Nothing
### Internal functions to allow estimation of calibration curves using the pseudo-value method.
#' Estimate data for calibration plots using pseudo-values.
#' @description
#' Called in calibmsm::calib_msm to apply the pseudo-value method.
#'
#' @details
#' Calls heavily on calibmsm::calc_obs_pv_boot to estimate observed transition probabilities.
#' Bootstrapping may be applied depending on user input.
#'
#' @returns A list of datasets for each calibration plot.
#'
#' @noRd
calib_pv <- function(data_ms,
data_raw,
tp_pred_plot,
j,
s,
t,
curve_type,
rcs_nk,
loess_span,
loess_degree,
loess_surface,
loess_statistics,
loess_trace_hat,
loess_cell,
loess_iterations,
loess_iterTrace,
pv_group_vars,
pv_n_pctls,
pv_precalc,
pv_ids,
CI,
CI_type,
CI_R_boot,
CI_seed,
transitions_out){
###
### Create the object of predicted risks over which the calibration plots will be plotted
### For calib_pv, this is the landmarked cohort of individuals, including those censored at time t,
### or tp_pred_plot if specified
if (is.null(tp_pred_plot)){
## Note that tp_pred has been added to data_raw and the predicted transition probabilities (and relevant transformations)
## are contained within this dataset.
data_to_plot <- apply_landmark(data_raw = data_raw, data_ms = data_ms, j = j, s = s, t = t, exclude_cens_t = FALSE)
} else if (!is.null(tp_pred_plot)){
data_to_plot <- tp_pred_plot
}
###
### Create plotdata object.
### 1) If a confidence interval was requested using bootstrapping, use calc_obs_pv_boot in conjuction with boot::boot.
### This must be done separately for each state.
### 2) If a confidence interval was requested using parametric form, call calc_obs_pv_boot once, specifying indices to be
### the sequence 1:nrow(data_raw), in order to calculate the plot data.
### 3) If a confidence interval was not requested, call calc_obs_pv_boot once, specifying indices to be
### the sequence 1:nrow(data_raw), in order to calculate the plot data.
### Note that 2) and 3) are the same. This is because the function calib_pseudo_func is dependent on CI and CI_type,
### which were defined as input into calib_pv. They will there give different output (as they should) when it is run.
if (CI != FALSE & CI_type == "bootstrap" & is.null(pv_ids)){
### Define alpha for CI's
alpha <- (1-CI/100)/2
### Create object to store plot data
plotdata <- vector("list", length(transitions_out))
### Cycle through states
for (state in 1:length(transitions_out)){
### Assign state_k
state_k <- transitions_out[state]
### Print progress
print(paste("Beginning bootstrapping for state = ", state_k, Sys.time()))
### Set seed for bootstrapping
if (!is.null(CI_seed)){
set.seed(CI_seed)
}
### Put function through bootstrap
boot_obs <- boot::boot(data_raw,
calc_obs_pv_boot,
R = CI_R_boot,
data_ms = data_ms,
data_to_plot = data_to_plot,
j = j,
s2 = s,
t = t,
curve_type = curve_type,
rcs_nk = rcs_nk,
loess_span = loess_span,
loess_degree = loess_degree,
loess_surface = loess_surface,
loess_statistics = loess_statistics,
loess_trace_hat = loess_trace_hat,
loess_cell = loess_cell,
loess_iterations = loess_iterations,
loess_iterTrace = loess_iterTrace,
pv_group_vars = pv_group_vars,
pv_n_pctls = pv_n_pctls,
pv_precalc = pv_precalc,
pv_ids = pv_ids,
CI = FALSE,
transitions_out = state_k,
boot_format = TRUE)
### Extract confidence bands
lower <- apply(boot_obs$t, 2, stats::quantile, probs = alpha, na.rm = TRUE)
upper <- apply(boot_obs$t, 2, stats::quantile, probs = 1-alpha, na.rm = TRUE)
### Produce a warning if any NA values
if(sum(is.na(boot_obs$t)) > 0){
warning(paste("WARNING, SOME BOOTSTRAPPED OBSERVED EVENT PROBABILITIES WERE NA FOR STATE", state_k, "\n",
"THERE ARE ", sum(apply(boot_obs$t, 1, function(x) {sum(is.na(x)) > 0})), " ITERATIONS WITH NA's \n",
"THE MEAN NUMBER OF NA's IN EACH ITERATION IS", mean(apply(boot_obs$t, 1, function(x) {sum(is.na(x))}))
))
}
### Assign output
if ("id" %in% colnames(data_to_plot)) {
plotdata[[state]] <- data.frame("id" = data_to_plot$id,
"pred" = data_to_plot[,paste("tp_pred", state_k, sep = "")],
"obs" = boot_obs$t0,
"obs_lower" = lower,
"obs_upper" = upper)
} else {
plotdata[[state]] <- data.frame(
"pred" = data_to_plot[,paste("tp_pred", state_k, sep = "")],
"obs" = boot_obs$t0,
"obs_lower" = lower,
"obs_upper" = upper)
}
}
} else {
### NB: calc_obs_pv_boot has the ability to output calibration curve with confidence interval estimated parametrically, as well as outputting
### data in boot format (a vector), which was utilised when CI_type = "bootstrap". Here, we specify boot_format = FALSE, which will allow the
