850_no_int <- fitme(cbind(twin_total, singleton_total) ~ 1 + births_total + (1 | pop),
family = binomial(link = "logit"),
data = data_all_post1850)
anova(fit_all_post1850, fit_all_post1850_no_int)
# chi2_LR df p_value
# p_v 3.129245 2 0.209167
# Compare datasets using models without last births -------------------------------
data_all_noLB_post1850 <- bind_rows(result_original_study$fits$fit_noLB_post1850$data,
result_estonian_study$fits$fit_noLB_post1850$data) |>
mutate(dataset = ifelse(pop == "EE", "EE", "original"))
fit_all_noLB_post1850 <- fitme(cbind(twin_total, singleton_total) ~ 1 + births_total*dataset + (1 | pop),
family = binomial(link = "logit"),
data = data_all_noLB_post1850)
fit_all_noLB_post1850_no_int <- fitme(cbind(twin_total, singleton_total) ~ 1 + births_total + (1 | pop),
family = binomial(link = "logit"),
data = data_all_noLB_post1850)
anova(fit_all_noLB_post1850, fit_all_noLB_post1850_no_int)
# chi2_LR df p_value
# p_v 0.003886339 2 0.9980587
# Preparing data for plots -------------------------------------------------
result_original_study$data_fig_2$results$last_birth <- TRUE
result_original_study$data_fig_2$results$pop <- "9 other European"
result_original_study$data_fig_2$results$pre1850_included <- TRUE
result_original_study$data_fig_2_noLB$results$last_birth <- FALSE
result_original_study$data_fig_2_noLB$results$pop <- "9 other European"
result_original_study$data_fig_2_noLB$results$pre1850_included <- TRUE
result_original_study$data_fig_2_post1850$results$last_birth <- TRUE
result_original_study$data_fig_2_post1850$results$pop <- "9 other European"
result_original_study$data_fig_2_post1850$results$pre1850_included <- FALSE
result_original_study$data_fig_2_noLB_post1850$results$last_birth <- FALSE
result_original_study$data_fig_2_noLB_post1850$results$pop <- "9 other European"
result_original_study$data_fig_2_noLB_post1850$results$pre1850_included <- FALSE
result_estonian_study$data_fig_2$results$last_birth <- TRUE
result_estonian_study$data_fig_2$results$pop <- "Estonian"
result_estonian_study$data_fig_2$results$pre1850_included <- FALSE
result_estonian_study$data_fig_2_noLB$results$last_birth <- FALSE
result_estonian_study$data_fig_2_noLB$results$pop <- "Estonian"
result_estonian_study$data_fig_2_noLB$results$pre1850_included <- TRUE
result_estonian_study$data_fig_2_post1850$results$last_birth <- TRUE
result_estonian_study$data_fig_2_post1850$results$pop <- "Estonian"
result_estonian_study$data_fig_2_post1850$results$pre1850_included <- TRUE
result_estonian_study$data_fig_2_noLB_post1850$results$last_birth <- FALSE
result_estonian_study$data_fig_2_noLB_post1850$results$pop <- "Estonian"
result_estonian_study$data_fig_2_noLB_post1850$results$pre1850_included <- FALSE
# Plotting ----------------------------------------------------------------
draw_plot(bind_rows(result_original_study$data_fig_2$results,
result_estonian_study$data_fig_2$results) |>
mutate(pop = relevel(as.factor(pop), ref = "Estonian")),
title = "With last births (no date restriction)") -> plot1
draw_plot(bind_rows(result_original_study$data_fig_2_noLB$results,
result_estonian_study$data_fig_2_noLB$results) |>
mutate(pop = relevel(as.factor(pop), ref = "Estonian")),
title = "Without last births (no date restriction)") +
theme(legend.position = "none") -> plot2
draw_plot(bind_rows(result_original_study$data_fig_2_post1850$results,
result_estonian_study$data_fig_2_post1850$results) |>
mutate(pop = relevel(as.factor(pop), ref = "Estonian")),
title = "With last births (mothers born 1850-1899)") +
theme(legend.position = "none") -> plot3
draw_plot(bind_rows(result_original_study$data_fig_2_noLB_post1850$results,
result_estonian_study$data_fig_2_noLB_post1850$results) |>
mutate(pop = relevel(as.factor(pop), ref = "Estonian")),
title = "Without last births (mothers born 1850-1899)") +
theme(legend.position = "none") -> plot4
legend <- get_legend(plot1 +
guides(color = guide_legend(nrow = 1)) +
theme(legend.position = "bottom", plot.margin = margin(t = 0, b = 0)))
plot1 <- plot1 + theme(legend.position = "none")
plot_grid(legend,
plot_grid(plot1, plot2, plot3, plot4, nrow = 2, labels = "auto") + theme(plot.margin = margin(r = 5)),
nrow = 2, rel_heights = c(0.15, 1))
ggsave(file = "figures/fig1_reply.pdf", width = 180, height = 180, units = "mm")
ggsave(file = "figures/fig1_reply.png", width = 180, height = 180, units = "mm")
courtiol/twinR documentation built on July 11, 2024, 12:04 a.m.
