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R/impute_categorical_covariates_once.R
In ImputeLongiCovs: Longitudinal Imputation of Categorical Variables via a Joint Transition Model
Defines functions
impute_categorical_covariates_once
#' impute_categorical_covariates_once
#'
#' impute_categorical_covariates_once imputes categorical covariates through a joint model that accommodates
#' initial, forward, backward, and intermittent transitions
#'
#' It encloses three different functions. The first deals with the initial and forward transitions, the second
#' with the intemittent and the third with the backward.
#'
#' @param input_data a data frame that contains the variables "state_from", which is the status at the beginning of the transition (say smoker in 2010),
#' "state_to", which is the status at the end of the transition (say ex-smoker in 2011) and "tran_Year", which is an integer that is equal
#' to the number of transitions (say tran_Year = 1, means that the transition from 2010 to 2011, tran_Year = 2, from 2011 to 2012, up to
#' the total number of transitions). Also, "prob_matrix" contains all the transitions ("initial", "forward", "backward", "intermittent") that were
#' calculated with the extract_probMatrix function
#' @param patient_id A character variable that specifies the column name with the unique Id of the patient
#' @param number_of_transitions The number of transitions needed. For example for years 2010, 2011 and 2012 there are 2 transitions.
#' @param covariates_initial The covariates to be used in the initial model
#' @param covariates_transition The covariates to be used in the transition model
#' @param missing_variable_levels The levels of the missing categorical outcome (e.g. "smoker", "ex-smoker", "never-smoker")
#' @param startingyear If the starting year per patient has no missing values, specify it
#' @param without_trans_prob This statement is useful when there are very high proportions of missing data and our initial and transition model cannot converge.
#' It provides the user with two options. One, to "notImpute", namely to return NA and two, to "ImputeEqualProbabilities", i.e., the user
#' can sample with equal probabilities.
#'
#' @importFrom nnet multinom
#' @importFrom stats complete.cases as.formula predict
#' @return a data frame with no missing values in the categorical outcome
#' @noRd
#'
#'
#' @examples
#' impute_categorical_covariates_once(analysis_data,
#' patient_id = "patient_id",
#' number_of_transitions = 2,
#' covariates_initial = c("cardio_state_from", "flu_vaccination_state_from"),
#' covariates_transition = c("cardio_state_to", "Diabetes_state_to", "flu_vaccination_state_to"),
#' missing_variable_levels = c("never-smoker", "ex-smoker", "smoker"),
#' startingyear = startingyear,
#' without_trans_prob = "notImpute")
impute_categorical_covariates_once <- function(input_data,
patient_id,
number_of_transitions,
covariates_initial = NULL,
covariates_transition = NULL,
missing_variable_levels,
startingyear = NULL,
without_trans_prob = c("notImpute", "ImputeEqualProbabilities")){
input_data <- as.data.frame(input_data)
if(!without_trans_prob %in% c("notImpute", "ImputeEqualProbabilities")){
stop("without_trans_prob should take notImpute or ImputeEqualProbabilities values")
}
if(!"state_from" %in% colnames(input_data)){
stop("state_from column does not exist")
}
if(!"state_to" %in% colnames(input_data)){
stop("state_to column does not exist")
}
if(!"tran_Year" %in% colnames(input_data)){
stop("tran_Year column does not exist")
}
if(!is.numeric(input_data$tran_Year) == T){
stop("tran_Year column should be integer")
}
input_data$state_from <- factor(as.character(input_data$state_from), levels = missing_variable_levels)
input_data$state_to <- factor(as.character(input_data$state_to), levels = missing_variable_levels)
unique_values_levels = unique(missing_variable_levels);unique_values_levels
unique_values_state_from = unique(input_data$state_from);unique_values_state_from
unique_values_state_to = unique(input_data$state_to);unique_values_state_to
if(any(unique_values_levels %in% unique_values_state_from == F)){
stop("All levels of missing_variable_levels vector should be present in the state_from column")
}
if(any(unique_values_levels %in% unique_values_state_to == F)){
stop("All levels of missing_variable_levels vector should be present in the state_to column")
}
observed_smoke_transition <- input_data[complete.cases(input_data),]
observed_smoke_initial <- input_data[complete.cases(input_data$state_from),]
draw_sample <- function(x, missing_variable_levels, without_trans_prob){
if (any(is.na(x))){
if (without_trans_prob == "notImpute"){
return(NA)
} else {
sample(missing_variable_levels, 1)
}
} else {
sample(missing_variable_levels, 1, prob = x)
}
}
if (is.null(covariates_initial)){
