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TT_analysis_1.Rmd
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# Maximum-Likelihood estimation of R
### Michelle Kendall and Christophe Fraser
```{r setup, include=FALSE}
knitr::opts_chunk$set(fig.width=10, fig.height=7, fig.cap="", cache=FALSE, echo = TRUE)
```
This code performs a Maximum-Likelihood estimation of R over fixed time periods before and after the Test and Trace programme, as reported in our [paper](https://doi.org/10.1016/S2589-7500(20)30241-7).
## Setup
### Load packages
```{r load.packages, message=FALSE}
library(EpiEstim)
library(incidence)
library(ggplot2)
library(stats4)
library(tidyverse)
library(RColorBrewer)
```
### Load data
From the working directory, fetch the daily case data:
```{r load.data, message=FALSE}
dat.UK.p1 <- read_csv("data/pillar1_case_data.csv") # local area pillar 1 data
dat.UK.p2 <- read.csv("data/pillar2_case_data.csv") # national pillars data including pillar 2
dat.IoW.p2 <- read.csv("data/pillar2_case_data_IoW.csv") # Isle of Wight pillar 2 data
dat.UK.both <- read.csv("data/combined_pillars_case_data.csv") # local combined pillars data
```
and the population size data:
```{r load.pop.data}
population.data <- read.csv("data/population_by_region.csv", stringsAsFactors = FALSE)
```
### Extract data
Extract relevant data
```{r cleaning}
# Extract relevant data:
dat.Eng.p1 <- dat.UK.p1 %>% filter(Country == "England") # England only
dat.IoW.p1 <- dat.Eng.p1 %>% filter(Area == "Isle of Wight") # IoW only
dat.Eng.both <- dat.UK.both %>% filter(`Area.type` == "Upper tier local authority") # UTLAs only
dat.Eng.both.clean <- dat.Eng.both %>% select("Date"=`Specimen.date`, "Area"=`Area.name`, "Cases"=`Daily.lab.confirmed.cases`) # only the necessary columns
dat.Eng.both.clean$Date <- as.Date(dat.Eng.both.clean$Date) # restore "date" property
```
## Analysis
### Combined pillars data
Calculate incidence for each area and overall:
```{r analysis.both.1, message=FALSE, warning=FALSE}
areas.alphabetical <- sort(unique(dat.Eng.both.clean$Area)) # get a list of utlas in alphabetical order
IoW.index <- which(areas.alphabetical == "Isle of Wight")
earliest.date <- min(as.Date(dat.Eng.both.clean$Date))
last.date <- max(as.Date(dat.Eng.both.clean$Date))
all.dates <- seq(earliest.date, last.date, by=1)
# Get incidence by area, filling in any missing dates with 0 cases
incidence.each.area <- sapply(areas.alphabetical, function(area) {
dat.area <- dat.Eng.both.clean %>% filter(Area == area)
dat.area <- rbind.data.frame(dat.area,
cbind.data.frame("Date" = as.Date(setdiff(all.dates, dat.area$Date), origin = "1970-01-01"),
"Area" = area,
"Cases" = 0)
)
dat.area$Cases[order(dat.area$Date)]
})
# extract the incidence table for the Isle of Wight
IoW.incidence <- cbind.data.frame(
"Date" = all.dates,
"Cases" = incidence.each.area[,IoW.index]
)
# and overall for England:
total.incidence <- cbind.data.frame(
"Date" = all.dates,
"Cases" = sapply(1:nrow(incidence.each.area), function(d) sum(incidence.each.area[d,]))
)
# these can be visualised for example like this:
TotalIncidencePlot <- ggplot(total.incidence, aes(x=Date, y=Cases)) +
geom_col(fill= brewer.pal(6,"Set2")[[3]]) +
scale_x_date(date_breaks = "2 weeks" , date_labels = "%b %d", limits=c(as.Date("2020-04-01"), last.date - 7)) +
ylab("Daily confirmed COVID-19\ncases by swab date") +
theme_bw(base_size = 16)
TotalIncidencePlot
```
For England and for the Isle of Wight create their incidence line lists and `incidence` objects using data from 5 days after the TT launch and ending 5 days before the end (to allow for missing data as cases where there are delays in reporting cases.)
