library(here)
here::i_am("MIPD/Precision_dosing_methods.qmd")
library(openMIPD)
library(dplyr)
library(ggplot2)
library(readr)
library(tidyr)
library(rpart.plot)
library(ggplot2)
library(patchwork)
library(mrgsolve)
library(kernlab)
library(purrr)
set.seed(1991)AMOX_CMIN_OBS_TRAIN <- read.csv(here("Data/AMOX_CMIN_OBS_TRAIN.csv"), quote = "") |>
mutate(
SEX_CAT = case_when(
SEX == 0 ~ "M",
SEX == 1 ~ "F"
)
) |>
rowwise() |>
mutate(CRCL_CKD_EPI_BSA_NORM = estimate_GFR(AGE,CREAT,SEX_CAT)) |>
ungroup() |>
mutate(CRCL_CKD_EPI_ABSOLUTE = CRCL_CKD_EPI_BSA_NORM * (BSA/1.73))
AMOX_CMIN_OBS_TEST <- read.csv(here("Data/AMOX_CMIN_OBS_TEST.csv"), quote = "") |>
mutate(
SEX_CAT = case_when(
SEX == 0 ~ "M",
SEX == 1 ~ "F"
)
) |>
rowwise() |>
mutate(CRCL_CKD_EPI_BSA_NORM = estimate_GFR(AGE,CREAT,SEX_CAT)) |>
ungroup() |>
mutate(CRCL_CKD_EPI_ABSOLUTE = CRCL_CKD_EPI_BSA_NORM * (BSA/1.73))perform_mrgsolve_prediction <- function(input_data,
mrgsolve_model_path,
model_name,
cmin_target) {
full_data <- select(input_data,-MODEL) #MODEL column identifies the model with which the prediction was made thus we have to drop it to be able to join later on
data_for_mrgsolve <- input_data |>
select(
ID,
TIME,
CREAT,
BURN,
ICU,
OBESE,
AGE,
SEX,
HT,
BSA,
DOSE_ADM,
FREQ,
DUR,
CMIN_IND,
MODEL_COHORT
) |> distinct()
mrgsolve_model <- mread_cache(mrgsolve_model_path)
mrgsolve_dose_data <-
rename(data_for_mrgsolve,
AMT = DOSE_ADM,
II = FREQ
) |>
mutate(RATE = AMT/DUR,
ADDL = TIME/II - 1,
TIME = 0,
EVID = 1,
CMT = 1)
mrgsolve_obs_data <- rename(data_for_mrgsolve,
AMT = DOSE_ADM,
II = FREQ
) |>
mutate(RATE = NA,
ADDL = NA,
EVID = 0,
CMT = 1)
mrgsolve_input_data <- bind_rows(mrgsolve_dose_data,
mrgsolve_obs_data) |>
arrange(ID,-EVID)
mrgsolve_model |>
data_set(mrgsolve_input_data) |>
zero_re() |>
mrgsim(obsonly = TRUE,
recover = colnames(mrgsolve_input_data)) |>
as_tibble() |>
rename(CMIN_PRED = IPRED) |>
mutate(MODEL = model_name) |>
select(ID,MODEL,CMIN_PRED) |>
right_join(full_data) |>
mutate(DOSE_PRED = cmin_target/CMIN_PRED * DOSE_ADM)
}AMOX_CMIN_PRED_TRAIN_CARLIER <- perform_mrgsolve_prediction(
input_data = AMOX_CMIN_OBS_TRAIN ,
mrgsolve_model_path = here(
"Simulations/amox_Carlier"
),
model_name = "CARLIER",
cmin_target = 60 #mg/L
)
AMOX_CMIN_PRED_TEST_CARLIER <- perform_mrgsolve_prediction(
input_data = AMOX_CMIN_OBS_TEST ,
mrgsolve_model_path = here(
"Simulations/amox_Carlier"
),
model_name = "CARLIER",
cmin_target = 60 #mg/L
) AMOX_CMIN_PRED_TRAIN_FOURNIER <- perform_mrgsolve_prediction(
input_data = AMOX_CMIN_OBS_TRAIN ,
mrgsolve_model_path = here(
"Simulations/amox_Fournier"
),
model_name = "FOURNIER",
cmin_target = 60 #mg/L
)
AMOX_CMIN_PRED_TEST_FOURNIER <- perform_mrgsolve_prediction(
input_data = AMOX_CMIN_OBS_TEST ,
mrgsolve_model_path = here(
"Simulations/amox_Fournier"
),
model_name = "FOURNIER",
cmin_target = 60 #mg/L
) AMOX_CMIN_PRED_TRAIN_MELLON <- perform_mrgsolve_prediction(
input_data = AMOX_CMIN_OBS_TRAIN ,
mrgsolve_model_path = here(
"Simulations/amox_Mellon"
),
model_name = "MELLON",
cmin_target = 60 #mg/L
)
AMOX_CMIN_PRED_TEST_MELLON <- perform_mrgsolve_prediction(
input_data = AMOX_CMIN_OBS_TEST ,
mrgsolve_model_path = here(
"Simulations/amox_Mellon"
),
model_name = "MELLON",
cmin_target = 60 #mg/L
) AMOX_CMIN_PRED_TRAIN_RAMBAUD <- perform_mrgsolve_prediction(
input_data = AMOX_CMIN_OBS_TRAIN ,
mrgsolve_model_path = here(
"Simulations/amox_Rambaud"
),
model_name = "RAMBAUD",
cmin_target = 60 #mg/L
)
AMOX_CMIN_PRED_TEST_RAMBAUD <- perform_mrgsolve_prediction(
input_data = AMOX_CMIN_OBS_TEST ,
mrgsolve_model_path = here(
"Simulations/amox_Rambaud"
),
model_name = "RAMBAUD",
cmin_target = 60 #mg/L
) AMOX_CMIN_TRAIN <- bind_rows(
AMOX_CMIN_PRED_TRAIN_CARLIER,
AMOX_CMIN_PRED_TRAIN_FOURNIER,
AMOX_CMIN_PRED_TRAIN_MELLON,
AMOX_CMIN_PRED_TRAIN_RAMBAUD
) |>
arrange(ID,MODEL) |>
mutate(REFERENCE = if_else(MODEL == MODEL_COHORT, 1, 0)) # Add a variable called REFERENCE which is 1 for the the line where the model used for simulation is the same as the model cohort (otherwise 0) and take only observed values
write.csv(AMOX_CMIN_TRAIN, here("Data/AMOX_CMIN_TRAIN.csv"), row.names = FALSE, quote = FALSE)
AMOX_CMIN_TEST <- bind_rows(
AMOX_CMIN_PRED_TEST_CARLIER,
AMOX_CMIN_PRED_TEST_FOURNIER,
AMOX_CMIN_PRED_TEST_MELLON,
AMOX_CMIN_PRED_TEST_RAMBAUD
) |>
arrange(ID,MODEL) |>
mutate(REFERENCE = if_else(MODEL == MODEL_COHORT, 1, 0)) # Add a variable called REFERENCE which is 1 for the the line where the model used for simulation is the same as the model cohort (otherwise 0) and take only observed values
write.csv(AMOX_CMIN_TEST, here("Data/AMOX_CMIN_TEST.csv"), row.names = FALSE, quote = FALSE)Visualization of the inter-individual variability of models by dividing PRED (predicted) values by IPRED (observed) both generated by the same model.
# CMIN
# Divide each PRED by the IPRED reference
AMOX_CMIN2 <- bind_rows(AMOX_CMIN_TRAIN,AMOX_CMIN_TEST) %>%
filter(REFERENCE == 1) |>
group_by(ID, MODEL) %>%
mutate(
ratio = (CMIN_PRED / CMIN_IND) * 100
) %>%
ungroup()
# Boxplot of ratios stratified by model
stratified_ratios_CMIN <- ggplot(AMOX_CMIN2, aes(x = MODEL, y = ratio, fill = MODEL)) +
geom_boxplot() +
geom_hline(yintercept = 80, linetype = "dashed", color = "red") +
geom_hline(yintercept = 125, linetype = "dashed", color = "red") +
labs(
title = "Predicted/observed ratios for the same model (Cmax)",
x = "MODEL",
y = "Ratio (%)"
) +
theme_minimal() +
theme(legend.position = "none") +
theme(
axis.text.x = element_text(angle = 20, hjust = 1, size = 16),
axis.text = element_text(size = 16),
axis.title = element_text(size = 20),
plot.title = element_text(size=20),
)
stratified_ratios_CMIN + scale_y_log10()
In this section, the focus is no longer solely on observed concentrations (IPRED), but the performance of the models is explored by illustrating how the predicted concentrations (PRED) for all the cohorts (not just for covariates on which the model was developed) compare the the observed concentration. Visualization of PRED/IPRED ratios. In all cases we compare PRED (predicted) values to a reference IPRED (observed), which is the IPRED of the model whose cohort was used to simulate a particular set of covariates. Red lines indicate the bioequivalence range of 80-125 %.
