library(tidyverse)
library(patchwork)
therapy_1 <- tibble(
  antibiotic = c("IV Piperacillin-tazobactam", "IV Piperacillin-tazobactam"),
  time_point = c("start", "end"),
  date = c("2023-04-10","2023-04-25")) %>% 
  mutate(date = as_date(date))
therapy_2 <-tibble(
  antibiotic = c("PO co-trimoxazole", "PO co-trimoxazole"),
  time_point = c("start", "end"),
  date = c("2023-04-10","2023-04-25")) %>% 
  mutate(date = as_date(date))
inflammatory_markers <- tibble(
  date = c("2023-04-10", "2023-04-12"),
  value = c("38.1", "37.8")) %>%
  mutate(date = as_date(date))
p1 <- therapy_1 %>%
  ggplot(aes(x = date)) +
  geom_line(aes(y = antibiotic, colour = antibiotic)) +
  theme(legend.position = "none")
p2 <- therapy_2 %>%
  ggplot(aes(x = date)) +
  geom_line(aes(y = antibiotic, colour = antibiotic)) +
  theme(legend.position = "none")
default <- inflammatory_markers %>%
  ggplot(aes(x = date)) +
  geom_point(aes(y = value))
desired <- inflammatory_markers %>%
  ggplot(aes(x = date)) +
  geom_point(aes(y = value)) +
  theme(axis.title.y = element_text(margin = margin(r = -160)))
# default output
p1 / default

# desired output
p1 / desired

# when length of y-axis labels shortened
p2 / desired

## adding a custom annotation to your inferior panel. 
desired <-
  inflammatory_markers %>%
  ggplot(aes(x = date)) +
  geom_point(aes(y = value)) +
  ## annotate with geom_text and not annotate, because you are using dates
  ## and you want to use "nudge_x" which doesn't work with annotate
  geom_text(
    data = data.frame(), aes(
      label = "value",
      x = min(inflammatory_markers$date),
      y = 1.5
    ),
    angle = 90, nudge_x = -.4
  ) +
  ## limit coordinates and turn clipping off
  coord_cartesian(xlim = range(inflammatory_markers$date), clip = "off") +
  ## remove y label
  labs(y = NULL)
# default output
p1 / desired

p2 / desired

library(egg)
ggarrange(p1, desired)

ggarrange(p2, desired)