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2021_pba_sim_casestudy2_model.R
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#R file for case study 2
#Probability bound analysis: A novel approach for quantifying parameter uncertainty in decision-analytic modeling and cost-effectiveness analysis
#author: Rowan Iskandar
#model file (used in 2021_pba_sim_casestudy2_analysis)
#based on
#Dong, Hengjin, and Martin Buxton. "Early assessment of the likely cost-effectiveness of a new technology: a Markov model with probabilistic sensitivity analysis of computer-assisted total knee replacement." International Journal of Technology Assessment in Health Care 22.2 (2006): 191-202.
#last updated: 13 August 2021
source("pbox.R") #make sure this file is at the same folder level
discount <- function(t,disc){
weight <- 1/(1+disc/12)^t
return(weight)
}
TKR_model_average <- function(
rr.CAS,
c.CAS,
p.tkr_init.tkr_normal, p.tkr_init.tkr_minor,p.tkr_init.tkr_serious,
p.tkr_normal.tkr_minor, p.tkr_normal.tkr_serious,p.tkr_normal.tkr_normal,
p.tkr_minor.tkr_normal,p.tkr_minor.tkr_serious, p.tkr_minor.revision_simple,p.tkr_minor.other_trt,p.tkr_minor.tkr_minor,
p.tkr_serious.tkr_minor,p.tkr_serious.revision_simple,p.tkr_serious.revision_complex,p.tkr_serious.other_trt,
p.tkr_normal_after_revision.revision_simple,p.tkr_normal_after_revision.revision_complex,p.tkr_normal_after_revision.tkr_normal_after_revision,
p.revision_simple.tkr_minor,p.revision_simple.tkr_serious,p.revision_simple.tkr_normal_after_revision,p.revision_simple.other_trt,
p.revision_complex.tkr_serious,p.revision_complex.tkr_normal_after_revision,
p.other_trt.tkr_minor,p.other_trt.tkr_serious,p.other_trt.tkr_normal_after_revision,p.other_trt.revision_simple,
p.tkr_normal.death,p.tkr_normal_after_revision.death,p.death,
c.tkr,
c.tkr_normal,
c.tkr_minor,
c.tkr_serious,
c.tkr_normal_after_revision,
c.revision_simple,
c.revision_complex,
c.other_trt,
c.death,
u.tkr,
u.tkr_normal,
u.tkr_minor,
u.tkr_serious,
u.tkr_normal_after_revision,
u.revision_simple,
u.revision_complex,
u.other_trt,
disc ,
num.states,
time.horizon,
init,
n,
WTP)
{
#1 tkr_init
#2 tkr_normal
#3 tkr_minor
#4 tkr_serious
#5 tkr_normal_after_revision
#6 revision_simple
#7 revision_complex
#8 other_trt
#9 death
mat.p <- matrix(rep(0,num.states*num.states),nrow=num.states,ncol=num.states)
mat.p.CAS <- matrix(rep(0,num.states*num.states),nrow=num.states,ncol=num.states)
p.tkr_init.tkr_serious.CAS <- (rr.CAS)*p.tkr_init.tkr_serious
p.tkr_normal.tkr_serious.CAS <- (rr.CAS)*p.tkr_normal.tkr_serious
p.tkr_minor.tkr_serious.CAS <- (rr.CAS)*p.tkr_minor.tkr_serious
p.revision_simple.tkr_serious.CAS <- (rr.CAS)*p.revision_simple.tkr_serious
p.revision_complex.tkr_serious.CAS <- (rr.CAS)*p.revision_complex.tkr_serious
p.other_trt.tkr_serious.CAS <- (rr.CAS)*p.other_trt.tkr_serious
mat.p[1,2] <- p.tkr_init.tkr_normal
mat.p[1,3] <- p.tkr_init.tkr_minor
mat.p[1,4] <- p.tkr_init.tkr_serious
mat.p[2,3] <- p.tkr_normal.tkr_minor
mat.p[2,4] <- p.tkr_normal.tkr_serious
mat.p[2,9] <- p.death + p.tkr_normal.death
mat.p[2,2] <- 1-sum(mat.p[2, -c(2)]) #p.tkr_normal.tkr_normal
mat.p[3,2] <- p.tkr_minor.tkr_normal
mat.p[3,4] <- p.tkr_minor.tkr_serious
mat.p[3,6] <- p.tkr_minor.revision_simple
mat.p[3,8] <- p.tkr_minor.other_trt
mat.p[3,9] <- p.death + p.tkr_normal.death
mat.p[3,3] <- 1-sum(mat.p[3, -c(3)]) #p.tkr_minor.tkr_minor
mat.p[4,3] <- p.tkr_serious.tkr_minor
mat.p[4,4] <- p.tkr_serious.other_trt
mat.p[4,6] <- p.tkr_serious.revision_simple
mat.p[4,7] <- p.tkr_serious.revision_complex
# mat.p[4,8] <- rowSums(mat.p[4, -4])
mat.p[4,9] <- p.death + p.tkr_normal.death
mat.p[5,6] <- p.tkr_normal_after_revision.revision_simple
mat.p[5,7] <- p.tkr_normal_after_revision.revision_complex
mat.p[5,9] <- p.death + p.tkr_normal_after_revision.death
mat.p[5,5] <- 1-sum(mat.p[5, -c(5)])
mat.p[6,3] <- p.revision_simple.tkr_minor
mat.p[6,4] <- p.revision_simple.tkr_serious
# mat.p[6,6] <- rowSums(mat.p[6, -6])
mat.p[6,8] <- p.revision_simple.other_trt
mat.p[6,9] <- p.death + p.tkr_normal_after_revision.death
mat.p[6,5] <- 1-sum(mat.p[6, -c(5)])
mat.p[7,4] <- p.revision_complex.tkr_serious
#mat.p[7,7] <- rowSums(mat.p[7, -7])