```{r analysis.both.2, warning=FALSE, message=FALSE}
start.date.IoW.both <- as.Date("2020-05-10")
start.date.Eng.both <- as.Date("2020-05-23")
end.date.both <- last.date - 5
IoW.both.linelist <- IoW.incidence$Date[1]
for(row in 1:nrow(IoW.incidence)){
if(IoW.incidence$Cases[row]>0){
for(case in 1:IoW.incidence$Cases[row]){
IoW.both.linelist <- c(IoW.both.linelist, IoW.incidence$Date[row])
}
}
}
IoW.both.linelist <- IoW.both.linelist[-1]
total.incidence$Cases[which(is.na(total.incidence$Cases))] <- 0
Eng.both.linelist <- total.incidence$Date[1]
for(row in 1:nrow(total.incidence)){
if(total.incidence$Cases[row]>0){
Eng.both.linelist <- c(Eng.both.linelist, rep(total.incidence$Date[row], total.incidence$Cases[row]))
}
}
Eng.both.linelist <- Eng.both.linelist[-1]
IoW.both.incidence <- incidence(IoW.both.linelist,
first_date = start.date.IoW.both,
last_date = end.date.both,
standard = FALSE)
Eng.both.incidence <- incidence(Eng.both.linelist,
first_date = start.date.Eng.both,
last_date = end.date.both,
standard = FALSE)
```
Prepare log-likelihood function:
```{r analysis.ll}
minusloglik <- function(i0, r, start.date, incidence.dates, incidence.counts) {
ll <- 0
for(row in 1:length(incidence.dates)){
model <- i0*exp(-r*as.numeric(difftime(start.date,incidence.dates[row],units=c("days"))))
ll <- ll + model - incidence.counts[row]*log(model)
}
return(ll)
}
```
Get Maximum-Likelihood estimates for the growth rate r:
```{r analysis.both.mle, warning=FALSE}
fit.mle.IoW.both <- mle(minusloglik,
start=list(i0=10, r=-0.01),
fixed=list(start.date=start.date.IoW.both,
incidence.dates=IoW.both.incidence$dates,
incidence.counts=IoW.both.incidence$counts)
)
summary(fit.mle.IoW.both)
fit.mle.Eng.both <- mle(minusloglik,
start=list(i0=1420, r=-0.02),
fixed=list(start.date=start.date.Eng.both,
incidence.dates=Eng.both.incidence$dates,
incidence.counts=Eng.both.incidence$counts))
summary(fit.mle.Eng.both)
```
### Pillar 1 data
Similarly for Pillar 1 alone:
```{r analysis.p1.1, message=FALSE, warning=FALSE}
dat.IoW.p1$Incidence <- rep(0,nrow(dat.IoW.p1))
dat.IoW.p1$Incidence[1] <- dat.IoW.p1$TotalCases[1]
for(row in 2:nrow(dat.IoW.p1)) {
dat.IoW.p1$Incidence[row] <- dat.IoW.p1$TotalCases[row] - dat.IoW.p1$TotalCases[row-1]
}
dat.Eng.p1 <- dat.UK.p1 %>% filter(Country == "England")
incidence.all.areas.p1 <- sapply(areas.alphabetical, function(area) {
dat.area <- dat.Eng.p1 %>% filter(Area == area)
new.dat.area <- data.frame("Date" = unique(dat.Eng.p1$Date))
new.dat.area$TotalCases <- sapply(new.dat.area$Date, function(d) (dat.area %>% filter(Date == d))$TotalCases)
# fill in the blanks
if (length(new.dat.area$TotalCases[[1]])==0) new.dat.area$TotalCases[[1]] <- 0
