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Fig5_sero_surveillance.R
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Fig5_sero_surveillance.R
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library(binom)
library(MASS)
library(randomForest)
library(pROC)
N_tree <- 10000 # 5000
N_rep <- 1000 # 1000
N_SS_cut <- 5000 # 5000
SS_seq <- seq(from=0, to=1, length=N_SS_cut)
set.seed(1234)
###################################
###################################
## ##
## #### #### ###### #### ##
## ## ## ## ## ## ## ## ##
## ## ## ###### ## ###### ##
## ## ## ## ## ## ## ## ##
## #### ## ## ## ## ## ##
## ##
###################################
###################################
AB_data <- read.csv("C:\\U\\CoronaVirus\\SeroSig_Phase2\\DATA\\SARS-CoV-2_serology.csv")
AB_data <- AB_data[-which(AB_data$days_post <= 10),]
N_positive <- length(which(AB_data$status == "positive"))
N_negative <- length(which(AB_data$status == "negative"))
site_update <- as.vector(AB_data$site)
site_update[which( AB_data$site == "Bichat" & AB_data$days_post <= 10 )] <- "Bichat_early"
site_update[which( AB_data$site == "Bichat" & AB_data$days_post > 10 )] <- "Bichat_late"
AB_data$site <- site_update
###################################
###################################
## ##
## ## #### # ## ###### ##
## ### ## ## ## ## ## ##
## ## ###### ###### ## ##
## ## ## ## ## ### ## ##
## #### ## ## ## ## ## ##
## ##
###################################
###################################
##N_dil_cut <- 10000
##
#3dil_cut <- exp(seq(from=log(1e-5), to=log(0.3), length=N_dil_cut))
dil_cut <- sort(unique(AB_data$Stri_IPP_IgG_dil))
dil_cut <- c( 1e-5, dil_cut, 0.5*(dil_cut[-1] + dil_cut[-length(dil_cut)]), 0.1 )
dil_cut <- sort(dil_cut)
N_dil_cut <- length(dil_cut)
#########################################################
## Calculation of 1 antigen sensitivity and specificity
## with uncertainty calculated with binomial distribution
sens_1ant_binom <- matrix(NA, ncol=3, nrow=N_dil_cut)
spec_1ant_binom <- matrix(NA, ncol=3, nrow=N_dil_cut)
colnames(sens_1ant_binom) <- c( "med", "lwr", "upr" )
colnames(spec_1ant_binom) <- c( "med", "lwr", "upr" )
for(i in 1:N_dil_cut)
{
N_pos <- length(which(is.na(AB_data$Stri_IPP_IgG_dil[which(AB_data$status == "positive")])==FALSE))
N_neg <- length(which(is.na(AB_data$Stri_IPP_IgG_dil[which(AB_data$status == "negative")])==FALSE))
sens_1ant_binom[i,1] <- length(which( AB_data$Stri_IPP_IgG_dil[which(AB_data$status == "positive")] > dil_cut[i] ))/N_pos
spec_1ant_binom[i,1] <- length(which( AB_data$Stri_IPP_IgG_dil[which(AB_data$status == "negative")] < dil_cut[i] ))/N_neg
sens_1ant_binom[i,2:3] <- as.numeric(as.vector(
binom.confint( sens_1ant_binom[i,1]*N_positive, N_positive, method="wilson")[1,5:6]
))
spec_1ant_binom[i,2:3] <- as.numeric(as.vector(
binom.confint( spec_1ant_binom[i,1]*N_negative, N_negative, method="wilson")[1,5:6]
))
}
#########################################################
## Calculation of 1 antigen sensitivity and specificity
## with cross-validated uncertainty
## (essentially bootstrapping)
Stri_IgG_pos <- AB_data$Stri_IPP_IgG_dil[which(AB_data$status == "positive")]
Stri_IgG_neg <- AB_data$Stri_IPP_IgG_dil[which(AB_data$status == "negative")]
sens_1ant_xval_mat <- matrix(NA, nrow=N_dil_cut, ncol=N_rep)
spec_1ant_xval_mat <- matrix(NA, nrow=N_dil_cut, ncol=N_rep)
for(n in 1:N_rep)
{