mat.p[7,9] <- p.death + p.tkr_normal_after_revision.death
mat.p[7,5] <- 1-sum(mat.p[7, -c(5)])
mat.p[8,3] <- p.other_trt.tkr_minor
mat.p[8,4] <- p.other_trt.tkr_serious
mat.p[8,7] <- p.other_trt.revision_simple
#mat.p[8,8] <- p.other_trt.revision_simple
mat.p[8,9] <- p.death + p.tkr_normal.death
mat.p[8,5] <- 1-sum(mat.p[8, -c(5)])
mat.p.CAS[1,4] <- p.tkr_init.tkr_serious.CAS
p.residual <- 1-(p.tkr_init.tkr_serious.CAS+p.tkr_init.tkr_normal+p.tkr_init.tkr_minor)
mat.p.CAS[1,2] <- p.tkr_init.tkr_normal + p.tkr_init.tkr_normal/(p.tkr_init.tkr_normal+p.tkr_init.tkr_minor)*p.residual
mat.p.CAS[1,3] <- p.tkr_init.tkr_minor + p.tkr_init.tkr_minor/(p.tkr_init.tkr_normal+p.tkr_init.tkr_minor)*p.residual
mat.p.CAS[2,3] <- p.tkr_normal.tkr_minor
mat.p.CAS[2,4] <- p.tkr_normal.tkr_serious.CAS
mat.p.CAS[2,9] <- p.death + p.tkr_normal.death
mat.p.CAS[2,2] <- 1-sum(mat.p.CAS[2, -c(2)]) #p.tkr_normal.tkr_normal
mat.p.CAS[3,2] <- p.tkr_minor.tkr_normal
mat.p.CAS[3,4] <- p.tkr_minor.tkr_serious.CAS
mat.p.CAS[3,6] <- p.tkr_minor.revision_simple
mat.p.CAS[3,8] <- p.tkr_minor.other_trt
mat.p.CAS[3,9] <- p.death + p.tkr_normal.death
mat.p.CAS[3,3] <- 1-sum(mat.p.CAS[3, -c(3)]) #p.tkr_minor.tkr_minor
mat.p.CAS[4,3] <- p.tkr_serious.tkr_minor
mat.p.CAS[4,4] <- p.tkr_serious.other_trt
mat.p.CAS[4,6] <- p.tkr_serious.revision_simple
mat.p.CAS[4,7] <- p.tkr_serious.revision_complex
# mat.p.CAS[4,8] <- rowSums(mat.p.CAS[4, -4])
mat.p.CAS[4,9] <- p.death + p.tkr_normal.death
mat.p.CAS[5,6] <- p.tkr_normal_after_revision.revision_simple
mat.p.CAS[5,7] <- p.tkr_normal_after_revision.revision_complex
mat.p.CAS[5,9] <- p.death + p.tkr_normal_after_revision.death
mat.p.CAS[5,5] <- 1-sum(mat.p.CAS[5, -c(5)])
mat.p.CAS[6,3] <- p.revision_simple.tkr_minor
mat.p.CAS[6,4] <- p.revision_simple.tkr_serious.CAS
# mat.p.CAS[6,6] <- rowSums(mat.p.CAS[6, -6])
mat.p.CAS[6,8] <- p.revision_simple.other_trt
mat.p.CAS[6,9] <- p.death + p.tkr_normal_after_revision.death
mat.p.CAS[6,5] <- 1-sum(mat.p.CAS[6, -c(5)])
mat.p.CAS[7,4] <- p.revision_complex.tkr_serious.CAS
#mat.p.CAS[7,7] <- rowSums(mat.p.CAS[7, -7])
mat.p.CAS[7,9] <- p.death + p.tkr_normal_after_revision.death
mat.p.CAS[7,5] <- 1-sum(mat.p.CAS[7,-c(5)])
mat.p.CAS[8,3] <- p.other_trt.tkr_minor
mat.p.CAS[8,4] <- p.other_trt.tkr_serious.CAS
mat.p.CAS[8,7] <- p.other_trt.revision_simple
#mat.p.CAS[8,8] <- p.other_trt.revision_simple
mat.p.CAS[8,9] <- p.death + p.tkr_normal.death
mat.p.CAS[8,5] <- 1-sum(mat.p.CAS[8, -c(5)])
#check matrix - rowsum == 1
mat <- rowSums(mat.p.CAS)
print(mat)
#utilities
utility <- c(u.tkr,
u.tkr_normal,
u.tkr_minor,
u.tkr_serious,
u.tkr_normal_after_revision,
u.revision_simple,
u.revision_complex,
u.other_trt,
0)
utility <- as.matrix(utility)
utility <-t(matrix(rep(utility,time.horizon+1),nrow=num.states,ncol=time.horizon+1))
cost <- c(c.tkr,
c.tkr_normal,
c.tkr_minor,
c.tkr_serious,
c.tkr_normal_after_revision,
c.revision_simple,
c.revision_complex,
c.other_trt,
c.death)
cost <- as.matrix(cost)
cost <-t(matrix(rep(cost,time.horizon+1),nrow=num.states,ncol=time.horizon+1))
cost.CAS <- c(c.tkr+c.CAS,
c.tkr_normal,
c.tkr_minor,
c.tkr_serious,
c.tkr_normal_after_revision,
c.revision_simple+c.CAS,
c.revision_complex+c.CAS,
c.other_trt,
c.death)
cost.CAS <- as.matrix(cost.CAS)
cost.CAS <-t(matrix(rep(cost.CAS,time.horizon+1),nrow=num.states,ncol=time.horizon+1))
#discount weight
disc.weight <- lapply(c(0:time.horizon),discount,disc=disc)
disc.weight <- as.matrix(unlist(disc.weight))
disc.weight <-matrix(rep(disc.weight,num.states),nrow=time.horizon+1,ncol=num.states)
#running
cohort <- matrix(rep(NA,num.states*(time.horizon+1)),nrow=time.horizon+1, ncol=num.states)
cohort.CAS <- matrix(rep(NA,num.states*(time.horizon+1)),nrow=time.horizon+1, ncol=num.states)
cohort[1,] <- init
cohort.CAS[1,] <- init
for(i in 2:(time.horizon+1)){
cohort[i,] <-cohort[i-1,]%*%mat.p
cohort.CAS[i,] <- cohort.CAS[i-1,]%*%mat.p.CAS
}
#calculate QoI
LE <- sum(cohort[,1:8])/n
mean.QALY <- sum((cohort*utility)*disc.weight)/n
mean.cost <- sum((cohort*cost)*disc.weight)/n
# QALY <- cohort%*%utility*disc.weight
# cost <- cohort%*%cost*disc.weight
QALY <- cohort*utility*disc.weight
cost <- cohort*cost*disc.weight