### confidence interval to be calculated parametrically.
### NB: If !is.null(pv_ids), i.e. pv_ids was specified, the function will just return a the pseudo-values themselves.
plotdata <- calc_obs_pv_boot(data_raw = data_raw,
indices = 1:nrow(data_raw),
data_ms = data_ms,
data_to_plot = data_to_plot,
j = j,
s2 = s,
t = t,
curve_type = curve_type,
rcs_nk = rcs_nk,
loess_span = loess_span,
loess_degree = loess_degree,
loess_surface = loess_surface,
loess_statistics = loess_statistics,
loess_trace_hat = loess_trace_hat,
loess_cell = loess_cell,
loess_iterations = loess_iterations,
loess_iterTrace = loess_iterTrace,
pv_group_vars = pv_group_vars,
pv_n_pctls = pv_n_pctls,
pv_precalc = pv_precalc,
pv_ids = pv_ids,
CI = CI,
CI_type = CI_type,
transitions_out = transitions_out,
boot_format = FALSE)
}
### Define combined output object
output_object_comb = list("plotdata" = plotdata)
return(output_object_comb)
}
#' Calculate pseudo-values and estimate observed event probabilities using pseudo-values.
#' @description
#' Estimate observed event probabilities for all states using pseudo-values.
#' Function is called by calibmsm::calib_pv, which is called by calibmsm::calib_msm.
#' This function does the heavy lifting, and has two major steps. First the pseudo-values
#' are calculated, taking advantage of functions calibmsm::calc_aj and calibmsm::calc_pv_aj.
#' Secondly, the pseudo-values are regressed on the predicted transition
#' probabilities, in order to generate fitted values (the observed event probabilities).
#' This second stage is implemented through the functions calibmsm::calc_obs_pv_rcs_model
#' or calibmsm::calc_obs_pv_loess_model.
#'
#' @details
#' Function written in a format so that it can be used in combination with \code{\link[boot]{boot}}
#' for bootstrapping. Specifying `indices = 1:nrow(data_raw)` will produce calibration
#' curves as normal.
#'
#' @returns If `boot_format = FALSE` a data.frame of predicted and observed event probabilities
#' is returned for each state in `transitions_out`. If boot_format = TRUE, a vector of observed
#' event probabilities is returned. Observed event probabilities are estimated for data points in
#' data_to_plot.
#'
#' @noRd
calc_obs_pv_boot <- function(data_raw,
indices,
data_ms,
data_to_plot,
j,
s2, # can't use 's' because it matches an argument for the boot function
t,
curve_type,
rcs_nk,
loess_span,
loess_degree,
loess_surface,
loess_statistics,
loess_trace_hat,
loess_cell,
loess_iterations,
loess_iterTrace,
pv_group_vars,
pv_n_pctls,
pv_precalc,
pv_ids,
CI,
CI_type,
transitions_out,
boot_format = FALSE){
### Create object 's' from 's2'
s <- s2
### If boot_format = TRUE and requested more than one state, stop
if (boot_format == TRUE & (length(transitions_out) > 1)){
stop("CANNOT OUTPUT IN BOOT FORMAT IF REQUESTING OBSERVED EVENT PROBABILITIES FOR MORE
THAN ONE STATE")
}
### The following steps will calculate the pseudo-values before fitting the calibration model
if (is.null(pv_precalc)){
###
### Apply bootstrapping
### Create bootstrapped dataset
data_raw_boot <- data_raw[indices, ]
### Create a new id for these individuals (calc_pv_aj relies on each individual having a unique identifier),
### meaning the duplicate values in the bootstrapped datasets will cause problems
data_raw_boot$id2 <- 1:nrow(data_raw_boot)
### Create bootstrapped data_ms (we replicate the choice of patients that was chosen in data_raw)
data_ms_boot <- apply_bootstrap_msdata(data_ms = data_ms, indices = indices)
### Extract transition matrix from original msdata object, as this will have been lost when bootstrapping
tmat <- attributes(data_ms)$trans
### Apply attribute tmat to the bootstrapped data_ms dataset
attributes(data_ms_boot)$trans <- tmat
### Set 'id' to be same as 'id2' in bootstrapped datasets, as the function calc_pv_aj works by removing individual
### with the 'id' variable
data_ms_boot$id <- data_ms_boot$id2
data_raw_boot$id <- data_raw_boot$id2
### Relabel data_ms_boot and data_raw_boot and remove '_boot' datasets
data_raw <- data_raw_boot
data_ms <- data_ms_boot
rm(data_raw_boot, data_ms_boot)
###
### Apply landmarking
### For calib_pv, we need to apply landmarking to both data_raw and data_ms
### We model the pseudo-values on the predicted transition probabilities in the bootstrapped data_raw dataset
### However the calculation of the pseudo-values must be done in the bootstrapped data_ms dataset
### Apply landmarking to data_raw and data_ms
data_raw_lmk_js <- apply_landmark(data_raw = data_raw,
data_ms = data_ms,
j = j,
s = s,
t = t,
exclude_cens_t = FALSE,
data_return = "data_raw")
data_ms_lmk_js <- apply_landmark(data_raw = data_raw,
data_ms = data_ms,
j = j,
s = s,
t = t,
exclude_cens_t = FALSE,
data_return = "data_ms")
