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08_model_calibration_calculation.R
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08_model_calibration_calculation.R
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#### Master Script 8: Calculate model calibration on validation set predictions ####
#
# Shubhayu Bhattacharyay, Matthew Wang, Eshan Joshi
# University of Cambridge
# Johns Hopkins University
# email address: [email protected]
#
### Contents:
# I. Initialization
# II. Calculate calibration curves of optimal (maximum AUC) GCSm-threshold detection model types
# III. Calculate calibration curves of optimal (maximum AUC) GOSE-threshold detection model types
# IV. Calculate calibration curves of optimal (maximum AUC) GOSE12m-threshold detection model types
## NOTE: Requires compilation of AUC metrics (performed in Master script 10)
### I. Initialization
# Load necessary packages
library(tidyverse)
library(rms)
library(foreach)
library(doParallel)
# Set the number of parallel cores
no.parallel.cores <- 10
registerDoParallel(cores = no.parallel.cores)
# Define number of bootstrap resamples
NUM.BOOTSTRAPS <- 1000
# Define common x-axis for calibration curve interpolation
X.INTERP <- seq(0,1,length = 200)
# Define function to calculate Integrated Calibration Index (ICI)
ICI <- function(probs,labels){
calibrated.model <- lowess(probs,labels,iter=0)
return(mean(abs(calibrated.model$y - calibrated.model$x)))
}
# Define function to calculate E50
E50 <- function(probs,labels){
calibrated.model <- lowess(probs,labels,iter=0)
return(median(abs(calibrated.model$y - calibrated.model$x)))
}
# Define function to calculate E90
E90 <- function(probs,labels){
calibrated.model <- lowess(probs,labels,iter=0)
return(quantile(abs(calibrated.model$y - calibrated.model$x),0.9))
}
# Define function to calculate Emax
Emax <- function(probs,labels){
calibrated.model <- lowess(probs,labels,iter=0)
return(max(abs(calibrated.model$y - calibrated.model$x)))
}
### II. Calculate calibration curves of optimal (maximum AUC) GCSm-threshold detection model types
## Determine optimal observation window for each threshold
# Load compiled AUC metrics
compiled.GCSm.AUC.df <- read.csv('../results/GCSm_threshold_prediction/compiled_metrics.csv') %>%
filter(Metrics == 'AUC')
# First, filter out significantly discriminating AUC, and determine maximum per observation window
opt.GCSm.signficant.AUC.df <- compiled.GCSm.AUC.df %>%
filter(lowerValues >= 0.50) %>%
group_by(Threshold) %>%
summarise(ObsWindow = ObsWindow[which.max(meanValue)],
meanAUC = max(meanValue),
medianAUC = medianValues[which.max(meanValue)],
lowerAUC = lowerValues[which.max(meanValue)],
upperAUC = upperValues[which.max(meanValue)])
# Then, for observation windows for which we cannot achieve significant discrimination, determine maximum AUC
opt.GCSm.nonsignficant.AUC.df <- compiled.GCSm.AUC.df %>%
filter(!(Threshold %in% opt.GCSm.signficant.AUC.df$Threshold)) %>%
group_by(Threshold) %>%
summarise(ObsWindow = ObsWindow[which.max(meanValue)],
meanAUC = max(meanValue),
medianAUC = medianValues[which.max(meanValue)],
lowerAUC = lowerValues[which.max(meanValue)],
upperAUC = upperValues[which.max(meanValue)])
# Compile the significant and non-significant AUC values to determine ROCs for plotting
opt.GCSm.AUC.df <- rbind(opt.GCSm.signficant.AUC.df,opt.GCSm.nonsignficant.AUC.df)
## Calculate calibration curve (with 95% CI - BBC-CV) of the optimal configurations
# Initialize empty dataframe to store ICIs across thresholds
compiled.GCSm.threshold.metrics <- as.data.frame(matrix(ncol = 8, nrow = 0))
# Iterate through each GCSm threshold
for (curr.thresh in opt.GCSm.AUC.df$Threshold){
# Extract observation window of current optimal configuration
curr.obs.window <- opt.GCSm.AUC.df$ObsWindow[opt.GCSm.AUC.df$Threshold == curr.thresh]
# Load compiled predictions of current threshold-observation window combination
curr.predictions <-