minor <- cohort[,3]
serious <- cohort[,4]
simple <- cohort[,6]
complex <- cohort[,7]
death <- cohort[,9]
LE.CAS <- sum(cohort.CAS[,1:8])/n
mean.QALY.CAS <- sum((cohort.CAS*utility)*disc.weight)/n
QALY.CAS <- (cohort.CAS*utility)*disc.weight
mean.cost.CAS <- sum((cohort.CAS*cost.CAS)*disc.weight)/n
QALY.CAS <- cohort.CAS*utility*disc.weight
cost.CAS <- cohort.CAS*cost.CAS*disc.weight
minor.CAS <- cohort.CAS[,3]
serious.CAS <- cohort.CAS[,4]
simple.CAS <- cohort.CAS[,6]
complex.CAS <- cohort.CAS[,7]
death.CAS <- cohort.CAS[,9]
NMB <- mean.QALY*WTP - mean.cost
NMB.CAS <- mean.QALY.CAS*WTP - mean.cost.CAS
INMB <- NMB.CAS-NMB
# if(objective.index==1){
# return(INMB)
# }
# else{
# return(-INMB)
# }
output <- list(INMB, LE, cost, mean.cost, QALY, mean.QALY, LE.CAS, cost.CAS, mean.cost.CAS, QALY.CAS, mean.QALY.CAS,
minor, serious, simple, complex, minor.CAS, serious.CAS, simple.CAS, complex.CAS,death,death.CAS, QALY, QALY.CAS)
return(output)
}
# p.tkr_minor.tkr_serious
# p.tkr_serious.tkr_minor
# p.revision_simple.other_trt
# p.other_trt.tkr_minor
# p.other_trt.tkr_serious
# p.other_trt.revision_simple
TKR_model <- function(list_params,
objective.index,
#rr.CAS,
c.CAS,
p.tkr_init.tkr_normal, p.tkr_init.tkr_minor,p.tkr_init.tkr_serious,
p.tkr_normal.tkr_minor, p.tkr_normal.tkr_serious,p.tkr_normal.tkr_normal,
p.tkr_minor.tkr_normal,
#p.tkr_minor.tkr_serious,
p.tkr_minor.revision_simple,p.tkr_minor.other_trt,p.tkr_minor.tkr_minor,
#p.tkr_serious.tkr_minor,
p.tkr_serious.revision_simple,p.tkr_serious.revision_complex,p.tkr_serious.other_trt,
p.tkr_normal_after_revision.revision_simple,p.tkr_normal_after_revision.revision_complex,p.tkr_normal_after_revision.tkr_normal_after_revision,
p.revision_simple.tkr_minor,p.revision_simple.tkr_serious,p.revision_simple.tkr_normal_after_revision,
#p.revision_simple.other_trt,
p.revision_complex.tkr_serious,p.revision_complex.tkr_normal_after_revision,
#p.other_trt.tkr_minor,p.other_trt.tkr_serious,
p.other_trt.tkr_normal_after_revision,
#p.other_trt.revision_simple,
p.tkr_normal.death,p.tkr_normal_after_revision.death,p.death,
c.tkr,
c.tkr_normal,
c.tkr_minor,
c.tkr_serious,
c.tkr_normal_after_revision,
c.revision_simple,
c.revision_complex,
c.other_trt,
c.death,
u.tkr,
u.tkr_normal,
u.tkr_minor,
u.tkr_serious,
u.tkr_normal_after_revision,
u.revision_simple,
u.revision_complex,
u.other_trt,
disc ,
num.states,
time.horizon,
init,
n,
WTP)
{
#1 tkr_init
#2 tkr_normal
#3 tkr_minor
#4 tkr_serious
#5 tkr_normal_after_revision
#6 revision_simple
#7 revision_complex
#8 other_trt
#9 death
rr.CAS <- list_params[1]
p.tkr_minor.tkr_serious <- list_params[2]
p.tkr_serious.tkr_minor <- list_params[3]
p.revision_simple.other_trt <- list_params[4]
p.other_trt.tkr_minor <- list_params[5]
p.other_trt.tkr_serious <- list_params[6]
p.other_trt.revision_simple <- list_params[7]
# print("---------")
# print("---------")
# print(rr.CAS)
# print("---------")
# print(p.tkr_init.tkr_serious)
# print("---------")
mat.p <- matrix(rep(0,num.states*num.states),nrow=num.states,ncol=num.states)
mat.p.CAS <- matrix(rep(0,num.states*num.states),nrow=num.states,ncol=num.states)
p.tkr_init.tkr_serious.CAS <- (1-rr.CAS)*p.tkr_init.tkr_serious
p.tkr_normal.tkr_serious.CAS <- (1-rr.CAS)*p.tkr_normal.tkr_serious
p.tkr_minor.tkr_serious.CAS <- (1-rr.CAS)*p.tkr_minor.tkr_serious
p.revision_simple.tkr_serious.CAS <- (1-rr.CAS)*p.revision_simple.tkr_serious
p.revision_complex.tkr_serious.CAS <- (1-rr.CAS)*p.revision_complex.tkr_serious
p.other_trt.tkr_serious.CAS <- (1-rr.CAS)*p.other_trt.tkr_serious
mat.p[1,2] <- p.tkr_init.tkr_normal
mat.p[1,3] <- p.tkr_init.tkr_minor
mat.p[1,4] <- p.tkr_init.tkr_serious
mat.p[2,3] <- p.tkr_normal.tkr_minor
mat.p[2,4] <- p.tkr_normal.tkr_serious
mat.p[2,9] <- p.death + p.tkr_normal.death
mat.p[2,2] <- 1-sum(mat.p[2, -c(2)]) #p.tkr_normal.tkr_normal
mat.p[3,2] <- p.tkr_minor.tkr_normal
mat.p[3,4] <- p.tkr_minor.tkr_serious
mat.p[3,6] <- p.tkr_minor.revision_simple
mat.p[3,8] <- p.tkr_minor.other_trt
mat.p[3,9] <- p.death + p.tkr_normal.death
mat.p[3,3] <- 1-sum(mat.p[3, -c(3)]) #p.tkr_minor.tkr_minor
mat.p[4,3] <- p.tkr_serious.tkr_minor
mat.p[4,4] <- p.tkr_serious.other_trt
mat.p[4,6] <- p.tkr_serious.revision_simple