formulainitial <- as.formula(paste("state_from ~ 1", sep = ""))
} else {
formulainitial <- as.formula(paste("state_from ~ ", paste(covariates_initial, collapse = "+"), sep = ""))
}
if (is.null(covariates_transition)){
formulatransition <- as.formula(paste("state_to ~ state_from", sep = ""))
} else {
formulatransition <- as.formula(paste("state_to ~ state_from + ", paste(covariates_transition, collapse = "+"), sep = ""))
}
modelFittransition <- try(multinom(as.formula(formulatransition), data = observed_smoke_transition, trace = FALSE))
if(is.character(modelFittransition)){
stop("Error: The transition model could not be fitted")
}
modelFitinitial <- try(multinom(as.formula(formulainitial), data = observed_smoke_initial, trace = FALSE))
if(is.character(modelFitinitial)){
stop("Error: The initial model could not be fitted")
}
if (is.null(startingyear)& any(input_data$prob_matrix %in% "initial" == T)){
#### 2.1 initial, forward function ####
initial_forward_function <- function(input_data = input_data,
number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels){
initialProbs <- predict(modelFitinitial, newdata = input_data[which(input_data$prob_matrix == "initial"), covariates_initial],"prob")
check_data <- input_data[which(input_data$prob_matrix == "initial"), covariates_initial]
if (nrow(check_data) > 1){
input_data$state_from[which(input_data$prob_matrix == "initial")] <- apply(initialProbs, 1, draw_sample, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
input_data$prob_matrix[which(input_data$prob_matrix == "initial")] <- "forward"
for (iYear in 1:number_of_transitions){
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from")])
} else {
newdata = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from", covariates_transition)]
}
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- apply(forwardProbabilities, 1, draw_sample, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
}
if (nrow(check_data) == 1){
input_data$state_from[which(input_data$prob_matrix == "initial")] <- draw_sample(initialProbs, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
input_data$prob_matrix[which(input_data$prob_matrix == "initial")] <- "forward"
for (iYear in 1:number_of_transitions){
if (iYear == 1){
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from")])
} else {
newdata = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from", covariates_transition)]
}
if (nrow(newdata) == 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- draw_sample(forwardProbabilities, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
if (nrow(newdata) > 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- apply(forwardProbabilities, 1, draw_sample, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob) #draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
}
if (iYear > 1){
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from")])
} else {
newdata = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from", covariates_transition)]
}
if (nrow(newdata) == 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
if (nrow(newdata) > 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- apply(forwardProbabilities, 1, draw_sample, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob) #draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
}
}
}
return(input_data)
}
check_data <- input_data[which(input_data$prob_matrix == "initial"), covariates_initial]
if (nrow(check_data) == 0){
initial_forward_data <- input_data
} else {
initial_forward_data <- initial_forward_function(input_data = input_data,
number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels)
}
} else {
initial_forward_function <- function(input_data = input_data,
number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels){
for (iYear in 1:number_of_transitions){
if (iYear == 1){
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from")])
} else {
newdata = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from", covariates_transition)]
}
if (nrow(newdata) == 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
if (nrow(newdata) > 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- apply(forwardProbabilities, 1, draw_sample, missing_variable_levels = missing_variable_levels) #draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
}
if (iYear > 1){
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from")])
} else {
newdata = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from", covariates_transition)]
}
if (nrow(newdata) == 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- draw_sample(forwardProbabilities, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
if (nrow(newdata) > 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- apply(forwardProbabilities, 1, draw_sample, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob) #draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