###
### Restructure mstate data so that time s = time 0, and relabel transitions to 1, 2,...
### This is required in order to estimate Aalen-Johansene estimator and calculate pseudo-values
### Reduce transition times by s and remove observations which now occur entirely prior to start up
data_ms_lmk_js <-
dplyr::mutate(data_ms_lmk_js,
Tstart = pmax(0, Tstart - s),
Tstop = pmax(0, Tstop - s),
time = Tstop - Tstart) |>
base::subset(!(Tstart == 0 & Tstop == 0))
###
### Remove observations for transitions which are not made in the landmarked cohort
### Otherwise mstate::msfit will throw out an unneccesary (in this context) warning
### Start by identifying which transitions these are
suppressMessages(zero_transition_table <- data_ms_lmk_js |>
dplyr::group_by(from, to) |>
dplyr::summarise(Frequency = sum(status)))
### Only edit data_ms if some transitions have a frequency of zero
if (any(zero_transition_table$Frequency == 0)){
### Extract the transitions
zero_transition_from <- zero_transition_table$from[zero_transition_table$Frequency == 0]
zero_transition_to <- zero_transition_table$to[zero_transition_table$Frequency == 0]
### Remove them from dataset
for (i in 1:length(zero_transition_from)){
data_ms_lmk_js <- base::subset(data_ms_lmk_js, !(from == zero_transition_from[i] & to == zero_transition_to[i]))
rm(i)
}
}
### Fit csh's with no predictors
strata <- survival::strata
csh_aj <- survival::coxph(survival::Surv(Tstart, Tstop, status) ~ strata(trans), data_ms_lmk_js)
### Extract numeric values for transitions that can occur in the landmarked cohort
landmark_transitions <- as.numeric(sapply(csh_aj[["xlevels"]]$`strata(trans)`, gsub, pattern = ".*=", replacement = ""))
### Create a mapping from the old transition numbers to new transition numbers which are in sequence
map_transitions <- data.frame("new" = 1:length(landmark_transitions),
"old" = landmark_transitions)
### Write a function to apply the mapping
map_func <- function(x){
if(!is.na(x)){
if(!(x %in% landmark_transitions)){
return(NA)
} else if (x %in% landmark_transitions)
return(map_transitions$new[map_transitions$old == x])
} else if (is.na(x))
return(NA)
}
### Create new tmat for the new transition numbers
tmat_lmk_js <- apply(tmat, c(1,2), map_func)
### Define max_state (note this be will the same as ncol(tmat))
max_state <- ncol(tmat_lmk_js)
######################################
### A) CALCULATE THE PSEUDO VALUES ###
######################################
### Data must now be split up into groups defined by predictor variables (pv_group_vars) and/or predicted risks (pv_n_pctls)
### Pseudo-values will be calculated seperately within each of these groups. We will also calculate
### the Aalen-Johansen estimate of observed risk within each of these groups to enable quicker
### estimation of pseudo-values
### To maximise code efficiency, there are some differences depending on whether groups have been defined using predictor
### variables or predicted risks.
### 1) If no grouping at all, just need to calculate pseudo-values for each individual within the entire group
### (don't need to do pseudo-values for each transition seperately, because the grouping is the same)
### 2) If grouping is only within variables, again, just need to calculate pseudo-values for each individual within the groups
### defined by the variables (don't need to do pseudo-values for each transition seperately, because the grouping is the same)