mat.p[4,7] <- p.tkr_serious.revision_complex
# mat.p[4,8] <- rowSums(mat.p[4, -4])
mat.p[4,9] <- p.death + p.tkr_normal.death
mat.p[5,6] <- p.tkr_normal_after_revision.revision_simple
mat.p[5,7] <- p.tkr_normal_after_revision.revision_complex
mat.p[5,9] <- p.death + p.tkr_normal_after_revision.death
mat.p[5,5] <- 1-sum(mat.p[5, -c(5)])
mat.p[6,3] <- p.revision_simple.tkr_minor
mat.p[6,4] <- p.revision_simple.tkr_serious
# mat.p[6,6] <- rowSums(mat.p[6, -6])
mat.p[6,8] <- p.revision_simple.other_trt
mat.p[6,9] <- p.death + p.tkr_normal_after_revision.death
mat.p[6,5] <- 1-sum(mat.p[6, -c(5)])
mat.p[7,4] <- p.revision_complex.tkr_serious
#mat.p[7,7] <- rowSums(mat.p[7, -7])
mat.p[7,9] <- p.death + p.tkr_normal_after_revision.death
mat.p[7,5] <- 1-sum(mat.p[7, -c(5)])
mat.p[8,3] <- p.other_trt.tkr_minor
mat.p[8,4] <- p.other_trt.tkr_serious
mat.p[8,7] <- p.other_trt.revision_simple
#mat.p[8,8] <- p.other_trt.revision_simple
mat.p[8,9] <- p.death + p.tkr_normal.death
mat.p[8,5] <- 1-sum(mat.p[8, -c(5)])
mat.p.CAS[1,4] <- p.tkr_init.tkr_serious.CAS
p.residual <- 1-(p.tkr_init.tkr_serious.CAS+p.tkr_init.tkr_normal+p.tkr_init.tkr_minor)
mat.p.CAS[1,2] <- p.tkr_init.tkr_normal + p.tkr_init.tkr_normal/(p.tkr_init.tkr_normal+p.tkr_init.tkr_minor)*p.residual
mat.p.CAS[1,3] <- p.tkr_init.tkr_minor + p.tkr_init.tkr_minor/(p.tkr_init.tkr_normal+p.tkr_init.tkr_minor)*p.residual
mat.p.CAS[2,3] <- p.tkr_normal.tkr_minor
mat.p.CAS[2,4] <- p.tkr_normal.tkr_serious.CAS
mat.p.CAS[2,9] <- p.death + p.tkr_normal.death
mat.p.CAS[2,2] <- 1-sum(mat.p.CAS[2, -c(2)]) #p.tkr_normal.tkr_normal
mat.p.CAS[3,2] <- p.tkr_minor.tkr_normal
mat.p.CAS[3,4] <- p.tkr_minor.tkr_serious.CAS
mat.p.CAS[3,6] <- p.tkr_minor.revision_simple
mat.p.CAS[3,8] <- p.tkr_minor.other_trt
mat.p.CAS[3,9] <- p.death + p.tkr_normal.death
mat.p.CAS[3,3] <- 1-sum(mat.p.CAS[3, -c(3)]) #p.tkr_minor.tkr_minor
mat.p.CAS[4,3] <- p.tkr_serious.tkr_minor
mat.p.CAS[4,4] <- p.tkr_serious.other_trt
mat.p.CAS[4,6] <- p.tkr_serious.revision_simple
mat.p.CAS[4,7] <- p.tkr_serious.revision_complex
# mat.p.CAS[4,8] <- rowSums(mat.p.CAS[4, -4])
mat.p.CAS[4,9] <- p.death + p.tkr_normal.death
mat.p.CAS[5,6] <- p.tkr_normal_after_revision.revision_simple
mat.p.CAS[5,7] <- p.tkr_normal_after_revision.revision_complex
mat.p.CAS[5,9] <- p.death + p.tkr_normal_after_revision.death
mat.p.CAS[5,5] <- 1-sum(mat.p.CAS[5, -c(5)])
mat.p.CAS[6,3] <- p.revision_simple.tkr_minor
mat.p.CAS[6,4] <- p.revision_simple.tkr_serious.CAS
# mat.p.CAS[6,6] <- rowSums(mat.p.CAS[6, -6])
mat.p.CAS[6,8] <- p.revision_simple.other_trt
mat.p.CAS[6,9] <- p.death + p.tkr_normal_after_revision.death
mat.p.CAS[6,5] <- 1-sum(mat.p.CAS[6, -c(5)])
mat.p.CAS[7,4] <- p.revision_complex.tkr_serious.CAS
#mat.p.CAS[7,7] <- rowSums(mat.p.CAS[7, -7])
mat.p.CAS[7,9] <- p.death + p.tkr_normal_after_revision.death
mat.p.CAS[7,5] <- 1-sum(mat.p.CAS[7,-c(5)])
mat.p.CAS[8,3] <- p.other_trt.tkr_minor
mat.p.CAS[8,4] <- p.other_trt.tkr_serious.CAS
mat.p.CAS[8,7] <- p.other_trt.revision_simple
#mat.p.CAS[8,8] <- p.other_trt.revision_simple
mat.p.CAS[8,9] <- p.death + p.tkr_normal.death
mat.p.CAS[8,5] <- 1-sum(mat.p.CAS[8, -c(5)])
#check matrix - rowsum == 1
# mat <- rowSums(mat.p.CAS)
# print(mat)
#
#
#utilities
utility <- c(u.tkr,
u.tkr_normal,
u.tkr_minor,
u.tkr_serious,
u.tkr_normal_after_revision,
u.revision_simple,
u.revision_complex,
u.other_trt,
0)
utility <- as.matrix(utility)
utility <-t(matrix(rep(utility,time.horizon+1),nrow=num.states,ncol=time.horizon+1))
cost <- c(c.tkr,
c.tkr_normal,
c.tkr_minor,
c.tkr_serious,
c.tkr_normal_after_revision,
c.revision_simple,
c.revision_complex,
c.other_trt,
c.death)
cost <- as.matrix(cost)
cost <-t(matrix(rep(cost,time.horizon+1),nrow=num.states,ncol=time.horizon+1))
cost.CAS <- c(c.tkr+c.CAS,
c.tkr_normal,
c.tkr_minor,
c.tkr_serious,
c.tkr_normal_after_revision,
c.revision_simple+c.CAS,
c.revision_complex+c.CAS,
c.other_trt,
c.death)
cost.CAS <- as.matrix(cost.CAS)
cost.CAS <-t(matrix(rep(cost.CAS,time.horizon+1),nrow=num.states,ncol=time.horizon+1))
#discount weight
disc.weight <- lapply(c(0:time.horizon),discount,disc=disc)
disc.weight <- as.matrix(unlist(disc.weight))
