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simulations.R
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library(tidyverse)
library(lme4)
library(arm)
library(merTools)
## Data Reading
rm(list = ls())
source("R/utils.R")
set.seed(987656)
select <- dplyr::select
# Elbow Radiographs
elbows <- readRDS("data/interim/train_elbows.rds")
elbowsBin <- readRDS("data/interim/train_elbows_bins.rds")
sort_raters <- elbowsBin %>%
group_by(RaterID) %>%
summarise(total_score = mean(rater_score)) %>%
arrange(desc(total_score)) %>%
pull(RaterID)
selected_raters <- sort_raters[seq(1, 226, 27)][c(1:4,6:9)]
# True values
n.sims <- 10000
n.items <- 80
n.learner <- length(unique(elbows$RaterID))
y <- elbows$Accuracy
## Transforming Data
# Rescale Sequence variable for fitting issues. If Sequence is left
# in its raw scale, glmer throws convergence warnings
elbows$sclSeq <- elbows$Sequence/20
######## Model Fitting #####
# Section 5 Models in the paper
# No pooling
m0 <- glm(Accuracy ~ sclSeq, data = elbows, family = binomial(link = "logit"))
# Multilevel Model - No diagnosis
m1 <- glmer(Accuracy ~ 1 + sclSeq + (1 + sclSeq|RaterID), data = elbows,
family = binomial(link = "logit"))
# Multilevel Model with Diagnosis
m2 <- glmer(Accuracy ~ 1 + sclSeq*CaseType2 + (1 + sclSeq|RaterID), data = elbows,
family = binomial(link = "logit"), control = glmerControl(optimizer = "bobyqa"))
saveRDS(m2, 'models/mlm_logistic_Dx.rds')
################### Model Evaluation #######################
## Simulations
## compute Real proportion of Correct Responses between all learners
##############################################################
###############################
### Mean and Standard Deviation of the
### total correct responses across all learners
###############################
m0.rep <- simulate_obs(m0, data = elbows, pooling = T, n_sims = n.sims)$sim_labels
m1.rep <- simulate_obs(m1, data = elbows, pooling = F, n_sims = n.sims)$sim_labels
m2.rep <- simulate_obs(m2, data = elbows, pooling = F, n_sims = n.sims)$sim_labels
g1 <- summary_stat_plot(y_sims = m0.rep, y_real = y, model = "Complete Pooling",
n_items = n.items, n_learners = n.learner)
g2 <- summary_stat_plot(y_sims = m1.rep, y_real = y, model = "MLM - No Diagnosis",
n_items = n.items, n_learners = n.learner)
g3 <- summary_stat_plot(y_sims = m2.rep, y_real = y, model = "MLM - With Diagnosis",
n_items = n.items, n_learners = n.learner)
## Mean
leg <- cowplot::get_legend(g1$mean_plot + theme(legend.position = "bottom"))
grid1 <- cowplot::plot_grid(g1$mean_plot + theme(legend.position = "none"),
g2$mean_plot + theme(legend.position = "none"),
g3$mean_plot + theme(legend.position = "none"), nrow = 1)
#800*320
cowplot::plot_grid(grid1, leg, nrow = 2, rel_heights = c(1, 0.1))
ggsave('sims_output/elbow-mean_sims.png', width = 8, height = 3.2, units = 'in')
## SD
leg <- cowplot::get_legend(g1$sd_plot + theme(legend.position = "bottom"))
grid1 <- cowplot::plot_grid(g1$sd_plot + theme(legend.position = "none"),
g2$sd_plot + theme(legend.position = "none"),
g3$sd_plot + theme(legend.position = "none"), nrow = 1)
cowplot::plot_grid(grid1, leg, nrow = 2, rel_heights = c(1, 0.1))
ggsave('sims_output/elbow-sd_sims.png', width = 8, height = 3.2, units = 'in')