for (i in 1:nrow(new.dat.area)) {
if (length(new.dat.area$TotalCases[[i]])==0) new.dat.area$TotalCases[[i]] <- new.dat.area$TotalCases[[i-1]]
}
new.dat.area$Incidence <- rep(0,nrow(new.dat.area))
new.dat.area$Incidence[[1]] <- new.dat.area$TotalCases[[1]]
for(row in 2:nrow(new.dat.area)) new.dat.area$Incidence[[row]] <- new.dat.area$TotalCases[[row]] - new.dat.area$TotalCases[[row-1]]
new.dat.area$Incidence
})
Eng.Pillar1 <- cbind.data.frame(
"Date" = unique(dat.Eng.p1$Date),
"Incidence" = sapply(1:nrow(incidence.all.areas.p1), function(row) {
sum(incidence.all.areas.p1[row,], na.rm=TRUE)
})
)
# linelists
IoW.p1.linelist <- dat.IoW.p1$Date[1]
for(row in 1:nrow(dat.IoW.p1)){
if(dat.IoW.p1$Incidence[row]>0){
for(case in 1:dat.IoW.p1$Incidence[row]){
IoW.p1.linelist <- c(IoW.p1.linelist, dat.IoW.p1$Date[row])
}
}
}
IoW.p1.linelist <- IoW.p1.linelist[-1]
Eng.p1.linelist <- Eng.Pillar1$Date[1]
for(row in 1:nrow(Eng.Pillar1)){
if ((!is.na(Eng.Pillar1$Incidence[row]))&&(Eng.Pillar1$Incidence[row]>0)){
Eng.p1.linelist <- c(Eng.p1.linelist, rep(Eng.Pillar1$Date[row], Eng.Pillar1$Incidence[row]))
}
}
Eng.p1.linelist <- Eng.p1.linelist[-1]
```
### Pillar 2 data
And Pillar 2:
```{r analysis.p2.1, message=FALSE, warning=FALSE}
dat.IoW.p2$specimen_date <- as.Date(as.character(dat.IoW.p2$specimen_date), "%d-%b-%y")
dat.IoW.p2$Pillar2 <- sapply(dat.IoW.p2$Pillar2, function(x)(if(!is.na(x)) return(x) else return(0)))
dat.UK.p2$Date.of.activity <- as.Date(dat.UK.p2$Date.of.activity, "%d/%m/%y")
UKPillar2 <- dat.UK.p2 %>% filter(Pillar == "Pillar 2 (excluding Wales)")
stopifnot(unique(UKPillar2$Nation) == "UK") # check we've just got the UK entries
UKPillar2$Daily.number.of.positive.cases <- sapply(UKPillar2$Daily.number.of.positive.cases, function(x)(if(!is.na(x)) return(x) else return(0)))
IoW.p2.linelist <- dat.IoW.p2$specimen_date[1]
for(row in 1:nrow(dat.IoW.p2)){
if(dat.IoW.p2$Pillar2[row]>0){
for(case in 1:dat.IoW.p2$Pillar2[row]){
IoW.p2.linelist <- c(IoW.p2.linelist, dat.IoW.p2$specimen_date[row])
}
}
}
IoW.p2.linelist <- IoW.p2.linelist[-1]
UK.p2.linelist <- UKPillar2$Date.of.activity[1]
for(row in 1:nrow(UKPillar2)){
if(UKPillar2$Daily.number.of.positive.cases[row]>0){
UK.p2.linelist <- c(UK.p2.linelist, rep(UKPillar2$Date.of.activity[row], UKPillar2$Daily.number.of.positive.cases[row]))
}
}
UK.p2.linelist <- UK.p2.linelist[-1]
```
Get `incidence` objects and Maximum-Likelihood estimates for the individual pillars data, starting 10 days after TT launch for Pillar 1 and 5 days after for Pillar 2 (to reflect the different typical times between symptom onset and swab).