Stri_IgG_pos_sub <- Stri_IgG_pos[sample( length(Stri_IgG_pos), (2/3)*length(Stri_IgG_pos) )]
Stri_IgG_neg_sub <- Stri_IgG_neg[sample( length(Stri_IgG_neg), (2/3)*length(Stri_IgG_neg) )]
for(i in 1:N_dil_cut)
{
sens_1ant_xval_mat[i,n] <- length(which( Stri_IgG_pos_sub > dil_cut[i] ))/length(Stri_IgG_pos_sub)
spec_1ant_xval_mat[i,n] <- length(which( Stri_IgG_neg_sub < dil_cut[i] ))/length(Stri_IgG_neg_sub)
}
}
sens_1ant_xval_quant <- matrix(NA, nrow=N_dil_cut, ncol=3)
spec_1ant_xval_quant <- matrix(NA, nrow=N_dil_cut, ncol=3)
colnames(sens_1ant_xval_quant) <- c( "med", "lwr", "upr" )
colnames(spec_1ant_xval_quant) <- c( "med", "lwr", "upr" )
for(i in 1:N_dil_cut)
{
sens_1ant_xval_quant[i,] <- quantile( sens_1ant_xval_mat[i,], prob=c(0.5, 0.025, 0.975) )
spec_1ant_xval_quant[i,] <- quantile( spec_1ant_xval_mat[i,], prob=c(0.5, 0.025, 0.975) )
}
##############################################################
##############################################################
## ##
## ## # ## ## ## ###### #### #### # ## ###### ##
## ## ## ## ## ## ## ## ## ## ## ## ## ##
## ####### ## ## ## ## ## ###### ### ## ## ##
## ## # ## ## ## ## ## ## ## ## ## ### ## ##
## ## ## ##### ##### ## #### ## ## ## ## ## ##
## ##
##############################################################
##############################################################
status <- AB_data$status
AB <- log(AB_data[,c(10:16,43:47,23:29,56:60)])
AB <- AB[,c(1,3,6,5,14,18)]
index_trim <- unique(which(is.na(AB)==TRUE, arr.ind=TRUE)[,1])
AB_trim <- AB[-index_trim,]
status_trim <- status[-index_trim]
##############################################
## Uncertainty in sensitivity and specificity
## for algorithm fitted to all the data
RF_multi_ant = randomForest( status_trim ~ ., data=AB_trim,
importance=TRUE, ntree=N_tree)
RF_multi_ant_ROC <- roc(status_trim, RF_multi_ant$votes[,2])
varImpPlot( RF_multi_ant )
N_SS_multi_ant <- length(RF_multi_ant_ROC$sensitivities)
##############################################
## Calculate uncertainty in sensitivity
sens_multi_ant_binom <- matrix(NA, nrow=length(RF_multi_ant_ROC$sensitivities), ncol=3)
colnames(sens_multi_ant_binom) <- c("med", "lwr", "upr")
for(i in 1:nrow(sens_multi_ant_binom))
{
N_pos <- length(which(status_trim=="positive"))
sens_multi_ant_binom[i,] <- as.numeric(as.vector(
binom.confint( RF_multi_ant_ROC$sensitivities[i]*N_pos,
N_pos, method="wilson")[1,4:6] ))
}
##############################################
## Calculate uncertainty in sensitivity
spec_multi_ant_binom <- matrix(NA, nrow=length(RF_multi_ant_ROC$specificities), ncol=3)
colnames(spec_multi_ant_binom) <- c("med", "lwr", "upr")
for(i in 1:nrow(spec_multi_ant_binom))
{
N_neg <- length(which(status_trim=="negative"))
spec_multi_ant_binom[i,] <- as.numeric(as.vector(
binom.confint( RF_multi_ant_ROC$specificities[i]*N_neg,
N_neg, method="wilson")[1,4:6] ))
}
####################################
####################################
## ##
## ## ## ## ## #### ## ##
## ## ## ## ## ## ## ## ##
## ### ## ## ###### ## ##
## ## ## ### ## ## ## ##
## ## ## # ## ## ##### ##
## ##
####################################
####################################
####################################
## Uncertainty in sensitivity and specificity
## for algorithmvia cross-validation - randomly
## leaving 1/3 out
#############################################################################
