Difference between revisions of "Epidemiological modelling"

library(OpasnetUtils)
library(ggplot2)

objects.latest("Op_fi4305", code_name = "alusta") # [[Pneumokokkirokote]]
objects.latest("Op_en6007", code_name = "answer") # [[OpasnetUtils/Drafts]]

openv.setN(100)

## Read the annual IPD and carriage incidence data.
## The 0 entries in IPD and carriage data are replaced by small values.
serotypes<-c(
"19F", "23F", "6B", "14", "9V", "4", "18C", "1", "7",
"6A", "19A", "3", "8", "9N", "10", "11", "12", "15",
"16", "20", "22", "23A", "33", "35", "38", "6C", "Oth")
car_under5<-c(
156030, 156030, 126990, 41200, 22290, 12830, 10130, 10, 14180,
54940, 24320, 12160, 1350, 20940, 4050, 72270, 10, 33100,
3380, 1350, 12160, 3380, 680, 30400, 4050, 27470, 24320 )
car_over5<-c(
168100, 314800, 256700, 209800, 114100, 62500, 200700, 100, 100,
158800, 54900, 30800, 8800, 8800, 20800, 97700, 100, 100,
191900, 25200, 72500, 22000, 100, 71300, 100, 79400, 330100 )
ipd_under5<-c(
7.78, 7.88, 24.39, 20.76, 2.91, 2.91, 6.64, 0.31, 3.02,
3.94, 9.88, 1.25, 0.10, 0.83, 0.41, 0.42, 0.21, 1.98,
0.21, 0.01, 0.93, 0.10, 0.42, 0.31, 0.42, 0.01, 0.73 )
ipd_over5<-c(
28.51, 53.72, 29.53, 99.43, 43.07, 76.99, 24.39, 6.58, 46.88,
17.42, 20.54, 55.04, 11.21, 25.20, 6.28, 12.76, 13.89, 9.18,
4.73, 3.29, 29.03, 4.40, 5.64, 12.41, 1.43, 5.50, 11.20 )

## Combine the data into 2 matrices of dimension 27*2:
IPD<-cbind(ipd_under5, ipd_over5)
Car<-cbind(car_under5, car_over5)

## Row numbers corresponding to the 3 different PCV formulations
## in matrices IPD and Car. Note: there is no serotype 5 in our data.
pcv7rows<-seq(7); pcv10rows<-seq(9); pcv13rows<-seq(12)


## Example S1.2A: Calculate the predicted incidence of IPD for the non-vaccine
## types(NVTs) under PCV13. The predictions are calculated separately for the
## two age classes. These are the values reported on the bottom panel in
## Figure 2 (there given as per 100K incidences).
postvacc <-Vaccination(IPD,Car,VT_rows=pcv13rows,p=1,q=1)


## Example S1.2B: Decrease in IPD incidence after adding a single new serotype
## to PCV13 separately for the two age categories.
next_under5<-NextVT(IPD[,1],Car[,1], VT_rows=pcv13rows,p=1)
next_over5 <-NextVT(IPD[,2],Car[,2], VT_rows=pcv13rows,p=1)

# Nämä taulukot kannattaisi transposata niin näyttäisivät siistimmiltä.

## Example S1.3A: The optimal sequence for under 5 year olds when replacement is 100%.
## The output shows the decreases in IPD incidence for each step,
## corresponding to Figure 5(C). The last serotype (row 27, the category "Other")
## is excluded from any vaccine composition but is taken into account as a
## replacing serotype at each stage.
opt<-OptimalSequence(IPD[,1],Car[,1],VT_rows=0,Excluded_rows=27,p=1.0,HowmanyAdded=20)


## Example S1.3B: The optimal sequence for the whole population when
## replacement is 50% and the current composition includes the PCV7 serotypes.
opt<-OptimalSequence(IPD,Car, VT_rows=pcv7rows,Excluded_rows=length(serotypes),
p=0.5,HowmanyAdded=17)


###################################

## Read the annual IPD and carriage incidence data.
## The 0 entries in IPD and carriage data are replaced by small values.