}
}
return(input_data)
}
}
initial_forward_data <- initial_forward_function(input_data = input_data,
number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels)
#### 2.2 intermittent function ####
imputeIntermittent <- function(input_data = input_data,
patient_id = patient_id,
from_state = from_state,
to_state = to_state,
year_missing = year_missing,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels){
# (A1) Create the function extratProb_new, which is amazing (change name "extratProb_new", and also explain why it is amazing)
extratProb_new <- function(diff_scenarios, prob_list){
trans_probs <- c()
trans_probs[1] <- prob_list[[1]][diff_scenarios[1,2]]
trans_probs <- unlist(trans_probs)
for (iROW in 2:length(prob_list)){
trans_probs[iROW] <- prob_list[[iROW]][diff_scenarios[iROW,1],diff_scenarios[iROW,2]]
}
return(prod(trans_probs))
}
# (A2) Need function to calculate all scenarios #
computeIndexTrans <- function(from_state, to_state, year_missing){
allPossibilities <- expand.grid(rep(list(1:length(missing_variable_levels)),year_missing))
finalScenarios <- as.matrix(cbind(rep(from_state, nrow(allPossibilities)), allPossibilities, rep(to_state, nrow(allPossibilities))))
colnames(finalScenarios) <- rownames(finalScenarios) <- NULL
return(finalScenarios)
}
# (A3) Need function to change Word to Numeric function #
changeWord2Num <- function(word2change, missing_variable_levels){
return(which(missing_variable_levels == word2change))
}
## computing the probability of each senario
from_state <- changeWord2Num(from_state, missing_variable_levels)
to_state <- changeWord2Num(to_state, missing_variable_levels)
allScenarios <- computeIndexTrans(from_state, to_state, year_missing)
probs_all_scenarios <- rep(NA, nrow(allScenarios))
prob_list <- list()
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[1, c("state_from")])
} else {
newdata = input_data[1, c("state_from", covariates_transition)]
}
prob_list[[1]] <- predict(modelFittransition, newdata = newdata, "prob")
for (iRow in 2:nrow(input_data)){
data2pred_list <- list()
for (ilevel in 1:length(missing_variable_levels)){
data2pred_list[[ilevel]] <- data.frame(state_from = missing_variable_levels[ilevel], input_data[iRow, covariates_transition])
}
data2pred <- do.call("rbind", data2pred_list)
prob_list[[iRow]] <- predict(modelFittransition, newdata = data2pred, "prob")
}
prob_list
probs_all_scenarios <- c()
for (iRow in 1:nrow(allScenarios)){
tmpScen <- allScenarios[iRow,]
allidx <- cbind(tmpScen[1:(length(tmpScen)-1)], tmpScen[2:length(tmpScen)])
probs_all_scenarios[iRow] <- extratProb_new(allidx, prob_list)
}
normalizedProbs <- probs_all_scenarios/sum(probs_all_scenarios)
imputedScenario <- sample(1:nrow(allScenarios), 1, prob = normalizedProbs)
imp2return <- allScenarios[imputedScenario,]
imp2returnInWords <- rep(NA,length(imp2return))
find_levels = unique(imp2return)
for (iWords in 1:length(find_levels)){
imp2returnInWords[which(imp2return == find_levels[iWords])] <- missing_variable_levels[find_levels[iWords]]
}
## These lines are for making scenarios in words if user is interested
# allScenariosInWords <- allScenarios
# allScenariosInWords[which(allScenarios == 1)] <- missing_variable_levels[1]
# allScenariosInWords[which(allScenarios == 2)] <- missing_variable_levels[2]
# allScenariosInWords[which(allScenarios == 3)] <- missing_variable_levels[3]
# allScenariosInWords[which(allScenarios == 4)] <- missing_variable_levels[4]
# allScenariosInWords[which(allScenarios == 5)] <- missing_variable_levels[5]
# allScenariosInWords[which(allScenarios == 6)] <- missing_variable_levels[6]
# allScenariosInWords[which(allScenarios == 7)] <- missing_variable_levels[7]
# allScenariosInWords[which(allScenarios == 8)] <- missing_variable_levels[8]
# allScenariosInWords[which(allScenarios == 9)] <- missing_variable_levels[9]
# allScenariosInWords[which(allScenarios == 10)] <- missing_variable_levels[10]
# rownames(allScenariosInWords) <- paste("Scenario", 1:nrow(allScenariosInWords))
# names(normalizedProbs) <- paste("Scenario", 1:nrow(allScenariosInWords))
#return(list(scenarios = allScenariosInWords, probs = normalizedProbs, imputedData = imp2returnInWords[-c(1,length(imp2returnInWords))]))
imputedData = imp2returnInWords[-c(1,length(imp2returnInWords))]
for (iRow in 1:nrow(input_data)){
if (is.na(input_data$state_to[iRow] == T)){
input_data$state_to[iRow] <- imputedData[iRow]
}
if (iRow == nrow(input_data)) break
input_data$state_from[iRow+1] <- imputedData[iRow]
}
return(input_data)
}
inter_missing <- initial_forward_data
inter_missing <- inter_missing[inter_missing$prob_matrix == "intermittent",]
if (nrow(inter_missing) > 0){
inter_missing$id_inter <- rep(0, nrow(inter_missing))
inter_missing$id_inter[which(!is.na(inter_missing$state_from))] <- 1
inter_missing$id_inter = cumsum(inter_missing$id_inter)
