Hips model 2: MC estimates for each strata - give
results for "Monte Carlo" columns in Table 2
Spiegelhalter, D.J. and Best, N.G. “Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness modelling”. Statistics in Medicine 22 , (2003), 3687-3709.
n = 10000 updates (1 per simulated patient) are required for this model; monitor C, mean.C, BL, mean.BL, BQ, mean.BQ.
Sections of the code that have changed from Model 1 are shown in bold
model {
for(k in 1 : K) { # loop over strata
# Cost and benefit equations
#######################
# Costs
for(t in 1 : N) {
ct[k, t] <- inprod(y[k, t, ], c[]) / pow(1 + delta.c, t - 1)
}
C[k] <- C0 + sum(ct[k, ])
# Benefits - life expectancy
for(t in 1 : N) {
blt[k, t] <- inprod(y[k, t, ], bl[]) / pow(1 + delta.b, t - 1)
}
BL[k] <- sum(blt[k, ])
# Benefits - QALYs
for(t in 1:N) {
bqt[k, t] <- inprod(y[k, t, ], bq[]) / pow(1 + delta.b, t - 1)
}
BQ[k] <- sum(bqt[k, ])
# Markov model probabilities:
#######################
# Transition matrix
for(t in 1 : N) {
Lambda[k, t, 1, 1] <- 1 - gamma[k, t] - lambda[k, t]
Lambda[k, t, 1, 2] <- gamma[k, t] * lambda.op
Lambda[k, t, 1, 3] <- gamma[k, t] *(1 - lambda.op)
Lambda[k, t, 1, 4] <- 0
Lambda[k, t, 1, 5] <- lambda[k, t]
Lambda[k, t, 2, 1] <- 0
Lambda[k, t, 2, 2] <- 0
Lambda[k, t, 2, 3] <- 0
Lambda[k, t, 2, 4] <- 0
Lambda[k, t, 2, 5] <- 1
Lambda[k, t, 3, 1] <- 0
Lambda[k, t, 3, 2] <- 0
Lambda[k, t, 3, 3] <- 0
Lambda[k, t, 3, 4] <- 1 - lambda[k, t]
Lambda[k, t, 3, 5] <- lambda[k, t]
Lambda[k, t, 4, 1] <- 0
Lambda[k, t, 4, 2] <- rho * lambda.op
Lambda[k, t, 4, 3] <- rho * (1 - lambda.op)
Lambda[k, t, 4, 4] <- 1 - rho - lambda[k, t]
Lambda[k, t, 4, 5] <- lambda[k, t]
Lambda[k, t, 5, 1] <- 0
Lambda[k, t, 5, 2] <- 0
Lambda[k, t, 5, 3] <- 0
Lambda[k, t, 5, 4] <- 0
Lambda[k, t, 5, 5] <- 1
gamma[k, t] <- h[k] * (t - 1)
}
# Marginal probability of being in each state at time 1
pi[k, 1, 1] <- 1 - lambda.op pi[k, 1, 2]<-0 pi[k, 1, 3] <- 0 pi[k, 1, 4] <- 0
pi[k, 1, 5] <- lambda.op
# state of each individual in strata k at time t =1
y[k,1,1 : S] ~ dmulti(pi[k,1, ], 1)
# state of each individual in strata k at time t > 1
for(t in 2 : N) {
for(s in 1:S) {
# sampling probabilities
pi[k, t, s] <- inprod(y[k, t - 1, ], Lambda[k, t, , s])
}
y[k, t, 1 : S] ~ dmulti(pi[k, t, ], 1)
}
}
# Mean of costs and benefits over strata
#################################
mean.C <- inprod(p.strata[], C[])
mean.BL <- inprod(p.strata[], BL[])
mean.BQ <- inprod(p.strata[], BQ[])
}
Data ( click to open )
Results
Overall SD for Monte Carlo estimates at bottom of Table 2 is just the weighted SD of the strata-specific Monte Carlo means