### 3) If grouping is done by predicted risk of each transition (with or without grouping by baseline variables),
### need to calculate pseudo-values for each individual seperately for each transition,
### as the ordering of individuals, and therefore group, will be different for each transition.
### Some references to other functions.
### calc_aj: function to calculate to Aalen-Johansen estimator
### calc_pv_aj: calculate pseudo-value for an individual based on the Aalen-Johansen estimator
### Write one function, which calculates Aalen-Johansen for a group (subset_ids), then calculates pseudo-values for individuals in that group
### Can also specify specific individuals to calculate pseudo-values for (pv_ids)
calc_pv_subgroup <- function(subset_ids, pv_ids = NULL){
### Calcuate Aalen-Johansen
obs_aj <- calc_aj(data_ms = base::subset(data_ms_lmk_js, id %in% subset_ids),
tmat = tmat_lmk_js,
t = t - s,
j = j)[["obs_aj"]]
### Now calculate pseudo-values for each individual
if (is.null(pv_ids)){
### Calculate pseudo-values (lapply part of function) and combine into dataset (rbind part of function)
pv_temp <- do.call("rbind",
lapply(subset_ids, calc_pv_aj,
data_ms = base::subset(data_ms_lmk_js, id %in% subset_ids),
obs_aj,
tmat = tmat_lmk_js,
n_cohort = length(subset_ids),
t = t - s,
j = j)
)
### Add id and columns names
pv_temp <- data.frame(subset_ids, pv_temp)
colnames(pv_temp) <- c("id", paste("pstate", 1:max_state, sep = ""))
} else if (!is.null(pv_ids)){
### Calculate pseudo-values (lapply part of function) and combine into dataset (rbind part of function)
pv_temp <- do.call("rbind",
lapply(pv_ids, calc_pv_aj,
data_ms = base::subset(data_ms_lmk_js, id %in% subset_ids),
obs_aj,
tmat = tmat_lmk_js,
n_cohort = length(subset_ids),
t = t - s,
j = j)
)
### Add id and columns names
pv_temp <- data.frame(pv_ids, pv_temp)
colnames(pv_temp) <- c("id", paste("pstate", 1:max_state, sep = ""))
}
return(pv_temp)
}
###
### APPLY calc_pv_subgroup WITHIN SUBGROUPS TO ESTIMATE PSEUDO-VALUES
###
if (is.null(pv_group_vars) & is.null(pv_n_pctls)){
###
### 1) No grouping
###
### For all individuals
if (is.null(pv_ids)){
### Calculate psuedo-value for each individual
pv_out <- calc_pv_subgroup(data_raw_lmk_js$id)
### For just individual specified in pv_ids
} else if (!is.null(pv_ids)){
### Calculate psuedo-value for each individual in pv_ids
pv_out <- calc_pv_subgroup(data_raw_lmk_js$id, pv_ids)
}
} else if (!is.null(pv_group_vars) & is.null(pv_n_pctls)) {
###
### 2) Grouping only by baseline variables
###
### Split data into groups defined by the variables in pv_group_vars
## Create formula to split the dataset by (by pv_group_vars)
split_formula <- stats::as.formula(paste("~ ", paste(pv_group_vars, collapse = "+"), sep = ""))
## Split the dataset into the respective groups
data_groups <- split(data_raw_lmk_js, split_formula)
### Get group ids for subgroups in which the pseudo-values need to be calculated
group_ids <- lapply(data_groups, function(x) as.numeric(x[,c("id")]))
### For all individuals
if (is.null(pv_ids)){
### Calculate pseudo-values in each subgroup
pv_out <- lapply(group_ids, calc_pv_subgroup)
### For just individual specified in pv_ids
} else if (!is.null(pv_ids)){
### Identify which pv_ids fit into which subgroup
group_pv_ids <- lapply(group_ids, function(x) x[x %in% pv_ids])
### Calculate pseudo-values in each subgroup, just for pv_ids
pv_out <- lapply(1:length(group_ids), function(x) {
if (length(group_pv_ids[[x]] > 0)){
calc_pv_subgroup(subset_ids = group_ids[[x]], pv_ids = group_pv_ids[[x]])
} else if (length(group_pv_ids[[x]] == 0)){
c()
}
})
}
### Combine into single dataset
pv_out <- do.call("rbind", pv_out)
### Sort by "id"
pv_out <- dplyr::arrange(pv_out, id)
} else if (is.null(pv_group_vars) & !is.null(pv_n_pctls)) {
###
### 3) Grouping only by predicted risk
###
### Write a function to calculate the pseudo-values for the transition probailities into a particular state,
### within subgroups defined by percentiles of the predicted transition probabilities into that state.
### Note that we now need to apply the function seperately to each state because the subgroups will change depending on the state of interest.