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## Analysis for reply to comment in NatCom
library(twinR)
library(spaMM)
library(doSNOW)
library(dplyr)
library(ggplot2)
library(cowplot)
nb_cores <- min(c(50L, parallel::detectCores() - 1))
spaMM.options(nb_cores = nb_cores)
# Functions definition -----------------------------------------------------
create_data_plots <- function(data, nb_boot){
## original data
data_births_monthly <- data
data_mothers_monthly <- aggregate_data(data_births_monthly)
## original data after dropping last births
data |>
mutate(last_birth = row_number() == n(), .by = "maternal_id") |>
filter(!last_birth) -> data_births_all_noLB
data_mothers_monthly_noLB <- aggregate_data(data_births_all_noLB)
## data without mothers born before 1850
data_births_all_post1850 <- data[data$maternal_birthyear >= 1850, ]
data_mothers_monthly_post1850 <- aggregate_data(data_births_all_post1850)
## data without LB and mothers born before 1850
data_births_all_noLB_post1850 <- data_births_all_noLB[data_births_all_noLB$maternal_birthyear >= 1850, ]
data_mothers_monthly_noLB_post1850 <- aggregate_data(data_births_all_noLB_post1850)
## original fit
fit <- fit_twinning.binomial(data_mothers_monthly)
## original fit without last birth
fit_noLB <- fit_twinning.binomial(data_mothers_monthly_noLB)
## original fit without data from mothers born before 1850
fit_post1850 <- fit_twinning.binomial(data_mothers_monthly_post1850)
## original fit without last births and without data from mothers born before 1850
fit_noLB_post1850 <- fit_twinning.binomial(data_mothers_monthly_noLB_post1850)
## original plot
min_births <- min(data_mothers_monthly$births_total)
max_births <- max(data_mothers_monthly$births_total)
data_fig_2 <- compute_predictions(fit,
newdata = data.frame(births_total = min_births:max_births),
nb_boot = nb_boot,
random = length(unique(data$pop)) > 1)
## predictions without last births
min_births_noLB <- min(data_mothers_monthly_noLB$births_total)
max_births_noLB <- max(data_mothers_monthly_noLB$births_total)
data_fig_2_noLB <- compute_predictions(fit_noLB,
newdata = data.frame(births_total = min_births_noLB:max_births_noLB),
nb_boot = nb_boot,
random = length(unique(data$pop)) > 1)
## predictions without mothers born before 1850
min_births_post1850 <- min(data_mothers_monthly_post1850$births_total)
max_births_post1850 <- max(data_mothers_monthly_post1850$births_total)
data_fig_2_post1850 <- compute_predictions(fit_post1850,
newdata = data.frame(births_total = min_births_post1850:max_births_post1850),
nb_boot = nb_boot,
random = length(unique(data$pop)) > 1)
## predictions without LB and without mothers born before 1850
min_births_noLB_post1850 <- min(data_mothers_monthly_noLB_post1850$births_total)
max_births_noLB_post1850 <- max(data_mothers_monthly_noLB_post1850$births_total)
data_fig_2_noLB_post1850 <- compute_predictions(fit_noLB_post1850,
newdata = data.frame(births_total = min_births_noLB_post1850:max_births_noLB_post1850),
nb_boot = nb_boot,
random = length(unique(data$pop)) > 1)
## return
list(data_fig_2 = data_fig_2,
data_fig_2_noLB = data_fig_2_noLB,
data_fig_2_post1850 = data_fig_2_post1850,
data_fig_2_noLB_post1850 = data_fig_2_noLB_post1850,
fits = list(fit = fit,
fit_noLB = fit_noLB,
fit_post1850 = fit_post1850,
fit_noLB_post1850 = fit_noLB_post1850))
}
draw_plot <- function(data, title = "") {
ggplot(data) +
aes(x = births_total, y = estimate, colour = pop) +
geom_ribbon(aes(ymin = lwr, ymax = upr, fill = pop), alpha = 0.3) +
geom_line(linewidth = 1) +
labs(title = title) +
scale_x_continuous(breaks = seq(1, 20, 2)) +
scale_y_continuous(trans = "logit",
breaks = seq(0.005, 0.03, by = 0.005)) +
scale_color_manual(values = c("purple4", "azure3")) +
scale_fill_manual(values = c("purple4", "azure3")) +