###### Aggregate Learning Curve #########
# Plot proportion: Selected test statistic
# Compute Aggregate proportion - observed
# Only done for the biggest model Eq 14
sim_ratio <- array(NA, c(n.items, n.sims))
sim_ratio <- apply(m2.rep, 2, test_ratio, n.items)
elbows %>%
group_by(Sequence) %>%
summarise(prop_correct = mean(Accuracy), n = n()) %>%
mutate(prop_se = sqrt(prop_correct*(1 - prop_correct)/n)) -> elbow_agg
elbow_agg %>%
ggplot(aes(x = Sequence, y = prop_correct)) +
geom_point() +
# geom_pointrange(aes(ymax = prop_correct + prop_se,
# ymin = prop_correct - prop_se), alpha = 0.4) +
geom_smooth(se = F) +
scale_y_continuous(limits = c(0.48, 0.81)) +
theme_classic() +
labs(y = "Proportion Correct", x = "Item in Sequence",
# title = "Aggregrate Learning Curve for learners",
title = "Observed Data - Elbow Dataset") -> p1
q50 <- apply(sim_ratio, 1, quantile, 0.5)
conf50 <- t(apply(sim_ratio, 1, quantile, c(0.25, 0.75)))
conf95 <- t(apply(sim_ratio, 1, quantile, c(0.025, 0.975)))
## Plot simulations vs Real Data
long_sims <- data.frame(cbind(q50, conf50, conf95)) %>%
mutate(n = 1:n())
names(long_sims)[1:5] <- c("mid50", "lb50", "ub50", "lb95", "ub95")
ggplot(long_sims, aes(x = n)) +
geom_linerange(aes(ymin = lb95, ymax = ub95, color = "95% PI"), alpha = 0.5, size = 1) +
geom_linerange(aes(ymin = lb50, ymax = ub50, color = "50% PI"), alpha = 0.8, size = 1.5) +
geom_point(data = elbow_agg, aes(x = Sequence, y = prop_correct, color = "Observed"), size = 1.5) +
# geom_line(aes(y = mid50, color = "Sim Median"), size = 1, alpha = 0.7) +
geom_smooth(aes(y = mid50, color = "Median Trend"), method = "loess", size = 1, se = F) +
scale_color_manual(name = "",
values = c(`Median Trend` = "darkred",
`50% PI`= "skyblue4",
`95% PI` = "gray65",
`Observed` = "black"),
guide = guide_legend(override.aes = list(linetype = c(rep("solid", 2), rep("blank", 2)),
shape = c(NA, NA, 16, 16)))) +
scale_y_continuous(limits = c(0.48, 0.81)) +
labs(y = "Proportion Correct", x = "Item in Sequence",
# title = "Aggregate Learning Curve for Learners",
title = "Model Simulated Data - Elbow Dataset") +
theme_classic() -> p2
cowplot::plot_grid(p1, p2, rel_widths = c(0.8, 1.1))
ggsave('sims_output/elbow-sims_v_observed.png', width = 8, height = 3.2, units = 'in')
#################################
#### New Data Predictions #######
elbows_test <- readRDS("data/interim/test_elbows.rds")
elbows_test$sclSeq <- (elbows_test$Sequence + 80)/20
test_items <- 20
test_learners <- length(unique(elbows_test$RaterID)) # same 226
y_test <- elbows_test$Accuracy
y_preds <- simulate(m2, nsim = n.sims, newdata = elbows_test)
true.mean <- mean(total_correct(y_test, test_items))
true.sd <- sd(total_correct(y_test, test_items))
pred_n.correct <- sapply(1:n.sims, function(s) total_correct(y_preds[,s], test_items))
pred.means <- data.frame(mean_correct = colMeans(pred_n.correct))
mean_summary <- mean(pred.means$mean_correct)
pred.sds <- data.frame(sd_correct = apply(pred_n.correct, 2, sd))
sd_summary <- mean(pred.sds$sd_correct)
pred.means %>%
ggplot(aes(x = mean_correct)) + geom_histogram(bins = 30, color = "darkgray", fill = "white", size = 0.5) +
geom_vline(aes(xintercept = true.mean, color = "True Mean"), size = 1.5) +
geom_vline(aes(xintercept = mean_summary + 0.06, color = "Simulations Mean"), size = 1) +