disc.weight <-matrix(rep(disc.weight,num.states),nrow=time.horizon+1,ncol=num.states)
#running
cohort <- matrix(rep(NA,num.states*(time.horizon+1)),nrow=time.horizon+1, ncol=num.states)
cohort.CAS <- matrix(rep(NA,num.states*(time.horizon+1)),nrow=time.horizon+1, ncol=num.states)
cohort[1,] <- init
cohort.CAS[1,] <- init
for(i in 2:(time.horizon+1)){
cohort[i,] <-cohort[i-1,]%*%mat.p
cohort.CAS[i,] <- cohort.CAS[i-1,]%*%mat.p.CAS
}
#calculate QoI
LE <- sum(cohort[,1:8])/n
mean.QALY <- sum((cohort*utility)*disc.weight)/n
mean.cost <- sum((cohort*cost)*disc.weight)/n
# QALY <- cohort%*%utility*disc.weight
# cost <- cohort%*%cost*disc.weight
QALY <- cohort*utility*disc.weight
cost <- cohort*cost*disc.weight
LE.CAS <- sum(cohort.CAS[,1:8])/n
mean.QALY.CAS <- sum((cohort.CAS*utility)*disc.weight)/n
mean.cost.CAS <- sum((cohort.CAS*cost.CAS)*disc.weight)/n
QALY.CAS <- cohort.CAS*utility*disc.weight
cost.CAS <- cohort.CAS*cost.CAS*disc.weight
NMB <- mean.QALY*WTP - mean.cost
NMB.CAS <- mean.QALY.CAS*WTP - mean.cost.CAS
INMB <- NMB.CAS-NMB
if(objective.index==1){
return(INMB)
}
else{
return(-INMB)
}
# output <- list(INMB, LE, cost, mean.cost, QALY, mean.QALY, LE.CAS, cost.CAS, mean.cost.CAS, QALY.CAS, mean.QALY.CAS)
# print(cost)
# return(output)
}
TKR_model_MC <- function(list_params,
#objective.index,
#rr.CAS,
c.CAS,
p.tkr_init.tkr_normal, p.tkr_init.tkr_minor,p.tkr_init.tkr_serious,
p.tkr_normal.tkr_minor, p.tkr_normal.tkr_serious,p.tkr_normal.tkr_normal,
p.tkr_minor.tkr_normal,
#p.tkr_minor.tkr_serious,
p.tkr_minor.revision_simple,p.tkr_minor.other_trt,p.tkr_minor.tkr_minor,
#p.tkr_serious.tkr_minor,
p.tkr_serious.revision_simple,p.tkr_serious.revision_complex,p.tkr_serious.other_trt,
p.tkr_normal_after_revision.revision_simple,p.tkr_normal_after_revision.revision_complex,p.tkr_normal_after_revision.tkr_normal_after_revision,
p.revision_simple.tkr_minor,p.revision_simple.tkr_serious,p.revision_simple.tkr_normal_after_revision,
#p.revision_simple.other_trt,
p.revision_complex.tkr_serious,p.revision_complex.tkr_normal_after_revision,
#p.other_trt.tkr_minor,p.other_trt.tkr_serious,
p.other_trt.tkr_normal_after_revision,
#p.other_trt.revision_simple,
p.tkr_normal.death,p.tkr_normal_after_revision.death,p.death,
c.tkr,
c.tkr_normal,
c.tkr_minor,
c.tkr_serious,
c.tkr_normal_after_revision,
c.revision_simple,
c.revision_complex,
c.other_trt,
c.death,
u.tkr,
u.tkr_normal,
u.tkr_minor,
u.tkr_serious,
u.tkr_normal_after_revision,
u.revision_simple,
u.revision_complex,
u.other_trt,
disc ,
num.states,
time.horizon,
init,
n,
WTP)
{
#1 tkr_init
#2 tkr_normal
#3 tkr_minor
#4 tkr_serious
#5 tkr_normal_after_revision
#6 revision_simple
#7 revision_complex
#8 other_trt
#9 death
rr.CAS <- list_params[[1]]
p.tkr_minor.tkr_serious <- list_params[[2]]
p.tkr_serious.tkr_minor <- list_params[[3]]
p.revision_simple.other_trt <- list_params[[4]]
p.other_trt.tkr_minor <- list_params[[5]]
p.other_trt.tkr_serious <- list_params[[6]]
p.other_trt.revision_simple <- list_params[[7]]
mat.p <- matrix(rep(0,num.states*num.states),nrow=num.states,ncol=num.states)
mat.p.CAS <- matrix(rep(0,num.states*num.states),nrow=num.states,ncol=num.states)
p.tkr_init.tkr_serious.CAS <- (1-rr.CAS)*p.tkr_init.tkr_serious
p.tkr_normal.tkr_serious.CAS <- (1-rr.CAS)*p.tkr_normal.tkr_serious
p.tkr_minor.tkr_serious.CAS <- (1-rr.CAS)*p.tkr_minor.tkr_serious
p.revision_simple.tkr_serious.CAS <- (1-rr.CAS)*p.revision_simple.tkr_serious
p.revision_complex.tkr_serious.CAS <- (1-rr.CAS)*p.revision_complex.tkr_serious
p.other_trt.tkr_serious.CAS <- (1-rr.CAS)*p.other_trt.tkr_serious
mat.p[1,2] <- p.tkr_init.tkr_normal
mat.p[1,3] <- p.tkr_init.tkr_minor
mat.p[1,4] <- p.tkr_init.tkr_serious
mat.p[2,3] <- p.tkr_normal.tkr_minor
mat.p[2,4] <- p.tkr_normal.tkr_serious
mat.p[2,9] <- p.death + p.tkr_normal.death
mat.p[2,2] <- 1-sum(mat.p[2, -c(2)]) #p.tkr_normal.tkr_normal
mat.p[3,2] <- p.tkr_minor.tkr_normal
mat.p[3,4] <- p.tkr_minor.tkr_serious
mat.p[3,6] <- p.tkr_minor.revision_simple
mat.p[3,8] <- p.tkr_minor.other_trt
mat.p[3,9] <- p.death + p.tkr_normal.death
mat.p[3,3] <- 1-sum(mat.p[3, -c(3)]) #p.tkr_minor.tkr_minor
mat.p[4,3] <- p.tkr_serious.tkr_minor
mat.p[4,4] <- p.tkr_serious.other_trt
