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:

- transitions occur at the end of each year,
- cost are counted starting from year 1, not year 0,
- treatment stops after 2 years,
- rounding errors.

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.

```
<- define_parameters(
par_mod rr = ifelse(markov_cycle <= 2, .509, 1),
cost_lami = ifelse(markov_cycle <= 2, 2086.5, 0),
cost_zido = 2278
)
<- define_transition(
mat_mono 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
)
<- define_transition(
mat_comb 350/1734*rr, 116/1734*rr, 17/1734*rr,
C, 0, C, 512/1258*rr, 15/1258*rr,
0, 0, C, 437/1749*rr,
0, 0, 0, 1.00
)
<- define_state(
A_mono cost_health = 2756,
cost_drugs = cost_zido,
cost_total = discount(
+ cost_drugs, .06, first = T),
cost_health life_year = 1
)<- define_state(
B_mono cost_health = 3052,
cost_drugs = cost_zido,
cost_total = discount(
+ cost_drugs, .06, first = T),
cost_health life_year = 1
)<- define_state(
C_mono cost_health = 9007,
cost_drugs = cost_zido,
cost_total = discount(
+ cost_drugs, .06, first = T),
cost_health life_year = 1
)<- define_state(
D_mono cost_health = 0,
cost_drugs = 0,
cost_total = discount(
+ cost_drugs, .06, first = T),
cost_health life_year = 0
)
<- define_state(
A_comb cost_health = 2756,
cost_drugs = cost_zido + cost_lami,
cost_total = discount(
+ cost_drugs, .06, first = T),
cost_health life_year = 1
)<- define_state(
B_comb cost_health = 3052,
cost_drugs = cost_zido + cost_lami,
cost_total = discount(
+ cost_drugs, .06, first = T),
cost_health life_year = 1
)<- define_state(
C_comb cost_health = 9007,
cost_drugs = cost_zido + cost_lami,
cost_total = discount(
+ cost_drugs, .06, first = T),
cost_health life_year = 1
)<- define_state(
D_comb cost_health = 0,
cost_drugs = 0,
cost_total = discount(
+ cost_drugs, .06, first = T),
cost_health life_year = 0
)
<- define_strategy(
mod_mono transition = mat_mono,
A_mono,
B_mono,
C_mono,
D_mono
)<- define_strategy(
mod_comb transition = mat_comb,
A_comb,
B_comb,
C_comb,
D_comb
)
<- run_model(
res_mod 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:

- Mortality rates are much higher in the book.

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
<- data.frame(
death_prob 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
<- define_parameters(
param 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 -
^ gamma)),
markov_cycle np1RR = 1 - exp(lambda * rrNP1 * ((markov_cycle - 1) ^ gamma -
^ gamma)),
markov_cycle
# 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
)
<- define_transition(
mat_standard 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
)
<- define_transition(
mat_np1 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
)
<- define_strategy(
mod_standard 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
)
)
<- define_strategy(
mod_np1 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
)
)
<- run_model(
res_mod 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)
```