idx.subj = unique(inter_missing[, patient_id])
bdd.changed_inter = inter_missing
for (i in 1:length(idx.subj)){
input.subj <- bdd.changed_inter[bdd.changed_inter[, patient_id] == idx.subj[i],]
inter_data = imputeIntermittent(input_data = input.subj, patient_id = patient_id, input.subj$state_from[1], input.subj$state_to[nrow(input.subj)], nrow(input.subj)-1,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels)
bdd.changed_inter[bdd.changed_inter[, patient_id] == idx.subj[i],] = inter_data
}
bdd.changed_inter$id_inter <- NULL
initial_forward_data <- initial_forward_data[initial_forward_data$prob_matrix != "intermittent",]
input_data <- rbind(initial_forward_data, bdd.changed_inter)
} else {
input_data <- initial_forward_data
}
#### 2.3 backward function ####
backward_function <- function(input_data = input_data,
patient_id = patient_id,
number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels){
for (iYear in number_of_transitions:1){
# Get initialProbs for each tran_Year starting from the last (i.e. 1st time that backward observation occurred)
initialProbs <- predict(modelFitinitial, newdata = input_data[which(input_data$tran_Year == iYear), covariates_initial], "prob")
# Create pseudo-observations for this patient for each tran_Year
data2pred_list <- list()
for (ilevel in 1:length(missing_variable_levels)){
data2pred_list[[ilevel]] <- data.frame(state_from = missing_variable_levels[ilevel], input_data[which(input_data$tran_Year == iYear), covariates_transition])
}
data2pred <- do.call("rbind", data2pred_list)
# Calculate transitionProbs on those pseudo-data
transitionProbs <- predict(modelFittransition, newdata = data2pred, "prob")
rownames(transitionProbs) <- missing_variable_levels
# Compute joint probabilities as product of (transitionProbs, initialProbs)
jointProbabilities_list <- list()
for (ilevel in 1:length(missing_variable_levels)){
jointProbabilities_list[[ilevel]] <- transitionProbs[ilevel,] * initialProbs[[ilevel]]
}
jointProbabilities <- do.call("rbind", jointProbabilities_list)
# Compute state_to initial probabilities
initialProbsStateTo <- apply(jointProbabilities, 2, sum)
# Compute backward probabilities as product of (transitionProbs, initialProbs)
backwardProbabilities_list <- list()
for (ilevel in 1:length(missing_variable_levels)){
backwardProbabilities_list[[ilevel]] <- jointProbabilities[,ilevel] / initialProbsStateTo[ilevel]
}
backwardProbabilities <- do.call("cbind", backwardProbabilities_list)
colnames(backwardProbabilities) <- missing_variable_levels; backwardProbabilities
status <- input_data$state_to[which(input_data$tran_Year == iYear)]
probs_back = backwardProbabilities[, status]
input_data$state_from[which(input_data$tran_Year == iYear)] <- draw_sample(probs_back, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
input_data$state_to[which(input_data$tran_Year == iYear-1)] <- input_data$state_from[which(input_data$tran_Year == iYear)]
# } else {
# warning(paste("For patient ", patient_id, " equal probabilities were used to generate backward probabilities"), sep = "")
# input_data$state_from[which(input_data$tran_Year == iYear)] <- sample(missing_variable_levels, 1)
# input_data$state_to[which(input_data$tran_Year == iYear-1)] <- input_data$state_from[which(input_data$tran_Year == iYear)]
#
# }
}
return(input_data)
}
back_missing <- initial_forward_data
back_missing <- back_missing[back_missing$prob_matrix == "backward",]
if (nrow(back_missing) > 0){
idx.subj = unique(back_missing[, patient_id])
bdd.changed_back = back_missing
for (i in 1:length(idx.subj)){
input.subj <- bdd.changed_back[bdd.changed_back[, patient_id] == idx.subj[i],]
number_of_transitions <- nrow(input.subj)
back_data = backward_function(input_data = input.subj, patient_id = patient_id, number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels)
bdd.changed_back[bdd.changed_back[, patient_id] == idx.subj[i],] = back_data
}
input_data <- input_data[input_data$prob_matrix != "backward",]
input_data <- rbind(input_data, bdd.changed_back)
input_data <- input_data[order(input_data[, patient_id], input_data$tran_Year),]
} else {
input_data <- input_data
}
return(list(input_data= input_data, modelFittransition= modelFittransition, modelFitinitial = modelFitinitial,
observed_smoke_transition = observed_smoke_transition,
observed_smoke_initial = observed_smoke_initial))
}
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Defines functions impute_categorical_covariates_once
#' impute_categorical_covariates_once
#'
#' impute_categorical_covariates_once imputes categorical covariates through a joint model that accommodates
#' initial, forward, backward, and intermittent transitions
#'
#' It encloses three different functions. The first deals with the initial and forward transitions, the second
#' with the intemittent and the third with the backward.