mat.p[4,6] <- p.tkr_serious.revision_simple
mat.p[4,7] <- p.tkr_serious.revision_complex
# mat.p[4,8] <- rowSums(mat.p[4, -4])
mat.p[4,9] <- p.death + p.tkr_normal.death
mat.p[5,6] <- p.tkr_normal_after_revision.revision_simple
mat.p[5,7] <- p.tkr_normal_after_revision.revision_complex
mat.p[5,9] <- p.death + p.tkr_normal_after_revision.death
mat.p[5,5] <- 1-sum(mat.p[5, -c(5)])
mat.p[6,3] <- p.revision_simple.tkr_minor
mat.p[6,4] <- p.revision_simple.tkr_serious
# mat.p[6,6] <- rowSums(mat.p[6, -6])
mat.p[6,8] <- p.revision_simple.other_trt
mat.p[6,9] <- p.death + p.tkr_normal_after_revision.death
mat.p[6,5] <- 1-sum(mat.p[6, -c(5)])
mat.p[7,4] <- p.revision_complex.tkr_serious
#mat.p[7,7] <- rowSums(mat.p[7, -7])
mat.p[7,9] <- p.death + p.tkr_normal_after_revision.death
mat.p[7,5] <- 1-sum(mat.p[7, -c(5)])
mat.p[8,3] <- p.other_trt.tkr_minor
mat.p[8,4] <- p.other_trt.tkr_serious
mat.p[8,7] <- p.other_trt.revision_simple
#mat.p[8,8] <- p.other_trt.revision_simple
mat.p[8,9] <- p.death + p.tkr_normal.death
mat.p[8,5] <- 1-sum(mat.p[8, -c(5)])
mat.p.CAS[1,4] <- p.tkr_init.tkr_serious.CAS
p.residual <- 1-(p.tkr_init.tkr_serious.CAS+p.tkr_init.tkr_normal+p.tkr_init.tkr_minor)
mat.p.CAS[1,2] <- p.tkr_init.tkr_normal + p.tkr_init.tkr_normal/(p.tkr_init.tkr_normal+p.tkr_init.tkr_minor)*p.residual
mat.p.CAS[1,3] <- p.tkr_init.tkr_minor + p.tkr_init.tkr_minor/(p.tkr_init.tkr_normal+p.tkr_init.tkr_minor)*p.residual
mat.p.CAS[2,3] <- p.tkr_normal.tkr_minor
mat.p.CAS[2,4] <- p.tkr_normal.tkr_serious.CAS
mat.p.CAS[2,9] <- p.death + p.tkr_normal.death
mat.p.CAS[2,2] <- 1-sum(mat.p.CAS[2, -c(2)]) #p.tkr_normal.tkr_normal
mat.p.CAS[3,2] <- p.tkr_minor.tkr_normal
mat.p.CAS[3,4] <- p.tkr_minor.tkr_serious.CAS
mat.p.CAS[3,6] <- p.tkr_minor.revision_simple
mat.p.CAS[3,8] <- p.tkr_minor.other_trt
mat.p.CAS[3,9] <- p.death + p.tkr_normal.death
mat.p.CAS[3,3] <- 1-sum(mat.p.CAS[3, -c(3)]) #p.tkr_minor.tkr_minor
mat.p.CAS[4,3] <- p.tkr_serious.tkr_minor
mat.p.CAS[4,4] <- p.tkr_serious.other_trt
mat.p.CAS[4,6] <- p.tkr_serious.revision_simple
mat.p.CAS[4,7] <- p.tkr_serious.revision_complex
# mat.p.CAS[4,8] <- rowSums(mat.p.CAS[4, -4])
mat.p.CAS[4,9] <- p.death + p.tkr_normal.death
mat.p.CAS[5,6] <- p.tkr_normal_after_revision.revision_simple
mat.p.CAS[5,7] <- p.tkr_normal_after_revision.revision_complex
mat.p.CAS[5,9] <- p.death + p.tkr_normal_after_revision.death
mat.p.CAS[5,5] <- 1-sum(mat.p.CAS[5, -c(5)])
mat.p.CAS[6,3] <- p.revision_simple.tkr_minor
mat.p.CAS[6,4] <- p.revision_simple.tkr_serious.CAS
# mat.p.CAS[6,6] <- rowSums(mat.p.CAS[6, -6])
mat.p.CAS[6,8] <- p.revision_simple.other_trt
mat.p.CAS[6,9] <- p.death + p.tkr_normal_after_revision.death
mat.p.CAS[6,5] <- 1-sum(mat.p.CAS[6, -c(5)])
mat.p.CAS[7,4] <- p.revision_complex.tkr_serious.CAS
#mat.p.CAS[7,7] <- rowSums(mat.p.CAS[7, -7])
mat.p.CAS[7,9] <- p.death + p.tkr_normal_after_revision.death
mat.p.CAS[7,5] <- 1-sum(mat.p.CAS[7,-c(5)])
mat.p.CAS[8,3] <- p.other_trt.tkr_minor
mat.p.CAS[8,4] <- p.other_trt.tkr_serious.CAS
mat.p.CAS[8,7] <- p.other_trt.revision_simple
#mat.p.CAS[8,8] <- p.other_trt.revision_simple
mat.p.CAS[8,9] <- p.death + p.tkr_normal.death
mat.p.CAS[8,5] <- 1-sum(mat.p.CAS[8, -c(5)])
#check matrix - rowsum == 1
# mat <- rowSums(mat.p.CAS)
# print(mat)
#
#
#utilities
utility <- c(u.tkr,
u.tkr_normal,
u.tkr_minor,
u.tkr_serious,
u.tkr_normal_after_revision,
u.revision_simple,
u.revision_complex,
u.other_trt,
0)
utility <- as.matrix(utility)
utility <-t(matrix(rep(utility,time.horizon+1),nrow=num.states,ncol=time.horizon+1))
cost <- c(c.tkr,
c.tkr_normal,
c.tkr_minor,
c.tkr_serious,
c.tkr_normal_after_revision,
c.revision_simple,
c.revision_complex,
c.other_trt,
c.death)
cost <- as.matrix(cost)
cost <-t(matrix(rep(cost,time.horizon+1),nrow=num.states,ncol=time.horizon+1))
cost.CAS <- c(c.tkr+c.CAS,
c.tkr_normal,
c.tkr_minor,
c.tkr_serious,
c.tkr_normal_after_revision,
c.revision_simple+c.CAS,
c.revision_complex+c.CAS,
c.other_trt,
c.death)
cost.CAS <- as.matrix(cost.CAS)
cost.CAS <-t(matrix(rep(cost.CAS,time.horizon+1),nrow=num.states,ncol=time.horizon+1))
#discount weight
disc.weight <- lapply(c(0:time.horizon),discount,disc=disc)