# CMIN
# Divide each PRED by the IPRED reference
AMOX_CMIN3 <- bind_rows(AMOX_CMIN_TRAIN,AMOX_CMIN_TEST) %>%
group_by(ID) %>%
mutate(
ref_CMIN = first(CMIN_IND[REFERENCE == 1], default = NA),
ratio = (CMIN_PRED / ref_CMIN) * 100
) %>%
ungroup()
# Boxplot of ratios stratified by model
perf_CMIN <- ggplot(AMOX_CMIN3, aes(x = MODEL, y = ratio, fill = MODEL)) +
geom_boxplot() +
scale_y_log10() +
geom_hline(yintercept = 80, linetype = "dashed", color = "red") +
geom_hline(yintercept = 125, linetype = "dashed", color = "red") +
labs(
title = "Boxplots of predicted/observed ratios (CMIN)",
x = "MODEL",
y = "Ratio (%)"
) +
theme_minimal() +
theme(legend.position = "none") +
theme(
axis.text.x = element_text(angle = 20, hjust = 1, size = 16),
axis.text = element_text(size = 16),
axis.title = element_text(size = 20),
plot.title = element_text(size=20),
)
perf_CMIN
explore_predictions <- function(data, conc_inf = 40, conc_sup = 80, freq_column = "FREQ") {
# Calculate true dose range and prediction correctness
data <- data %>%
mutate(
DOSE_inf = (conc_inf / CMIN_IND) * DOSE_ADM,
DOSE_sup = (conc_sup / CMIN_IND) * DOSE_ADM
) %>%
mutate(
Prediction_correctness = ifelse(
(DOSE_PRED >= DOSE_inf & DOSE_PRED <= DOSE_sup),
"Correct", "Incorrect"
)
) %>%
drop_na(Prediction_correctness) %>%
mutate(
Dosing = case_when(
Prediction_correctness == "Correct" ~ "On target",
DOSE_PRED < DOSE_inf ~ "Underdosed",
DOSE_PRED > DOSE_sup ~ "Overdosed"
)
)
# Proportions of under- and overdosing
dosing <- data %>%
count(Dosing) %>%
mutate(
Proportion = n / sum(n) * 100,
Dosing = factor(Dosing, levels = c("Overdosed", "On target", "Underdosed")),
Label = paste0(Dosing, "\n", round(Proportion), "%")
)
# Over/underdosed graph
p1 <- ggplot(dosing, aes(x = "", y = Proportion, fill = Dosing)) +
geom_bar(stat = "identity", width = 0.5) +
geom_text(aes(label = Label), position = position_stack(vjust = 0.5), color = "white", size = 5) +
scale_fill_manual(values = c("Underdosed" = "darkorange", "On target" = "chartreuse4", "Overdosed" = "#A91A27")) +
labs(y = "%", x = NULL, title = "Target attainment", fill = "Dosing Category") +
theme_minimal() +
theme(
axis.text.x = element_blank(),
axis.ticks.x = element_blank(),
plot.title = element_text(size = 20),
axis.text = element_text(size = 16),
axis.title = element_text(size = 20),
legend.position = "none"
) +
scale_y_continuous(breaks = seq(0, 100, by = 10)) +
coord_cartesian(ylim = c(0, 100))
# CREAT binning (based on the American Kidney Fund's categories)
data <- data %>%
mutate(
CREAT_bin = case_when(# males
SEX == 0 ~ cut(
CREAT,
breaks = c(0, 0.7, 1.3, Inf),
labels = c("Below normal", "Normal", "Above normal"),
right = FALSE
),
SEX == 1 ~ cut( # females
CREAT,
breaks = c(0, 0.6, 1.1, Inf),
labels = c("Below normal", "Normal", "Above normal"),
right = FALSE
)
)
)
# Binning stats
bin_summary <- data %>%
group_by(CREAT_bin, Prediction_correctness) %>%
summarise(Count = n(), .groups = "drop") %>%
pivot_wider(names_from = Prediction_correctness, values_from = Count, values_fill = 0) %>%
mutate(Proportion_Correct = (Correct / (Correct + Incorrect)) * 100)
# Binning graph
p2 <- ggplot(bin_summary, aes(x = CREAT_bin, y = Proportion_Correct)) +
geom_bar(stat = "identity", fill = "chartreuse4", color = "chartreuse4", size = 1) +
geom_text(aes(label = round(Proportion_Correct)), vjust = -0.5, size = 5, color = "black") +
labs(title = "Target attainement by serum creatinine level", x = "Serum creatinine", y = "Correct predictions (%)") +
theme_minimal() +
theme(
plot.title = element_text(size = 24),
axis.text = element_text(size = 14),
axis.title = element_text(size = 16)
) +
scale_y_continuous(limits = c(0, 100), breaks = seq(0, 100, by = 20))
# CRCL binning for chronic kidney disease categories
data <- data %>%
mutate(
CRCL_bin = cut(
CRCL_CKD_EPI_ABSOLUTE,
breaks = c(0, 30, 60, 90, 130, Inf),
labels = c("0-30", "31-60", "61-90", "90-130", "> 130"),
right = FALSE
)
)
# Binning stats
bin_summary <- data %>%
group_by(CRCL_bin, Prediction_correctness) %>%
summarise(Count = n(), .groups = "drop") %>%
pivot_wider(names_from = Prediction_correctness, values_from = Count, values_fill = 0) %>%
mutate(Proportion_Correct = (Correct / (Correct + Incorrect)) * 100)
# Binning graph
p3 <- ggplot(bin_summary, aes(x = CRCL_bin, y = Proportion_Correct)) +
geom_bar(stat = "identity", fill = "chartreuse4", color = "chartreuse4", size = 1) +
geom_text(aes(label = round(Proportion_Correct)), vjust = -0.5, size = 5, color = "black") +
labs(title = "Target attainement by creatinine clearance category", x = "Creatinine clearance (mL/min)", y = "Correct predictions (%)") +
theme_minimal() +
theme(
plot.title = element_text(size = 24),
axis.text = element_text(size = 14),
axis.title = element_text(size = 16)
) +
scale_y_continuous(limits = c(0, 100), breaks = seq(0, 100, by = 20))
# Summary statistics
summary_stats <- data %>%
group_by(Prediction_correctness) %>%
summarise(
mean_CREAT = mean(CREAT, na.rm = TRUE),
sd_CREAT = sd(CREAT, na.rm = TRUE),
mean_WT = mean(WT, na.rm = TRUE),
sd_WT = sd(WT, na.rm = TRUE),
mean_AGE = mean(AGE, na.rm = TRUE),
sd_AGE = sd(AGE, na.rm = TRUE),
Count = n()
) %>%
mutate(Proportion = Count / sum(Count))
correct_proportion <- summary_stats %>%
filter(Prediction_correctness == "Correct") %>%
pull(Proportion)
message(sprintf("Proportion of 'correct' predictions: %.2f%%", correct_proportion * 100))
return(list(
target_attainment = p1,
creat_plot = p2,
crcl_plot = p3,
summary_stats = summary_stats
))
}# In this specific case predictions were already
# created before, thus "making predictions"
# simply involve loading them and filtering for the correct model
AMOX_CMIN_PRED_TRAIN_CARLIER <- read_csv(
here("Data/AMOX_CMIN_TRAIN.csv")
) |>
filter(MODEL == "CARLIER")
AMOX_CMIN_PRED_TEST_CARLIER <- read_csv(
here("Data/AMOX_CMIN_TEST.csv")
) |>
filter(MODEL == "CARLIER")results_carlier_train <- explore_predictions(AMOX_CMIN_PRED_TRAIN_CARLIER)
results_carlier_train$target_attainment 
creat_plot_carlier_train <- results_carlier_train$creat_plot
creat_plot_carlier_train
crcl_plot_carlier_train <- results_carlier_train$crcl_plot
crcl_plot_carlier_train
results_carlier_train$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 0.982 0.558 79.0 14.2 64.1 17.2 512
2 Incorrect 0.912 0.606 86.4 19.0 57.4 15.6 1363
# ℹ 1 more variable: Proportion <dbl>results_carlier_test <- explore_predictions(AMOX_CMIN_PRED_TEST_CARLIER)
results_carlier_test$target_attainment 
creat_plot_carlier_test <- results_carlier_test$creat_plot
creat_plot_carlier_test
crcl_plot_carlier_test <- results_carlier_test$crcl_plot
crcl_plot_carlier_test
results_carlier_test$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 1.02 0.593 79.7 14.8 65.1 17.3 171
2 Incorrect 0.921 0.571 86.3 19.7 57.9 15.6 429
# ℹ 1 more variable: Proportion <dbl># In this specific case predictions were already
# created before, thus "making predictions"
# simply involve loading them and filtering for the correct model
AMOX_CMIN_PRED_TRAIN_FOURNIER <- read_csv(
here("Data/AMOX_CMIN_TRAIN.csv")
) |>
filter(MODEL == "FOURNIER")
AMOX_CMIN_PRED_TEST_FOURNIER <- read_csv(
here("Data/AMOX_CMIN_TEST.csv")
) |>
filter(MODEL == "FOURNIER")results_fournier_train <- explore_predictions(AMOX_CMIN_PRED_TRAIN_FOURNIER)
results_fournier_train$target_attainment 
creat_plot_fournier_train <- results_fournier_train$creat_plot
creat_plot_fournier_train
crcl_plot_fournier_train <- results_fournier_train$crcl_plot
crcl_plot_fournier_train
results_fournier_train$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 0.965 0.608 80.7 16.1 64.1 17.9 605
2 Incorrect 0.914 0.586 86.1 18.7 56.9 15.0 1270
# ℹ 1 more variable: Proportion <dbl>results_fournier_test <- explore_predictions(AMOX_CMIN_PRED_TEST_FOURNIER)
results_fournier_test$target_attainment 
creat_plot_fournier_test <- results_fournier_test$creat_plot
creat_plot_fournier_test
crcl_plot_fournier_test <- results_fournier_test$crcl_plot
crcl_plot_fournier_test
results_fournier_test$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 0.907 0.432 79.0 15.8 62.7 16.9 191
2 Incorrect 0.970 0.635 86.9 19.4 58.6 16.0 409
# ℹ 1 more variable: Proportion <dbl># In this specific case predictions were already
# created before, thus "making predictions"
# simply involve loading them and filtering for the correct model
AMOX_CMIN_PRED_TRAIN_MELLON <- read_csv(
here("Data/AMOX_CMIN_TRAIN.csv")
) |>
filter(MODEL == "MELLON")
AMOX_CMIN_PRED_TEST_MELLON <- read_csv(
here("Data/AMOX_CMIN_TEST.csv")
) |>
filter(MODEL == "MELLON")results_mellon_train <- explore_predictions(AMOX_CMIN_PRED_TRAIN_MELLON)
results_mellon_train$target_attainment 
creat_plot_mellon_train <- results_mellon_train$creat_plot
creat_plot_mellon_train
crcl_plot_mellon_train <- results_mellon_train$crcl_plot
crcl_plot_mellon_train
results_mellon_train$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 0.681 0.177 94.9 19.3 52.9 11.9 290
2 Incorrect 0.977 0.630 82.4 17.2 60.4 16.8 1585
# ℹ 1 more variable: Proportion <dbl>results_mellon_test <- explore_predictions(AMOX_CMIN_PRED_TEST_MELLON)
results_mellon_test$target_attainment 
creat_plot_mellon_test <- results_mellon_test$creat_plot
creat_plot_mellon_test
crcl_plot_mellon_test <- results_mellon_test$crcl_plot
crcl_plot_mellon_test
results_mellon_test$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 0.713 0.184 93.0 21.8 49.5 13.1 87
2 Incorrect 0.990 0.612 82.9 17.7 61.7 16.2 513
# ℹ 1 more variable: Proportion <dbl># In this specific case predictions were already
# created before, thus "making predictions"
# simply involve loading them and filtering for the correct model
AMOX_CMIN_PRED_TRAIN_RAMBAUD <- read_csv(
here("Data/AMOX_CMIN_TRAIN.csv")
) |>
filter(MODEL == "RAMBAUD")
AMOX_CMIN_PRED_TEST_RAMBAUD <- read_csv(
here("Data/AMOX_CMIN_TEST.csv")
) |>
filter(MODEL == "RAMBAUD")results_rambaud_train <- explore_predictions(AMOX_CMIN_PRED_TRAIN_RAMBAUD)
results_rambaud_train$target_attainment 
creat_plot_rambaud_train <- results_rambaud_train$creat_plot
creat_plot_rambaud_train
crcl_plot_rambaud_train <- results_rambaud_train$crcl_plot
crcl_plot_rambaud_train
results_rambaud_train$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 1.07 0.492 77.4 13.6 70.9 14.6 329
2 Incorrect 0.901 0.609 85.9 18.6 56.7 15.6 1546
# ℹ 1 more variable: Proportion <dbl>results_rambaud_test <- explore_predictions(AMOX_CMIN_PRED_TEST_RAMBAUD)
results_rambaud_test$target_attainment 
creat_plot_rambaud_test <- results_rambaud_test$creat_plot
creat_plot_rambaud_test
crcl_plot_rambaud_test <- results_rambaud_test$crcl_plot
crcl_plot_rambaud_test
results_rambaud_test$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 1.09 0.645 76.5 15.2 70.1 14.1 104
2 Incorrect 0.921 0.560 86.1 19.0 57.8 16.0 496
# ℹ 1 more variable: Proportion <dbl>This is an ensembling method where a PopPK model is built based on data simulated with the four models (Carlier, Fournier, Mellon, and Rambaud).
The model is built on the training set used for the ensembling algorithms and tested on the test set. The data is rich and does not contain below quantification limit concentrations. The 3 three compartment structural model was a better fit than a two compartment one (OFV drop < 0.1 %), however as the estimate of the second peripheral volume was negligeable (< 1 L), the two-compartment model was preferred. The pharmacostatistical model is developed using the automatic statistical model building tool in Monolix 2024R1. The best model has IIV on all parameters with no covariance between them. The error model is combined with log-normal distribution.
The covariate model is built using the automatic SCM tool of Monolix with respective forward and backward p values of 5 and 1 % (Likelihood Ratio Test). CREAT and WT were added on the clearance.
AMOX_CMIN_PRED_TEST_META <- perform_mrgsolve_prediction(
input_data = AMOX_CMIN_OBS_TEST ,
mrgsolve_model_path = here(
"MIPD/amox_Meta"
),
model_name = "META",
cmin_target = 60 #mg/L
) results_meta_test <- explore_predictions(AMOX_CMIN_PRED_TEST_META)
results_meta_test$target_attainment 
creat_plot_meta_test <- results_meta_test$creat_plot
creat_plot_meta_test
crcl_plot_meta_test <- results_meta_test$crcl_plot
crcl_plot_meta_test
results_meta_test$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 0.839 0.301 86.3 20.4 60.4 15.7 168
2 Incorrect 0.993 0.651 83.6 17.9 59.7 16.6 432
# ℹ 1 more variable: Proportion <dbl>Based on the our standard dose screening, out of five potential dosing regimens guided by the SPILF recommendation and hospital practices, 200 mg/kg is selected as standard dose reference as it gave the highest target attainment on clinical data.
AMOX_CMIN_PRED_TRAIN_STD <- AMOX_CMIN_TRAIN %>%
mutate(DOSE_PRED = (200 * WT) / (24/FREQ)) %>%
dplyr::select(ID, CREAT, WT, BURN, SEX, AGE, HT, FREQ, DOSE_ADM, DOSE_PRED, CMIN_IND, SEX, BSA, CRCL_CKD_EPI_ABSOLUTE) %>%
distinct()
AMOX_CMIN_PRED_TEST_STD <- AMOX_CMIN_TEST %>%
mutate(DOSE_PRED = (200 * WT) / (24/FREQ)) %>%
dplyr::select(ID, CREAT, WT, BURN, SEX, AGE, HT, FREQ, DOSE_ADM, DOSE_PRED, CMIN_IND, SEX, BSA, CRCL_CKD_EPI_ABSOLUTE) %>%
distinct()results_standard_train <- explore_predictions(AMOX_CMIN_PRED_TRAIN_STD)
results_standard_train$target_attainment 
results_standard_train$creat_plot
results_standard_train$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 1.19 0.743 76.9 12.0 70.1 14.5 291
2 Incorrect 0.883 0.549 85.7 18.7 57.2 15.8 1584
# ℹ 1 more variable: Proportion <dbl>results_standard_test <- explore_predictions(AMOX_CMIN_PRED_TEST_STD)
results_standard_test$target_attainment 
results_standard_test$creat_plot
results_standard_test$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 1.10 0.511 77.7 13.2 70.4 13.7 93
2 Incorrect 0.923 0.587 85.6 19.3 58.0 16.1 507
# ℹ 1 more variable: Proportion <dbl>All the models are given the same weight (one quarter in this case). The performance of the models or the development cohort characteristics are not taken into account.