#'
#' @param input_data a data frame that contains the variables "state_from", which is the status at the beginning of the transition (say smoker in 2010),
#' "state_to", which is the status at the end of the transition (say ex-smoker in 2011) and "tran_Year", which is an integer that is equal
#' to the number of transitions (say tran_Year = 1, means that the transition from 2010 to 2011, tran_Year = 2, from 2011 to 2012, up to
#' the total number of transitions). Also, "prob_matrix" contains all the transitions ("initial", "forward", "backward", "intermittent") that were
#' calculated with the extract_probMatrix function
#' @param patient_id A character variable that specifies the column name with the unique Id of the patient
#' @param number_of_transitions The number of transitions needed. For example for years 2010, 2011 and 2012 there are 2 transitions.
#' @param covariates_initial The covariates to be used in the initial model
#' @param covariates_transition The covariates to be used in the transition model
#' @param missing_variable_levels The levels of the missing categorical outcome (e.g. "smoker", "ex-smoker", "never-smoker")
#' @param startingyear If the starting year per patient has no missing values, specify it
#' @param without_trans_prob This statement is useful when there are very high proportions of missing data and our initial and transition model cannot converge.
#' It provides the user with two options. One, to "notImpute", namely to return NA and two, to "ImputeEqualProbabilities", i.e., the user
#' can sample with equal probabilities.
#'
#' @importFrom nnet multinom
#' @importFrom stats complete.cases as.formula predict
#' @return a data frame with no missing values in the categorical outcome
#' @noRd
#'
#'
#' @examples
#' impute_categorical_covariates_once(analysis_data,
#' patient_id = "patient_id",
#' number_of_transitions = 2,
#' covariates_initial = c("cardio_state_from", "flu_vaccination_state_from"),
#' covariates_transition = c("cardio_state_to", "Diabetes_state_to", "flu_vaccination_state_to"),
#' missing_variable_levels = c("never-smoker", "ex-smoker", "smoker"),
#' startingyear = startingyear,
#' without_trans_prob = "notImpute")
impute_categorical_covariates_once <- function(input_data,
patient_id,
number_of_transitions,
covariates_initial = NULL,
covariates_transition = NULL,
missing_variable_levels,
startingyear = NULL,
without_trans_prob = c("notImpute", "ImputeEqualProbabilities")){
input_data <- as.data.frame(input_data)
if(!without_trans_prob %in% c("notImpute", "ImputeEqualProbabilities")){
stop("without_trans_prob should take notImpute or ImputeEqualProbabilities values")
}
if(!"state_from" %in% colnames(input_data)){
stop("state_from column does not exist")
}
if(!"state_to" %in% colnames(input_data)){
stop("state_to column does not exist")
}
if(!"tran_Year" %in% colnames(input_data)){
stop("tran_Year column does not exist")
}
if(!is.numeric(input_data$tran_Year) == T){
stop("tran_Year column should be integer")
}
input_data$state_from <- factor(as.character(input_data$state_from), levels = missing_variable_levels)
input_data$state_to <- factor(as.character(input_data$state_to), levels = missing_variable_levels)
unique_values_levels = unique(missing_variable_levels);unique_values_levels
unique_values_state_from = unique(input_data$state_from);unique_values_state_from
unique_values_state_to = unique(input_data$state_to);unique_values_state_to
if(any(unique_values_levels %in% unique_values_state_from == F)){
stop("All levels of missing_variable_levels vector should be present in the state_from column")
}
if(any(unique_values_levels %in% unique_values_state_to == F)){
stop("All levels of missing_variable_levels vector should be present in the state_to column")
}
observed_smoke_transition <- input_data[complete.cases(input_data),]
observed_smoke_initial <- input_data[complete.cases(input_data$state_from),]
draw_sample <- function(x, missing_variable_levels, without_trans_prob){
if (any(is.na(x))){
if (without_trans_prob == "notImpute"){
return(NA)
} else {
sample(missing_variable_levels, 1)
}
} else {
sample(missing_variable_levels, 1, prob = x)
}
}
if (is.null(covariates_initial)){
formulainitial <- as.formula(paste("state_from ~ 1", sep = ""))
} else {
formulainitial <- as.formula(paste("state_from ~ ", paste(covariates_initial, collapse = "+"), sep = ""))
}
if (is.null(covariates_transition)){
formulatransition <- as.formula(paste("state_to ~ state_from", sep = ""))
} else {
formulatransition <- as.formula(paste("state_to ~ state_from + ", paste(covariates_transition, collapse = "+"), sep = ""))
}
modelFittransition <- try(multinom(as.formula(formulatransition), data = observed_smoke_transition, trace = FALSE))