```{r incidence.p1.and.p2, message=FALSE, warning=FALSE}
start.date.IoW.p1 <- as.Date("2020-05-15")
start.date.IoW.p2 <- as.Date("2020-05-10")
start.date.Eng.p1 <- as.Date("2020-05-28")
start.date.UK.p2 <- as.Date("2020-05-23")
end.date.IoW.p1 <- max(Eng.Pillar1$Date) - 5
end.date.Eng.p1 <- max(Eng.Pillar1$Date) - 5
end.date.UK.p2 <- max(UKPillar2$Date.of.activity, na.rm = TRUE) - 5
end.date.IoW.p2 <- end.date.UK.p2 # there were no more cases after the 13th
IoW.p1.incidence <- incidence(IoW.p1.linelist,
first_date = start.date.IoW.p1,
last_date = end.date.IoW.p1,
standard = FALSE)
Eng.p1.incidence <- incidence(Eng.p1.linelist,
first_date = start.date.Eng.p1,
last_date = end.date.Eng.p1,
standard = FALSE)
IoW.p2.incidence <- incidence(IoW.p2.linelist,
first_date = start.date.IoW.p2,
last_date = end.date.IoW.p2,
standard = FALSE)
UK.p2.incidence <- incidence(UK.p2.linelist,
first_date = start.date.UK.p2,
last_date = end.date.UK.p2,
standard = FALSE)
```
```{r mle.p1.and.p2, warning=FALSE}
fit.mle.IoW.p1 <- mle(minusloglik,
start=list(i0=10, r=-0.01),
fixed=list(start.date=start.date.IoW.p1,
incidence.dates=IoW.p1.incidence$dates,
incidence.counts=IoW.p1.incidence$counts)
)
summary(fit.mle.IoW.p1)
fit.mle.Eng.p1 <- mle(minusloglik,
start=list(i0=10, r=-0.03),
fixed=list(start.date=start.date.Eng.p1,
incidence.dates=Eng.p1.incidence$dates,
incidence.counts=Eng.p1.incidence$counts))
summary(fit.mle.Eng.p1)
fit.mle.IoW.p2 <- mle(minusloglik,
start=list(i0=10, r=-0.01),
fixed=list(start.date=start.date.IoW.p2,
incidence.dates=IoW.p2.incidence$dates,
incidence.counts=IoW.p2.incidence$counts)
)
summary(fit.mle.IoW.p2)
fit.mle.UK.p2 <- mle(minusloglik,
start=list(i0=10, r=-0.02),
fixed=list(start.date=start.date.UK.p2,
incidence.dates=UK.p2.incidence$dates,
incidence.counts=UK.p2.incidence$counts))
summary(fit.mle.UK.p2)
```
Plot these results for comparison:
```{r IoW.vs.national}
# function to convert from growth rate r to reproduction number R
alpha <- 6.6
beta <- 1.2
R <- function(r) ((beta + r)/beta)^alpha
# gather results, converting r to R:
results.for.plotting <- cbind.data.frame(
"Where" =c(rep("Isle of Wight",3), rep("National",3)),
"Pillar" = c(1,2,"combined",1,2,"combined"),
"R" = c(R(attributes(fit.mle.IoW.p1)$coef[[2]]),
R(attributes(fit.mle.IoW.p2)$coef[[2]]),
R(attributes(fit.mle.IoW.both)$coef[[2]]),
R(attributes(fit.mle.Eng.p1)$coef[[2]]),
R(attributes(fit.mle.UK.p2)$coef[[2]]),
R(attributes(fit.mle.Eng.both)$coef[[2]])
),
"lower" = c(R(attributes(fit.mle.IoW.p1)$coef[[2]] - attributes(summary(fit.mle.IoW.p1))$coef[[4]]),
R(attributes(fit.mle.IoW.p2)$coef[[2]] - attributes(summary(fit.mle.IoW.p2))$coef[[4]]),
R(attributes(fit.mle.IoW.both)$coef[[2]] - attributes(summary(fit.mle.IoW.both))$coef[[4]]),
R(attributes(fit.mle.Eng.p1)$coef[[2]] - attributes(summary(fit.mle.Eng.p1))$coef[[4]]),
R(attributes(fit.mle.UK.p2)$coef[[2]] - attributes(summary(fit.mle.UK.p2))$coef[[4]]),
R(attributes(fit.mle.Eng.both)$coef[[2]] - attributes(summary(fit.mle.Eng.both))$coef[[4]])
),
"upper" = c(R(attributes(fit.mle.IoW.p1)$coef[[2]] + attributes(summary(fit.mle.IoW.p1))$coef[[4]]),
R(attributes(fit.mle.IoW.p2)$coef[[2]] + attributes(summary(fit.mle.IoW.p2))$coef[[4]]),
R(attributes(fit.mle.IoW.both)$coef[[2]] + attributes(summary(fit.mle.IoW.both))$coef[[4]]),
R(attributes(fit.mle.Eng.p1)$coef[[2]] + attributes(summary(fit.mle.Eng.p1))$coef[[4]]),
R(attributes(fit.mle.UK.p2)$coef[[2]] + attributes(summary(fit.mle.UK.p2))$coef[[4]]),
R(attributes(fit.mle.Eng.both)$coef[[2]] + attributes(summary(fit.mle.Eng.both))$coef[[4]])
)
)
ggplot(results.for.plotting, aes(x=Where, y=R, fill=Pillar)) +
geom_bar(stat="identity", color="black",
position=position_dodge(0.9)) +
geom_errorbar(aes(ymin=lower, ymax=upper), width=.4,
position=position_dodge(.9)) +
scale_fill_manual(values=brewer.pal(6, "Set2")[1:3]) +
xlab("") +
ylim(0,1) +
theme_bw(base_size = 16)
```
We use likelihood ratio tests to obtain p-values for the differences in R seen between the Isle of Wight and the national level.