AMOX_CMIN_PRED_TRAIN_UNINF_MOD_ENS <- AMOX_CMIN_TRAIN %>%
mutate(WEIGHT = 0.25) %>% # Add uniform weight
mutate(WEIGHTED_PRED = CMIN_PRED * WEIGHT) %>% # Weigh prediction
group_by(ID) %>%
mutate(WEIGHTED_PREDICTION = sum(WEIGHTED_PRED)) %>% # Ensemble weighted predictions
ungroup() %>%
dplyr::select(ID, CREAT, WT, BURN, SEX, AGE, HT, FREQ, DOSE_ADM, WEIGHTED_PREDICTION, CMIN_IND, SEX, CRCL_CKD_EPI_ABSOLUTE) %>%
distinct() %>%
dplyr::mutate(DOSE_PRED = (60/WEIGHTED_PREDICTION) * DOSE_ADM) # Administered dose extrapolation to reach 60 mg/L
AMOX_CMIN_PRED_TEST_UNINF_MOD_ENS <- AMOX_CMIN_TEST %>%
mutate(WEIGHT = 0.25) %>% # Add uniform weight
mutate(WEIGHTED_PRED = CMIN_PRED * WEIGHT) %>% # Weigh prediction
group_by(ID) %>%
mutate(WEIGHTED_PREDICTION = sum(WEIGHTED_PRED)) %>% # Ensemble weighted predictions
ungroup() %>%
dplyr::select(ID, CREAT, WT, BURN, SEX, AGE, HT, FREQ, DOSE_ADM, WEIGHTED_PREDICTION, CMIN_IND, SEX, CRCL_CKD_EPI_ABSOLUTE) %>%
distinct() %>%
dplyr::mutate(DOSE_PRED = (60/WEIGHTED_PREDICTION) * DOSE_ADM) # Administered dose extrapolation to reach 60 mg/Lresults_uninf_mod_ens_train <- explore_predictions(AMOX_CMIN_PRED_TRAIN_UNINF_MOD_ENS)
results_uninf_mod_ens_train$target_attainment 
results_uninf_mod_ens_train$creat_plot
results_uninf_mod_ens_train$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 0.939 0.468 82.8 17.8 62.0 17.0 613
2 Incorrect 0.927 0.646 85.1 18.2 57.8 15.8 1262
# ℹ 1 more variable: Proportion <dbl>results_uninf_mod_ens_test <- explore_predictions(AMOX_CMIN_PRED_TEST_UNINF_MOD_ENS)
results_uninf_mod_ens_test$target_attainment 
results_uninf_mod_ens_test$creat_plot
results_uninf_mod_ens_test$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 0.937 0.515 82.2 18.6 62.3 16.6 194
2 Incorrect 0.956 0.607 85.5 18.7 58.8 16.2 406
# ℹ 1 more variable: Proportion <dbl>The nomogram developed by Rambaud et al. (2020) in Nantes which predicts the dose in endocarditis patients based solely on absolute glomerular filtration rate.
The daily dose in g to reach 20 mg/L is predicted by the nomogram based on CRCL in mL/min (x) estimated using the CKD-EPI equation \[ \text{Dose} = 0.0001x^2 + 0.0613x + 1.157 \] and then extrapolated to attain 60 mg/L.
Although the nomogram has been validated only for CRCL between 30 and 120 mL/min and continuous infusion, in this study, it was also evaluated in patients with CRCL outside of this range and applied to intermittent infusion.
AMOX_CMIN_PRED_TRAIN_NOMOGRAM <- AMOX_CMIN_TRAIN %>%
dplyr::select(ID, CREAT, WT, BURN, SEX, AGE, HT, FREQ, DOSE_ADM, CMIN_IND, SEX, CRCL_CKD_EPI_ABSOLUTE) %>%
mutate(DOSE_PRED = ((0.0001 * CRCL_CKD_EPI_ABSOLUTE^2 + 0.0613 * CRCL_CKD_EPI_ABSOLUTE + 1.157) * 3000) / (24/FREQ)) |>
distinct()
AMOX_CMIN_PRED_TEST_NOMOGRAM <- AMOX_CMIN_TEST %>%
dplyr::select(ID, CREAT, WT, BURN, SEX, AGE, HT, FREQ, DOSE_ADM, CMIN_IND, SEX, CRCL_CKD_EPI_ABSOLUTE) %>%
mutate(DOSE_PRED = ((0.0001 * CRCL_CKD_EPI_ABSOLUTE^2 + 0.0613 * CRCL_CKD_EPI_ABSOLUTE + 1.157) * 3000) / (24/FREQ)) |>
distinct() results_nomogram_train <- explore_predictions(AMOX_CMIN_PRED_TRAIN_NOMOGRAM)
results_nomogram_train$target_attainment 
results_nomogram_train$creat_plot
results_nomogram_train$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 1.04 0.431 75.6 12.6 67.7 15.7 360
2 Incorrect 0.905 0.623 86.4 18.6 57.2 15.8 1515
# ℹ 1 more variable: Proportion <dbl>results_nomogram_test <- explore_predictions(AMOX_CMIN_PRED_TEST_NOMOGRAM)
results_nomogram_test$target_attainment 
results_nomogram_test$creat_plot
results_nomogram_test$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 1.12 0.587 77.0 13.6 69.8 15.1 129
2 Incorrect 0.904 0.568 86.4 19.4 57.2 15.7 471
# ℹ 1 more variable: Proportion <dbl>This method is used to attribute weights to models based on their probability to give correct predictions for a set of covariates.
The method is based on Agema et al. (2024).
Bioequivalence ratios between \(Cmin_{\text{pred}}\) and \(Cmin_{\text{ind}}\) are calculated and transformed to a binary variable based on if the ratio is in the bioequivalence range [0.80-1.25] or not. This categorical variable is called CORRECT.
First, for each set of covariates, the ratios between the predicted values of the 4 models are compared to the true value. Then, we add the variable CORRECT which takes the value of YES if the ratio is in the bioequivalence range, and the value of NO, if not.
Then, decision tree is developed where the predictors are the seven covariates and a binary variable indicating continuous or intermittent infusion (CON), and the target variable is the categorical variable named CORRECT. A decision tree is fitted separately for each MODEL where the following parameters need to be defined
- Complexity – a penalty that the information gain has to overcome to add a split. A higher complexity value leads to a smaller tree meaning that subjects are divided into smaller number of categories, so their scores will be less diverse. Comlexity is found by automatic hyperparameter tuning based on cross-validation error.
Minsplit – minimum number of samples to split a node (smaller value, deeper tree).
Minbucket – minimum number of samples in the terminal node (smaller value, deeper tree). Minsplit and minbucket in the range of 2-30 range does not affect the results , so 4 is fixed as a value to have deeper trees.
- xval – number of cross validations. 10-fold cross validation is used (the same number as for the ML methods).
- splitting criterion - entropy or Gini impurity. Gini meausures the frequency (f) with which an element is misclassified:
\[ Gini\ impurity = 2 \cdot f \cdot \left(1 - f \right) \ \] Entropy (called information in rpart) measures the disorder of the predictors as a function of the target:
\[ Entropy = f \cdot log_2(f) \]
Normally, the two splitting criteria give similar results. Entropy is more computationally complex as it uses logarithms.
For certain models, the root node is not split any further (same model score for all subjects).
In the obtained leaf_results table, only the leaf nodes are included with the following columns
node - node number
var - splitting variable (it always says leaf, as only leaves are included in the table)
n- number of subjects per node
wt - subject weight (all the subject have the same weight)
dev - Gini index
yval - the predicted class
ncompete - Alternative splitting variables that were not selected for a node but give slightly worse performance than the selected variable. As only leaves are included, there are no competing splitting variables.
nsurrogate - Used for missing values. Not applicable to leaves.
yval2[, 2] - number of NO for the CORRECT variable
yval2[, 3] - number of YES
yval2[, 4] - proportion of NO
yval2[, 5] - proportion of YES
prob_yes - same as yval2[, 5], this column is used later to attribute model weights
n_obs - number of observations
To this table, in the path column is added containing all the decisions that led to that particular leaf. Then, this string is transformed to lower and upper limits for continuous and categories for categorical covariates. If there are no upper or lower limits or selected categories, NA is added.
In the original method ( Agema et al. (2024)), the leaves are selected with at least a YES proportion of 0.5 and then the selected models are taken into account with equal weight. Here, all models are used with their respective YES proportions. This way, no subject will end up without a model, and the weights will be more nuancedly calculated. Then, for each subject, the four corresponding nodes are found based on its covariates (one for each model). The probabilites (proportions) of having YES (=prob_yes or score) are normalized by their sum for each subject, so that the scores of the models for a subject will always add up to 1. These normalized scores (=weights) are used to ensemble the model predictions.
Finally, the method is tested by ensembling the predictions of the test data using the weights calibrated base on the training data. The administered dose is extrapolated by dividing the weighted concentration prediction by the target concentration (= 60 mg/L).
Our openMIPD package is used to apply this method.
