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Optimum_PF_x_ALLpc.R
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Optimum_PF_x_ALLpc.R
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#Plot the OR (Vaccine Efficacy Odds) efficacy/(1-efficacy)
#SPECIFICALLY,
#we only minimise the error at the central (50%) mark.
rm(list=ls())
require(tidyverse)
#The Problem:
#We have data: y0, y25, y50, y75 that we want to scale like so:
#y0*x = y25
#y0*(x^2) = y50
#y0*(x^3) = y75
#No x will fit perfectly, but what's the best we can do?
#----------------------------
#Build y vectors, one for AZ, one for PF, one for infectiousness combined
#AZ ones correspond all to 1 dose: VE against (i) severe disease, (ii) infection
y0_AZ <- c(0.8/(1-0.8), 0.63/(1-0.63) )
y25_AZ <- c(0.64/(1-0.64), 0.5/(1-0.5))
y50_AZ <- c(0.4/(1-0.4), 0.1/(1-0.1))
y75_AZ <- c(0.2/(1-0.2), 0)
y100_AZ <- y75_AZ
#PF values correspond to VE against (i/ii) severe disease 1dose/2dose (iii/iv) infection 1dose/2dose (v) infectiousness (1 dose)
y0_PF <- c(0.8/(1-0.8), 0.95/(1-0.95), 0.65/(1-0.65), 0.86/(1-0.86))
y25_PF <- c(0.8/(1-0.8), 0.95/(1-0.95), 0.65/(1-0.65), 0.85/(1-0.85))
y50_PF <- c(0.7/(1-0.7), 0.9/(1-0.9), 0.55/(1-0.55), 0.75/(1-0.75))
y75_PF <- c(0.6/(1-0.6), 0.85/(1-0.85), 0.45/(1-0.45), 0.55/(1-0.55))
y100_PF <- y75_PF
#Lastly we do a separate one for infectious values (1 dose) of either AZ or PF
y0_infect <- 0.45/(1-0.45)
y25_infect <- 0.45/(1-0.45)
y50_infect <- 0.2/(1-0.2)
y75_infect <- 0
y100_infect <- y75_infect
#----------------------------------------
#PF
#Assume the same worst case is 100%.
error_x_PF <- function(x) {
#Allocate memory:
y25_estimate_PF <- c(0,0,0,0)
y50_estimate_PF <- c(0,0,0,0)
y100_estimate_PF <- c(0,0,0,0)
y25_estimate_PF <- (x)*y0_PF
y50_estimate_PF <- (x^2)*y0_PF
y100_estimate_PF <- (x^4)*y0_PF
y25_estimate_PF_probability <- y25_estimate_PF/(y25_estimate_PF+1)
y25_PF_probability <- y25_PF/(y25_PF+1)
y50_estimate_PF_probability <- y50_estimate_PF/(y50_estimate_PF+1)
y50_PF_probability <- y50_PF/(y50_PF+1)
y100_estimate_PF_probability <- y100_estimate_PF/(y100_estimate_PF+1)
y100_PF_probability <- y100_PF/(y100_PF+1)
error_amt <- (sum((abs(y50_estimate_PF_probability - y50_PF_probability))^2 ) + sum( (abs(y100_estimate_PF_probability - y100_PF_probability))^2 ) + sum( (abs(y25_estimate_PF_probability - y25_PF_probability))^2) )
return(error_amt)
}
optim_PF <- optimize(error_x_PF, interval = c(0,1))
optim_x_PF <- optim_PF$minimum
optim_x_PF_error <- optim_PF$objective
#----------------------------
#Okay, now we want to plot it
######
#PF
######
percent_mark <- seq(0,100, length.out = 101)
# Severe Disease (1 dose)
sev_disease_efficacy <- (0.8/(1-0.8))*(optim_x_PF^(percent_mark/25))
#Convert back to probability:
sev_disease_efficacy <- sev_disease_efficacy/(sev_disease_efficacy+1)
Table_Data <- data.frame(percent_mark = c(0, 25, 50, 100), sev_disease_efficacy = c(0.8, 0.8, 0.7, 0.6))
Mapped_Data <- data.frame(percent_mark = percent_mark, sev_disease_efficacy = sev_disease_efficacy)
ggplot(data=Mapped_Data, aes(x=percent_mark, y=sev_disease_efficacy, group=1)) +
geom_line(color="skyblue", size = 2) +
geom_point(data = Table_Data, color = 'firebrick', shape = 5, size = 5, stroke = 2)+
labs(title="Severe Disease (1 dose)",
x ="Vaccine Escape Percentage", y = "VE") +
geom_path(data = data.frame(percent_mark = c(50, 50), sev_disease_efficacy = c(0.7, sev_disease_efficacy[51]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+
geom_path(data = data.frame(percent_mark = c(25, 25), sev_disease_efficacy = c(0.8, sev_disease_efficacy[26]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+
geom_path(data = data.frame(percent_mark = c(100, 100), sev_disease_efficacy = c(0.6, sev_disease_efficacy[101]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+ylim(0.2,1) +
theme_classic() +
theme(
plot.title = element_text( size=14, face="bold"),
axis.title.x = element_text(size=18),
axis.title.y = element_text(size=18),
axis.text = element_text(size=14)
) -> PF_sev_dis_1dose_50_fit
# Severe Disease (2 doses)
sev_dis_efficacy <- (0.95/(1-0.95))*(optim_x_PF^(percent_mark/25))
#Convert back to probability:
sev_dis_efficacy <- sev_dis_efficacy/(sev_dis_efficacy+1)
Table_Data <- data.frame(percent_mark = c(0, 25, 50, 100), sev_dis_efficacy = c(0.95, 0.95, 0.9, 0.85))