IPD <- Ovariable("IPD", ddata = "Op_fi4305.pneumokokki_vaestossa")
IPD@data <- IPD@data[IPD@data$Observation == "Incidence" , colnames(IPD@data) != "Observation"]

Car <- Ovariable("Car", ddata = "Op_fi4305.pneumokokki_vaestossa")
Car@data <- Car@data[Car@data$Observation == "Carrier" , colnames(Car@data) != "Observation"]

servac <- Ovariable("servac", data = data.frame(
	Vaccine = rep(c("Current", "New"), each = length(serotypes)),
	Serotype = serotypes,
	Result = as.numeric(c(
		serotypes %in% c("19F", "23F", "6B", "14", "9V", "4", "18C", "1", "7"),
		serotypes %in% servac_user
	))
))

p_user<-q_user<-adultcarriers<-1

p <- Ovariable("p", data = data.frame(Result = p_user))
q <- EvalOutput(Ovariable("q", data = data.frame(Result = q_user))) 
# EvalOutput must be used because q is mentioned twice in the code and there will otherwise be a merge mismatch.

# The true number of adult carriers may actually be larger than estimated. This adjusts for that.
Car <- Car * Ovariable("adjust", data = data.frame(Age = c("Under 5", "Over 5"), Result = c(1, adultcarriers)))

VacCar <- EvalOutput(VacCar)
VacIPD <- EvalOutput(VacIPD)

if (1==0) {
cat("servac\n")
oprint(summary(servac))


cat("Number of carriers\n")
oprint(summary(VacCar))
cat("Incidence of invasive pneumococcal disease.\n")
oprint(summary(VacIPD))  }




if("Iter" %in% colnames(VacCar@output)) N <- max(VacCar@output$Iter) else N <- 1

if (1==0) {ggplot(VacCar@output, aes(x = Serotype, weight = result(VacCar) / N, fill = Vaccine)) + geom_bar(position = "dodge") + theme_gray(base_size = 24) + 
	labs(title = "Carriers", y = "Number of carriers in Finland") }

ggplot(VacIPD@output, aes(x = Serotype, weight = result(VacIPD) / N, fill = Vaccine)) + geom_bar(position = "dodge") + theme_gray(base_size = 24) +
	labs(title = "Incidence of invasive pneumococcal disease", y = "Number of cases per year")

ggplot(VacIPD@output, aes(x = Vaccine, weight = result(VacIPD) / N, fill = Age)) + geom_bar(position = "stack") + theme_gray(base_size = 24) +
	labs(title = "Incidence of invasive pneumococcal disease", y = "Number of cases per year")

library(OpasnetUtils)

#S1.4. The R-functions
###############################################################################
##
## R code for the core methods introduced in
## Markku Nurhonen and Kari Auranen:
## "Optimal serotype compositions for pneumococcal conjugate
## vaccination under serotype replacement",
## PLoS Computational Biology, 2014.
##
###############################################################################
## List of arguments common to most functions:
##
## IPD = matrix of IPD incidences by age class (columns) and serotype (rows)
## Car = corresponding matrix of carriage incidences
## VT_rows = vector of the row numbers in matrices IPD and Car
## corresponding to vaccine types (VT_rows=0 for no vaccination)
## p = proportion of lost VT carriage which is replaced by NVT carriage
## q = proportion of VT carriage lost either due to elimination or replacement
##
## This code includes 4 functions:
## Vaccination, NextVT, OptimalSequence and OptimalVacc.
##

Vaccination<-function(IPD,Car,VT_rows,p,q) {
	##
	## Result:
	## A list of 2 matrices: IPD and carriage incidences
	## after vaccination (corresponding to matrices IPD and Car).
	## [Markku Nurhonen 2013]
	##
	if (VT_rows[1]>0) {
		IPD<-as.matrix(IPD); Car<-as.matrix(Car)
		# Post vaccination carriage incidences
		Car_Total<-t(matrix(apply(Car,2,sum),dim(Car)[2],dim(Car)[1]))
		Car2<-Car; Car2[VT_rows,]<-0
		Car_NVT<-t(matrix(apply(Car2,2,sum),dim(Car2)[2],dim(Car2)[1]))
		Car_VT<-Car_Total-Car_NVT
		CarNew<-q*(1+p*Car_VT/Car_NVT)*Car2+(1-q)*Car
		# Post vaccination IPD incidences
		NVT_rows<-seq(dim(IPD)[1])[-1*VT_rows]
		# CCR=Case-to-carrier ratios
		CCR<-IPD/Car ; IPDNew<-0*IPD
		# Apply the equation appearing above
		# equation (1) in text for each serotype.
		# First term applies to NVTs.
		IPDNew[VT_rows,]<-(1-q)*IPD[VT_rows,]
		# Second term applies to NVTs.
		IPDNew[NVT_rows,]<-((Car_NVT+p*q*Car_VT)*(Car/Car_NVT)*CCR)[NVT_rows,]
		}
	else {
		IPDNew<-IPD; CarNew<-Car
	}
	list(IPDNew,CarNew) 
}