AMOX_CMIN_TRAINED_CT <- classification_tree_model_ensembling_train(
data = AMOX_CMIN_TRAIN,
target_variable = "CMIN",
continuous_cov = c("WT", "CREAT", "AGE"),
categorical_cov = c("OBESE", "ICU", "BURN", "SEX", "CON"))
[1] "Confusion matrix for model: CARLIER"
node number: 1
root
[1] "Confusion matrix for model: FOURNIER"
node number: 1
root
[1] "Confusion matrix for model: MELLON"
node number: 1
root
[1] "Confusion matrix for model: RAMBAUD"
node number: 2
root
CON=0
node number: 12
root
CON=1
CREAT< 0.5407
AGE< 50.43
node number: 26
root
CON=1
CREAT< 0.5407
AGE>=50.43
AGE>=74.79
node number: 108
root
CON=1
CREAT< 0.5407
AGE>=50.43
AGE< 74.79
CREAT>=0.4709
AGE< 63.61
node number: 109
root
CON=1
CREAT< 0.5407
AGE>=50.43
AGE< 74.79
CREAT>=0.4709
AGE>=63.61
node number: 55
root
CON=1
CREAT< 0.5407
AGE>=50.43
AGE< 74.79
CREAT< 0.4709
node number: 56
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT< 62.11
node number: 228
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE< 64.82
node number: 916
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE>=64.82
AGE>=69.52
CREAT< 1.194
node number: 1834
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE>=64.82
AGE>=69.52
CREAT>=1.194
CREAT>=1.741
node number: 3670
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE>=64.82
AGE>=69.52
CREAT>=1.194
CREAT< 1.741
WT< 76.98
node number: 29368
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE>=64.82
AGE>=69.52
CREAT>=1.194
CREAT< 1.741
WT>=76.98
AGE< 81.84
OBESE=0
CREAT< 1.239
node number: 58738
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE>=64.82
AGE>=69.52
CREAT>=1.194
CREAT< 1.741
WT>=76.98
AGE< 81.84
OBESE=0
CREAT>=1.239
CREAT>=1.298
node number: 58739
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE>=64.82
AGE>=69.52
CREAT>=1.194
CREAT< 1.741
WT>=76.98
AGE< 81.84
OBESE=0
CREAT>=1.239
CREAT< 1.298
node number: 58740
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE>=64.82
AGE>=69.52
CREAT>=1.194
CREAT< 1.741
WT>=76.98
AGE< 81.84
OBESE=1
AGE>=77.57
CREAT>=1.355
node number: 58741
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE>=64.82
AGE>=69.52
CREAT>=1.194
CREAT< 1.741
WT>=76.98
AGE< 81.84
OBESE=1
AGE>=77.57
CREAT< 1.355
node number: 29371
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE>=64.82
AGE>=69.52
CREAT>=1.194
CREAT< 1.741
WT>=76.98
AGE< 81.84
OBESE=1
AGE< 77.57
node number: 7343
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE>=64.82
AGE>=69.52
CREAT>=1.194
CREAT< 1.741
WT>=76.98
AGE>=81.84
node number: 459
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT>=71.67
AGE>=64.82
AGE< 69.52
node number: 460
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT< 71.67
WT< 69.69
SEX=1
node number: 1844
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT< 71.67
WT< 69.69
SEX=0
WT< 67.65
WT>=63.78
node number: 1845
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT< 71.67
WT< 69.69
SEX=0
WT< 67.65
WT< 63.78
node number: 923
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT< 71.67
WT< 69.69
SEX=0
WT>=67.65
node number: 231
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT< 102
WT>=62.11
WT< 71.67
WT>=69.69
node number: 29
root
CON=1
CREAT>=0.5407
CREAT>=1.146
WT>=102
node number: 60
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT< 56.88
node number: 488
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT>=1.04
node number: 1956
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT>=84.27
node number: 7828
root
CON=1
CREAT>=0.5407
CREAT< 1.146
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WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
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node number: 31316
root
CON=1
CREAT>=0.5407
CREAT< 1.146
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WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
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CREAT>=0.7009
node number: 62634
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
CREAT< 0.7382
CREAT< 0.7009
WT< 70.5
node number: 62635
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
CREAT< 0.7382
CREAT< 0.7009
WT>=70.5
node number: 31318
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
CREAT>=0.7382
WT< 61.96
node number: 250552
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
CREAT>=0.7382
WT>=61.96
AGE>=60.53
AGE< 69.15
AGE>=67.93
node number: 1002212
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
CREAT>=0.7382
WT>=61.96
AGE>=60.53
AGE< 69.15
AGE< 67.93
AGE< 65.49
WT>=70.42
node number: 1002213
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
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CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
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WT>=61.96
AGE>=60.53
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AGE< 67.93
AGE< 65.49
WT< 70.42
node number: 501107
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
CREAT>=0.7382
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AGE>=60.53
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AGE< 67.93
AGE>=65.49
node number: 1002216
root
CON=1
CREAT>=0.5407
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AGE< 81.53
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WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
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WT>=61.96
AGE>=60.53
AGE>=69.15
CREAT>=0.8211
WT>=66.9
WT< 76.18
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root
CON=1
CREAT>=0.5407
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AGE< 81.53
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WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
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WT>=61.96
AGE>=60.53
AGE>=69.15
CREAT>=0.8211
WT>=66.9
WT>=76.18
node number: 501109
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
CREAT>=0.7382
WT>=61.96
AGE>=60.53
AGE>=69.15
CREAT>=0.8211
WT< 66.9
node number: 250555
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
CREAT>=0.7382
WT>=61.96
AGE>=60.53
AGE>=69.15
CREAT< 0.8211
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root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE>=51.17
AGE>=55.7
CREAT>=0.7382
WT>=61.96
AGE< 60.53
node number: 3915
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT< 86.58
WT< 84.27
AGE< 51.17
node number: 3916
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT>=86.58
AGE< 51.92
AGE>=44.95
node number: 3917
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT>=86.58
AGE< 51.92
AGE< 44.95
node number: 15672
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT>=86.58
AGE>=51.92
CREAT< 0.926
CREAT>=0.795
CREAT< 0.8616
node number: 15673
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT>=86.58
AGE>=51.92
CREAT< 0.926
CREAT>=0.795
CREAT>=0.8616
node number: 7837
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT>=86.58
AGE>=51.92
CREAT< 0.926
CREAT< 0.795
node number: 3919
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT< 1.055
CREAT< 1.04
WT>=86.58
AGE>=51.92
CREAT>=0.926
node number: 245
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT>=58.14
CREAT>=1.055
node number: 123
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE< 81.53
WT>=56.88
WT< 58.14
node number: 248
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE>=81.53
WT< 80.57
AGE>=84.67
AGE< 86.04
node number: 996
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE>=81.53
WT< 80.57
AGE>=84.67
AGE>=86.04
CREAT< 0.7409
WT< 60.25
node number: 997
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE>=81.53
WT< 80.57
AGE>=84.67
AGE>=86.04
CREAT< 0.7409
WT>=60.25
node number: 1996
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE>=81.53
WT< 80.57
AGE>=84.67
AGE>=86.04
CREAT>=0.7409
CREAT>=0.8719
WT>=61.77
node number: 1997
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE>=81.53
WT< 80.57
AGE>=84.67
AGE>=86.04
CREAT>=0.7409
CREAT>=0.8719
WT< 61.77
node number: 999
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE>=81.53
WT< 80.57
AGE>=84.67
AGE>=86.04
CREAT>=0.7409
CREAT< 0.8719
node number: 125
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE>=81.53
WT< 80.57
AGE< 84.67
node number: 63
root
CON=1
CREAT>=0.5407
CREAT< 1.146
AGE>=81.53
WT>=80.57To evaluate the method training, the decision trees and their corresponding confusion matrices are visualized. On the visualized nodes, the first line indicates the target variable majority class in that node (YES/NO), the second line the proportion of correct predictions (= proportion of YES), and the third line the percentage of subjects in that particular node.
AMOX_CMIN_TRAINED_CT$plot$obj
n= 1875
node), split, n, loss, yval, (yprob)
* denotes terminal node
1) root 1875 234 NO (0.875200000 0.124800000)
2) CON=0 1425 5 NO (0.996491228 0.003508772) *
3) CON=1 450 221 YES (0.491111111 0.508888889)
6) CREAT< 0.5406907 30 8 NO (0.733333333 0.266666667)
12) AGE< 50.42605 7 0 NO (1.000000000 0.000000000) *
13) AGE>=50.42605 23 8 NO (0.652173913 0.347826087)
26) AGE>=74.79412 7 0 NO (1.000000000 0.000000000) *
27) AGE< 74.79412 16 8 NO (0.500000000 0.500000000)
54) CREAT>=0.4709054 11 3 NO (0.727272727 0.272727273)
108) AGE< 63.61155 6 0 NO (1.000000000 0.000000000) *
109) AGE>=63.61155 5 2 YES (0.400000000 0.600000000) *
55) CREAT< 0.4709054 5 0 YES (0.000000000 1.000000000) *
7) CREAT>=0.5406907 420 199 YES (0.473809524 0.526190476)
14) CREAT>=1.146159 167 76 NO (0.544910180 0.455089820)
28) WT< 101.9952 161 70 NO (0.565217391 0.434782609)
56) WT< 62.10829 11 1 NO (0.909090909 0.090909091) *
57) WT>=62.10829 150 69 NO (0.540000000 0.460000000)
114) WT>=71.66666 117 48 NO (0.589743590 0.410256410)
228) AGE< 64.82186 22 3 NO (0.863636364 0.136363636) *
229) AGE>=64.82186 95 45 NO (0.526315789 0.473684211)
458) AGE>=69.51973 78 32 NO (0.589743590 0.410256410)
916) CREAT< 1.194147 8 1 NO (0.875000000 0.125000000) *
917) CREAT>=1.194147 70 31 NO (0.557142857 0.442857143)
1834) CREAT>=1.741118 11 2 NO (0.818181818 0.181818182) *
1835) CREAT< 1.741118 59 29 NO (0.508474576 0.491525424)
3670) WT< 76.98115 15 4 NO (0.733333333 0.266666667) *
3671) WT>=76.98115 44 19 YES (0.431818182 0.568181818)
7342) AGE< 81.84138 36 18 NO (0.500000000 0.500000000)
14684) OBESE=0 18 7 NO (0.611111111 0.388888889)
29368) CREAT< 1.238723 4 0 NO (1.000000000 0.000000000) *
29369) CREAT>=1.238723 14 7 NO (0.500000000 0.500000000)
58738) CREAT>=1.298427 8 2 NO (0.750000000 0.250000000) *
58739) CREAT< 1.298427 6 1 YES (0.166666667 0.833333333) *
14685) OBESE=1 18 7 YES (0.388888889 0.611111111)
29370) AGE>=77.56952 9 4 NO (0.555555556 0.444444444)
58740) CREAT>=1.354561 4 1 NO (0.750000000 0.250000000) *
58741) CREAT< 1.354561 5 2 YES (0.400000000 0.600000000) *
29371) AGE< 77.56952 9 2 YES (0.222222222 0.777777778) *
7343) AGE>=81.84138 8 1 YES (0.125000000 0.875000000) *
459) AGE< 69.51973 17 4 YES (0.235294118 0.764705882) *
115) WT< 71.66666 33 12 YES (0.363636364 0.636363636)