### In 1) and 2), we could calculate the pseudo-values for all states simultaneously within each subgroup.
apply_calc_pv_subgroup_pctls <- function(state_k){
### Split data by predicted risk of state k
data_pctls <- base::split(data_raw_lmk_js,
cut(data_raw_lmk_js[,paste("tp_pred", state_k, sep = "")],
breaks = stats::quantile(data_raw_lmk_js[,paste("tp_pred", state_k, sep = "")],
seq(0,1,1/pv_n_pctls)),
include.lowest = TRUE))
### Get group ids for subgroups
group_ids <- lapply(data_pctls, function(x) as.numeric(x[,c("id")]))
### For all individuals
if (is.null(pv_ids)){
### Calculate pseudo-values in each subgroup
pv_temp <- lapply(group_ids, calc_pv_subgroup)
### For just individual specified in pv_ids
} else if (!is.null(pv_ids)){
### Identify which pv_ids fit into which subgroup
group_pv_ids <- lapply(group_ids, function(x) x[x %in% pv_ids])
### Calculate pseudo-values in each subgroup, just for pv_ids
pv_temp <- lapply(1:length(group_ids), function(x) {
if (length(group_pv_ids[[x]] > 0)){
calc_pv_subgroup(subset_ids = group_ids[[x]], pv_ids = group_pv_ids[[x]])
} else if (length(group_pv_ids[[x]] == 0)){
c()
}
})
}
### Combine into single dataset
pv_temp <- do.call("rbind", pv_temp)
### Add id, and only retain the pseudo-value for the state of interest (that we sorted the data by)
### The pseudo-values for each state are calculated seperately
pv_temp <- pv_temp[, c("id", paste("pstate", state_k, sep = ""))]
### Sort by "id"
pv_temp <- dplyr::arrange(pv_temp, id)
return(pv_temp)
}
### Calculate pseudo-values in each subgroup
pv_out <- lapply(transitions_out, apply_calc_pv_subgroup_pctls)
### Combine into a single dataset
pv_out <- Reduce(function(...) merge(..., by = "id", all.x = TRUE), pv_out)
### Arrange
pv_out <- dplyr::arrange(pv_out, id)
} else if (!is.null(pv_group_vars) & !is.null(pv_n_pctls)) {
###
### 4) Grouping by baseline variables and predicted risk
###
### Again, we must go separate for each state
apply_calc_pv_subgroup_pctls_vars <- function(state_k){
###
### Split data into groups defined by the variables in pv_group_vars, and then predicted risk of transition k
###
### Start by splitting up data by baseline variables
### Create formula to split the dataset by (by pv_group_vars)
split_formula <- stats::as.formula(paste("~ ", paste(pv_group_vars, collapse = "+"), sep = ""))
### Split the dataset into the respective groups
data_groups <- split(data_raw_lmk_js, split_formula)
###
### Split each dataset of data_groups into groups defined by percentile of predicted risk for state k
### Write a function to do this
split_group_by_pctl <- function(data_in){
base::split(data_in,
cut(data_in[,paste("tp_pred", state_k, sep = "")],
breaks = stats::quantile(data_in[,paste("tp_pred", state_k, sep = "")],
seq(0,1,1/pv_n_pctls)),
include.lowest = TRUE))
}
### Apply to each group in data_groups
data_groups_pctls <- lapply(data_groups, split_group_by_pctl)
### Create a single list containing each of these datasets
data_groups_pctls <- unlist(data_groups_pctls, recursive = FALSE)
### Get group ids for subgroups
group_ids <- lapply(data_groups_pctls, function(x) as.numeric(x[,c("id")]))
### For all individuals
if (is.null(pv_ids)){
### Calculate pseudo-values in each subgroup
pv_temp <- lapply(group_ids, calc_pv_subgroup)
### For just individual specified in pv_ids
} else if (!is.null(pv_ids)){
### Identify which pv_ids fit into which subgroup
group_pv_ids <- lapply(group_ids, function(x) x[x %in% pv_ids])
### Calculate pseudo-values in each subgroup, just for pv_ids
pv_temp <- lapply(1:length(group_ids), function(x) {
if (length(group_pv_ids[[x]] > 0)){
calc_pv_subgroup(subset_ids = group_ids[[x]], pv_ids = group_pv_ids[[x]])
} else if (length(group_pv_ids[[x]] == 0)){
c()
}
})
}
### Combine into single dataset
pv_temp <- do.call("rbind", pv_temp)
### Add id, and only retain the pseudo-value for the state of interest (that we sorted the data by)
### The pseudo-values for each state are calculated seperately
pv_temp <- pv_temp[, c("id", paste("pstate", state_k, sep = ""))]
### Sort by "id"
pv_temp <- dplyr::arrange(pv_temp, id)
return(pv_temp)
}
### Calculate pseudo-values in each subgroup
pv_out <- lapply(transitions_out, apply_calc_pv_subgroup_pctls_vars)
### Combine into a single dataset
pv_out <- Reduce(function(...) merge(..., by = "id", all.x = TRUE), pv_out)
### Arrange
pv_out <- dplyr::arrange(pv_out, id)
}
##########################################
### PSEUDO-VALUES HAVE BEEN CALCULATED ###
### STORED IN PV_OUT ###
##########################################