```{r lrtests, warning=FALSE, message=FALSE}
# prepare function for Maximum-likelihood estimation where we allow r to vary between the two datasets:
minusloglik.both.different.rs <- function(i0_1, i0_2, r_1, r_2, start.date, incidence.dates_1, incidence.dates_2, incidence.counts_1, incidence.counts_2) {
ll_1 <- 0
for(row in 1:length(incidence.dates_1)){
model_1 <- i0_1*exp(-r_1*as.numeric(difftime(start.date,incidence.dates_1[row],units=c("days"))))
ll_1 <- ll_1 + model_1 - incidence.counts_1[row]*log(model_1)
}
ll_2 <- 0
for(row in 1:length(incidence.dates_2)){
model_2 <- i0_2*exp(-r_2*as.numeric(difftime(start.date,incidence.dates_2[row],units=c("days"))))
ll_2 <- ll_2 + model_2 - incidence.counts_2[row]*log(model_2)
}
return(ll_1 + ll_2)
}
#... and where we force r to be the same for both
minusloglik.both.same.r <- function(i0_1, i0_2, r, start.date, incidence.dates_1, incidence.dates_2, incidence.counts_1, incidence.counts_2) {
ll_1 <- 0
for(row in 1:length(incidence.dates_1)){
model_1 <- i0_1*exp(-r*as.numeric(difftime(start.date,incidence.dates_1[row],units=c("days"))))
ll_1 <- ll_1 + model_1 - incidence.counts_1[row]*log(model_1)
}
ll_2 <- 0
for(row in 1:length(incidence.dates_2)){
model_2 <- i0_2*exp(-r*as.numeric(difftime(start.date,incidence.dates_2[row],units=c("days"))))
ll_2 <- ll_2 + model_2 - incidence.counts_2[row]*log(model_2)
}
return(ll_1 + ll_2)
}
# Pillar 1:
fit.mle.both.different.rs.p1 <- mle(minusloglik.both.different.rs,
start=list(i0_1=attributes(fit.mle.Eng.p1)$coef[[1]],
i0_2=attributes(fit.mle.IoW.p1)$coef[[1]],
r_1=attributes(fit.mle.Eng.p1)$coef[[2]],
r_2=attributes(fit.mle.IoW.p1)$coef[[2]]),
fixed=list(start.date=start.date.Eng.p1,
incidence.dates_1=Eng.p1.incidence$dates,
incidence.dates_2=IoW.p1.incidence$dates,
incidence.counts_1=Eng.p1.incidence$counts,
incidence.counts_2=IoW.p1.incidence$counts)
)
summary(fit.mle.both.different.rs.p1)
# versus
fit.mle.both.same.r.p1 <- mle(minusloglik.both.same.r,
start=list(i0_1=attributes(fit.mle.Eng.p1)$coef[[1]],
i0_2=attributes(fit.mle.IoW.p1)$coef[[1]],
r=attributes(fit.mle.IoW.p1)$coef[[2]]),
fixed=list(start.date=start.date.Eng.p1,
incidence.dates_1=Eng.p1.incidence$dates,
incidence.dates_2=IoW.p1.incidence$dates,
incidence.counts_1=Eng.p1.incidence$counts,
incidence.counts_2=IoW.p1.incidence$counts)
)
summary(fit.mle.both.same.r.p1)
# likelihood ratio test
ll.diff.p1 <- attributes(fit.mle.both.different.rs.p1)$details$value - attributes(fit.mle.both.same.r.p1)$details$value
1 - pchisq(-2*ll.diff.p1, df=1) # p-value for the Pillar 1 difference
# Pillar 2
fit.mle.both.different.rs.p2 <- mle(minusloglik.both.different.rs,
start=list(i0_1=attributes(fit.mle.UK.p2)$coef[[1]],
i0_2=attributes(fit.mle.IoW.p2)$coef[[1]],
r_1=attributes(fit.mle.UK.p2)$coef[[2]],
r_2=attributes(fit.mle.IoW.p2)$coef[[2]]),
fixed=list(start.date=start.date.UK.p2,
incidence.dates_1=UK.p2.incidence$dates,
incidence.dates_2=IoW.p2.incidence$dates,