230) WT< 69.6873 23 11 NO (0.521739130 0.478260870)
460) SEX=1 4 0 NO (1.000000000 0.000000000) *
461) SEX=0 19 8 YES (0.421052632 0.578947368)
922) WT< 67.64966 13 6 NO (0.538461538 0.461538462)
1844) WT>=63.77837 9 3 NO (0.666666667 0.333333333) *
1845) WT< 63.77837 4 1 YES (0.250000000 0.750000000) *
923) WT>=67.64966 6 1 YES (0.166666667 0.833333333) *
231) WT>=69.6873 10 0 YES (0.000000000 1.000000000) *
29) WT>=101.9952 6 0 YES (0.000000000 1.000000000) *
15) CREAT< 1.146159 253 108 YES (0.426877470 0.573122530)
30) AGE< 81.5308 191 92 YES (0.481675393 0.518324607)
60) WT< 56.88156 8 2 NO (0.750000000 0.250000000) *
61) WT>=56.88156 183 86 YES (0.469945355 0.530054645)
122) WT>=58.14381 179 86 YES (0.480446927 0.519553073)
244) CREAT< 1.055043 164 82 NO (0.500000000 0.500000000)
488) CREAT>=1.039779 5 0 NO (1.000000000 0.000000000) *
489) CREAT< 1.039779 159 77 YES (0.484276730 0.515723270)
978) WT< 86.58055 119 56 NO (0.529411765 0.470588235)
1956) WT>=84.27392 5 0 NO (1.000000000 0.000000000) *
1957) WT< 84.27392 114 56 NO (0.508771930 0.491228070)
3914) AGE>=51.17455 101 46 NO (0.544554455 0.455445545)
7828) AGE< 55.70456 13 2 NO (0.846153846 0.153846154) *
7829) AGE>=55.70456 88 44 NO (0.500000000 0.500000000)
15658) CREAT< 0.7382098 24 8 NO (0.666666667 0.333333333)
31316) CREAT>=0.7008613 5 0 NO (1.000000000 0.000000000) *
31317) CREAT< 0.7008613 19 8 NO (0.578947368 0.421052632)
62634) WT< 70.50466 10 2 NO (0.800000000 0.200000000) *
62635) WT>=70.50466 9 3 YES (0.333333333 0.666666667) *
15659) CREAT>=0.7382098 64 28 YES (0.437500000 0.562500000)
31318) WT< 61.95855 8 2 NO (0.750000000 0.250000000) *
31319) WT>=61.95855 56 22 YES (0.392857143 0.607142857)
62638) AGE>=60.52909 48 21 YES (0.437500000 0.562500000)
125276) AGE< 69.14929 20 8 NO (0.600000000 0.400000000)
250552) AGE>=67.92727 6 0 NO (1.000000000 0.000000000) *
250553) AGE< 67.92727 14 6 YES (0.428571429 0.571428571)
501106) AGE< 65.48585 10 4 NO (0.600000000 0.400000000)
1002212) WT>=70.41755 6 1 NO (0.833333333 0.166666667) *
1002213) WT< 70.41755 4 1 YES (0.250000000 0.750000000) *
501107) AGE>=65.48585 4 0 YES (0.000000000 1.000000000) *
125277) AGE>=69.14929 28 9 YES (0.321428571 0.678571429)
250554) CREAT>=0.8210599 21 9 YES (0.428571429 0.571428571)
501108) WT>=66.90488 12 5 NO (0.583333333 0.416666667)
1002216) WT< 76.17987 8 2 NO (0.750000000 0.250000000) *
1002217) WT>=76.17987 4 1 YES (0.250000000 0.750000000) *
501109) WT< 66.90488 9 2 YES (0.222222222 0.777777778) *
250555) CREAT< 0.8210599 7 0 YES (0.000000000 1.000000000) *
62639) AGE< 60.52909 8 1 YES (0.125000000 0.875000000) *
3915) AGE< 51.17455 13 3 YES (0.230769231 0.769230769) *
979) WT>=86.58055 40 14 YES (0.350000000 0.650000000)
1958) AGE< 51.91959 10 4 NO (0.600000000 0.400000000)
3916) AGE>=44.95318 5 1 NO (0.800000000 0.200000000) *
3917) AGE< 44.95318 5 2 YES (0.400000000 0.600000000) *
1959) AGE>=51.91959 30 8 YES (0.266666667 0.733333333)
3918) CREAT< 0.9259867 21 8 YES (0.380952381 0.619047619)
7836) CREAT>=0.7950074 9 4 NO (0.555555556 0.444444444)
15672) CREAT< 0.8615979 5 1 NO (0.800000000 0.200000000) *
15673) CREAT>=0.8615979 4 1 YES (0.250000000 0.750000000) *
7837) CREAT< 0.7950074 12 3 YES (0.250000000 0.750000000) *
3919) CREAT>=0.9259867 9 0 YES (0.000000000 1.000000000) *
245) CREAT>=1.055043 15 4 YES (0.266666667 0.733333333) *
123) WT< 58.14381 4 0 YES (0.000000000 1.000000000) *
31) AGE>=81.5308 62 16 YES (0.258064516 0.741935484)
62) WT< 80.57075 46 16 YES (0.347826087 0.652173913)
124) AGE>=84.67447 34 15 YES (0.441176471 0.558823529)
248) AGE< 86.03799 6 1 NO (0.833333333 0.166666667) *
249) AGE>=86.03799 28 10 YES (0.357142857 0.642857143)
498) CREAT< 0.7409344 8 3 NO (0.625000000 0.375000000)
996) WT< 60.2531 4 0 NO (1.000000000 0.000000000) *
997) WT>=60.2531 4 1 YES (0.250000000 0.750000000) *
499) CREAT>=0.7409344 20 5 YES (0.250000000 0.750000000)
998) CREAT>=0.8718551 12 5 YES (0.416666667 0.583333333)
1996) WT>=61.77331 6 2 NO (0.666666667 0.333333333) *
1997) WT< 61.77331 6 1 YES (0.166666667 0.833333333) *
999) CREAT< 0.8718551 8 0 YES (0.000000000 1.000000000) *
125) AGE< 84.67447 12 1 YES (0.083333333 0.916666667) *
63) WT>=80.57075 16 0 YES (0.000000000 1.000000000) *
$snipped.nodes
NULL
$xlim
[1] 0 1
$ylim
[1] 0 1
$x
[1] 0.148649696 0.004955367 0.292344025 0.040148286 0.022018600 0.058277971
[7] 0.039081834 0.077474109 0.064676684 0.056145067 0.073208300 0.090271534
[13] 0.544539764 0.303378654 0.192284341 0.107334767 0.277233914 0.181586493
[19] 0.124398000 0.238774986 0.165456405 0.141461234 0.189451577 0.158524467
[25] 0.220378688 0.175587700 0.265169675 0.235309017 0.205448358 0.192650934
[31] 0.218245783 0.209714167 0.226777400 0.265169675 0.252372250 0.243840633
[37] 0.260903867 0.277967100 0.295030333 0.312093567 0.372881335 0.348352938
[43] 0.329156800 0.367549075 0.354751650 0.346220033 0.363283267 0.380346500
[49] 0.397409733 0.414472967 0.785700875 0.604773217 0.431536200 0.778010235
[55] 0.697903437 0.554753074 0.448599433 0.660906714 0.543680302 0.465662667
[61] 0.621697937 0.521784708 0.482725900 0.560843515 0.512586558 0.499789133
[67] 0.525383983 0.516852367 0.533915600 0.609100472 0.550978833 0.667222110
[73] 0.629896287 0.587238204 0.568042067 0.606434342 0.593636917 0.585105300
[79] 0.602168533 0.619231767 0.672554371 0.657624042 0.644826617 0.636295000
[85] 0.653358233 0.670421467 0.687484700 0.704547933 0.721611167 0.778133127
[91] 0.747206017 0.738674400 0.755737633 0.809060237 0.794129908 0.781332483
[97] 0.772800866 0.789864100 0.806927333 0.823990566 0.841053800 0.858117033
[103] 0.966628533 0.938634165 0.899708664 0.875180266 0.924237062 0.900775116
[109] 0.892243500 0.909306733 0.947699008 0.934901583 0.926369966 0.943433200
[115] 0.960496433 0.977559666 0.994622900
$y
[1] 0.98311135 0.01001217 0.93655158 0.88999181 0.01001217 0.84343204
[7] 0.01001217 0.79687227 0.75031250 0.01001217 0.01001217 0.01001217
[13] 0.88999181 0.84343204 0.79687227 0.01001217 0.75031250 0.70375273
[19] 0.01001217 0.65719296 0.61063319 0.01001217 0.56407342 0.01001217
[25] 0.51751365 0.01001217 0.47095388 0.42439411 0.37783434 0.01001217
[31] 0.33127457 0.01001217 0.01001217 0.37783434 0.33127457 0.01001217
[37] 0.01001217 0.01001217 0.01001217 0.01001217 0.70375273 0.65719296
[43] 0.01001217 0.61063319 0.56407342 0.01001217 0.01001217 0.01001217
[49] 0.01001217 0.01001217 0.84343204 0.79687227 0.01001217 0.75031250
[55] 0.70375273 0.65719296 0.01001217 0.61063319 0.56407342 0.01001217
[61] 0.51751365 0.47095388 0.01001217 0.42439411 0.37783434 0.01001217
[67] 0.33127457 0.01001217 0.01001217 0.37783434 0.01001217 0.33127457
[73] 0.28471481 0.23815504 0.01001217 0.19159527 0.14503550 0.01001217
[79] 0.01001217 0.01001217 0.23815504 0.19159527 0.14503550 0.01001217
[85] 0.01001217 0.01001217 0.01001217 0.01001217 0.01001217 0.56407342
[91] 0.51751365 0.01001217 0.01001217 0.51751365 0.47095388 0.42439411
[97] 0.01001217 0.01001217 0.01001217 0.01001217 0.01001217 0.01001217
[103] 0.79687227 0.75031250 0.70375273 0.01001217 0.65719296 0.61063319
[109] 0.01001217 0.01001217 0.61063319 0.56407342 0.01001217 0.01001217
[115] 0.01001217 0.01001217 0.01001217
$branch.x
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
x 0.1486497 0.004955367 0.2923440 0.04014829 0.02201860 0.05827797 0.03908183
NA 0.004955367 0.2923440 0.04014829 0.02201860 0.05827797 0.03908183
NA 0.148649696 0.1486497 0.29234403 0.04014829 0.04014829 0.05827797
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
x 0.07747411 0.06467668 0.05614507 0.07320830 0.09027153 0.5445398 0.3033787
0.07747411 0.06467668 0.05614507 0.07320830 0.09027153 0.5445398 0.3033787
0.05827797 0.07747411 0.06467668 0.06467668 0.07747411 0.2923440 0.5445398
[,15] [,16] [,17] [,18] [,19] [,20] [,21]
x 0.1922843 0.1073348 0.2772339 0.1815865 0.1243980 0.2387750 0.1654564
0.1922843 0.1073348 0.2772339 0.1815865 0.1243980 0.2387750 0.1654564
0.3033787 0.1922843 0.1922843 0.2772339 0.1815865 0.1815865 0.2387750
[,22] [,23] [,24] [,25] [,26] [,27] [,28]
x 0.1414612 0.1894516 0.1585245 0.2203787 0.1755877 0.2651697 0.2353090
0.1414612 0.1894516 0.1585245 0.2203787 0.1755877 0.2651697 0.2353090
0.1654564 0.1654564 0.1894516 0.1894516 0.2203787 0.2203787 0.2651697
[,29] [,30] [,31] [,32] [,33] [,34] [,35]
x 0.2054484 0.1926509 0.2182458 0.2097142 0.2267774 0.2651697 0.2523723
0.2054484 0.1926509 0.2182458 0.2097142 0.2267774 0.2651697 0.2523723
0.2353090 0.2054484 0.2054484 0.2182458 0.2182458 0.2353090 0.2651697
[,36] [,37] [,38] [,39] [,40] [,41] [,42]
x 0.2438406 0.2609039 0.2779671 0.2950303 0.3120936 0.3728813 0.3483529
0.2438406 0.2609039 0.2779671 0.2950303 0.3120936 0.3728813 0.3483529
0.2523723 0.2523723 0.2651697 0.2651697 0.2387750 0.2772339 0.3728813
[,43] [,44] [,45] [,46] [,47] [,48] [,49]
x 0.3291568 0.3675491 0.3547517 0.3462200 0.3632833 0.3803465 0.3974097
0.3291568 0.3675491 0.3547517 0.3462200 0.3632833 0.3803465 0.3974097
0.3483529 0.3483529 0.3675491 0.3547517 0.3547517 0.3675491 0.3728813
[,50] [,51] [,52] [,53] [,54] [,55] [,56]
x 0.4144730 0.7857009 0.6047732 0.4315362 0.7780102 0.6979034 0.5547531
0.4144730 0.7857009 0.6047732 0.4315362 0.7780102 0.6979034 0.5547531
0.3033787 0.5445398 0.7857009 0.6047732 0.6047732 0.7780102 0.6979034
[,57] [,58] [,59] [,60] [,61] [,62] [,63]
x 0.4485994 0.6609067 0.5436803 0.4656627 0.6216979 0.5217847 0.4827259
0.4485994 0.6609067 0.5436803 0.4656627 0.6216979 0.5217847 0.4827259
0.5547531 0.5547531 0.6609067 0.5436803 0.5436803 0.6216979 0.5217847
[,64] [,65] [,66] [,67] [,68] [,69] [,70]
x 0.5608435 0.5125866 0.4997891 0.5253840 0.5168524 0.5339156 0.6091005
0.5608435 0.5125866 0.4997891 0.5253840 0.5168524 0.5339156 0.6091005
0.5217847 0.5608435 0.5125866 0.5125866 0.5253840 0.5253840 0.5608435
[,71] [,72] [,73] [,74] [,75] [,76] [,77]
x 0.5509788 0.6672221 0.6298963 0.5872382 0.5680421 0.6064343 0.5936369
0.5509788 0.6672221 0.6298963 0.5872382 0.5680421 0.6064343 0.5936369
0.6091005 0.6091005 0.6672221 0.6298963 0.5872382 0.5872382 0.6064343
[,78] [,79] [,80] [,81] [,82] [,83] [,84]
x 0.5851053 0.6021685 0.6192318 0.6725544 0.6576240 0.6448266 0.6362950
0.5851053 0.6021685 0.6192318 0.6725544 0.6576240 0.6448266 0.6362950
0.5936369 0.5936369 0.6064343 0.6298963 0.6725544 0.6576240 0.6448266
[,85] [,86] [,87] [,88] [,89] [,90] [,91]
x 0.6533582 0.6704215 0.6874847 0.7045479 0.7216112 0.7781331 0.7472060
0.6533582 0.6704215 0.6874847 0.7045479 0.7216112 0.7781331 0.7472060
0.6448266 0.6576240 0.6725544 0.6672221 0.6216979 0.6609067 0.7781331
[,92] [,93] [,94] [,95] [,96] [,97] [,98]
x 0.7386744 0.7557376 0.8090602 0.7941299 0.7813325 0.7728009 0.7898641
0.7386744 0.7557376 0.8090602 0.7941299 0.7813325 0.7728009 0.7898641
0.7472060 0.7472060 0.7781331 0.8090602 0.7941299 0.7813325 0.7813325
[,99] [,100] [,101] [,102] [,103] [,104] [,105]
x 0.8069273 0.8239906 0.8410538 0.8581170 0.9666285 0.9386342 0.8997087
