The `heemod`

package provides a number of ways to estimate
transition probabilities from survival distributions. Survival
distributions can come from at least three different sources:

- User-definded parametric distributions.
- Fitted parametric distributions with
`flexsurv::flexsurvreg()`

. - Fitted Kaplan-Meiers with
`survival::survfit()`

.

Once defined, each of these types of distributions can be combined and modified using a standard set of operations.

User-defined parametric distributions are created using the
`define_survival()`

and `define_spline_survival()`

functions:

```
surv_dist_1 <- define_survival(
distribution = "exp",
rate = .5
)
surv_dist_2 <- define_spline_survival(
scale = "odds",
gamma = c(-11.643, 1.843, 0.208),
knots = c(4.077537, 5.883183, 6.458338)
)
```

`## Le chargement a nécessité le package : flexsurv`

Fitted parametric models are created using
`flexsurv::flexsurvreg()`

and
`flexsurv::flexsurvspline()`

:

`## Le chargement a nécessité le package : survival`

```
fit_w <- flexsurvreg(
formula = Surv(futime, fustat) ~ 1,
data = ovarian, dist = "weibull"
)
plot(fit_w)
```

```
fit_spl <- flexsurvspline(
formula = Surv(futime, fustat) ~ 1,
data = ovarian,
scale = "odds",
k=1
)
plot(fit_spl)
```

Fitted models can include covariates. In order to use a model with
covariates in heemod, you can use the `set_covariates()`

function on the fitted model and provide as additional arguments the
covariate values you want to model. You can also provide a data frame of
covariate levels to aggregate survival probabilites over different
groups. By default, heemod will aggregate over predicted survival
probabilities for each subject in the dataset to which the model was
fit.

```
fit_cov <- flexsurvreg(
formula = Surv(rectime, censrec) ~ group,
dist = "weibull",
data = bc
)
plot(fit_cov)
```

```
fitcov_good <- set_covariates(fit_cov, group = "Good")
fitcov_medium <- set_covariates(fit_cov, group = "Medium")
fitcov_poor <- set_covariates(fit_cov, group = "Poor")
```

Similar functionality is also available for Kaplan-Meiers created
using `survival::survfit()`

Once defined, treatment effects of various types can be applied to any survival distribution:

- Hazard ratio:
`apply_hr()`

. - Odds ratio:
`apply_or()`

. - Acceleration factor:
`apply_af()`

.

In addition, distributions can be combined using a variety of operations:

- Join survival distributions together:
`join()`

. - Mix two (or more) survival distributions:
`mix()`

. - Combine two (or more) survival distributions as independent risks:
`add_hazards()`

.

```
km_poor_join <- join(
km_poor,
fitcov_poor,
at = 365
)
models_all <- mix(
fitcov_good, fitcov_medium, fitcov_poor,
weights = c(0.25, 0.25, 0.5)
)
combined_risks <- add_hazards(
fit_w, fitcov_good
)
```

The transition or survival probabilities are computed with
`compute_surv()`

. Time (usually `model_time`

or
`state_time`

) needs to be passed to the function as a
`time`

argument.

`## [1] 8.780223e-06 2.271877e-05 3.500128e-05 4.649850e-05 5.747782e-05`

All these operations can be chained with the `%>%`

piping operator.

```
fit_cov %>%
set_covariates(group = "Good") %>%
apply_hr(hr = 2) %>%
join(
fitcov_poor,
at = 3
) %>%
mix(
fitcov_medium,
weights = c(0.25, 0.75)
) %>%
add_hazards(
fit_w
) %>%
compute_surv(time = 1:5)
```

`## [1] 0.0004011356 0.0004736851 0.0005069766 0.0005490092 0.0005692261`

For the example we define a simple model with only 1 strategy.

```
param <- define_parameters(
p1 = compute_surv(
surv_dist_1,
time = model_time # can also be state_time
),
p2 = km_1 %>%
join(fit_w, at = 730) %>%
compute_surv(
time = model_time,
cycle_length = 365 # time is in days in km_medium, in years in model_time
)
)
tm <- define_transition(
C, p1 - p2, p2,
0, C, p2,
0, 0, C
)
```

`## No named state -> generating names.`

```
sA <- define_state(
cost = 10, ut = 1
)
sB <- define_state(
cost = 20, ut = .5
)
sC <- define_state(
cost = 0, ut = 0
)
stratTM <- define_strategy(
transition = tm,
A = sA, B = sB, C = sC
)
resTM <- run_model(
parameters = param,
stratTM,
cycles = 15,
cost = cost, effect = ut
)
```

`## No named model -> generating names.`

```
## No covariates provided, returning aggregate survival across all subjects.
## No covariates provided, returning aggregate survival across all subjects.
```

A partitioned survival model can also be computed:

```
ps <- define_part_surv(
pfs = surv_dist_1,
os = km_1 %>%
join(fit_w, at = 730),
cycle_length = c(1, 365) # 1 for pfs, 365 for os
)
```

`## No named state -> generating names.`

```
stratPS <- define_strategy(
transition = ps,
A = sA, B = sB, C = sC
)
resPS <- run_model(
stratPS,
cycles = 15,
cost = cost, effect = ut
)
```

`## No named model -> generating names.`

```
## No covariates provided, returning aggregate survival across all subjects.
## No covariates provided, returning aggregate survival across all subjects.
```