## Random forests classifier for disjoint training and testing data
RF_multi_ant_SS = function( AB_train, status_train, AB_test, status_test, antigen_list )
{
AB_train = as.matrix(AB_train[,antigen_list])
if( length(which(is.na(AB_train))) > 0 )
{
status_train = status_train[-which(is.na(AB_train), arr.ind=TRUE)[,1]]
AB_train = AB_train[-which(is.na(AB_train), arr.ind=TRUE)[,1],]
}
AB_test = as.matrix(AB_test[,antigen_list])
if( length(which(is.na(AB_test))) > 0 )
{
status_test = status_test[-which(is.na(AB_test), arr.ind=TRUE)[,1]]
AB_test = AB_test[-which(is.na(AB_test), arr.ind=TRUE)[,1],]
}
############################################
## Fit Rforest and create prediction object
tryCatch(
{
RF_multi_ant = randomForest( as.factor(status_train) ~ ., data=as.data.frame(AB_train),
importance=TRUE, ntree=N_tree )
RF_multi_ant_pred_obj = predict( RF_multi_ant, newdata=AB_test, predict.all=TRUE)
RF_multi_ant_votes = rowSums(RF_multi_ant_pred_obj$individual=="negative")/N_tree
RF_multi_ant_roc <- roc(status_test, RF_multi_ant_votes)
}, error=function(e){ NULL }
)
SS_mat = cbind( RF_multi_ant_roc$sensitivities, RF_multi_ant_roc$specificities )
colnames(SS_mat) = c("sens", "spec" )
SS_mat
}
#############################################################################
## Cross-validated random forests classification algorithm
RF_multi_ant_SS_xval = function( AB_dd, status_data, antigen_list, train_prop, N_rep )
{
AB_class <- list()
for(n in 1:N_rep)
{
############################################
## Prepare testing and training data
index_train = sample( nrow(AB_dd), train_prop*nrow(AB_dd) )
index_test = setdiff( 1:nrow(AB_dd), index_train )
status_train = status_data[index_train]
status_test = status_data[index_test]
AB_train = AB_dd[index_train,]
AB_test = AB_dd[index_test,]
AB_class[[n]] = RF_multi_ant_SS( AB_train, status_train, AB_test, status_test, antigen_list )
}
AB_class
}
#########################################
## Cross-validated algorithm (mixed)
RF_multi_ant_xval_rep <- RF_multi_ant_SS_xval( AB, status, antigen_list=c(1,2,3,4,5,6), train_prop=2/3, N_rep=N_rep )
#########################################
## Cross-validated variation in sensitivity
RF_multi_ant_xval_se_vary_sp_fix <- matrix(NA, nrow=N_SS_cut, ncol=N_rep)
for(n in 1:N_rep)
{
for(i in 1:N_SS_cut)
{
RF_multi_ant_xval_se_vary_sp_fix[i,n] <- RF_multi_ant_xval_rep[[n]][min(which(RF_multi_ant_xval_rep[[n]][,2] > SS_seq[i])),1]
}
}
RF_multi_ant_xval_se_vary_sp_fix[N_SS_cut,] <- 0
RF_multi_ant_xval_se_vary_sp_fix_quant <- matrix(NA, nrow=N_SS_cut, ncol=3)
colnames(RF_multi_ant_xval_se_vary_sp_fix_quant) <- c("med", "lwr", "upr")
for(i in 1:N_SS_cut)
{
RF_multi_ant_xval_se_vary_sp_fix_quant[i,] <- quantile( RF_multi_ant_xval_se_vary_sp_fix[i,], prob=c(0.5, 0.025, 0.975) )
}
#########################################
## Cross-validated variation in specificity
RF_multi_ant_xval_se_fix_sp_vary <- matrix(NA, nrow=N_SS_cut, ncol=N_rep)
for(n in 1:N_rep)
{
for(i in 1:N_SS_cut)
{
RF_multi_ant_xval_se_fix_sp_vary[i,n] <- RF_multi_ant_xval_rep[[n]][min(which(RF_multi_ant_xval_rep[[n]][,1] < SS_seq[i])),2]
}
}
RF_multi_ant_xval_se_fix_sp_vary[1,] <- 1
RF_multi_ant_xval_se_fix_sp_vary_quant <- matrix(NA, nrow=N_SS_cut, ncol=3)
colnames(RF_multi_ant_xval_se_fix_sp_vary_quant) <- c("med", "lwr", "upr")
for(i in 1:N_SS_cut)
{
RF_multi_ant_xval_se_fix_sp_vary_quant[i,] <- quantile( RF_multi_ant_xval_se_fix_sp_vary[i,], prob=c(0.5, 0.025, 0.975) )
}