theme_twin(larger = 0.8) +
coord_cartesian(xlim = c(1, 18), ylim = c(0.008, 0.03)) +
labs(y = "Per-birth twin. prob.",
x = "Maternal total births",
colour = "Populations",
fill = "Populations") +
theme(legend.direction = "vertical", legend.title.align = 0.5)
}
# Fitting the models --------------------------------------------------------
data_births_all_EE <- readRDS(paste0(system.file(package = "twinR"), "/extdata/data_births_all_EE.rds"))
data_births_all_EE$monthly <- TRUE
data_births_all_EE$pop <- "EE"
data_births_all |>
count(maternal_id, maternal_birthyear) |>
count(maternal_id) |>
filter(n > 1) |>
pull(maternal_id) -> ID_wrong_maternal_year ## a few data preparation error exist for Norway
## this applies to maternal birth years which we did not use before
data_births_all |>
filter(!maternal_id %in% ID_wrong_maternal_year) -> data_births_all2
nb_boot <- 5000 ## use > 1000 for plots
result_estonian_study <- create_data_plots(data = data_births_all_EE, nb_boot = nb_boot)
result_original_study <- create_data_plots(data = data_births_all2, nb_boot = nb_boot)
# Extracting info on datasets ---------------------------------------------
## Estonia all data
length(unique(result_estonian_study$fits$fit$data$maternal_id)) # 125575 mothers
sum(result_estonian_study$fits$fit$data$births_total) # 417418 birth events
## Estonia without last births
length(unique(result_estonian_study$fits$fit_noLB$data$maternal_id)) # 98183 mothers
sum(result_estonian_study$fits$fit_noLB$data$births_total) # 291843 birth events
## Original all data
length(unique(result_original_study$fits$fit$data$maternal_id)) # 23267 mothers
sum(result_original_study$fits$fit$data$births_total) # 115963 birth events
## Original without last births
length(unique(result_original_study$fits$fit_noLB$data$maternal_id)) # 20309 mothers
sum(result_original_study$fits$fit_noLB$data$births_total) # 92696 birth events
## Original no pre 1850
length(unique(result_original_study$fits$fit_post1850$data$maternal_id)) # 5410 mothers
sum(result_original_study$fits$fit_post1850$data$births_total) # 24735 birth events
## Original no pre 1850 without last births
length(unique(result_original_study$fits$fit_noLB_post1850$data$maternal_id)) # 4549 mothers
sum(result_original_study$fits$fit_noLB_post1850$data$births_total) # 19325 birth events
## Mothers born before 1850 in original data:
data_births_all2 |>
select(-maternal_age) |>
mutate(post_1850 = maternal_birthyear >= 1850) |>
summarise(n = length(unique(maternal_id)), .by = c("post_1850")) |>
mutate(pct = 100 * n / sum(n))
# A tibble: 2 × 3
# post_1850 n pct
# <lgl> <int> <dbl>
# 1 FALSE 17857 76.7
# 2 TRUE 5410 23.3
# Compare datasets using models with last births -------------------------------
data_all_post1850 <- bind_rows(result_original_study$fits$fit_post1850$data,
result_estonian_study$fits$fit_post1850$data) |>
mutate(dataset = ifelse(pop == "EE", "EE", "original"))
fit_all_post1850 <- fitme(cbind(twin_total, singleton_total) ~ 1 + births_total*dataset + (1 | pop),
family = binomial(link = "logit"),
data = data_all_post1850)
fit_all_post1850_no_int <- fitme(cbind(twin_total, singleton_total) ~ 1 + births_total + (1 | pop),
family = binomial(link = "logit"),
data = data_all_post1850)
anova(fit_all_post1850, fit_all_post1850_no_int)
# chi2_LR df p_value
# p_v 3.129245 2 0.209167
# Compare datasets using models without last births -------------------------------
data_all_noLB_post1850 <- bind_rows(result_original_study$fits$fit_noLB_post1850$data,
result_estonian_study$fits$fit_noLB_post1850$data) |>
mutate(dataset = ifelse(pop == "EE", "EE", "original"))
fit_all_noLB_post1850 <- fitme(cbind(twin_total, singleton_total) ~ 1 + births_total*dataset + (1 | pop),
family = binomial(link = "logit"),