incidence.counts_1=UK.p2.incidence$counts,
incidence.counts_2=IoW.p2.incidence$counts)
)
summary(fit.mle.both.different.rs.p2)
# versus
fit.mle.both.same.r.p2 <- mle(minusloglik.both.same.r,
start=list(i0_1=attributes(fit.mle.UK.p2)$coef[[1]],
i0_2=attributes(fit.mle.IoW.p2)$coef[[1]],
r=attributes(fit.mle.IoW.p2)$coef[[2]]),
fixed=list(start.date=start.date.UK.p2,
incidence.dates_1=UK.p2.incidence$dates,
incidence.dates_2=IoW.p2.incidence$dates,
incidence.counts_1=UK.p2.incidence$counts,
incidence.counts_2=IoW.p2.incidence$counts)
)
summary(fit.mle.both.same.r.p2)
# likelihood ratio test
ll.diff.p2 <- attributes(fit.mle.both.different.rs.p2)$details$value - attributes(fit.mle.both.same.r.p2)$details$value
1 - pchisq(-2*ll.diff.p2, df=1) # p-value for the Pillar 2 difference
# Combined pillars
fit.mle.both.different.rs.both <- mle(minusloglik.both.different.rs,
start=list(i0_1=attributes(fit.mle.Eng.both)$coef[[1]],
i0_2=attributes(fit.mle.IoW.both)$coef[[1]],
r_1=attributes(fit.mle.Eng.both)$coef[[2]],
r_2=attributes(fit.mle.IoW.both)$coef[[2]]),
fixed=list(start.date=start.date.Eng.both,
incidence.dates_1=Eng.both.incidence$dates,
incidence.dates_2=IoW.both.incidence$dates,
incidence.counts_1=Eng.both.incidence$counts,
incidence.counts_2=IoW.both.incidence$counts)
)
summary(fit.mle.both.different.rs.both)
# versus
fit.mle.both.same.r.both <- mle(minusloglik.both.same.r,
start=list(i0_1=attributes(fit.mle.Eng.both)$coef[[1]],
i0_2=attributes(fit.mle.IoW.both)$coef[[1]],
r=attributes(fit.mle.IoW.both)$coef[[2]]),
fixed=list(start.date=start.date.Eng.both,
incidence.dates_1=Eng.both.incidence$dates,
incidence.dates_2=IoW.both.incidence$dates,
incidence.counts_1=Eng.both.incidence$counts,
incidence.counts_2=IoW.both.incidence$counts)
)
summary(fit.mle.both.same.r.both)
# likelihood ratio test
ll.diff.both <- attributes(fit.mle.both.different.rs.both)$details$value - attributes(fit.mle.both.same.r.both)$details$value
1 - pchisq(-2*ll.diff.both, df=1) # p-value for the combined pillars difference
```
### Comparing R before and after the Test and Trace launch
Finally, using the Pillar 1 data we estimate R in each Upper Tier Local Authority before and after the Test and Trace launch:
```{r p1.pre, warning=FALSE, message=FALSE}
r.pre.TT <- sapply(areas.alphabetical, function(area) {
dat.this.area <- dat.UK.p1 %>% filter(Area == area)
dat.this.area$Incidence <- rep(0,nrow(dat.this.area))
dat.this.area$Incidence[1] <- dat.this.area$TotalCases[1]
for(row in 2:nrow(dat.this.area)) {
dat.this.area$Incidence[row] <- dat.this.area$TotalCases[row] - dat.this.area$TotalCases[row-1]
}
this.area.p1.linelist <- dat.this.area$Date[1]
for(row in 1:nrow(dat.this.area)){
if(dat.this.area$Incidence[row]>0){
for(case in 1:dat.this.area$Incidence[row]){
this.area.p1.linelist <- c(this.area.p1.linelist, dat.this.area$Date[row])
}
}
}
this.area.p1.linelist <- this.area.p1.linelist[-1]
this.area.incidence <- incidence(this.area.p1.linelist,