disc.weight <- as.matrix(unlist(disc.weight))
disc.weight <-matrix(rep(disc.weight,num.states),nrow=time.horizon+1,ncol=num.states)
#running
cohort <- matrix(rep(NA,num.states*(time.horizon+1)),nrow=time.horizon+1, ncol=num.states)
cohort.CAS <- matrix(rep(NA,num.states*(time.horizon+1)),nrow=time.horizon+1, ncol=num.states)
cohort[1,] <- init
cohort.CAS[1,] <- init
for(i in 2:(time.horizon+1)){
cohort[i,] <-cohort[i-1,]%*%mat.p
cohort.CAS[i,] <- cohort.CAS[i-1,]%*%mat.p.CAS
}
#calculate QoI
LE <- sum(cohort[,1:8])/n
mean.QALY <- sum((cohort*utility)*disc.weight)/n
mean.cost <- sum((cohort*cost)*disc.weight)/n
# QALY <- cohort%*%utility*disc.weight
# cost <- cohort%*%cost*disc.weight
QALY <- cohort*utility*disc.weight
cost <- cohort*cost*disc.weight
LE.CAS <- sum(cohort.CAS[,1:8])/n
mean.QALY.CAS <- sum((cohort.CAS*utility)*disc.weight)/n
mean.cost.CAS <- sum((cohort.CAS*cost.CAS)*disc.weight)/n
QALY.CAS <- cohort.CAS*utility*disc.weight
cost.CAS <- cohort.CAS*cost.CAS*disc.weight
NMB <- mean.QALY*WTP - mean.cost
NMB.CAS <- mean.QALY.CAS*WTP - mean.cost.CAS
INMB <- NMB.CAS-NMB
return(INMB)
}
fun_pba <- function(list.params, #list of parameters that are varied - PSA
#list.params.other, # list ofparams - not varied
disc ,
num.states,
time.horizon,
init,
n,
WTP,
index_slice, pbox.int, index.array){
# trt.index, #which strategy: 1: novel TAH, 2:syncardia
# #outcome.index=1, #which outcome: 1:cost, 2: effect
#########################################
#rr.CAS,
c.CAS <- unlist(list.params[1])
p.tkr_init.tkr_normal <- unlist( list.params[2])
p.tkr_init.tkr_minor <- unlist( list.params[3])
p.tkr_init.tkr_serious<- unlist( list.params[4])
p.tkr_normal.tkr_minor <- unlist( list.params[5])
p.tkr_normal.tkr_serious <- unlist( list.params[6])
p.tkr_normal.tkr_normal <- unlist(list.params[7])
p.tkr_minor.tkr_normal <- unlist( list.params[8])
#p.tkr_minor.tkr_serious,
p.tkr_minor.revision_simple <- unlist( list.params[9])
p.tkr_minor.other_trt <- unlist( list.params[10])
p.tkr_minor.tkr_minor <- unlist(list.params[11])
#p.tkr_serious.tkr_minor,
p.tkr_serious.revision_simple <- unlist(list.params[12])
p.tkr_serious.revision_complex <- unlist( list.params[13])
p.tkr_serious.other_trt <- unlist(list.params[14])
p.tkr_normal_after_revision.revision_simple <- unlist( list.params[15])
p.tkr_normal_after_revision.revision_complex <- unlist(list.params[16])
p.tkr_normal_after_revision.tkr_normal_after_revision <- unlist( list.params[17])
p.revision_simple.tkr_minor <- unlist( list.params[18])
p.revision_simple.tkr_serious <- unlist( list.params[19])
p.revision_simple.tkr_normal_after_revision <- unlist( list.params[20])
#p.revision_simple.other_trt,
p.revision_complex.tkr_serious <- unlist(list.params[21])
p.revision_complex.tkr_normal_after_revision <- unlist(list.params[22])
#p.other_trt.tkr_minor,p.other_trt.tkr_serious <- list.params[1]
p.other_trt.tkr_normal_after_revision <- unlist( list.params[23])
#p.other_trt.revision_simple,
p.tkr_normal.death <- unlist( list.params[24])
p.tkr_normal_after_revision.death <- unlist(list.params[25])
p.death <- unlist(list.params[26])
c.tkr <- unlist(list.params[27])
c.tkr_normal <- unlist(list.params[28])
c.tkr_minor <- unlist(list.params[29])
c.tkr_serious <- unlist( list.params[30])
c.tkr_normal_after_revision <- unlist( list.params[31])
c.revision_simple <- unlist( list.params[32])
c.revision_complex <- unlist( list.params[33])
c.other_trt <- unlist( list.params[34])
c.death <- unlist( list.params[35])
u.tkr<- unlist( list.params[36])
u.tkr_normal <- unlist( list.params[37])
u.tkr_minor <- unlist( list.params[38])
u.tkr_serious <- unlist( list.params[39])
u.tkr_normal_after_revision <- unlist( list.params[40])
u.revision_simple <- unlist( list.params[41])
u.revision_complex <- unlist( list.params[42])
u.other_trt <- unlist( list.params[43])
#########################################
dim_slice <- length(index_slice) #size of set K (equation 12) or the number of possible partitions
result_list <- c(rep(0,(dim_slice*3)))
dim(result_list) <- c(dim_slice,3)
#pbox.int <- pbox.int[ , , ,trt.index]
#pbox.int <- pbox.int[ , , ,trt.index]
num.pbox.param <- dim(pbox.int)[1] #get the number of pbox params
for (i in 1:dim_slice){