0.8069273 0.8239906 0.8410538 0.8581170 0.9666285 0.9386342 0.8997087
0.7941299 0.8090602 0.6979034 0.7780102 0.7857009 0.9666285 0.9386342
[,106] [,107] [,108] [,109] [,110] [,111] [,112]
x 0.8751803 0.9242371 0.9007751 0.8922435 0.9093067 0.9476990 0.9349016
0.8751803 0.9242371 0.9007751 0.8922435 0.9093067 0.9476990 0.9349016
0.8997087 0.8997087 0.9242371 0.9007751 0.9007751 0.9242371 0.9476990
[,113] [,114] [,115] [,116] [,117]
x 0.9263700 0.9434332 0.9604964 0.9775597 0.9946229
0.9263700 0.9434332 0.9604964 0.9775597 0.9946229
0.9349016 0.9349016 0.9476990 0.9386342 0.9666285
$branch.y
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
y 1.001852 0.02875275 0.9552922 0.9087324 0.02875275 0.8621726 0.02875275
NA 0.95837830 0.9583783 0.9118185 0.86525877 0.8652588 0.81869900
NA 0.95837830 0.9583783 0.9118185 0.86525877 0.8652588 0.81869900
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
y 0.8156129 0.7690531 0.02875275 0.02875275 0.02875275 0.9087324 0.8621726
0.8186990 0.7721392 0.72557946 0.72557946 0.77213923 0.9118185 0.8652588
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[49] NA NA 0.79678042 0.61457435 NA 0.78908978
[55] 0.71239207 0.56881557 NA 0.67070785 0.55475985 NA
[61] 0.63405589 0.53286425 NA 0.57661056 0.52835361 NA
[67] 0.53518512 NA NA 0.61890161 NA 0.67958007
[73] 0.64097583 0.59959616 NA 0.61751389 0.60471646 NA
[79] NA NA 0.68959983 0.66870359 0.65462775 NA
[85] NA NA NA NA NA 0.78921267
[91] 0.75956397 NA NA 0.82482728 0.80989695 0.79709953
[97] NA NA NA NA NA NA
[103] 0.97642967 0.95099212 0.91078821 NA 0.94000411 0.91057625
[109] NA NA 0.96474446 0.94598113 NA NA
[115] NA NA NA
$split.box$y2
[1] 0.9654449 NA 0.9188851 0.8723253 NA 0.8257656 NA
[8] 0.7792058 0.7326460 NA NA NA 0.8723253 0.8257656
[15] 0.7792058 NA 0.7326460 0.6860863 NA 0.6395265 0.5929667
[22] NA 0.5464070 NA 0.4998472 NA 0.4532874 0.4067277
[29] 0.3601679 NA 0.3136081 NA NA 0.3601679 0.3136081
[36] NA NA NA NA NA 0.6860863 0.6395265
[43] NA 0.5929667 0.5464070 NA NA NA NA
[50] NA 0.8257656 0.7792058 NA 0.7326460 0.6860863 0.6395265
[57] NA 0.5929667 0.5464070 NA 0.4998472 0.4532874 NA
[64] 0.4067277 0.3601679 NA 0.3136081 NA NA 0.3601679
[71] NA 0.3136081 0.2670483 0.2204886 NA 0.1739288 0.1273690
[78] NA NA NA 0.2204886 0.1739288 0.1273690 NA
[85] NA NA NA NA NA 0.5464070 0.4998472
[92] NA NA 0.4998472 0.4532874 0.4067277 NA NA
[99] NA NA NA NA 0.7792058 0.7326460 0.6860863
[106] NA 0.6395265 0.5929667 NA NA 0.5929667 0.5464070
[113] NA NA NA NA NAAMOX_CMIN_TRAINED_CT_confusion_matrix <- AMOX_CMIN_TRAINED_CT$confusion_matrix
print(AMOX_CMIN_TRAINED_CT_confusion_matrix)$CARLIER
$FOURNIER
$MELLON
$RAMBAUD
cfit_list <- AMOX_CMIN_TRAINED_CT$cfit_list
# Export the plot of the four trees
jpeg(here("Figures/S7.jpg"), width = 7, height = 7, units = "in", res = 300)
n_trees <- length(cfit_list)
par(mfrow = c(ceiling(n_trees / 2), 2))
for (model_name in names(cfit_list)) {
rpart.plot(cfit_list[[model_name]],
main = model_name,
roundint = FALSE)
}
dev.off()png
2 # Export the plot of the four confusion matrices
confusion_plot <-
(AMOX_CMIN_TRAINED_CT_confusion_matrix$CARLIER + ggtitle("Carlier")) +
(AMOX_CMIN_TRAINED_CT_confusion_matrix$FOURNIER + ggtitle("Fournier")) +
(AMOX_CMIN_TRAINED_CT_confusion_matrix$MELLON + ggtitle("Mellon")) +
(AMOX_CMIN_TRAINED_CT_confusion_matrix$RAMBAUD + ggtitle("Rambaud")) +
plot_layout(ncol = 2)
ggsave(here("Figures/S8.jpg"),
plot = confusion_plot,
width = 7, height = 7, units = "in", dpi = 600)AMOX_CMIN_PRED_TEST_CT <- classification_tree_model_ensembling_test(
test_data = AMOX_CMIN_TEST,
train_results = AMOX_CMIN_TRAINED_CT) To evaluate the method, a predictions as a function of observed concentrations goodness of fit plot is presented as well a boxplot indicating the predicted/observed ratios in %. Then, the average model weights are plotted, stratified by covariate categories/quantiles.
test_data_CT <- AMOX_CMIN_PRED_TEST_CT$test_results
AMOX_CMIN_PRED_TEST_CT$GOF_plot
AMOX_CMIN_PRED_TEST_CT$Boxplot
# Plots showing the average attributed weight stratified by covariates
weight_BURN_CT <- generate_weight_plot(test_data_CT, "BURN", is_categorical = TRUE)
weight_ICU_CT <- generate_weight_plot(test_data_CT, "ICU", is_categorical = TRUE)
weight_OBESE_CT <- generate_weight_plot(test_data_CT, "OBESE", is_categorical = TRUE)
weight_CREAT_CT <- generate_weight_plot(test_data_CT, "CREAT", is_categorical = FALSE)
weight_WT_CT <- generate_weight_plot(test_data_CT, "WT", is_categorical = FALSE)
weight_AGE_CT <- generate_weight_plot(test_data_CT, "AGE", is_categorical = FALSE)
weight_SEX_CT <- generate_weight_plot(test_data_CT, "SEX", is_categorical = TRUE)
weight_CON_CT <- generate_weight_plot(test_data_CT, "CON", is_categorical = TRUE)
weight_BURN_CT
weight_ICU_CT
weight_OBESE_CT
weight_CREAT_CT
weight_WT_CT
weight_AGE_CT
weight_SEX_CT
weight_CON_CT
# Print overall average weight
test_data_CT %>%
group_by(MODEL) %>%
summarise(avg_weight = mean(WEIGHT, na.rm = TRUE))# A tibble: 4 × 2
MODEL avg_weight
<chr> <dbl>
1 CARLIER 0.319
2 FOURNIER 0.389
3 MELLON 0.179
4 RAMBAUD 0.113# Extrapolate dose based on the ensembled concentrations and compare it to the true simulated dose.
test_data_CT <- test_data_CT %>%
dplyr::filter(REFERENCE == 1) %>%
dplyr::mutate(DOSE_PRED = (60/WEIGHTED_PREDICTION) * DOSE_ADM) # Administered dose extrapolation to reach 60 mg/L
final_results_CT <- explore_predictions(test_data_CT)
final_results_CT$target_attainment 
crcl_plot_CT <- final_results_CT$crcl_plot
crcl_plot_CT
final_results_CT$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 0.966 0.513 79.0 15.5 64.2 15.7 186
2 Incorrect 0.943 0.606 86.8 19.5 58.0 16.3 414
# ℹ 1 more variable: Proportion <dbl># Keep data for method ensembling
test_data_CT_ens <- test_data_CT %>%
dplyr::mutate(CT = DOSE_PRED) %>%
dplyr::select("ID","CT")This method is similar to the previous decision tree-based method, with the difference that not prediction correctness is used as a target variable, but the log-transformed prediction/observation ratio:
\[ \text{Ratio} = \left( log (\frac{predicted}{true}) \right) \]
Therefore these are not classification, but regression trees.
Our openMIPD package is used to apply this method.
train_results_RT <- regression_tree_model_ensembling_train(
data = AMOX_CMIN_TRAIN,
target_variable = "CMIN",
continuous_cov = c("WT", "CREAT", "AGE"),
categorical_cov = c("OBESE", "ICU", "BURN", "SEX", "CON"))
To evaluate the method training, the regression trees are visualized. On the visualized nodes, the first line indicates average log-transformed prediction/observation ratio and the second line, percentage of subjects in that particular node.
model_trees <- train_results_RT$model_trees
print(model_trees)$CARLIER
n= 1875
node), split, n, deviance, yval
* denotes terminal node
1) root 1875 2722.349000 0.7215246
2) ICU=1 1400 1254.040000 0.3662242
4) BURN=0 925 584.076200 0.1997434 *
5) BURN=1 475 594.401200 0.6904237
10) CREAT< 0.5087704 76 103.572900 -0.4073936
20) AGE>=90.55131 9 12.324480 -2.1388150 *
21) AGE< 90.55131 67 60.643800 -0.1748146 *
11) CREAT>=0.5087704 399 381.786200 0.8995317
22) CREAT< 0.9848673 253 225.506200 0.6357652 *
23) CREAT>=0.9848673 146 108.176100 1.3566070 *
3) ICU=0 475 770.676800 1.7687260
6) CREAT< 0.6594764 202 182.581600 1.3189530 *
7) CREAT>=0.6594764 273 516.995300 2.1015250
14) CREAT>=0.6603812 270 469.309000 2.0584990
28) WT>=110.0654 116 171.808100 1.7276860 *
29) WT< 110.0654 154 275.244000 2.3076830 *
15) CREAT< 0.6603812 3 2.202036 5.9738390 *
$FOURNIER
n= 1875
node), split, n, deviance, yval
* denotes terminal node
1) root 1875 2668.353000 0.29249860
2) ICU=1 1400 1254.534000 -0.06534612
4) CREAT>=1.279099 304 218.536600 -0.49097220
8) BURN=0 214 122.258400 -0.73177000
16) CON=0 98 44.940400 -1.29009300 *
17) CON=1 116 20.960400 -0.26008340 *
9) BURN=1 90 54.365010 0.08159171 *
5) CREAT< 1.279099 1096 965.650100 0.05271073 *
3) ICU=0 475 706.159000 1.34719900
6) CREAT< 0.6594764 202 172.563800 0.99242950 *
7) CREAT>=0.6594764 273 489.359400 1.60970200
14) CREAT>=0.6603812 270 440.864100 1.56628600 *
15) CREAT< 0.6603812 3 2.182976 5.51710600 *
$MELLON
n= 1875
node), split, n, deviance, yval
* denotes terminal node
1) root 1875 32866.19000 -2.52319600
2) CON=1 450 118.99190 -9.50437800
4) CREAT>=1.123887 175 37.91400 -9.89345100 *
5) CREAT< 1.123887 275 37.72864 -9.25678500 *
3) CON=0 1425 3889.82100 -0.31861170
6) CREAT>=1.153214 228 306.36100 -2.37156900
12) BURN=0 120 96.38875 -3.02996000 *
13) BURN=1 108 100.15760 -1.64002300 *
7) CREAT< 1.153214 1197 2439.48900 0.07242771
14) ICU=1 724 1282.75200 -0.44429380
28) CREAT>=0.6333707 396 497.33880 -0.93833000
56) AGE>=52.98266 243 240.10380 -1.25474200 *
57) AGE< 52.98266 153 194.26780 -0.43579410 *
29) CREAT< 0.6333707 328 572.07040 0.15216460
58) AGE>=47.39281 233 427.46600 -0.07053408 *
59) AGE< 47.39281 95 104.70730 0.69836230 *
15) ICU=0 473 667.53890 0.86335030 *
$RAMBAUD
n=1873 (2 observations effacées parce que manquantes)
node), split, n, deviance, yval
* denotes terminal node
1) root 1873 63965.02000 -8.089378000
2) CON=0 1423 25214.15000 -10.645500000
4) CREAT< 1.209516 1215 15077.22000 -11.650850000
8) ICU=1 741 7335.49100 -13.440420000
16) CREAT< 0.8776082 574 4308.17400 -14.240640000
32) BURN=0 287 950.34510 -15.400710000 *
33) BURN=1 287 2585.36900 -13.080580000 *
17) CREAT>=0.8776082 167 1396.37900 -10.689950000
34) BURN=0 79 353.27190 -12.157220000 *
35) BURN=1 88 720.34340 -9.372733000 *
9) ICU=0 474 1658.77700 -8.853227000
18) CREAT< 0.7359913 314 440.58620 -9.616361000 *
19) CREAT>=0.7359913 160 676.45370 -7.355578000
38) SEX=0 59 213.14900 -8.431385000 *
39) SEX=1 101 355.13170 -6.727137000 *
5) CREAT>=1.209516 208 1735.59100 -4.772933000
10) CREAT< 1.859952 134 606.10390 -6.273502000
20) CREAT< 1.487287 72 250.51200 -7.370088000
40) BURN=0 42 79.34322 -8.173240000 *
41) BURN=1 30 106.14740 -6.245676000 *
21) CREAT>=1.487287 62 168.46720 -5.000047000
42) BURN=0 32 22.69181 -6.179260000 *
43) BURN=1 30 53.81415 -3.742221000 *
11) CREAT>=1.859952 74 281.38510 -2.055687000
22) CREAT< 2.391933 33 73.24242 -3.498949000 *
23) CREAT>=2.391933 41 84.07702 -0.894038000 *
3) CON=1 450 52.32690 -0.006339534 *# Export the plot of the four trees
jpeg(here("Figures/S9.jpg"), width = 7, height = 7, units = "in", res = 300)
n_trees <- length(model_trees)
par(mfrow = c(ceiling(n_trees / 2), 2))
for (model_name in names(model_trees)) {
rpart.plot(model_trees[[model_name]],
main = model_name,
roundint = FALSE)
}
dev.off()png
2 test_results_RT <- regression_tree_model_ensembling_test(
test_data = AMOX_CMIN_TEST,
train_results = train_results_RT) To evaluate the method, a predictions as a function of observed concentrations goodness of fit plot is presented as well a boxplot indicating the predicted/observed ratios in %. Then, the average model weights are plotted, stratified by covariate categories/quantiles.