NextVT<-function(IPD,Car,VT_rows,p) {
	##
	## Result:
	## A vector of decreases in IPD due to adding a serotype
	## to the vaccine. If VT_rows=0, initially no vaccination.
	## For row indexes incuded in VT_rows, the result is 0.
	## [Markku Nurhonen 2013]
	##
	IPD<-as.matrix(IPD); Car<-as.matrix(Car)
	
	## VaccMat = IPD and Car matrices after vaccination
	VaccMat<-Vaccination(IPD,Car,VT_rows,p,1)
	IPD<-VaccMat[[1]]; Car<-VaccMat[[2]]
	
	## Total_IPD,Total_Car = Matrices corresponding to
	## overall IPD and carriage in each age class.
	Total_IPD<-t(matrix(apply(IPD,2,sum),dim(IPD)[2],dim(IPD)[1]))
	Total_Car<-t(matrix(apply(Car,2,sum),dim(Car)[2],dim(Car)[1]))
	
	## Effect = decrease in IPD when one serotype is added to the vaccine.
	## See equation (3) in text.
	Effect<-(Total_IPD-IPD)*((IPD/(Total_IPD-IPD))-(p*Car/(Total_Car-Car)))
	
	## Special case when only one NVT remains.
	IPD_nonzero<-which(apply(IPD,1,sum)!=0)
	if (length(IPD_nonzero)==1) {Effect[IPD_nonzero,]<-IPD[IPD_nonzero,]}

	## Result is obtained after summation over age classes.
	apply(Effect,1,sum) 
}

OptimalSequence<-function(IPD,Car,VT_rows,Excluded_rows,p,HowmanyAdded) {
	##
	## Starting from VTs indicated by the vector VT_rows
	## (VT_rows=0, for no vaccination) sequentially add new VTs
	## to the vaccine composition s.t. at each step the optimal
	## serotype (corresponding to largest decrease in IPD) is added.
	##
	## Excluded_rows = Vector of indexes of the rows in matrices
	## IPD and Car corresponding to serotypes that are not to
	## be included in a vaccine composition, e.g. a row
	## corresponding to a group of serotypes labelled "Other".
	## Enter Excluded_rows=0 for no excluded serotypes.
	## HowmanyAdded = number of VTs to be added.
	##
	## Result:
	## Matrix of dimension 2*HowmanyAdded with 1st row indicating
	## the row numbers of added serotypes in the order they appear
	## in the sequence. The 2nd row lists the decreases in IPD
	## due to addition of each type. [Markku Nurhonen 2013]
	##
	IPD<-as.matrix(IPD); Car<-as.matrix(Car)
	## First check the maximum possible number of added VTs.
	VT_howmany<-length(VT_rows)
	if (VT_rows[1]==0) {VT_howmany<-0}
	Excluded_howmany<-length(Excluded_rows)
	if (Excluded_rows[1]==0) {Excluded_howmany<-0}
	HowmanyAdded<-min(HowmanyAdded,dim(IPD)[1]-(VT_howmany+Excluded_howmany))
	BestVTs<-BestEffects<-rep(0,HowmanyAdded)
	## Sequential procedure: at each step find the best additional VT.
	for (i in 1:HowmanyAdded) {
		## Effects = Decrease in IPD after addition of each serotype
		Effects<-NextVT(IPD,Car,VT_rows,p)
		## Set Effects for VTs and excluded types equal to small values
		## so that none of these will be selected as the next VT.
		minvalue<- -2*max(abs(Effects))
		if (Excluded_howmany>0) {Effects[Excluded_rows]<-minvalue}
		if (VT_rows[1]>0) {Effects[VT_rows]<-minvalue}
		## BestVTs[i] = Index of serotype with maximum decrease in IPD.
		BestVTs[i]<-order(-1*Effects)[1]
		## BestEffects[i] = Decrese in IPD due to addition of BestVTs[i]
		## to the vaccine.
		BestEffects[i]<-Effects[BestVTs[i]]
		VT_rows<-c(VT_rows,BestVTs[i])
		if (VT_rows[1]==0) {VT_rows<-VT_rows[-1]}
		VaccMat<-Vaccination(IPD,Car,VT_rows,p,1)
		IPD<-VaccMat[[1]]; Car<-VaccMat[[2]] 
	}
	t(matrix(c(BestVTs,BestEffects),HowmanyAdded,2)) 
}