Mapped_Data <- data.frame(percent_mark = percent_mark, sev_dis_efficacy = sev_dis_efficacy)
ggplot(data=Mapped_Data, aes(x=percent_mark, y=sev_dis_efficacy, group=1)) +
geom_line(color="skyblue", size = 2) +
geom_point(data = Table_Data, color = 'firebrick', shape = 5, size = 5, stroke = 2)+
labs(title="Severe Disease (2 dose)",
x ="Vaccine Escape Percentage", y = "VE") +
geom_path(data = data.frame(percent_mark = c(50, 50), sev_dis_efficacy = c(0.9, sev_dis_efficacy[51]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+
geom_path(data = data.frame(percent_mark = c(25, 25), sev_dis_efficacy = c(0.95, sev_dis_efficacy[26]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+
geom_path(data = data.frame(percent_mark = c(100, 100), sev_dis_efficacy = c(0.85, sev_dis_efficacy[101]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+ylim(0.2,1) +
theme_classic() +
theme(
plot.title = element_text( size=14, face="bold"),
axis.title.x = element_text(size=18),
axis.title.y = element_text(size=18),
axis.text = element_text(size=14)
) -> PF_sev_dis_2dose_50_fit
# Infection (1 dose)
infection_efficacy <- (0.65/(1-0.65))*(optim_x_PF^(percent_mark/25))
#Convert back to probability:
infection_efficacy <- infection_efficacy/(infection_efficacy+1)
Table_Data <- data.frame(percent_mark = c(0, 25, 50, 100), infection_efficacy = c(0.65, 0.65, 0.55, 0.45))
Mapped_Data <- data.frame(percent_mark = percent_mark, infection_efficacy = infection_efficacy)
ggplot(data=Mapped_Data, aes(x=percent_mark, y=infection_efficacy, group=1)) +
geom_line(color="skyblue", size = 2) +
geom_point(data = Table_Data, color = 'firebrick', shape = 5, size = 5, stroke = 2)+
labs(title="Infection (1 dose)",
x ="Vaccine Escape Percentage", y = "VE") +
geom_path(data = data.frame(percent_mark = c(50, 50), infection_efficacy = c(0.55, infection_efficacy[51]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+
geom_path(data = data.frame(percent_mark = c(25, 25), infection_efficacy = c(0.65, infection_efficacy[26]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+
geom_path(data = data.frame(percent_mark = c(100, 100), infection_efficacy = c(0.45, infection_efficacy[101]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+ylim(0.2,1) +
theme_classic() +
theme(
plot.title = element_text( size=14, face="bold"),
axis.title.x = element_text(size=18),
axis.title.y = element_text(size=18),
axis.text = element_text(size=14)
) -> PF_sinfection_1dose_50_fit
# Infection (2 doses)
infection_efficacy <- (0.86/(1-0.86))*(optim_x_PF^(percent_mark/25))
#Convert back to probability:
infection_efficacy <- infection_efficacy/(infection_efficacy+1)
Table_Data <- data.frame(percent_mark = c(0, 25, 50, 100), infection_efficacy = c(0.86, 0.85, 0.75, 0.55))
Mapped_Data <- data.frame(percent_mark = percent_mark, infection_efficacy = infection_efficacy)
ggplot(data=Mapped_Data, aes(x=percent_mark, y=infection_efficacy, group=1)) +
geom_line(color="skyblue", size = 2) +
geom_point(data = Table_Data, color = 'firebrick', shape = 5, size = 5, stroke = 2)+
labs(title="Infection (2 doses)",
x ="Vaccine Escape Percentage", y = "VE") +
geom_path(data = data.frame(percent_mark = c(50, 50), infection_efficacy = c(0.75, infection_efficacy[51]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+
geom_path(data = data.frame(percent_mark = c(25, 25), infection_efficacy = c(0.85, infection_efficacy[26]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+
geom_path(data = data.frame(percent_mark = c(100, 100), infection_efficacy = c(0.55, infection_efficacy[101]) ),
size = 1, colour = "#EC7014",
arrow = arrow(type = "open", angle = 40, length = unit(0.1, "inches"))
)+ ylim(0.2,1) +
theme_classic() +
theme(
plot.title = element_text( size=14, face="bold"),
axis.title.x = element_text(size=18),
axis.title.y = element_text(size=18),
axis.text = element_text(size=14)
) -> PF_sinfection_2dose_50_fit
require(cowplot)
plot_grid(PF_sev_dis_1dose_50_fit, PF_sev_dis_2dose_50_fit, PF_sinfection_1dose_50_fit, PF_sinfection_2dose_50_fit, labels = c('A', 'B', 'C', 'D'), label_size = 12) -> p
#Make a title
title <- ggdraw() + draw_label("PF Vaccine Efficacy (x ~ 0.762)", fontface='bold')
#Add title:
plot_grid(title, p, ncol=1, rel_heights=c(0.1, 1)) -> plot2 # rel_heights values control title margins