data = data_all_noLB_post1850)
fit_all_noLB_post1850_no_int <- fitme(cbind(twin_total, singleton_total) ~ 1 + births_total + (1 | pop),
family = binomial(link = "logit"),
data = data_all_noLB_post1850)
anova(fit_all_noLB_post1850, fit_all_noLB_post1850_no_int)
# chi2_LR df p_value
# p_v 0.003886339 2 0.9980587
# Preparing data for plots -------------------------------------------------
result_original_study$data_fig_2$results$last_birth <- TRUE
result_original_study$data_fig_2$results$pop <- "9 other European"
result_original_study$data_fig_2$results$pre1850_included <- TRUE
result_original_study$data_fig_2_noLB$results$last_birth <- FALSE
result_original_study$data_fig_2_noLB$results$pop <- "9 other European"
result_original_study$data_fig_2_noLB$results$pre1850_included <- TRUE
result_original_study$data_fig_2_post1850$results$last_birth <- TRUE
result_original_study$data_fig_2_post1850$results$pop <- "9 other European"
result_original_study$data_fig_2_post1850$results$pre1850_included <- FALSE
result_original_study$data_fig_2_noLB_post1850$results$last_birth <- FALSE
result_original_study$data_fig_2_noLB_post1850$results$pop <- "9 other European"
result_original_study$data_fig_2_noLB_post1850$results$pre1850_included <- FALSE
result_estonian_study$data_fig_2$results$last_birth <- TRUE
result_estonian_study$data_fig_2$results$pop <- "Estonian"
result_estonian_study$data_fig_2$results$pre1850_included <- FALSE
result_estonian_study$data_fig_2_noLB$results$last_birth <- FALSE
result_estonian_study$data_fig_2_noLB$results$pop <- "Estonian"
result_estonian_study$data_fig_2_noLB$results$pre1850_included <- TRUE
result_estonian_study$data_fig_2_post1850$results$last_birth <- TRUE
result_estonian_study$data_fig_2_post1850$results$pop <- "Estonian"
result_estonian_study$data_fig_2_post1850$results$pre1850_included <- TRUE
result_estonian_study$data_fig_2_noLB_post1850$results$last_birth <- FALSE
result_estonian_study$data_fig_2_noLB_post1850$results$pop <- "Estonian"
result_estonian_study$data_fig_2_noLB_post1850$results$pre1850_included <- FALSE
# Plotting ----------------------------------------------------------------
draw_plot(bind_rows(result_original_study$data_fig_2$results,
result_estonian_study$data_fig_2$results) |>
mutate(pop = relevel(as.factor(pop), ref = "Estonian")),
title = "With last births (no date restriction)") -> plot1
draw_plot(bind_rows(result_original_study$data_fig_2_noLB$results,
result_estonian_study$data_fig_2_noLB$results) |>
mutate(pop = relevel(as.factor(pop), ref = "Estonian")),
title = "Without last births (no date restriction)") +
theme(legend.position = "none") -> plot2
draw_plot(bind_rows(result_original_study$data_fig_2_post1850$results,
result_estonian_study$data_fig_2_post1850$results) |>
mutate(pop = relevel(as.factor(pop), ref = "Estonian")),
title = "With last births (mothers born 1850-1899)") +
theme(legend.position = "none") -> plot3
draw_plot(bind_rows(result_original_study$data_fig_2_noLB_post1850$results,
result_estonian_study$data_fig_2_noLB_post1850$results) |>
mutate(pop = relevel(as.factor(pop), ref = "Estonian")),
title = "Without last births (mothers born 1850-1899)") +
theme(legend.position = "none") -> plot4
legend <- get_legend(plot1 +
guides(color = guide_legend(nrow = 1)) +
theme(legend.position = "bottom", plot.margin = margin(t = 0, b = 0)))
plot1 <- plot1 + theme(legend.position = "none")
plot_grid(legend,
plot_grid(plot1, plot2, plot3, plot4, nrow = 2, labels = "auto") + theme(plot.margin = margin(r = 5)),
nrow = 2, rel_heights = c(0.15, 1))
ggsave(file = "figures/fig1_reply.pdf", width = 180, height = 180, units = "mm")
ggsave(file = "figures/fig1_reply.png", width = 180, height = 180, units = "mm")
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