read.csv(file.path('../results/GCSm_threshold_prediction',
paste0(sprintf('%05.2f', curr.obs.window), '_h_obs_window'),
paste0(curr.thresh,'_compiled_predictions.csv')))
# Identify unique UPIs available
unique.UPIs <- unique(curr.predictions$UPI)
# Once bootstrap samples have been confirmed, begin parallel bootstrapping
compiled.GCSm.threshold.calibration <- foreach(icount(NUM.BOOTSTRAPS), .combine=rbind) %dopar%{
# Keep drawing sample until both cases are present in both in- and out-sample cases
fail.condition <- TRUE
while(fail.condition){
curr.UPI.resample <- sample(unique.UPIs,length(unique.UPIs),replace = T)
# Extract in-sample and out-sample UPIs
curr.in.sample <- sort(unique(curr.UPI.resample))
curr.out.sample <- sort(unique.UPIs[! unique.UPIs %in% curr.in.sample])
# Divide in-sample and out-sample predictions
curr.in.sample.preds <- curr.predictions %>% filter(UPI %in% curr.in.sample)
curr.out.sample.preds <- curr.predictions %>% filter(UPI %in% curr.out.sample)
# If the necessary condition is met, we may break out of the while loop
if ((length(unique(curr.in.sample.preds$TrueLabel)) == 2) &
(length(unique(curr.out.sample.preds$TrueLabel)) == 2)){
fail.condition <- FALSE
}
}
# Determine optimal configuration in current resample for calibration based on in-sample ICI
opt.config <- curr.in.sample.preds %>%
group_by(ConfigIdx) %>%
summarise(ICIvalues = ICI(Prob,TrueLabel)) %>%
top_n(-1,ICIvalues)
# Calculate ICI and calibration curve for current optimal configuration
curr.config.out.sample.preds <- curr.out.sample.preds %>% filter(ConfigIdx == opt.config$ConfigIdx)
curr.ICI <- ICI(curr.config.out.sample.preds$Prob,curr.config.out.sample.preds$TrueLabel)
curr.E50 <- E50(curr.config.out.sample.preds$Prob,curr.config.out.sample.preds$TrueLabel)
curr.E90 <- E90(curr.config.out.sample.preds$Prob,curr.config.out.sample.preds$TrueLabel)
curr.Emax <- Emax(curr.config.out.sample.preds$Prob,curr.config.out.sample.preds$TrueLabel)
curr.config.out.calibrated.model <- lowess(curr.config.out.sample.preds$Prob,curr.config.out.sample.preds$TrueLabel,iter=0)
curr.calib.curve <- approx(x = curr.config.out.calibrated.model$x,
y = curr.config.out.calibrated.model$y,
xout = X.INTERP)
# Return dataframe row of compiled information
data.frame(
Threshold = curr.thresh,
ObsWindow = curr.obs.window,
ConfigIdx = opt.config$ConfigIdx,
PredProb = curr.calib.curve$x,
TrueProb = curr.calib.curve$y,
ICI = curr.ICI,
E50 = curr.E50,
E90 = curr.E90,
Emax = curr.Emax
)
}
# Derive 95% confidence intervals from compiled calibration axes
summ.GCSm.threshold.calibration <- compiled.GCSm.threshold.calibration %>%
group_by(Threshold,ObsWindow,PredProb) %>%
summarise(meanTrueProb = mean(TrueProb,na.rm = T),
medianTrueProb = median(TrueProb,na.rm = T),
lowerTrueProb = quantile(TrueProb,.025,na.rm = T,),
upperTrueProb = quantile(TrueProb,.975,na.rm = T,))
# Save summarized calibration curve
write.csv(summ.GCSm.threshold.calibration,
file.path('../results/GCSm_threshold_prediction',
paste0(curr.thresh, '_calibration_curve.csv')),
row.names = F)
# Derive 95% of compiled ICI values as well as optimal configuration index
summ.GCSm.threshold.metrics <- compiled.GCSm.threshold.calibration %>%
dplyr::select(-c(PredProb,TrueProb)) %>%
distinct() %>%
pivot_longer(cols = -c(Threshold,ObsWindow,ConfigIdx),names_to = 'Metric',values_to = 'Value') %>%
group_by(Threshold,ObsWindow,Metric) %>%
summarise(meanValue = mean(Value,na.rm = T),
medianValue = median(Value,na.rm = T),
lowerValue = quantile(Value,.025,na.rm = T,),
upperValue = quantile(Value,.975,na.rm = T,),
optConfigIdx = unique(ConfigIdx)[which.max(table(ConfigIdx))])
# Append to compiled metric dataframe
compiled.GCSm.threshold.metrics <- rbind(compiled.GCSm.threshold.metrics,summ.GCSm.threshold.metrics)
# Status update on completion of threshold
print(paste(curr.thresh,'complete.'))
