The purpose of this vignette is to present how to reproduce exactly the results from Decision Modelling for Health Economic Evaluation. While other vignettes such as vignette("c-homogeneous", "heemod"), vignette("d-non-homogeneous", "heemod") or vignette("e-probabilistic", "heemod") are greatly inspired from this book, key elements differ (mostly for the sake of clarity) and thus results differ, sometimes significantly, from the book. Here we show how to exactly reproduce the results with the heemod package.
Key differences in DMHEE:
It is possible to reproduce 1. and 2. by making transition happen at the end of each year with method = “end”. Since with this method the transition occur 1 year after the beginning, costs should be discounted from the first cycle with the argument first = TRUE in discount(). Point 3. is reproduced by making rr and cost_lami a time changing variable like this rr = ifelse(markov_cycle <= 2, .509, 1.00).
The last point is reproduced by writing transition probabilities as fractions.
par_mod <- define_parameters(
rr = ifelse(markov_cycle <= 2, .509, 1),
cost_lami = ifelse(markov_cycle <= 2, 2086.5, 0),
cost_zido = 2278
)
mat_mono <- define_transition(
1251/1734, 350/1734, 116/1734, 17/1734,
0, 731/1258, 512/1258, 15/1258,
0, 0, 1312/1749, 437/1749,
0, 0, 0, 1.00
)
mat_comb <- define_transition(
C, 350/1734*rr, 116/1734*rr, 17/1734*rr,
0, C, 512/1258*rr, 15/1258*rr,
0, 0, C, 437/1749*rr,
0, 0, 0, 1.00
)
A_mono <- define_state(
cost_health = 2756,
cost_drugs = cost_zido,
cost_total = discount(
cost_health + cost_drugs, .06, first = T),
life_year = 1
)
B_mono <- define_state(
cost_health = 3052,
cost_drugs = cost_zido,
cost_total = discount(
cost_health + cost_drugs, .06, first = T),
life_year = 1
)
C_mono <- define_state(
cost_health = 9007,
cost_drugs = cost_zido,
cost_total = discount(
cost_health + cost_drugs, .06, first = T),
life_year = 1
)
D_mono <- define_state(
cost_health = 0,
cost_drugs = 0,
cost_total = discount(
cost_health + cost_drugs, .06, first = T),
life_year = 0
)
A_comb <- define_state(
cost_health = 2756,
cost_drugs = cost_zido + cost_lami,
cost_total = discount(
cost_health + cost_drugs, .06, first = T),
life_year = 1
)
B_comb <- define_state(
cost_health = 3052,
cost_drugs = cost_zido + cost_lami,
cost_total = discount(
cost_health + cost_drugs, .06, first = T),
life_year = 1
)
C_comb <- define_state(
cost_health = 9007,
cost_drugs = cost_zido + cost_lami,
cost_total = discount(
cost_health + cost_drugs, .06, first = T),
life_year = 1
)
D_comb <- define_state(
cost_health = 0,
cost_drugs = 0,
cost_total = discount(
cost_health + cost_drugs, .06, first = T),
life_year = 0
)
mod_mono <- define_strategy(
transition = mat_mono,
A_mono,
B_mono,
C_mono,
D_mono
)
mod_comb <- define_strategy(
transition = mat_comb,
A_comb,
B_comb,
C_comb,
D_comb
)
res_mod <- run_model(
mono = mod_mono,
comb = mod_comb,
parameters = par_mod,
cycles = 20,
cost = cost_total,
effect = life_year,
method = "end",
init = c(1, 0, 0, 0)
)
summary(res_mod)Key difference in DMHEE:
This can be corrected by using a user-specified mortality table and then fetch the values with:
look_up(death_prob, age = age, sex = sex, bin = "age")# a function to return age-related mortality rate
# given age and sex
death_prob <- data.frame(
age = rep(seq(35, 85, 10), each = 2),
sex = rep(1:0, 6),
value = c(
1.51e-3, .99e-3, 3.93e-3,
2.6e-3, 10.9e-3, 6.7e-3,
31.6e-3, 19.3e-3, 80.1e-3,
53.5e-3, 187.9e-3, 154.8e-3
)
)
death_prob
param <- define_parameters(
age_init = 60,
sex = 0,
# age increases with cycles
age = age_init + markov_cycle,
# operative mortality rates
omrPTHR = .02,
omrRTHR = .02,
# re-revision mortality rate
rrr = .04,
# parameters for calculating primary revision rate
cons = -5.490935,
ageC = -.0367022,
maleC = .768536,
lambda = exp(cons + ageC * age_init + maleC * sex),
lngamma = 0.3740968,
gamma = exp(lngamma),
lnrrNP1 = -1.344474,
rrNP1 = exp(lnrrNP1),
# revision probability of primary procedure
standardRR = 1 - exp(lambda * ((markov_cycle - 1) ^ gamma -
markov_cycle ^ gamma)),
np1RR = 1 - exp(lambda * rrNP1 * ((markov_cycle - 1) ^ gamma -
markov_cycle ^ gamma)),
# age-related mortality rate
sex_cat = ifelse(sex == 0, "FMLE", "MLE"),
mr = look_up(death_prob, age = age, sex = sex, bin = "age"),
u_successP = .85,
u_revisionTHR = .30,
u_successR = .75,
c_revisionTHR = 5294
)
mat_standard <- define_transition(
state_names = c(
"PrimaryTHR",
"SuccessP",
"RevisionTHR",
"SuccessR",
"Death"
),
0, C, 0, 0, omrPTHR,
0, C, standardRR, 0, mr,
0, 0, 0, C, omrRTHR+mr,
0, 0, rrr, C, mr,
0, 0, 0, 0, 1
)
mat_np1 <- define_transition(
state_names = c(
"PrimaryTHR",
"SuccessP",
"RevisionTHR",
"SuccessR",
"Death"
),
0, C, 0, 0, omrPTHR,
0, C, np1RR, 0, mr,
0, 0, 0, C, omrRTHR+mr,
0, 0, rrr, C, mr,
0, 0, 0, 0, 1
)
mod_standard <- define_strategy(
transition = mat_standard,
PrimaryTHR = define_state(
utility = 0,
cost = 394
),
SuccessP = define_state(
utility = discount(u_successP, .015),
cost = 0
),
RevisionTHR = define_state(
utility = discount(u_revisionTHR, .015),
cost = discount(c_revisionTHR, .06)
),
SuccessR = define_state(
utility = discount(u_successR, .015),
cost = 0
),
Death = define_state(
utility = 0,
cost = 0
)
)
mod_np1 <- define_strategy(
transition = mat_np1,
PrimaryTHR = define_state(
utility = 0,
cost = 579
),
SuccessP = define_state(
utility = discount(u_successP, .015),
cost = 0
),
RevisionTHR = define_state(
utility = discount(u_revisionTHR, .015),
cost = discount(c_revisionTHR, .06)
),
SuccessR = define_state(
utility = discount(u_successR, .015),
cost = 0
),
Death = define_state(
utility = 0,
cost = 0
)
)
res_mod <- run_model(
standard = mod_standard,
np1 = mod_np1,
parameters = param,
cycles = 60,
cost = cost,
effect = utility,
method = "beginning",
init = c(1, 0, 0, 0, 0)
)
summary(res_mod)