if(is.character(modelFittransition)){
stop("Error: The transition model could not be fitted")
}
modelFitinitial <- try(multinom(as.formula(formulainitial), data = observed_smoke_initial, trace = FALSE))
if(is.character(modelFitinitial)){
stop("Error: The initial model could not be fitted")
}
if (is.null(startingyear)& any(input_data$prob_matrix %in% "initial" == T)){
#### 2.1 initial, forward function ####
initial_forward_function <- function(input_data = input_data,
number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels){
initialProbs <- predict(modelFitinitial, newdata = input_data[which(input_data$prob_matrix == "initial"), covariates_initial],"prob")
check_data <- input_data[which(input_data$prob_matrix == "initial"), covariates_initial]
if (nrow(check_data) > 1){
input_data$state_from[which(input_data$prob_matrix == "initial")] <- apply(initialProbs, 1, draw_sample, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
input_data$prob_matrix[which(input_data$prob_matrix == "initial")] <- "forward"
for (iYear in 1:number_of_transitions){
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from")])
} else {
newdata = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from", covariates_transition)]
}
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- apply(forwardProbabilities, 1, draw_sample, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
}
if (nrow(check_data) == 1){
input_data$state_from[which(input_data$prob_matrix == "initial")] <- draw_sample(initialProbs, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
input_data$prob_matrix[which(input_data$prob_matrix == "initial")] <- "forward"
for (iYear in 1:number_of_transitions){
if (iYear == 1){
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from")])
} else {
newdata = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from", covariates_transition)]
}
if (nrow(newdata) == 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- draw_sample(forwardProbabilities, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
if (nrow(newdata) > 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- apply(forwardProbabilities, 1, draw_sample, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob) #draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
}
if (iYear > 1){
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from")])
} else {
newdata = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from", covariates_transition)]
}
if (nrow(newdata) == 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
if (nrow(newdata) > 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- apply(forwardProbabilities, 1, draw_sample, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob) #draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
}
}
}
return(input_data)
}
check_data <- input_data[which(input_data$prob_matrix == "initial"), covariates_initial]
if (nrow(check_data) == 0){
initial_forward_data <- input_data
} else {
initial_forward_data <- initial_forward_function(input_data = input_data,
number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels)
}
} else {
initial_forward_function <- function(input_data = input_data,
number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels){
for (iYear in 1:number_of_transitions){
if (iYear == 1){
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from")])
} else {
newdata = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from", covariates_transition)]
}
if (nrow(newdata) == 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
if (nrow(newdata) > 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- apply(forwardProbabilities, 1, draw_sample, missing_variable_levels = missing_variable_levels) #draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
}
if (iYear > 1){
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from")])
} else {
newdata = input_data[which(input_data$prob_matrix == "forward"& input_data$tran_Year == iYear & is.na(input_data$state_from) == F), c("state_from", covariates_transition)]
}
if (nrow(newdata) == 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- draw_sample(forwardProbabilities, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
if (nrow(newdata) > 1){
forwardProbabilities <- predict(modelFittransition, newdata = newdata, "prob")
input_data$state_to[which(input_data$prob_matrix == "forward" & input_data$tran_Year == iYear & is.na(input_data$state_from) == F)] <- apply(forwardProbabilities, 1, draw_sample, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob) #draw_sample(forwardProbabilities, missing_variable_levels)
if (iYear == nrow(input_data)) break
input_data$state_from[which(input_data$tran_Year == iYear+1)] <- input_data$state_to[which(input_data$tran_Year == iYear)]