}
# Save compiled metrics
write.csv(compiled.GCSm.threshold.metrics,'../results/GCSm_threshold_prediction/calibration_metrics.csv',row.names = F)
### III. Calculate calibration curves of optimal (maximum AUC) GOSE-threshold detection model types
## Determine optimal observation window for each threshold
# Load compiled AUC metrics
compiled.GOSE.AUC.df <- read.csv('../results/GOSE_threshold_prediction/compiled_metrics.csv') %>%
filter(Metrics == 'AUC')
# First, filter out significantly discriminating AUC, and determine maximum per observation window
opt.GOSE.signficant.AUC.df <- compiled.GOSE.AUC.df %>%
filter(lowerValues >= 0.50) %>%
group_by(Threshold) %>%
summarise(ObsWindow = ObsWindow[which.max(meanValue)],
meanAUC = max(meanValue),
medianAUC = medianValues[which.max(meanValue)],
lowerAUC = lowerValues[which.max(meanValue)],
upperAUC = upperValues[which.max(meanValue)])
# Then, for observation windows for which we cannot achieve significant discrimination, determine maximum AUC
opt.GOSE.nonsignficant.AUC.df <- compiled.GOSE.AUC.df %>%
filter(!(Threshold %in% opt.GOSE.signficant.AUC.df$Threshold)) %>%
group_by(Threshold) %>%
summarise(ObsWindow = ObsWindow[which.max(meanValue)],
meanAUC = max(meanValue),
medianAUC = medianValues[which.max(meanValue)],
lowerAUC = lowerValues[which.max(meanValue)],
upperAUC = upperValues[which.max(meanValue)])
# Compile the significant and non-significant AUC values to determine ROCs for plotting
opt.GOSE.AUC.df <- rbind(opt.GOSE.signficant.AUC.df,opt.GOSE.nonsignficant.AUC.df)
## Calculate calibration curve (with 95% CI - BBC-CV) of the optimal configurations
# Initialize empty dataframe to store ICIs across thresholds
compiled.GOSE.threshold.metrics <- as.data.frame(matrix(ncol = 8, nrow = 0))
# Iterate through each GOSE threshold
for (curr.thresh in opt.GOSE.AUC.df$Threshold){
# Extract observation window of current optimal configuration
curr.obs.window <- opt.GOSE.AUC.df$ObsWindow[opt.GOSE.AUC.df$Threshold == curr.thresh]
# Load compiled predictions of current threshold-observation window combination
curr.predictions <-
read.csv(file.path('../results/GOSE_threshold_prediction',
paste0(sprintf('%05.2f', curr.obs.window), '_h_obs_window'),
paste0(curr.thresh,'_compiled_predictions.csv')))
# Identify unique UPIs available
unique.UPIs <- unique(curr.predictions$UPI)
# Once bootstrap samples have been confirmed, begin parallel bootstrapping
compiled.GOSE.threshold.calibration <- foreach(icount(NUM.BOOTSTRAPS), .combine=rbind) %dopar%{
# Keep drawing sample until both cases are present in both in- and out-sample cases
fail.condition <- TRUE
while(fail.condition){
curr.UPI.resample <- sample(unique.UPIs,length(unique.UPIs),replace = T)
# Extract in-sample and out-sample UPIs
curr.in.sample <- sort(unique(curr.UPI.resample))
curr.out.sample <- sort(unique.UPIs[! unique.UPIs %in% curr.in.sample])
# Divide in-sample and out-sample predictions
curr.in.sample.preds <- curr.predictions %>% filter(UPI %in% curr.in.sample)
curr.out.sample.preds <- curr.predictions %>% filter(UPI %in% curr.out.sample)
# If the necessary condition is met, we may break out of the while loop
if ((length(unique(curr.in.sample.preds$TrueLabel)) == 2) &
(length(unique(curr.out.sample.preds$TrueLabel)) == 2)){
fail.condition <- FALSE
}
}
# Determine optimal configuration in current resample for calibration based on in-sample ICI
opt.config <- curr.in.sample.preds %>%
group_by(ConfigIdx) %>%
summarise(ICIvalues = ICI(Prob,TrueLabel)) %>%
top_n(-1,ICIvalues)
# Calculate ICI and calibration curve for current optimal configuration
curr.config.out.sample.preds <- curr.out.sample.preds %>% filter(ConfigIdx == opt.config$ConfigIdx)
curr.ICI <- ICI(curr.config.out.sample.preds$Prob,curr.config.out.sample.preds$TrueLabel)
curr.E50 <- E50(curr.config.out.sample.preds$Prob,curr.config.out.sample.preds$TrueLabel)
curr.E90 <- E90(curr.config.out.sample.preds$Prob,curr.config.out.sample.preds$TrueLabel)
curr.Emax <- Emax(curr.config.out.sample.preds$Prob,curr.config.out.sample.preds$TrueLabel)
curr.config.out.calibrated.model <- lowess(curr.config.out.sample.preds$Prob,curr.config.out.sample.preds$TrueLabel,iter=0)
curr.calib.curve <- approx(x = curr.config.out.calibrated.model$x,
y = curr.config.out.calibrated.model$y,
xout = X.INTERP)
# Return dataframe row of compiled information
data.frame(
Threshold = curr.thresh,
ObsWindow = curr.obs.window,
ConfigIdx = opt.config$ConfigIdx,
PredProb = curr.calib.curve$x,
TrueProb = curr.calib.curve$y,
ICI = curr.ICI,
E50 = curr.E50,
E90 = curr.E90,
Emax = curr.Emax
)
}
# Derive 95% confidence intervals from compiled calibration axes
summ.GOSE.threshold.calibration <- compiled.GOSE.threshold.calibration %>%
group_by(Threshold,ObsWindow,PredProb) %>%