####################################
####################################
## ##
## #### ## ## ##### ## ## ##
## ## ## ## ## ## ## ## ##
## #### ## ## ##### ## ## ##
## ## ## ## ## ## ### ##
## #### #### ## ## # ##
## ##
####################################
####################################
####################################
## ##
## Multiple antigens ##
## ##
####################################
SS_multi_ant <- matrix(NA, nrow=N_SS_multi_ant, ncol=2+2*N_rep)
colnames(SS_multi_ant) <- c("sens_hat", "spec_hat", 1:(2*N_rep))
for(j in 1:N_rep)
{
colnames(SS_multi_ant)[2+j] <- paste("sens_rep_", j, sep="")
colnames(SS_multi_ant)[N_rep+2+j] <- paste("spec_rep_", j, sep="")
}
SS_multi_ant[,1] <- RF_multi_ant_ROC$sensitivities
SS_multi_ant[,2] <- RF_multi_ant_ROC$specificities
for(i in 1:N_SS_multi_ant)
{
for(j in 1:N_rep)
{
sens_index <- max(which(RF_multi_ant_ROC$sensitivities[i] < RF_multi_ant_xval_rep[[j]][,1]))
SS_multi_ant[i,2+N_rep+j] <- RF_multi_ant_xval_rep[[j]][sens_index,2]
spec_index <- max(which(RF_multi_ant_ROC$specificities[i] > RF_multi_ant_xval_rep[[j]][,2]))+1
SS_multi_ant[i,2+j] <- RF_multi_ant_xval_rep[[j]][spec_index,1]
}
}
SS_multi_ant[which(SS_multi_ant[,1]==1),3:(2+N_rep)] <- 1
SS_multi_ant[which(SS_multi_ant[,1]==1),(3+N_rep):(2+2*N_rep)] <- 0
####################################
## ##
## Single antigen ##
## ##
####################################
SS_one_ant <- matrix(NA, nrow=N_dil_cut, ncol=2+2*N_rep)
colnames(SS_one_ant) <- c("sens_hat", "spec_hat", 1:(2*N_rep))
for(j in 1:N_rep)
{
colnames(SS_one_ant)[2+j] <- paste("sens_rep_", j, sep="")
colnames(SS_one_ant)[N_rep+2+j] <- paste("spec_rep_", j, sep="")
}
SS_one_ant[,1] <- sens_1ant_binom[,1]
SS_one_ant[,2] <- spec_1ant_binom[,1]
for(i in 1:N_dil_cut)
{
for(j in 1:N_rep)
{
sens_index <- max(which(sens_1ant_binom[i,1] < sens_1ant_xval_mat[,j]))
SS_one_ant[i,2+N_rep+j] <- spec_1ant_xval_mat[sens_index,j]
spec_index <- max(which(spec_1ant_binom[i,1] > spec_1ant_xval_mat[,j]))+1
SS_one_ant[i,2+j] <- sens_1ant_xval_mat[spec_index,j]
}
}
SS_one_ant[which(SS_one_ant[,1]==1),3:(2+N_rep)] <- 1
SS_one_ant[which(SS_one_ant[,2]==0),3:(2+N_rep)] <- 1
SS_one_ant[which(SS_one_ant[,1]==1),(3+N_rep):(2+2*N_rep)] <- 0
#####################
#####################
## ##
## ##### ## ## ##
## ## ## ##
## #### ## ##
## ## ## ##
## #### ## ## ##
## ##
#####################
#####################
T_prev <- 0.05
########################################################
## ##
## Multi-antigen: 5% true prevalence ##
## ##
########################################################
M_multi_ant_5prev <- T_prev*SS_multi_ant[,(2+1):(2+N_rep)] + (1 - T_prev)*(1 - SS_multi_ant[,(2+N_rep+1):(2+2*N_rep)])
M_multi_ant_5prev_quant <- matrix(NA, nrow=N_SS_multi_ant, ncol=3)
colnames(M_multi_ant_5prev_quant) <- c("med", "lwr", "upr")
for(i in 1:N_SS_multi_ant)
{
M_multi_ant_5prev_quant[i,] <- quantile( M_multi_ant_5prev[i,], prob=c(0.5, 0.025, 0.975) )
}
##################################################
## Variation in sensitivity and specificity
spec_mat <- matrix( rep(RF_multi_ant_ROC$specificities, N_rep), ncol=N_rep)
sens_mat <- matrix( rep(RF_multi_ant_ROC$sensitivities, N_rep), ncol=N_rep)
##################################################
## Adjusted prevalence
A_multi_ant_5prev <- (M_multi_ant_5prev + spec_mat - 1)/( sens_mat + spec_mat - 1)
A_multi_ant_5prev[which(A_multi_ant_5prev < 0, arr.ind=TRUE)] <- 0