k <- index_slice[i] #get current index from the set of indices (K in equation 12)
#getting lower and upper bounds of each parameter
# lbound <-rep(0,num.pbox.param)
# ubound <-rep(0,num.pbox.param)
lbound <- matrix(rep(0,num.pbox.param*2),nrow=num.pbox.param,ncol=2)
ubound <- matrix(rep(0,num.pbox.param*2),nrow=num.pbox.param,ncol=2)
for (j in 1:num.pbox.param){
# lbound <- c(pbox.int[3,index.array[k,1],1],pbox.int[5,index.array[k,2],1])
# ubound <- c(pbox.int[3,index.array[k,1],2],pbox.int[5,index.array[k,2],2])
for (jj in 1:2){
lbound[j,jj] <- pbox.int[j,index.array[k,j],1,jj]
ubound[j,jj] <- pbox.int[j,index.array[k,j],2,jj]
}
}
#using auglag
objective.index=2
x.0 <-(lbound[,1]+ubound[,1])/2
# print(lbound[,1])
# print(x.0)
# print(ubound[,1])
# print("---------------------")
#temporary fix due to lbound is higher than ubound (vice versa) - not yet fixed as of 15 May 2021
bound.compare <- (lbound[,1] < ubound[,1])
lbound_2 <- lbound
ubound_2 <- ubound
for (i.bound in 1:length(ubound[,1])){
if(bound.compare[i.bound]==FALSE){
lbound_2[i.bound,1] <- ubound[i.bound,1]
ubound_2[i.bound,1] <- lbound[i.bound,1]
}
}
ubound <- ubound_2
lbound <- lbound_2
optim.max <- bobyqa(lbound[,1],TKR_model,lbound[,1],ubound[,1],
nl.info = FALSE, control=list(xtol_rel=1e-9, maxeval=1000),
objective.index,
#rr.CAS,
c.CAS,
p.tkr_init.tkr_normal, p.tkr_init.tkr_minor,p.tkr_init.tkr_serious,
p.tkr_normal.tkr_minor, p.tkr_normal.tkr_serious,p.tkr_normal.tkr_normal,
p.tkr_minor.tkr_normal,
#p.tkr_minor.tkr_serious,
p.tkr_minor.revision_simple,p.tkr_minor.other_trt,p.tkr_minor.tkr_minor,
#p.tkr_serious.tkr_minor,
p.tkr_serious.revision_simple,p.tkr_serious.revision_complex,p.tkr_serious.other_trt,
p.tkr_normal_after_revision.revision_simple,p.tkr_normal_after_revision.revision_complex,p.tkr_normal_after_revision.tkr_normal_after_revision,
p.revision_simple.tkr_minor,p.revision_simple.tkr_serious,p.revision_simple.tkr_normal_after_revision,
#p.revision_simple.other_trt,
p.revision_complex.tkr_serious,p.revision_complex.tkr_normal_after_revision,
#p.other_trt.tkr_minor,p.other_trt.tkr_serious,
p.other_trt.tkr_normal_after_revision,
#p.other_trt.revision_simple,
p.tkr_normal.death,p.tkr_normal_after_revision.death,p.death,
c.tkr,
c.tkr_normal,
c.tkr_minor,
c.tkr_serious,
c.tkr_normal_after_revision,
c.revision_simple,
c.revision_complex,
c.other_trt,
c.death,
u.tkr,
u.tkr_normal,
u.tkr_minor,
u.tkr_serious,
u.tkr_normal_after_revision,
u.revision_simple,
u.revision_complex,
u.other_trt,
disc ,
num.states,
time.horizon,
init,
n,
WTP)
#min
objective.index=1
optim.min <- bobyqa(lbound[,1],TKR_model,lbound[,1],ubound[,1],
nl.info = FALSE, control=list(xtol_rel=1e-9, maxeval=1000),
objective.index,
#rr.CAS,
c.CAS,
p.tkr_init.tkr_normal, p.tkr_init.tkr_minor,p.tkr_init.tkr_serious,
p.tkr_normal.tkr_minor, p.tkr_normal.tkr_serious,p.tkr_normal.tkr_normal,
p.tkr_minor.tkr_normal,
#p.tkr_minor.tkr_serious,
p.tkr_minor.revision_simple,p.tkr_minor.other_trt,p.tkr_minor.tkr_minor,
#p.tkr_serious.tkr_minor,
p.tkr_serious.revision_simple,p.tkr_serious.revision_complex,p.tkr_serious.other_trt,
p.tkr_normal_after_revision.revision_simple,p.tkr_normal_after_revision.revision_complex,p.tkr_normal_after_revision.tkr_normal_after_revision,
p.revision_simple.tkr_minor,p.revision_simple.tkr_serious,p.revision_simple.tkr_normal_after_revision,
#p.revision_simple.other_trt,
p.revision_complex.tkr_serious,p.revision_complex.tkr_normal_after_revision,
#p.other_trt.tkr_minor,p.other_trt.tkr_serious,
p.other_trt.tkr_normal_after_revision,
#p.other_trt.revision_simple,
p.tkr_normal.death,p.tkr_normal_after_revision.death,p.death,
c.tkr,
c.tkr_normal,
c.tkr_minor,
c.tkr_serious,
c.tkr_normal_after_revision,
c.revision_simple,
c.revision_complex,
c.other_trt,
c.death,
u.tkr,
u.tkr_normal,
u.tkr_minor,
u.tkr_serious,
u.tkr_normal_after_revision,
u.revision_simple,
u.revision_complex,
u.other_trt,
disc ,
num.states,
time.horizon,
init,
n,
WTP)
#
# optim.min <- directL(TAH.model.single.run_par_inmb,lbound[,1],ubound[,1],
# nl.info = FALSE, control=list(xtol_rel=1e-9, maxeval=1000),
# objective.index=objective.index, #change sign objective function: 1: positive, 2: negative