### If pv_ids was specified, we just want to return
### the pseudo-values and nothing else,
### as no point modelling on a subset of the dataset
if (!is.null(pv_ids)){
### Assign column names
colnames(pv_out)[-1] <- paste("pv_state", transitions_out, sep = "")
### Assign output_object
output_object <- pv_out
}
### If pv_ids was not specified, and we have calculated psudo-values for entire cohort,
### generate the observed event probabilities for each state by regressing the calculated pseudo-values
### on the predicted transition probabilities
if (is.null(pv_ids)){
###
### Create object to store output
output_object <- vector("list", length(transitions_out))
names(output_object) <- paste("state", transitions_out, sep = "")
###
### Loop through and generate observed event probabilities
for (state in 1:length(transitions_out)){
### Assign state_k
state_k <- transitions_out[state]
### Calculate observed event probabilities
if (curve_type == "loess"){
obs <- calc_obs_pv_loess_model(pred = data_raw_lmk_js[,paste("tp_pred", state_k, sep = "")],
pv = pv_out[,paste("pstate", state_k, sep = "")],
data_to_plot = data_to_plot[,paste("tp_pred", state_k, sep = "")],
loess_span = loess_span,
loess_degree = loess_degree,
loess_surface = loess_surface,
loess_statistics = loess_statistics,
loess_trace_hat = loess_trace_hat,
loess_cell = loess_cell,
loess_iterations = loess_iterations,
loess_iterTrace = loess_iterTrace,
CI = CI,
CI_type = CI_type)
} else if (curve_type == "rcs"){
obs <- calc_obs_pv_rcs_model(pred = data_raw_lmk_js[,paste("tp_pred", state_k, sep = "")],
pv = pv_out[,paste("pstate", state_k, sep = "")],
data_to_plot = data_to_plot[,paste("tp_pred", state_k, sep = "")],
rcs_nk = rcs_nk,
CI = CI,
CI_type = CI_type)
}
### Create output object
if ("id" %in% colnames(data_to_plot)) {
output_object[[state]] <- data.frame(
"id" = data_to_plot$id,
"pred" = data_to_plot[,paste("tp_pred", state_k, sep = "")],
obs,
"pv" = pv_out[,paste("pstate", state_k, sep = "")])
} else {
output_object[[state]] <- data.frame(
"pred" = data_to_plot[,paste("tp_pred", state_k, sep = "")],
obs,
"pv" = pv_out[,paste("pstate", state_k, sep = "")])
}
}
###
### If boot_format is true, just return the observed event probabilities for the first state
if(boot_format == TRUE){
output_object <- output_object[[1]]$obs
}
### If pseudo-values have been user-inputted, skip the majority of steps and just fit the calibration model using pv_precalc and data_raw
}
} else if (!is.null(pv_precalc)){
###
### Create object to store output
output_object <- vector("list", length(transitions_out))
names(output_object) <- paste("state", transitions_out, sep = "")
###
### Loop through and generate observed event probabilities
for (state in 1:length(transitions_out)){
### Assign state_k
state_k <- transitions_out[state]
### Calculate observed event probabilities
if (curve_type == "loess"){
obs <- calc_obs_pv_loess_model(pred = data_raw[,paste("tp_pred", state_k, sep = "")],
pv = pv_precalc[,paste("pstate", state_k, sep = "")],
data_to_plot = data_to_plot[,paste("tp_pred", state_k, sep = "")],
loess_span = loess_span,
loess_degree = loess_degree,
loess_surface = loess_surface,
loess_statistics = loess_statistics,
loess_trace_hat = loess_trace_hat,
loess_cell = loess_cell,
loess_iterations = loess_iterations,
loess_iterTrace = loess_iterTrace,
CI = CI,
CI_type = CI_type)
} else if (curve_type == "rcs"){
obs <- calc_obs_pv_rcs_model(pred = data_raw[,paste("tp_pred", state_k, sep = "")],
pv = pv_precalc[,paste("pstate", state_k, sep = "")],
data_to_plot = data_to_plot[,paste("tp_pred", state_k, sep = "")],
rcs_nk = rcs_nk,
CI = CI,
CI_type = CI_type)
}
### Create output object
if ("id" %in% colnames(data_to_plot)){
output_object[[state]] <- data.frame(
"id" = data_to_plot$id,
"pred" = data_to_plot[,paste("tp_pred", state_k, sep = "")],
obs,
"pv" = pv_precalc[,paste("pstate", state_k, sep = "")])
} else {
output_object[[state]] <- data.frame(
"pred" = data_to_plot[,paste("tp_pred", state_k, sep = "")],
obs,
"pv" = pv_precalc[,paste("pstate", state_k, sep = "")])
}
}
}
return(output_object)
}
#' Estimate Aalen-Johansen estimator for a cohort of individuals
#'
#' @description
#' Estimates Aalen-Johansen estimator for the transition probabilities in cohort data_ms.
#' Estimates transition probabilities at time t if in state j at time 0
#' The Aalen-Johansen estimator for the entire cohort (including individual person_id_eval)
#' is inputted manually (obs_aj), to speed up computational time if calculating pseudo-values
#' for multiple individuals from the same cohort.