A_multi_ant_5prev[which(is.na(A_multi_ant_5prev) == TRUE, arr.ind=TRUE)] <- 0
A_multi_ant_5prev_quant <- matrix(NA, nrow=N_SS_multi_ant, ncol=3)
colnames(A_multi_ant_5prev_quant) <- c("med", "lwr", "upr")
for(i in 1:N_SS_multi_ant)
{
A_multi_ant_5prev_quant[i,] <- quantile( A_multi_ant_5prev[i,], prob=c(0.5, 0.025, 0.975) )
}
##################################################
## Relative error in adjusted prevalence
##A_multi_ant_5prev_rel_error <- abs(A_multi_ant_5prev/T_prev)
A_multi_ant_5prev_rel_error <- abs(A_multi_ant_5prev - T_prev)/T_prev
A_multi_ant_5prev_rel_error <- rowSums(A_multi_ant_5prev_rel_error)/N_rep
##################################################
## Absolute error in adjusted prevalence
A_multi_ant_5prev_abs_error <- abs(A_multi_ant_5prev - T_prev)
A_multi_ant_5prev_abs_error <- rowSums(A_multi_ant_5prev_abs_error)/N_rep
########################################################
## ##
## Single antigen: 5% true prevalence ##
## ##
########################################################
M_one_ant_5prev <- T_prev*SS_one_ant[,(2+1):(2+N_rep)] + (1 - T_prev)*(1 - SS_one_ant[,(2+N_rep+1):(2+2*N_rep)])
M_one_ant_5prev_quant <- matrix(NA, nrow=N_dil_cut, ncol=3)
colnames(M_one_ant_5prev_quant) <- c("med", "lwr", "upr")
for(i in 1:N_dil_cut)
{
M_one_ant_5prev_quant[i,] <- quantile( M_one_ant_5prev[i,], prob=c(0.5, 0.025, 0.975) )
}
##################################################
## Variation in sensitivity and specificity
spec_mat <- matrix( rep(spec_1ant_binom[,1], N_rep), ncol=N_rep)
sens_mat <- matrix( rep(sens_1ant_binom[,1], N_rep), ncol=N_rep)
##################################################
## Adjusted prevalence
A_one_ant_5prev <- (M_one_ant_5prev + spec_mat - 1)/( sens_mat + spec_mat - 1)
A_one_ant_5prev[which(A_one_ant_5prev < 0, arr.ind=TRUE)] <- 0
A_one_ant_5prev[which(is.na(A_one_ant_5prev) == TRUE, arr.ind=TRUE)] <- 0
A_one_ant_5prev_quant <- matrix(NA, nrow=N_dil_cut, ncol=3)
colnames(A_one_ant_5prev_quant) <- c("med", "lwr", "upr")
for(i in 1:N_dil_cut)
{
A_one_ant_5prev_quant[i,] <- quantile( A_one_ant_5prev[i,], prob=c(0.5, 0.025, 0.975) )
}
##################################################
## Relative error in adjusted prevalence
##A_one_ant_5prev_rel_error <- abs(A_one_ant_5prev/T_prev)
A_one_ant_5prev_rel_error <- abs(A_one_ant_5prev - T_prev)/T_prev
A_one_ant_5prev_rel_error <- rowSums(A_one_ant_5prev_rel_error)/N_rep
##################################################
## Absolute error in adjusted prevalence
A_one_ant_5prev_abs_error <- abs(A_one_ant_5prev - T_prev)
A_one_ant_5prev_abs_error <- rowSums(A_one_ant_5prev_abs_error)/N_rep
########################################################
########################################################
## ##
## #### ##### ###### #### ##### ##### #### ##
## ## ## ## ## ## ## ## ## ## ## ## ##
## ## ## ##### ## #### ##### #### ## ##
## ## ## ## ## ## ## ## ## ## ##
## #### ## ## #### ## ##### #### ##
## ##
########################################################
########################################################
drop_sens <- which(RF_multi_ant_ROC$sensitivities == 1)
drop_sens <- drop_sens[-length(drop_sens)]
drop_spec <- which(RF_multi_ant_ROC$specificities==1)
drop_spec <- drop_spec[-1]
drop_multi <- c(drop_sens, drop_spec)
########################################################
## ##
## Multi-antigen prevalence estimating function ##
## ##
########################################################