theme_classic() +
scale_y_continuous(expand = c(0, 0)) + scale_x_continuous(breaks = seq(14, 16, 0.5)) +
scale_color_discrete(name = "") +
labs(title = "Testing Data", x = "Mean of Correct Responses")
pred.sds %>%
ggplot(aes(x = sd_correct)) + geom_histogram(bins = 30, color = "darkgray", fill = "white", size = 0.5) +
geom_vline(aes(xintercept = true.sd, color = "True Mean"), size = 1.5) +
geom_vline(aes(xintercept = sd_summary + 0.06, color = "Simulations SD"), size = 1) +
theme_classic() +
scale_y_continuous(expand = c(0, 0)) +
scale_color_discrete(name = "") +
labs(title = "Testing Data", x = "SD of Correct Responses")
###### Prediction of next 20 items ######
#### Aggregate Learning Curve #########
pred_ratio <- array(NA, c(test_items, n.sims))
pred_ratio <- apply(y_preds, 2, test_ratio, test_items)
q50 <- apply(pred_ratio, 1, quantile, 0.5)
conf50 <- t(apply(pred_ratio, 1, quantile, c(0.25, 0.75)))
conf95 <- t(apply(pred_ratio, 1, quantile, c(0.025, 0.975)))
## Plot simulations vs Real Data
long_sims <- data.frame(cbind(q50, conf50, conf95)) %>%
mutate(n = 1:n())
names(long_sims)[1:5] <- c("mid50", "lb50", "ub50", "lb95", "ub95")
elbows_test %>%
group_by(Sequence) %>%
summarise(prop_correct = mean(Accuracy), n = n()) %>%
mutate(prop_se = sqrt(prop_correct*(1 - prop_correct)/n)) -> elbow_agg_test
ggplot(long_sims, aes(x = n + 80)) +
geom_linerange(aes(ymin = lb95, ymax = ub95, color = "95% PI"), alpha = 0.5, size = 1) +
geom_linerange(aes(ymin = lb50, ymax = ub50, color = "50% PI"), alpha = 0.8, size = 1.5) +
geom_point(data = elbow_agg_test, aes(x = Sequence + 80, y = prop_correct, color = "Observed"), size = 1.5) +
# geom_line(aes(y = mid50, color = "Sim Median"), size = 1, alpha = 0.7) +
geom_smooth(aes(y = mid50, color = "Median Trend"), method = "loess", size = 1, se = F) +
scale_color_manual(
name = "",
values = c(`Median Trend` = "darkred",
`50% PI`= "skyblue4",
`95% PI` = "gray65",
`Observed` = "black"),
guide = guide_legend(override.aes = list(linetype = c(rep("solid", 2), rep("blank", 2)),
shape = c(NA, NA, 16, 16)))) +
scale_x_continuous() +
labs(y = "Proportion Correct", x = "Item in Sequence",
title = "Aggregate Learning Curve for Learners",
subtitle = "Held-out Data - Elbow Dataset") +
theme_classic() # -> p2
cowplot::plot_grid(p1, p2, rel_widths = c(0.8, 1.1))
########## Prediction Intervals ############
m0_preds <- arm::sim(m0, n.sims)
X <- cbind(rep(1, nrow(elbows_test)), elbows_test$sclSeq)
p.sim <- sapply(1:n.sims, function(s) invlogit(X %*% coef(m0_preds)[s,]))
conf95 <- t(apply(p.sim, 1, quantile, c(0.025, 0.5, 0.975)))
p.intervals <- cbind(elbows_test, conf95) %>%
filter(RaterID %in% selected_raters, Sequence == 1) %>%
arrange(factor(RaterID, levels = selected_raters))
test_df <- expand.grid(RaterID = selected_raters, sclSeq = 4.05)
m1_preds <- predictInterval(m1, newdata = test_df, n.sims = n.sims, type = "probability", include.resid.var = F)
round(m1_preds, 2)
test_df <- expand.grid(RaterID = selected_raters, sclSeq = 4.05, CaseType2 = "Normal")
m2_preds <- predictInterval(m2, newdata = test_df, n.sims = n.sims, type = "probability", include.resid.var = F)
round(m2_preds, 2)
test_df <- expand.grid(RaterID = selected_raters, sclSeq = 4.05, CaseType2 = "Abnormal/Other")