#'
#' Function is called in calibmsm::calc_obs_pv_boot
#'
#' @param data_ms Validation data in `msdata` format
#' @param tmat Transition probability matrix
#' @param t Follow up time at which calibration is to be assessed
#' @param j Landmark state at which predictions were made
#'
#' @noRd
calc_aj <- function(data_ms, tmat, t, j){
### Assign max state number
max_state <- ncol(tmat)
### Fit csh's with no predictors
strata <- survival::strata
csh_aj <- survival::coxph(survival::Surv(Tstart, Tstop, status) ~ strata(trans), data_ms)
### Calculate cumulative incidence functions using the new transition matrix
suppressWarnings(
msfit_aj <- mstate::msfit(csh_aj, trans = tmat)
)
### Calculate Aalen-Johansen estimator
suppressWarnings(
pt_aj <- mstate::probtrans(msfit_aj, predt = 0)
)
### Note that warnings are suppressed at both these stages because user will be warned if there are states which can possibly be moved to, but no individual
### makes this transition, resulting in zero probabilities. For example in our vignette example, this happens when individuals are in
### starting state for 100 days, by definition they can no longer have an adverse event, and mstate gives a warning:
### "In max(x[!is.na(x)]) : no non-missing arguments to max; returning -Inf"
### There are no problems with this, as it just returns a zero probability of being in that state in the next step (mstate::probtrans), which
### A) is correct, and B) we aren't interested in those states anyway
### Extract the closest time in the data to the time we want to evaluate at
t_dat <- pt_aj[[j]]$time[max(which(pt_aj[[j]]$time <= t))]
### Extract AJ estimator at this time point
obs_aj <- pt_aj[[j]][pt_aj[[j]]$time == t_dat, paste("pstate", 1:max_state, sep = "")]
### Extract AJ standard error at this time point
obs_aj_se <- pt_aj[[j]][pt_aj[[j]]$time == t_dat, paste("se", 1:max_state, sep = "")]
### Create output object
output_object <- list("obs_aj" = obs_aj, "obs_aj_se" = obs_aj_se)
return(output_object)
}
#' Estimate pseudo-values for the transition probabilities based on the Aalen-Johansen estimator
#'
#' @description
#' Estimates the pseudo-values for an individual (person_id_eval) from cohort data_ms.
#' Calculates psuedo-values for transition probabilities at time t if in state j at time 0
#' The Aalen-Johansen estimator for the entire cohort (including individual person_id_eval)
#' is inputted manually (obs_aj), to speed up computaitonal time if calculating pseudo-values
#' for multiple individuals from the same cohort.
#'
#' Function is called in calibmsm::calc_obs_pv_boot
#'
#' @param person_id_eval id of individual to calculate the pseudo-value for
#' @param data_ms Validation data in `msdata` format
#' @param obs_aj Aalen-Johansen estimator of the transition probabilities in the entire cohort (not excluding person_id_eval)
#' @param tmat Transition probability matrix
#' @param n_cohort Size of cohort (number of unique entries in data_ms)
#' @param t Follow up time at which calibration is to be assessed
#' @param j Landmark state at which predictions were made
#'
#' @noRd
calc_pv_aj <- function(person_id_eval, data_ms, obs_aj, tmat, n_cohort, t, j){
### Calculate AJ estimate without patient in dataset
est_drop_pat <- calc_aj(subset(data_ms, id != person_id_eval),
tmat = tmat,
t = t,
j = j)
### Retain just the estimate (not the standard error)
est_drop_pat <- est_drop_pat[["obs_aj"]]
### Calculate the pseudo-value
pv_pat <- n_cohort*obs_aj - (n_cohort-1)*est_drop_pat
return(pv_pat)
}
#' Estimate observed event probabilities using pseudo-values and loess smoothers.
#' @description
#' Estimate observed event probabilities for a given input vector of pseudo-values and
#' predicted transition probabilities. This function is called in calibmsm::calc_obs_pv_boot.
#'
#' @returns A vector of observed event probabilities.
#'
#' @noRd
calc_obs_pv_loess_model <- function(pred, pv, data_to_plot,
loess_span,
loess_degree,
loess_surface,
loess_statistics,
loess_trace_hat,
loess_cell,
loess_iterations,
loess_iterTrace,
CI,
CI_type){
### Fit model
if (CI != FALSE){
if (CI_type == "parametric"){
loess_model <- stats::loess(pv ~ pred,
span = loess_span,
degree = loess_degree,
control = stats::loess.control(surface = loess_surface,
statistics = loess_statistics,
trace.hat = loess_trace_hat,
cell = loess_cell,
iterations = loess_iterations,
iterTrace = loess_iterTrace))
}
} else {
### If not requiring standard errors for parametric confidence, let statistics = "none" for computational efficiency
loess_model <- stats::loess(pv ~ pred,
span = loess_span,
degree = loess_degree,
control = stats::loess.control(surface = loess_surface,
statistics = "none",
trace.hat = loess_trace_hat,
cell = loess_cell,
iterations = loess_iterations,
iterTrace = loess_iterTrace))
}
## Calculate predicted observed probabilities (and confidence intervals if requested using parametric approach)
## Note we do not calculate standard errors if confidence interval has been requested using the bootstrap (or if no CI requested)