T_prev_multi_ant_func <- function( T_prevv, plot_out=TRUE )
{
M_prev <- T_prevv*SS_multi_ant[,(2+1):(2+N_rep)] + (1 - T_prevv)*(1 - SS_multi_ant[,(2+N_rep+1):(2+2*N_rep)])
M_prev_quant <- matrix(NA, nrow=N_SS_multi_ant, ncol=3)
colnames(M_prev_quant) <- c("med", "lwr", "upr")
for(i in 1:N_SS_multi_ant)
{
M_prev_quant[i,] <- quantile( M_prev[i,], prob=c(0.5, 0.025, 0.975) )
}
##################################################
## Variation in sensitivity and specificity
spec_mat <- matrix( rep(RF_multi_ant_ROC$specificities, N_rep), ncol=N_rep)
sens_mat <- matrix( rep(RF_multi_ant_ROC$sensitivities, N_rep), ncol=N_rep)
##################################################
## Adjusted prevalence
A_prev <- (M_prev + spec_mat - 1)/( sens_mat + spec_mat - 1)
A_prev[which(A_prev < 0, arr.ind=TRUE)] <- 0
A_prev[which(is.na(A_prev) == TRUE, arr.ind=TRUE)] <- 0
A_prev_quant <- matrix(NA, nrow=N_SS_multi_ant, ncol=3)
colnames(A_prev_quant) <- c("med", "lwr", "upr")
for(i in 1:N_SS_multi_ant)
{
A_prev_quant[i,] <- quantile( A_prev[i,], prob=c(0.5, 0.025, 0.975) )
}
##################################################
## Relative error in adjusted prevalence
##A_prev_rel_error <- abs(A_prev - T_prevv)/T_prevv
##A_prev_rel_error <- rowSums(A_prev_rel_error)/N_rep
A_prev_rel_error <- abs(A_prev - T_prevv)/T_prevv
A_prev_rel_error <- rowSums(A_prev_rel_error)/N_rep
##################################################
## Absolute error in adjusted prevalence
##A_prev_abs_error <- abs(A_prev - T_prevv)
##A_prev_abs_error <- rowSums(A_prev_abs_error)/N_rep
A_prev_abs_error <- abs(A_prev - T_prevv)
A_prev_abs_error <- rowSums(A_prev_abs_error)/N_rep
##################################################
##################################################
## Summarise findings in a plot
if( plot_out==TRUE )
{
par(mfrow=c(2,2))
par(mar=c(3,3,2,1))
##################################################
## Panel A: measured prevalence
plot(x=100, y=100, type='l', lty="dashed",
xlim=c(0,0.1), ylim=c(0,0.5),
#xaxs='i', yaxs='i',
xlab="1 - specificity", ylab="prevalence",
main="(A) Measured prevalence")
points( x=1 - RF_multi_ant_ROC$specificities, y=M_prev_quant[,1],
type='l', lwd=2, col="black" )
for(i in 1:N_SS_multi_ant)
{
polygon(x=1 - RF_multi_ant_ROC$specificities[c(i-1,i,i,i-1)],
y=c( M_prev_quant[c(i,i),2], M_prev_quant[c(i-1,i-1),3] ),
col=rgb(190/256,190/256,190/256,0.4), border=NA)
}
points(x=c(0,1), y=rep(T_prevv,2), type='l', col="red")
##################################################
## Panel B: adjusted prevalence
plot(x=100, y=100, type='l', lty="dashed",
xlim=c(0,0.1), ylim=c(0,0.5),
#xaxs='i', yaxs='i',
xlab="1 - specificity", ylab="prevalence",
main="(B) Adjusted prevalence")
points( x=1 - RF_multi_ant_ROC$specificities, y=A_prev_quant[,1],
type='l', lwd=2, col="black" )
for(i in 1:N_SS_multi_ant)
{
polygon(x=1 - RF_multi_ant_ROC$specificities[c(i-1,i,i,i-1)],
y=c( A_prev_quant[c(i,i),2], A_prev_quant[c(i-1,i-1),3] ),
col=rgb(190/256,190/256,190/256,0.4), border=NA)
}
points(x=c(0,1), y=rep(T_prevv,2), type='l', col="red")
##################################################
## Panel C: Expected relative error
plot(x=1 - RF_multi_ant_ROC$specificities, y=A_prev_rel_error,
type='l', lwd=2, col="black",
xlim=c(0,0.1), log="y",
#xaxs='i', yaxs='i',
xlab="1 - specificity",
main="(C) Expected relative error")