OptimalVacc<-function(IPD,Car,VT_rows,p,q,HowmanyAdded) {
	##
	## Result:
	## A list of 3 elements: (1) Row numbers of serotypes in the optimal
	## vaccine composition (2)-(3) IPD and carriage incidences
	## by serotype and age class corresponding to the optimal
	## vaccine formed using the sequential procedure in the
	## function OptimalSequence. [Markku Nurhonen 2013]
	##
	Additional_VTs<-OptimalSequence(IPD,Car,VT_rows,p,HowmanyAdded)[1,]
	All_VTs<-c(VT_rows,Additional_VTs)
	if (All_VTs[1]==0) All_VTs<-All_VTs[-1]
	VaccMat<-Vaccination(IPD,Car,All_VTs,p,q)
	list(All_VTs,VaccMat[[1]],VaccMat[[2]]) 
}

VacCar <- Ovariable("VacCar",
	dependencies = data.frame(Name = c(
		"IPD", # incidence of pneumococcus disease
		"Car", # number of carriers of pneumococcus
		"servac", # ovariable of serotypes in vaccine (1 for serotypes in a vaccine, otherwise result is 0)
		"p", # proportion of eliminated VT carriage that is replaced by NVT carriage
		"q" # proportion of of VT carriage eliminated by vaccine
	)), 
	formula = function(...) {
		## Result:
		## An ovariable of carriage incidences
		## after vaccination (corresponding to Car).
		## [Markku Nurhonen 2013, Jouni Tuomisto 2014]
		# Post vaccination carriage incidences
		
		# Sum over serotypes and drop extra columns
		Car_Total<- unkeep(oapply(Car, cols = "Serotype", FUN = sum) * 1, prevresults = TRUE)
		# Car2 is a temporary ovariable with NVT carriers only
		Car2 <- unkeep(Car * (1 - servac), prevresults = TRUE) # Take only NVT carriers
			
		Car_NVT <- oapply(Car2, cols = "Serotype", FUN = sum) # Carriers of serotypes not in vaccine (NVT)
		Car_VT <- Car_Total - Car_NVT # Carriers of vaccine serotypes

		CarNew <- q * (1 + p * Car_VT / Car_NVT) * Car2 + (1 - q) * Car

		return(CarNew)
	}
)
		
VacIPD <- Ovariable("VacIPD",
	dependencies = data.frame(Name = c(
		"IPD", # incidence of pneumococcus disease
		"Car", # number of carriers of pneumococcus
		"servac", # ovariable of serotypes in vaccine (1 for serotypes in a vaccine, otherwise result is 0)
		"p", # proportion of eliminated VT carriage that is replaced by NVT carriage
		"q" # proportion of of VT carriage eliminated by vaccine
	)), 
	formula = function(...) {
		## Result:
		## An ovariable of IPD incidence
		## after vaccination (corresponding to ovariable IPD).
		## [Markku Nurhonen 2013, Jouni Tuomisto 2014]
		
		# Post vaccination carriage incidences (same code as in VacCar)
			
		Car_Total <- unkeep(oapply(Car, cols = "Serotype", FUN = sum) * 1, prevresults = TRUE) # Sums over serotypes
		Car2 <- unkeep(Car * (1 - servac), prevresults = TRUE)
			
		Car_NVT <- oapply(Car2, cols = "Serotype", FUN = sum) # Carriers of serotypes not in vaccine (NVT)
		Car_VT <- Car_Total - Car_NVT # Carriers of vaccine serotypes
		CarNew <- q * (1 + p * Car_VT / Car_NVT) * Car2 + (1 - q) * Car
			
		# Post vaccination IPD incidences
		# CCR=Case-to-carrier ratios
		CCR <- IPD / Car

		# Apply the equation appearing above
		# equation (1) in text for each serotype.
		# First term applies to VTs.
		IPDNewVT <- (1 - q) * IPD * servac

		# Second term applies to NVTs.
		IPDNewNVT <- (Car_NVT + p * q * Car_VT) * (Car / Car_NVT) * CCR * (1 - servac)

		IPDNew <- IPDNewVT + IPDNewNVT

		return(IPDNew) 
	}
)

objects.store(Vaccination, NextVT, OptimalSequence, OptimalVacc, VacCar, VacIPD)

cat("the functions Vaccination, NextVT, OptimalSequence, OptimalVacc sekä ovariablet VacCar, VacIPD are now saved. \n")