m2_preds <- predictInterval(m2, newdata = test_df, n.sims = n.sims, type = "probability", include.resid.var = F)
round(m2_preds, 2)
no_pool <- elbows %>%
filter(RaterID %in% selected_raters) %>%
group_by(RaterID) %>%
do(single_glm = glm(Accuracy ~ sclSeq, data = ., family = binomial))%>%
arrange(factor(RaterID, levels = selected_raters))
x_tilde <- c(1, 4.05)
sim_list <- lapply(no_pool$single_glm, function(x) coef(arm::sim(x, n.sims)))
no_pool.sim <- sapply(sim_list, function(x) sapply(1:n.sims, function(s) invlogit(x_tilde %*% x[s,])))
round(t(apply(no_pool.sim, 2, quantile, c(0.025, 0.5, 0.975))),2)
elbows_test %>%
filter(RaterID %in% selected_raters) %>%
group_by(RaterID) %>%
summarise(mean_score = mean(Accuracy))%>%
arrange(factor(RaterID, levels = selected_raters)) %>%
mutate(mean_score = round(mean_score, 2))
#### Confidence Intervals ####
m <- random_intercept
coef(m)[["RaterID"]] %>%
rownames_to_column("RaterID") %>%
filter(RaterID == 47)
m.sims <- arm::sim(m, 1e4)
int_sims <- fixef(m)[1] + m.sims@ranef$RaterID[,,1]
slp_sims <- fixef(m)[2] + m.sims@ranef$RaterID[,,2]
data.frame(t(apply(int_sims, 2, quantile, c(0.025, 0.975)))) %>%
rownames_to_column("RaterID") %>% filter(RaterID == 47)
df_intercept %>% filter(RaterID == 47)
confint(m)
# Beyond this point is only the ECG Data set, most of the code is
# the same except for the prediction on new data.
#----------------------------------------------------------------
########################## ECGs #################################
rm(list = ls())
source("R/utils.R")
ecg <- readRDS("data/interim/ecg_set1.rds")
ecg_test <- readRDS("data/interim/ecg_set2.rds")
# True values
n.sims <- 10000
n.items <- 100
n.learner <- length(unique(ecg$userId))
y <- ecg$correctDx
y_test <- ecg_test$correctDx
## Transforming Data
# Rescale Sequence variable for fitting issues. If Sequence is left
# in its raw scale, glmer throws convergence warnings (one reason to move to rstanarm)
ecg$sclSeq <- ecg$Sequence/20
ecg_test$sclSeq <- ecg_test$Sequence/20
######## Model Fitting #######
# Section 5 Models in the paper
m0 <- glm(correctDx ~ sclSeq, data = ecg, family = binomial(link = "logit"))
# ECG Data
m0.ecg <- glmer(correctDx ~ 1 + sclSeq + (1 + sclSeq|userId), data = ecg,
family = binomial(link = "logit"))
m1.ecg <- glmer(correctDx ~ 1 + sclSeq*caseType2 + (1 + sclSeq|userId), data = ecg,
family = binomial(link = "logit"), control = glmerControl(optimizer = "bobyqa"))
################### Model Evaluation ###############
## Simulations
####################################################
###############################
### Mean and Standard Deviation of the
### total correct responses across all learners
###############################
m0.rep <- simulate_obs(m0, data = ecg, pooling = T, n_sims = n.sims)$sim_labels
m1.rep <- simulate_obs(m0.ecg, data = ecg, pooling = F, n_sims = n.sims)$sim_labels
m2.rep <- simulate_obs(m1.ecg, data = ecg, pooling = F, n_sims = n.sims)$sim_labels
g1 <- summary_stat_plot(y_sims = m0.rep, y_real = y, model = "Complete Pooling",
n_items = n.items, n_learners = n.learner)
g2 <- summary_stat_plot(y_sims = m1.rep, y_real = y, model = "MLM - No Diagnosis",
n_items = n.items, n_learners = n.learner)
g3 <- summary_stat_plot(y_sims = m2.rep, y_real = y,