##################################################
## Panel D: Expected relative error
plot(x=1 - RF_multi_ant_ROC$specificities, y=A_prev_abs_error,
type='l', lwd=2, col="black",
xlim=c(0,0.1),
#xaxs='i', yaxs='i',
xlab="1 - specificity",
main="(D) Expected absolute error")
}
##################################################
##################################################
## Summarise findings in a plot
sens_out <- RF_multi_ant_ROC$sensitivities#[which( RF_multi_ant_ROC$specificities > 0 & RF_multi_ant_ROC$specificities < 1 )]
spec_out <- RF_multi_ant_ROC$specificities#[which( RF_multi_ant_ROC$specificities > 0 & RF_multi_ant_ROC$specificities < 1 )]
A_prev_rel_error_out <- A_prev_rel_error#[which( RF_multi_ant_ROC$specificities > 0 & RF_multi_ant_ROC$specificities < 1 )]
A_prev_abs_error_out <- A_prev_abs_error#[which( RF_multi_ant_ROC$specificities > 0 & RF_multi_ant_ROC$specificities < 1 )]
OUTP <- c( sens_out[which.min(A_prev_rel_error_out)],
spec_out[which.min(A_prev_rel_error_out)],
min(A_prev_rel_error_out),
min(A_prev_abs_error_out) )
OUTP
}
########################################################
## ##
## Single antigen prevalence estimating function ##
## ##
########################################################
T_prev_1ant_func <- function( T_prevv, plot_out=TRUE )
{
##################################################
## Measured prevalence
M_prev <- T_prevv*SS_one_ant[,(2+1):(2+N_rep)] + (1 - T_prevv)*(1 - SS_one_ant[,(2+N_rep+1):(2+2*N_rep)])
M_prev_quant <- matrix(NA, nrow=N_dil_cut, ncol=3)
colnames(M_prev_quant) <- c("med", "lwr", "upr")
for(i in 1:N_dil_cut)
{
M_prev_quant[i,] <- quantile( M_prev[i,], prob=c(0.5, 0.025, 0.975) )
}
##################################################
## Variation in sensitivity and specificity
#spec_mat <- matrix( rep(spec_1ant_xval_quant[,1], N_rep), ncol=N_rep)
#sens_mat <- matrix( rep(sens_1ant_xval_quant[,1], N_rep), ncol=N_rep)
spec_mat <- matrix( rep(spec_1ant_binom[,1], N_rep), ncol=N_rep)
sens_mat <- matrix( rep(sens_1ant_binom[,1], N_rep), ncol=N_rep)
##################################################
## Adjusted prevalence
A_prev <- (M_prev + spec_mat - 1)/( sens_mat + spec_mat - 1)
A_prev[which(A_prev < 0, arr.ind=TRUE)] <- 0
A_prev[which(is.na(A_prev) == TRUE, arr.ind=TRUE)] <- 0
A_prev_quant <- matrix(NA, nrow=N_dil_cut, ncol=3)
colnames(A_prev_quant) <- c("med", "lwr", "upr")
for(i in 1:N_dil_cut)
{
A_prev_quant[i,] <- quantile( A_prev[i,], prob=c(0.5, 0.025, 0.975) )
}
##################################################
## Relative error in adjusted prevalence
##A_prev_rel_error <- abs(A_prev/T_prevv)
A_prev_rel_error <- abs(A_prev - T_prevv)/T_prevv
A_prev_rel_error <- rowSums(A_prev_rel_error)/N_rep
##################################################
## Absolute error in adjusted prevalence
A_prev_abs_error <- abs(A_prev - T_prevv)
A_prev_abs_error <- rowSums(A_prev_abs_error)/N_rep
##################################################
##################################################
## Summarise findings in a plot
if( plot_out==TRUE )
{
par(mfrow=c(2,2))
##################################################
## Panel A: measured prevalence
plot(x=100, y=100, type='l', lty="dashed",
xlim=c(0,0.1), ylim=c(0,0.5),
#xaxs='i', yaxs='i',
xlab="1 - specificity", ylab="prevalence",
main="(A) Measured prevalence")
points( x=1 - spec_1ant_binom[,1], y=M_prev_quant[,1],
type='l', lwd=2, col="black" )