}
}
}
return(input_data)
}
}
initial_forward_data <- initial_forward_function(input_data = input_data,
number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels)
#### 2.2 intermittent function ####
imputeIntermittent <- function(input_data = input_data,
patient_id = patient_id,
from_state = from_state,
to_state = to_state,
year_missing = year_missing,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels){
# (A1) Create the function extratProb_new, which is amazing (change name "extratProb_new", and also explain why it is amazing)
extratProb_new <- function(diff_scenarios, prob_list){
trans_probs <- c()
trans_probs[1] <- prob_list[[1]][diff_scenarios[1,2]]
trans_probs <- unlist(trans_probs)
for (iROW in 2:length(prob_list)){
trans_probs[iROW] <- prob_list[[iROW]][diff_scenarios[iROW,1],diff_scenarios[iROW,2]]
}
return(prod(trans_probs))
}
# (A2) Need function to calculate all scenarios #
computeIndexTrans <- function(from_state, to_state, year_missing){
allPossibilities <- expand.grid(rep(list(1:length(missing_variable_levels)),year_missing))
finalScenarios <- as.matrix(cbind(rep(from_state, nrow(allPossibilities)), allPossibilities, rep(to_state, nrow(allPossibilities))))
colnames(finalScenarios) <- rownames(finalScenarios) <- NULL
return(finalScenarios)
}
# (A3) Need function to change Word to Numeric function #
changeWord2Num <- function(word2change, missing_variable_levels){
return(which(missing_variable_levels == word2change))
}
## computing the probability of each senario
from_state <- changeWord2Num(from_state, missing_variable_levels)
to_state <- changeWord2Num(to_state, missing_variable_levels)
allScenarios <- computeIndexTrans(from_state, to_state, year_missing)
probs_all_scenarios <- rep(NA, nrow(allScenarios))
prob_list <- list()
if (is.null(covariates_transition)){
newdata = data.frame(state_from = input_data[1, c("state_from")])
} else {
newdata = input_data[1, c("state_from", covariates_transition)]
}
prob_list[[1]] <- predict(modelFittransition, newdata = newdata, "prob")
for (iRow in 2:nrow(input_data)){
data2pred_list <- list()
for (ilevel in 1:length(missing_variable_levels)){
data2pred_list[[ilevel]] <- data.frame(state_from = missing_variable_levels[ilevel], input_data[iRow, covariates_transition])
}
data2pred <- do.call("rbind", data2pred_list)
prob_list[[iRow]] <- predict(modelFittransition, newdata = data2pred, "prob")
}
prob_list
probs_all_scenarios <- c()
for (iRow in 1:nrow(allScenarios)){
tmpScen <- allScenarios[iRow,]
allidx <- cbind(tmpScen[1:(length(tmpScen)-1)], tmpScen[2:length(tmpScen)])
probs_all_scenarios[iRow] <- extratProb_new(allidx, prob_list)
}
normalizedProbs <- probs_all_scenarios/sum(probs_all_scenarios)
imputedScenario <- sample(1:nrow(allScenarios), 1, prob = normalizedProbs)
imp2return <- allScenarios[imputedScenario,]
imp2returnInWords <- rep(NA,length(imp2return))
find_levels = unique(imp2return)
for (iWords in 1:length(find_levels)){
imp2returnInWords[which(imp2return == find_levels[iWords])] <- missing_variable_levels[find_levels[iWords]]
}
## These lines are for making scenarios in words if user is interested
# allScenariosInWords <- allScenarios
# allScenariosInWords[which(allScenarios == 1)] <- missing_variable_levels[1]
# allScenariosInWords[which(allScenarios == 2)] <- missing_variable_levels[2]
# allScenariosInWords[which(allScenarios == 3)] <- missing_variable_levels[3]
# allScenariosInWords[which(allScenarios == 4)] <- missing_variable_levels[4]
# allScenariosInWords[which(allScenarios == 5)] <- missing_variable_levels[5]
# allScenariosInWords[which(allScenarios == 6)] <- missing_variable_levels[6]
# allScenariosInWords[which(allScenarios == 7)] <- missing_variable_levels[7]
# allScenariosInWords[which(allScenarios == 8)] <- missing_variable_levels[8]
# allScenariosInWords[which(allScenarios == 9)] <- missing_variable_levels[9]
# allScenariosInWords[which(allScenarios == 10)] <- missing_variable_levels[10]
# rownames(allScenariosInWords) <- paste("Scenario", 1:nrow(allScenariosInWords))
# names(normalizedProbs) <- paste("Scenario", 1:nrow(allScenariosInWords))
#return(list(scenarios = allScenariosInWords, probs = normalizedProbs, imputedData = imp2returnInWords[-c(1,length(imp2returnInWords))]))
imputedData = imp2returnInWords[-c(1,length(imp2returnInWords))]
for (iRow in 1:nrow(input_data)){
if (is.na(input_data$state_to[iRow] == T)){
input_data$state_to[iRow] <- imputedData[iRow]
}
if (iRow == nrow(input_data)) break
input_data$state_from[iRow+1] <- imputedData[iRow]
}
return(input_data)
}
inter_missing <- initial_forward_data
inter_missing <- inter_missing[inter_missing$prob_matrix == "intermittent",]
if (nrow(inter_missing) > 0){