model = "MLM - With Diagnosis", n.items, n.learner)
## Mean
leg <- cowplot::get_legend(g1$mean_plot + theme(legend.position = "bottom"))
grid1 <- cowplot::plot_grid(g1$mean_plot + theme(legend.position = "none"),
g2$mean_plot + theme(legend.position = "none"),
g3$mean_plot + theme(legend.position = "none"), nrow = 1)
cowplot::plot_grid(grid1, leg, nrow = 2, rel_heights = c(1, 0.1))
## SD
leg <- cowplot::get_legend(g1$sd_plot + theme(legend.position = "bottom"))
grid1 <- cowplot::plot_grid(g1$sd_plot + theme(legend.position = "none"),
g2$sd_plot + theme(legend.position = "none"),
g3$sd_plot + theme(legend.position = "none"), nrow = 1)
cowplot::plot_grid(grid1, leg, nrow = 2, rel_heights = c(1, 0.1))
###### Aggregate Learning Curve #########
# Plot proportion: Selected test statistic
# Compute Aggregate proportion - observed
# Only done for the biggest model Eq 14
source("R/utils.R")
sim_ratio <- array(NA, c(n.items, n.sims))
sim_ratio <- apply(m2.rep, 2, test_ratio, n.items)
ecg %>%
group_by(Sequence) %>%
summarise(prop_correct = mean(correctDx), n = n()) %>%
mutate(prop_se = sqrt(prop_correct*(1 - prop_correct)/n)) -> ecg_agg
ecg_agg %>%
ggplot(aes(x = Sequence, y = prop_correct)) +
geom_point() +
# geom_pointrange(aes(ymax = prop_correct + prop_se,
# ymin = prop_correct - prop_se), alpha = 0.4) +
geom_smooth(se = F) +
scale_y_continuous(limits = c(0.37, 0.72)) +
theme_classic() +
labs(y = "Proportion Correct", x = "Number of Items",
# title = "Population Level Learning Curve",
title = "Observed Data - ECG Dataset") -> p1
q50 <- apply(sim_ratio, 1, quantile, 0.5)
conf50 <- t(apply(sim_ratio, 1, quantile, c(0.25, 0.75)))
conf95 <- t(apply(sim_ratio, 1, quantile, c(0.025, 0.975)))
## Plot simulations vs Real Data
long_sims <- data.frame(cbind(q50, conf50, conf95)) %>%
mutate(n = 1:n())
names(long_sims)[1:5] <- c("mid50", "lb50", "ub50", "lb95", "ub95")
# ecg_agg_test$key <- "real"
ggplot(long_sims, aes(x = n)) +
geom_linerange(aes(ymin = lb95, ymax = ub95, color = "95% PI"), alpha = 0.5, size = 1) +
geom_linerange(aes(ymin = lb50, ymax = ub50, color = "50% PI"), alpha = 0.8, size = 1.5) +
geom_point(data = ecg_agg, aes(x = Sequence, y = prop_correct, color = "Observed"), size = 1.5) +
# geom_line(aes(y = mid50, color = "Sim Median"), size = 1, alpha = 0.7) +
geom_smooth(aes(y = mid50, color = "Median Trend"), method = "loess", size = 1, se = F) +
scale_color_manual(
name = "",
values = c(
`Median Trend` = "darkred",
`50% PI`= "skyblue4",
`95% PI` = "gray65",
`Observed` = "black"),
guide = guide_legend(override.aes = list(linetype = c(rep("solid", 2), rep("blank", 2)),
shape = c(NA, NA, 16, 16)))) +
scale_y_continuous(limits = c(0.37, 0.72)) +
labs(y = "Proportion Correct", x = "Number of Items",
# title = "Population Level Learning Curve",
title = "Model Simulated Data - ECG Dataset") +
theme_classic() -> p2
cowplot::plot_grid(p1, p2, rel_widths = c(0.8, 1.1))
new_sims <- simulate(m1.ecg, allow.new.levels = T, newdata = ecg_test,
nsim = n.sims, re.form = NA)
new_ratio <- array(NA, c(n.items, n.sims))
new_ratio <- apply(new_sims, 2, test_ratio, n.items)
ecg_test %>%
group_by(Sequence) %>%
summarise(prop_correct = mean(correctDx), n = n()) %>%
mutate(prop_se = sqrt(prop_correct*(1 - prop_correct)/n)) -> ecg_agg_test