test_data_RT <- test_results_RT$test_results
test_results_RT$GOF_plot
test_results_RT$Boxplot
# Plots showing the average attributed weight stratified by covariates
weight_BURN_RT <- generate_weight_plot(test_data_RT, "BURN", is_categorical = TRUE)
weight_ICU_RT <- generate_weight_plot(test_data_RT, "ICU", is_categorical = TRUE)
weight_OBESE_RT <- generate_weight_plot(test_data_RT, "OBESE", is_categorical = TRUE)
weight_CREAT_RT <- generate_weight_plot(test_data_RT, "CREAT", is_categorical = FALSE)
weight_WT_RT <- generate_weight_plot(test_data_RT, "WT", is_categorical = FALSE)
weight_AGE_RT <- generate_weight_plot(test_data_RT, "AGE", is_categorical = FALSE)
weight_SEX_RT <- generate_weight_plot(test_data_RT, "SEX", is_categorical = TRUE)
weight_CON_RT <- generate_weight_plot(test_data_RT, "CON", is_categorical = TRUE)
weight_BURN_RT
weight_ICU_RT
weight_OBESE_RT <- weight_OBESE_RT +
labs(title = "RT inf ens weight attribution, stratified by OBESE")
ggsave(filename = here("Figures/S10b.jpg"),
plot = weight_OBESE_RT,
width = 8, height = 6, dpi = 600)
weight_CREAT_RT
weight_WT_RT
weight_AGE_RT
weight_SEX_RT
weight_CON_RT
test_data_RT %>%
group_by(MODEL) %>%
summarise(avg_weight = mean(WEIGHT, na.rm = TRUE))# A tibble: 4 × 2
MODEL avg_weight
<chr> <dbl>
1 CARLIER 0.163
2 FOURNIER 0.419
3 MELLON 0.179
4 RAMBAUD 0.239# Extrapolate dose based on the ensembled concentrations and compare it to the true simulated dose.
test_data_RT <- test_data_RT %>%
dplyr::filter(REFERENCE == 1) %>%
dplyr::mutate(DOSE_PRED = (60/WEIGHTED_PREDICTION) * DOSE_ADM) # Administered dose extrapolation to reach 60 mg/L
final_results_RT <- explore_predictions(test_data_RT)
final_results_RT$target_attainment 
crcl_plot_RT <- final_results_RT$crcl_plot
crcl_plot_RT
final_results_RT$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 1.01 0.575 80.4 17.3 62.4 16.7 216
2 Incorrect 0.915 0.579 86.7 19.1 58.5 16.0 384
# ℹ 1 more variable: Proportion <dbl># Keep data for method ensembling
test_data_RT_ens <- test_data_RT %>%
dplyr::mutate(RT = DOSE_PRED) %>%
dplyr::select("ID","RT")This method is used to attribute weights to models based on their performance in different subgroups and on the overall performance of models in different subgroups.
The method is based on Agema et al. (2024).
To calculate model influence, first, differences are calculated between \(Cmin_{\text{pred}}\) and \(Cmin_{\text{ind}}\) for a particular set of covariates. Then we use this difference to calculate pooled MPE and RMSE values for each model. MPE and rRMSE will be used to calculate scores as discussed in a later section.
The data is divided into subgroups. For categorical covariates (ICU, BURN, OBESE, SEX, CON (indicating continuous infusion)), a subgroup is a category, thus we have two-two-two-two-two subgroups for ICU, BURN, SEX, OBESE, and CON. Continuous covariates (WT, CREAT, AGE) are divided into four quantiles, and each quantile will represent a subgroup.
First, ratios are calculated between\(Cmin_{\text{pred}}\) and the \(Cmin_{\text{ind}}\) for a particular set of covariates. For each sugbroup we will calculate the proportion of ratios outside the bioequivalence range of [0.80-1.25]. This proportion will represent subgroup influence. The logic behind giving more influence to subgroups with more ratios outside the bioequivalence range is that sugbroup having overall good predictions (many ratios inside the bioequivalence range), means that we can use any of the models for that subgroup, thus its influence will be lower in attributing model weights. A model having a good performance in a sugbroup with bad predictions (many ratios outside the bioequivalence range) will be preferred to a model having good performance in a subgroup having overall good predictions.
Scores are calculated with a negative exponential function: \[ \text{Score}_{\text{MPE}} = e^{\text{penalty} \cdot |\text{MPE}|} \] \[ \text{Score}_{\text{RMSE}} = e^{\text{penalty} \cdot |\text{RMSE}|} \]Model score is the product of RMSE and MPE scores. \[ \text{Score}_{\text{Carlier}} = \text{Score}_{\text{RMSE}} \cdot \text{Score}_{\text{MPE}} \] Model score is normalized by the sum of scores. \[ \text{Influence}_{\text{Carlier}} = \frac{\text{Score}_{\text{Carlier}}}{\sum \text{Score}} \] For this negative exponential calculation, the two penalties have to be defined
To test the algorithm we check to which 8 subgroups (ICU, BURN, WT, CREAT, OBESE, SEX, AGE, CON (= continuous or intermittant infusion)) a subject belongs, and we add the obtain the corresponding model and influence scores from the all_scores table. We normalize the four subgroup influences by their sum (so they add up to 1 for that subject). Then, for each subgroup we multiply the model influences with the normalized subgroup influence. As a product of this multiplication we have a model weights for each of the four models for each of the four subgroups. For each model, we add the four weights (for example Carlier weight for ICU = 0, Carlier weight for BURN = 1 etc). As a final step, we normalize the weights of the models by their sum so they add up to 1 for each subject. Then, we ensemble the separate Cmax predictions of the four models based on their weight. The administered dose is extrapolated by dividing the weighted concentration prediction by the target concentration (= 60 mg/L).
The penalties are automatically tuned based on the percentage of correct dose predictions.
Our openMIPD package is used to apply this method.
AMOX_CMIN_TRAIN <- AMOX_CMIN_TRAIN %>%
mutate(dosing_reg_strata = paste0(DOSE_ADM,FREQ,DUR))
wme_tuning <- weighed_model_ensembling_tuning(
train_data = AMOX_CMIN_TRAIN,
target_variable = "CMIN",
continuous_cov = c("WT", "CREAT", "AGE"),
categorical_cov = c("OBESE", "ICU", "BURN", "SEX","CON"),
penalties_grid = NULL,
conc_inf = 40, conc_sup = 80, conc_target = 60,
freq_column = "FREQ",
cv_stratification_col = "dosing_reg_strata",
target_log_dose = TRUE)
wme_tuning$best_pen_RMSE[1] -4wme_tuning$best_pen_MPE[1] -2To visualize method training, the mean percentage error (MPE) and relative root mean squared error (RMSE) for each model in each covariate quantile/category is plotted as well as subgroup influences (the proportion of incorrect predictions for each covariate quantile/category, all models included).
training_results_WME <- weighed_model_ensembling_train(
data = AMOX_CMIN_TRAIN,
target_variable = "CMIN",
pen_RMSE = wme_tuning$best_pen_RMSE,
pen_MPE = wme_tuning$best_pen_MPE,
continuous_cov = c("WT", "CREAT", "AGE"),
categorical_cov = c("OBESE", "ICU", "BURN", "SEX", "CON"))all_scores <- training_results_WME$all_scores
print(all_scores)# A tibble: 88 × 10
COVARIATE QUANTILE SUBGROUP_INFLUENCE MODEL MPE RMSE MODEL_INFLUENCE
<chr> <chr> <dbl> <chr> <dbl> <dbl> <dbl>
1 AGE 18.3-49.4 0.897 CARLIER 13.0 2.23 6.81e-16
2 AGE 18.3-49.4 0.897 FOURNIER 7.12 1.27 4.11e- 9
3 AGE 18.3-49.4 0.897 MELLON 4.75 2.37 5.58e- 9
4 AGE 18.3-49.4 0.897 RAMBAUD 0.954 1.62 2.28e- 4
5 AGE 49.4-57.3 0.884 CARLIER 13.5 1.39 6.83e-15
6 AGE 49.4-57.3 0.884 FOURNIER 8.69 1.03 4.65e-10
7 AGE 49.4-57.3 0.884 MELLON 5.11 2.44 2.09e- 9
8 AGE 49.4-57.3 0.884 RAMBAUD 0.918 1.05 2.35e- 3
9 AGE 57.3-69.5 0.836 CARLIER 3.81 1.06 7.07e- 6
10 AGE 57.3-69.5 0.836 FOURNIER 2.31 0.802 3.99e- 4
# ℹ 78 more rows
# ℹ 3 more variables: LABEL <chr>, lower <dbl>, upper <dbl>MPE_plot <- training_results_WME$MPE_plot
MPE_plot
ggsave(filename = here("Figures/S13.jpg"),
plot = MPE_plot,
width = 8, height = 6, dpi = 600)
RMSE_plot <- training_results_WME$RMSE_plot
RMSE_plot
ggsave(filename = here("Figures/S14.jpg"),
plot = RMSE_plot,
width = 8, height = 6, dpi = 600)
SUBGROUP_INFLUENCE_plot <- training_results_WME$SUBGROUP_INFLUENCE_plot
SUBGROUP_INFLUENCE_plot
ggsave(filename = here("Figures/S15.jpg"),
plot = SUBGROUP_INFLUENCE_plot,
width = 8, height = 6, dpi = 600)test_results_WME <- weighed_model_ensembling_test(
train_results = training_results_WME,
test_data = AMOX_CMIN_TEST)To evaluate the method, a predictions as a function of observed concentrations goodness of fit plot is presented as well a boxplot indicating the predicted/observed ratios in %. Then, the average model weights are plotted, stratified by covariate categories/quantiles.
test_data_WME <- test_results_WME$test_results
test_results_WME$GOF_plot
test_results_WME$Boxplot
# Plots showing the average attributed weight stratified by covariates
weight_BURN_WME <- generate_weight_plot(test_data_WME, "BURN", is_categorical = TRUE)
weight_ICU_WME <- generate_weight_plot(test_data_WME, "ICU", is_categorical = TRUE)
weight_OBESE_WME <- generate_weight_plot(test_data_WME, "OBESE", is_categorical = TRUE)
weight_CREAT_WME <- generate_weight_plot(test_data_WME, "CREAT", is_categorical = FALSE)
weight_WT_WME <- generate_weight_plot(test_data_WME, "WT", is_categorical = FALSE)
weight_AGE_WME <- generate_weight_plot(test_data_WME, "AGE", is_categorical = FALSE)
weight_SEX_WME <- generate_weight_plot(test_data_WME, "SEX", is_categorical = TRUE)
weight_CON_WME <- generate_weight_plot(test_data_WME, "CON", is_categorical = TRUE)
weight_BURN_WME
weight_ICU_WME
weight_OBESE_WME
weight_CREAT_WME
weight_WT_WME
weight_AGE_WME
weight_SEX_WME
weight_CON_WME
weight_OBESE_WME
test_data_WME %>%
group_by(MODEL) %>%
summarise(avg_weight = mean(WEIGHT, na.rm = TRUE))# A tibble: 4 × 2
MODEL avg_weight
<chr> <dbl>
1 CARLIER 0.0554
2 FOURNIER 0.152
3 MELLON 0.00578
4 RAMBAUD 0.787 # Extrapolate dose based on the ensembled concentrations and compare it to the true simulated dose.
test_data_WME <- test_data_WME %>%
dplyr::filter(REFERENCE == 1) %>%
dplyr::mutate(DOSE_PRED = (60/WEIGHTED_PREDICTION) * DOSE_ADM) # Administered dose extrapolation to reach 60 mg/L
final_results_WME <- explore_predictions(test_data_WME)
final_results_WME$target_attainment 
crcl_plot_WME <- final_results_WME$crcl_plot
crcl_plot_WME
final_results_WME$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 1.04 0.616 78.0 15.0 65.8 16.2 135
2 Incorrect 0.921 0.565 86.5 19.1 58.2 16.0 462
# ℹ 1 more variable: Proportion <dbl># Keep data for method ensembling
test_data_WME_ens <- test_data_WME %>%
dplyr::mutate(WME = DOSE_PRED) %>%
dplyr::select("ID","WME")In FAMD, Principal Component Analyisis (PCA) is applied to continuous covariates and multiple correspondence analysis (MCA) to categorical covariates. FAMD is an unsupervised machine learning algorithm which is based on dimensionality reduction. Principal components are uncorrelated linear combinations of initial variables. They are directions in the variable space, perpendicular to each other that explain a maximum variance of the data. The first principal component explains most of the variance, as it has most of the dispersion of the data points along it, then the subsequent ones explain less and less and if a certain percentage (in this case, 90 %) of the data variance is explained, no more principal components are added. This process simplifies the dataset while retaining most of the relevant information.