inter_missing$id_inter <- rep(0, nrow(inter_missing))
inter_missing$id_inter[which(!is.na(inter_missing$state_from))] <- 1
inter_missing$id_inter = cumsum(inter_missing$id_inter)
idx.subj = unique(inter_missing[, patient_id])
bdd.changed_inter = inter_missing
for (i in 1:length(idx.subj)){
input.subj <- bdd.changed_inter[bdd.changed_inter[, patient_id] == idx.subj[i],]
inter_data = imputeIntermittent(input_data = input.subj, patient_id = patient_id, input.subj$state_from[1], input.subj$state_to[nrow(input.subj)], nrow(input.subj)-1,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels)
bdd.changed_inter[bdd.changed_inter[, patient_id] == idx.subj[i],] = inter_data
}
bdd.changed_inter$id_inter <- NULL
initial_forward_data <- initial_forward_data[initial_forward_data$prob_matrix != "intermittent",]
input_data <- rbind(initial_forward_data, bdd.changed_inter)
} else {
input_data <- initial_forward_data
}
#### 2.3 backward function ####
backward_function <- function(input_data = input_data,
patient_id = patient_id,
number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels){
for (iYear in number_of_transitions:1){
# Get initialProbs for each tran_Year starting from the last (i.e. 1st time that backward observation occurred)
initialProbs <- predict(modelFitinitial, newdata = input_data[which(input_data$tran_Year == iYear), covariates_initial], "prob")
# Create pseudo-observations for this patient for each tran_Year
data2pred_list <- list()
for (ilevel in 1:length(missing_variable_levels)){
data2pred_list[[ilevel]] <- data.frame(state_from = missing_variable_levels[ilevel], input_data[which(input_data$tran_Year == iYear), covariates_transition])
}
data2pred <- do.call("rbind", data2pred_list)
# Calculate transitionProbs on those pseudo-data
transitionProbs <- predict(modelFittransition, newdata = data2pred, "prob")
rownames(transitionProbs) <- missing_variable_levels
# Compute joint probabilities as product of (transitionProbs, initialProbs)
jointProbabilities_list <- list()
for (ilevel in 1:length(missing_variable_levels)){
jointProbabilities_list[[ilevel]] <- transitionProbs[ilevel,] * initialProbs[[ilevel]]
}
jointProbabilities <- do.call("rbind", jointProbabilities_list)
# Compute state_to initial probabilities
initialProbsStateTo <- apply(jointProbabilities, 2, sum)
# Compute backward probabilities as product of (transitionProbs, initialProbs)
backwardProbabilities_list <- list()
for (ilevel in 1:length(missing_variable_levels)){
backwardProbabilities_list[[ilevel]] <- jointProbabilities[,ilevel] / initialProbsStateTo[ilevel]
}
backwardProbabilities <- do.call("cbind", backwardProbabilities_list)
colnames(backwardProbabilities) <- missing_variable_levels; backwardProbabilities
status <- input_data$state_to[which(input_data$tran_Year == iYear)]
probs_back = backwardProbabilities[, status]
input_data$state_from[which(input_data$tran_Year == iYear)] <- draw_sample(probs_back, missing_variable_levels = missing_variable_levels, without_trans_prob = without_trans_prob)
input_data$state_to[which(input_data$tran_Year == iYear-1)] <- input_data$state_from[which(input_data$tran_Year == iYear)]
# } else {
# warning(paste("For patient ", patient_id, " equal probabilities were used to generate backward probabilities"), sep = "")
# input_data$state_from[which(input_data$tran_Year == iYear)] <- sample(missing_variable_levels, 1)
# input_data$state_to[which(input_data$tran_Year == iYear-1)] <- input_data$state_from[which(input_data$tran_Year == iYear)]
#
# }
}
return(input_data)
}
back_missing <- initial_forward_data
back_missing <- back_missing[back_missing$prob_matrix == "backward",]
if (nrow(back_missing) > 0){
idx.subj = unique(back_missing[, patient_id])
bdd.changed_back = back_missing
for (i in 1:length(idx.subj)){
input.subj <- bdd.changed_back[bdd.changed_back[, patient_id] == idx.subj[i],]
number_of_transitions <- nrow(input.subj)
back_data = backward_function(input_data = input.subj, patient_id = patient_id, number_of_transitions = number_of_transitions,
covariates_initial = covariates_initial,
covariates_transition = covariates_transition,
missing_variable_levels = missing_variable_levels)
bdd.changed_back[bdd.changed_back[, patient_id] == idx.subj[i],] = back_data
}
input_data <- input_data[input_data$prob_matrix != "backward",]
input_data <- rbind(input_data, bdd.changed_back)
input_data <- input_data[order(input_data[, patient_id], input_data$tran_Year),]
} else {
input_data <- input_data
}
return(list(input_data= input_data, modelFittransition= modelFittransition, modelFitinitial = modelFitinitial,
observed_smoke_transition = observed_smoke_transition,
observed_smoke_initial = observed_smoke_initial))
}
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