if (CI != FALSE){
if (CI_type == "parametric"){
## Need to split up individuals into smaller grouped otherwise predict.loess with SE = TRUE will give an
## error, as it will create a matrix that is too large.
## Split data into groups of size 10000
data_to_plot_list <- split(data_to_plot,
rep(1:ceiling(length(data_to_plot)/10000), each = 10000, length.out = length(data_to_plot)))
## Define alpha for CIs
alpha <- (1-CI/100)/2
## Predict observed and create data frame
obs_data <- lapply(1:length(data_to_plot_list),
function(x) {
## Predict observed
obs <- predict(loess_model, newdata = data_to_plot_list[[x]], se = TRUE)
## Put into dataframe
obs_df <- data.frame("obs" = obs$fit,
"obs_lower" = obs$fit - stats::qnorm(1-alpha)*obs$se,
"obs_upper" = obs$fit + stats::qnorm(1-alpha)*obs$se)
## Return
return(obs_df)
})
## Combine into one data frame
obs_data <- do.call("rbind", obs_data)
}
} else {
## Predict observed
obs <- predict(loess_model, newdata = data_to_plot)
## Put into dataframe
obs_data <- data.frame("obs" = obs)
}
### Return obs_data
return(obs_data)
}
#' Estimate observed event probabilities using pseudo-values and restricted cubic splines.
#' @description
#' Estimate observed event probabilities for a given input vector of pseudo-values and
#' predicted transition probabilities. This function is called in calibmsm::calc_obs_pv_boot.
#'
#' @returns A vector of observed event probabilities.
#'
#' @noRd
calc_obs_pv_rcs_model <- function(pred, pv, data_to_plot, rcs_nk, CI, CI_type){
### Start by transforming pred onto logit scale
pred_logit <- log(pred/(1-pred))
### Create spline terms based on predicted risks
rcs_pred <- Hmisc::rcspline.eval(pred_logit, nk=rcs_nk, inclx=T)
colnames(rcs_pred) <- paste("rcs_x", 1:ncol(rcs_pred), sep = "")
knots_pred <- attr(rcs_pred,"knots")
### Create spline terms in data_to_plot (using same knot locations derived from the predicted risks)
### Note that if data_to_plot == pred, these will be the same
### First transform onto logit scale
data_to_plot <- log(data_to_plot/(1 - data_to_plot))
### Create spline terms
rcs_data_to_plot <- data.frame(Hmisc::rcspline.eval(data_to_plot, knots = knots_pred, inclx=T))
colnames(rcs_data_to_plot) <- paste("rcs_x", 1:ncol(rcs_data_to_plot), sep = "")
### Create dataset in which to fit the model
data_rcs <- data.frame("pv" = pv, rcs_pred)
### Define equation
eq_LHS <- paste("pv ~ ", sep = "")
eq_RHS <- paste("rcs_x", 1:ncol(rcs_data_to_plot), sep = "", collapse = "+")
eq_rcs <- stats::formula(paste(eq_LHS, eq_RHS, sep = ""))
## Fit the model using logit link function
rcs_model <- stats::glm(eq_rcs, data = data_rcs, family = stats::gaussian(link = "logit"), start = rep(0, ncol(rcs_pred) + 1))
## Calculate predicted observed probabilities (and confidence intervals if requested using parametric approach)
## Note we do not calculate standard errors if confidence interval has been requested using the bootstrap
if (CI == FALSE){
## Predict observed
obs <- predict(rcs_model, newdata = rcs_data_to_plot, type = "link")
## Put into dataframe
obs_data <- data.frame("obs" = 1/(1+exp(-obs)))
} else if (CI != FALSE){
if (CI_type == "bootstrap"){
## Predict observed
obs <- predict(rcs_model, newdata = rcs_data_to_plot, type = "link")
## Put into data frame
obs_data <- data.frame("obs" = 1/(1+exp(-obs)))
} else if (CI_type == "parametric"){
## Predict observed
obs <- predict(rcs_model, newdata = rcs_data_to_plot, type = "link", se.fit = TRUE)
## Define alpha for CIs
alpha <- (1-CI/100)/2
## Put into dataframe
obs_data <- data.frame("obs" = 1/(1+exp(-obs$fit)),
"obs_lower" = 1/(1+exp(-(obs$fit - stats::qnorm(1-alpha)*obs$se.fit))),
"obs_upper" = 1/(1+exp(-(obs$fit + stats::qnorm(1-alpha)*obs$se.fit)))
)
}
}
### Return obs_data
return(obs_data)
}
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