Nearest neighbors is a classification technique that relies on the proximity of a data point to different classes in a variable space. To measure proximity, we can use euclidean distance, which is the length of a straight line connecting to points, or the Mahalanobis distance which accounts for variance and correlation between the variables as well. Mahalanobis distances are calculated between the centroids (geometric means) of model cohorts and a new subject. Model weights were calculated by taking the normalized reciprocal of these distances.
Our openMIPD package is used to apply this method.
train_result_FAMD <- famd_train(
train = AMOX_CMIN_TRAIN,
continuous_cov = c("WT", "CREAT", "AGE"),
categorical_cov = c("OBESE", "ICU", "BURN", "SEX"),
target_variable = "CMIN")To visualize the model, the contribution of covariates to the first (left) and second (right) principal component ar visualized for FAMD. Notably, BURN contributed the least to the first dimension, and the most to the second. The contribution of continuous covariates to the first and second principal components in PCA is also plotted. WT contributes the most to the results, and CREAT the least (out of the continuous covariates). CREAT and age are positively correlated as the angle between them is smaller, while between CREAT and WT there is an important negative correlation.
train_result_FAMD$principal_components eigenvalue percentage of variance cumulative percentage of variance
comp 1 3.2226916 46.038451 46.03845
comp 2 1.2679382 18.113402 64.15185
comp 3 0.9498823 13.569747 77.72160
comp 4 0.6445674 9.208106 86.92971
comp 5 0.5435385 7.764835 94.69454contrib_dim1 <- train_result_FAMD$contrib_dim1
contrib_dim1 
ggsave(filename = here("Figures/S11a.jpg"),
plot = contrib_dim1,
width = 8, height = 6, dpi = 600)
contrib_dim2 <- train_result_FAMD$contrib_dim2
contrib_dim2 
ggsave(filename = here("Figures/S11b.jpg"),
plot = contrib_dim2,
width = 8, height = 6, dpi = 600)
contrib_quant_var <- train_result_FAMD$contrib_quant_var
contrib_quant_var
ggsave(filename = here("Figures/S12.jpg"),
plot = contrib_quant_var,
width = 8, height = 6, dpi = 600)test_result_FAMD <- famd_test(
test = AMOX_CMIN_TEST,
train_results = train_result_FAMD)To evaluate the method, a predictions as a function of observed concentrations goodness of fit plot is presented as well as the average model weights are plotted, stratified by covariate categories/quantiles.
test_data_FAMD <- test_result_FAMD$test_results
test_result_FAMD$GOF_plot
weight_BURN_FAMD <- generate_weight_plot(test_data_FAMD, "BURN", is_categorical = TRUE)
weight_ICU_FAMD <- generate_weight_plot(test_data_FAMD, "ICU", is_categorical = TRUE)
weight_OBESE_FAMD <- generate_weight_plot(test_data_FAMD, "OBESE", is_categorical = TRUE)
weight_CREAT_FAMD <- generate_weight_plot(test_data_FAMD, "CREAT", is_categorical = FALSE)
weight_WT_FAMD <- generate_weight_plot(test_data_FAMD, "WT", is_categorical = FALSE)
weight_AGE_FAMD <- generate_weight_plot(test_data_FAMD, "AGE", is_categorical = FALSE)
weight_SEX_FAMD <- generate_weight_plot(test_data_FAMD, "SEX", is_categorical = TRUE)
weight_BURN_FAMD
weight_ICU_FAMD
weight_OBESE_FAMD
weight_CREAT_FAMD
weight_AGE_FAMD
weight_SEX_FAMD
weight_OBESE_FAMD <- weight_OBESE_FAMD +
labs(title = "FAMD weight attribution, stratified by OBESE")
ggsave(filename = here("Figures/S10a.jpg"),
plot = weight_OBESE_FAMD,
width = 8, height = 6, dpi = 600)
test_data_FAMD %>%
group_by(MODEL) %>%
summarise(avg_weight = mean(WEIGHT, na.rm = TRUE))# A tibble: 4 × 2
MODEL avg_weight
<chr> <dbl>
1 CARLIER 0.248
2 FOURNIER 0.257
3 MELLON 0.189
4 RAMBAUD 0.306# Extrapolate dose based on the ensembled concentrations and compare it to the true simulated dose.
test_data_FAMD <- test_data_FAMD %>%
dplyr::filter(REFERENCE == 1) %>%
dplyr::mutate(DOSE_PRED = (60/WEIGHTED_PREDICTION) * DOSE_ADM) # Administered dose extrapolation to reach 60 mg/L
final_results_FAMD <- explore_predictions(test_data_FAMD)
final_results_FAMD$target_attainment 
crcl_plot_FAMD <- final_results_FAMD$crcl_plot
crcl_plot_FAMD
final_results_FAMD$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 0.967 0.510 82.1 18.6 62.1 16.5 222
2 Incorrect 0.941 0.616 85.7 18.7 58.6 16.2 378
# ℹ 1 more variable: Proportion <dbl># Keep data for method ensembling
test_data_FAMD_ens <- test_data_FAMD %>%
dplyr::mutate(FAMD = DOSE_PRED) %>%
dplyr::select("ID","FAMD")Ensembling for machine learning (XGBoost, Random forest, k nearest neighobrs, support vector machine) and PopPK ensembling (classification tree informed ensembling, regression tree informed ensembling, weighed model ensembling, FAMD). A dose prediction to reach 60 mg/L is made for each subject and the method with the dose prediction closest to the true dose is selected. A classification tree is trained to predict the most suited dose for each subject.
# First prediction for the four single ML algorithms
# For ML, take only one line per patient (the true concentration)
train <- AMOX_CMIN_TRAIN %>%
dplyr::filter(REFERENCE == 1) %>%
mutate(II = FREQ) %>%
mutate(INF = 24/FREQ)
test <- AMOX_CMIN_TEST %>%
dplyr::filter(REFERENCE == 1) %>%
mutate(II = FREQ) %>%
mutate(INF = 24/FREQ)
test_data_ML <- machine_learning(train = train, test = test, continuous_cov = c("WT", "CREAT", "AGE"),
categorical_cov = c("OBESE", "ICU", "BURN", "SEX", "INF"), target_variable = "CMIN", target_concentration = 60)set.seed(1991)
conflicted::conflicts_prefer(dplyr::filter)
# Put together the predictions of the 8 methods
datasets <- list(test_data_ML, test_data_WME_ens, test_data_FAMD_ens, test_data_RT_ens, test_data_CT_ens)
# Merge the datasets
data <- reduce(datasets, full_join, by = "ID") %>% arrange(ID)
# Divide the data to training and test data (50-50)
idx <- seq_len(nrow(data)) %% 2 == 1
train_data <- data[idx, ]
test_data <- data[!idx, ]
# Add the name of the best method (whose dose prediction is the closest to the target dose) in a new column called Method
methods <- c("RF", "XGB", "KNN", "SVM", "WME", "CT", "RT", "FAMD")
train_data <- train_data %>%
rowwise() %>%
dplyr::mutate(
Method = methods[which.min(abs(c_across(all_of(methods)) - DOSE_TARGET))]
) %>%
ungroup()
# Range for complexity parameter to test (based on cross-validation)
cp_values <- seq(0.001, 0.04, by = 0.001)
# Convert categorical variables to factors
train_data <- train_data %>%
dplyr::mutate(across(c(Method, ICU, BURN, OBESE, SEX), as.factor))
# Perform cross-validation for each complexity value
cv_results <- sapply(cp_values, function(cp) {
ensfit <- rpart(
Method ~ WT + CREAT + ICU + BURN + OBESE + AGE + SEX,
data = train_data,
method = 'class',
parms = list(split = "information"),
control = rpart.control(
cp = cp,
xval = 10,
minsplit = 4,
minbucket = 4
)
)
min(ensfit$cptable[, "xerror"])
})
# Get the minimal cross validation error
min_error <- min(cv_results)
# Choose largest complexity parameter among those achieving the minimum error
best_cp <- max(cp_values[cv_results == min_error])# Refit the tree
ensfit <- rpart(
Method ~ WT + CREAT + ICU + BURN + OBESE + AGE + SEX,
data = train_data,
method = 'class',
parms = list(split = "information"),
control = rpart.control(
cp = best_cp,
xval = 10,
minsplit = 4,
minbucket = 4
)
)
saveRDS(ensfit, file = "ensfit.rds")The classification tree is plotted indicating the best-suited method for each subject group.
# Plot the tree
ens_plot <- rpart.plot(ensfit, type = 3, extra = 0, cex.main = 1.25, cex = 1, box.palette = "Blues", main = paste("Method ensembling", "(cp =", best_cp, ")"))
print(ens_plot)$obj
n= 300
node), split, n, loss, yval, (yprob)
* denotes terminal node
1) root 300 247 FAMD (0.13 0.18 0.16 0.14 0.06 0.13 0.09 0.12)
2) BURN=1 75 55 CT (0.27 0.11 0.19 0.08 0.053 0.12 0.16 0.027) *
3) BURN=0 225 180 FAMD (0.089 0.2 0.15 0.16 0.062 0.13 0.067 0.15) *
$snipped.nodes
NULL
$xlim
[1] 0 1
$ylim
[1] 0 1
$x
[1] 0.5131127 0.1403557 0.8858696
$y
[1] 1.09542725 0.05022487 0.05022487
$branch.x
[,1] [,2] [,3]
x 0.5131127 0.1403557 0.8858696
NA 0.1403557 0.8858696
NA 0.5131127 0.5131127
$branch.y
[,1] [,2] [,3]
y 1.095427 0.1011043 0.1011043
NA 1.0954273 1.0954273
NA 1.0954273 1.0954273
$labs
[1] NA "CT" "FAMD"
$cex
[1] 1
$boxes
$boxes$x1
[1] NA 0.1109523 0.8355855
$boxes$y1
[1] NA 0.03326507 0.03326507
$boxes$x2
[1] NA 0.1697591 0.9361537
$boxes$y2
[1] NA 0.1011043 0.1011043
$split.labs
[1] ""
$split.cex
[1] 1 1 1
$split.box
$split.box$x1
[1] 0.07711707 NA NA
$split.box$y1
[1] 0.9868845 NA NA
$split.box$x2
[1] 0.2035944 NA NA
$split.box$y2
[1] 1.054724 NA NAjpeg(here("Figures/S18.jpg"), width = 8, height = 6, units = "in", res = 400)
rpart.plot(ensfit, type = 3, extra = 0, cex = 1, cex.main = 1.25, box.palette = "Blues", main = "Method ensembling")
dev.off()png
2 # Get for which patient which method is the best
leaves <- rownames(ensfit$frame)[ensfit$frame$var == "<leaf>"]
paths <- path.rpart(ensfit, leaves, print.it = FALSE)
leaf_classes <- ensfit$frame$yval[which(ensfit$frame$var == "<leaf>")]
leaf_labels <- as.character(attr(ensfit, "ylevels")[leaf_classes])
leaf_summary <- data.frame(
Method = leaf_labels,
Path = sapply(paths, function(path) paste(path, collapse = " & "))
)
print(leaf_summary) Method Path
2 CT root & BURN=1
3 FAMD root & BURN=0# Make predictions for the test data
test_data <- test_data %>%
mutate(across(c(ICU, BURN, OBESE, SEX), as.factor))
test_data$Method <- predict(ensfit, newdata = test_data, type = "class")
# Add the dose prediction of the best predicted method
test_data_results <- test_data %>%
rowwise() %>%
dplyr::mutate(DOSE_PRED = cur_data()[[Method]]) %>%
ungroup()results_ens <- explore_predictions(test_data_results)
results_ens$target_attainment 
crcl_plot_ens <- results_ens$crcl_plot
crcl_plot_ens
results_ens$summary_stats # A tibble: 2 × 9
Prediction_correctness mean_CREAT sd_CREAT mean_WT sd_WT mean_AGE sd_AGE Count
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
1 Correct 0.896 0.362 82.3 19.4 63.4 15.5 115
2 Incorrect 0.883 0.543 86.1 18.2 57.7 15.5 185
# ℹ 1 more variable: Proportion <dbl>