for(i in 1:N_dil_cut)
{
polygon(x=1 - spec_1ant_binom[c(i-1,i,i,i-1),1],
y=c( M_prev_quant[c(i,i),2], M_prev_quant[c(i-1,i-1),3] ),
col=rgb(190/256,190/256,190/256,0.4), border=NA)
}
points(x=c(0,1), y=rep(T_prevv,2), type='l', col="red")
##################################################
## Panel B: adjusted prevalence
plot(x=100, y=100, type='l', lty="dashed",
xlim=c(0,0.1), ylim=c(0,0.5),
#xaxs='i', yaxs='i',
xlab="1 - specificity", ylab="prevalence",
main="(B) Adjusted prevalence")
points( x=1 - spec_1ant_binom[,1], y=A_prev_quant[,1],
type='l', lwd=2, col="black" )
for(i in 1:N_dil_cut)
{
polygon(x=1 - spec_1ant_binom[c(i-1,i,i,i-1),1],
y=c( A_prev_quant[c(i,i),2], A_prev_quant[c(i-1,i-1),3] ),
col=rgb(190/256,190/256,190/256,0.4), border=NA)
}
points(x=c(0,1), y=rep(T_prevv,2), type='l', col="red")
##################################################
## Panel C: Expected relative error
plot(x=1 - spec_1ant_binom[,1], y=A_prev_rel_error,
type='l', lwd=2, col="black",
xlim=c(0,0.1), log="y",
#xaxs='i', yaxs='i',
xlab="1 - specificity",
main="(C) Expected relative error")
##################################################
## Panel D: Expected relative error
plot(x=1 - spec_1ant_binom[,1], y=A_prev_abs_error,
type='l', lwd=2, col="black",
xlim=c(0,0.1),
#xaxs='i', yaxs='i',
xlab="1 - specificity",
main="(D) Expected absolute error")
}
##################################################
##################################################
## Summarise findings in a plot
sens_out <- sens_1ant_binom#[which( spec_1ant_binom[,1] > 0 & spec_1ant_binom[,1] < 1 ),1]
spec_out <- spec_1ant_binom#[which( spec_1ant_binom[,1] > 0 & spec_1ant_binom[,1] < 1 ),1]
A_prev_rel_error_out <- A_prev_rel_error#[which( spec_1ant_binom[,1] > 0 & spec_1ant_binom[,1] < 1 )]
A_prev_abs_error_out <- A_prev_abs_error#[which( spec_1ant_binom[,1] > 0 & spec_1ant_binom[,1] < 1 )]
OUTP <- c( sens_out[which.min(A_prev_rel_error_out)],
spec_out[which.min(A_prev_rel_error_out)],
min(A_prev_rel_error_out),
min(A_prev_abs_error_out) )
OUTP
}
########################################################
## ##
## Calculate optimum sensitivity and specificity ##
## as a function of prevalence ##
## ##
########################################################
N_T_prev <- 3000
T_prev_seq <- exp(seq(from=log(0.0001), to=log(1), length=N_T_prev))
T_prev_multi_ant <- matrix(NA, nrow=N_T_prev, ncol=4)
colnames(T_prev_multi_ant) <- c("sensitivity", "specificity", "rel_error", "abs_error")
for(k in 1:N_T_prev)
{
T_prev_multi_ant[k,] <- T_prev_multi_ant_func( T_prev_seq[k], plot_out=FALSE )
}
T_prev_1ant <- matrix(NA, nrow=N_T_prev, ncol=4)
colnames(T_prev_1ant) <- c("sensitivity", "specificity", "rel_error", "abs_error")
for(k in 1:N_T_prev)
{
T_prev_1ant[k,] <- T_prev_1ant_func( T_prev_seq[k], plot_out=FALSE )
}
save.image("Fig5_sero_surveillance.RData")
##################################
##################################
## ##
## ##### ## #### ###### ##
## ## ## ## ## ## ## ##
## ##### ## ## ## ## ##
## ## ## ## ## ## ##
## ## ##### #### ## ##
## ##
##################################
##################################
PP <- 10
tiff(file="Fig5_sero_surveillance.tif", width=25, height=40, units="cm", res=500)
lay.mat <- rbind( c( 1, 1 ),
c( 2, 2 ),
c( 3, 4 ),
c( 5, 5 ),
c( 6, 7 ),
c( 8, 8 ),
c( 9,10 ),
c(11,11 ) )
layout(lay.mat, heights=c(20,1.5,10,1.5,10,1.5,10,11), widths=c(1,1))
layout.show(11)