first_date = as.Date("2020-03-01"),
last_date = as.Date("2020-05-04"),
standard = FALSE)
fit.mle.this.area <- mle(minusloglik,
start=list(i0=10, r=-0.01),
fixed=list(start.date=start.date.Eng.p1,
incidence.dates=this.area.incidence$dates,
incidence.counts=this.area.incidence$counts))
c(mean=attributes(fit.mle.this.area)$coef[[2]], sd =attributes(summary(fit.mle.this.area))$coef[[4]])
})
# convert from growth rate r to reproduction number R
R.pre.TT <- cbind.data.frame("Area" = areas.alphabetical,
"R" = R(r.pre.TT["mean",]),
"IoW" = rep(FALSE, length(areas.alphabetical)))
R.pre.TT[which(R.pre.TT[,"Area"] == "Isle of Wight"), "IoW"] <- TRUE # "is it the Isle of Wight" column for plotting
head(R.pre.TT)
```
```{r p1.post, warning=FALSE, message=FALSE}
r.post.TT <- sapply(areas.alphabetical[-104], function(area) { # Rutland causes an error (too few cases)
dat.this.area <- dat.UK.p1 %>% filter(Area == area)
dat.this.area$Incidence <- rep(0,nrow(dat.this.area))
dat.this.area$Incidence[1] <- dat.this.area$TotalCases[1]
for(row in 2:nrow(dat.this.area)) {
dat.this.area$Incidence[row] <- dat.this.area$TotalCases[row] - dat.this.area$TotalCases[row-1]
}
this.area.p1.linelist <- dat.this.area$Date[1]
for(row in 1:nrow(dat.this.area)){
if(dat.this.area$Incidence[row]>0){
for(case in 1:dat.this.area$Incidence[row]){
this.area.p1.linelist <- c(this.area.p1.linelist, dat.this.area$Date[row])
}
}
}
this.area.p1.linelist <- this.area.p1.linelist[-1]
this.area.incidence <- incidence(this.area.p1.linelist,
first_date = start.date.Eng.p1,
last_date = end.date.Eng.p1,
standard = FALSE)
fit.mle.this.area <- mle(minusloglik,
start=list(i0=10, r=-0.01),
fixed=list(start.date=start.date.Eng.p1,
incidence.dates=this.area.incidence$dates,
incidence.counts=this.area.incidence$counts))
c(mean=attributes(fit.mle.this.area)$coef[[2]], sd =attributes(summary(fit.mle.this.area))$coef[[4]])
})
# convert from growth rate r to reproduction number R
R.post.TT <- cbind.data.frame("Area" = areas.alphabetical[-104],
"R" = R(r.post.TT["mean",]),
"IoW" = rep(FALSE, length(areas.alphabetical) - 1))
R.post.TT[which(R.post.TT[,"Area"] == "Isle of Wight"), "IoW"] <- TRUE # "is it the Isle of Wight" column for plotting
# use previous estimate for Isle of Wight, which has a different start date (earlier launch of TT)
R.post.TT[which(R.post.TT[,"Area"] == "Isle of Wight"),"R"] <- R(attributes(fit.mle.IoW.p1)$coef[[2]])
head(R.post.TT)
```
Plot these values as histograms with the Isle of Wight highlighted in red:
```{r plot.histograms}
ggplot(R.pre.TT, aes(fill=IoW)) +
geom_histogram(aes(R), bins=50) +
xlab("R") +
ylab("Frequency") +
scale_fill_manual(values=c(brewer.pal(6, "Set1")[[2]],"red")) +
guides(fill=FALSE) +
theme_bw(base_size = 16)
ggplot(R.post.TT, aes(fill=IoW)) +
geom_histogram(aes(R), bins=50) +
xlab("R") +
ylab("Frequency") +
scale_fill_manual(values=c(brewer.pal(6, "Set1")[[2]],"red")) +
guides(fill=FALSE) +
theme_bw(base_size = 16)
```