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-defined parametric distributions with
`define_surv_dist()`

or`define_surv_spline()`

. - Fitted survival models with a Kaplan-Meier estimator or parametric distributions with
`define_surv_fit()`

- Survival Tables with
`define_surv_table()`

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_surv_dist()`

and `define_surv_spline()`

functions:

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

`## Loading required namespace: flexsurv`

Fitted Kaplan-Meier curves are created using `survival::survfit()`

wrapped into `define_surv_fit()`

`library(flexsurv)`

`## Loading required package: survival`

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

```
<- flexsurvspline(
fit_spl formula = Surv(futime, fustat) ~ 1,
data = ovarian,
scale = "odds",
k=1
|>
) define_surv_fit()
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 probabilities over different groups. By default, heemod will aggregate over predicted survival probabilities for each subject in the dataset to which the model was fit.

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

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

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

Similar functionality is also available for fitted parametric models created using `flexsurv::flexsurvreg()`

and `flexsurv::flexsurvspline()`

wrapped into `define_surv_fit()`

```
library(survival)
<- survfit(
km_1 formula = Surv(futime, fustat) ~ 1,
data = ovarian
|>
) define_surv_fit()
<- survfit(
km_cov formula = Surv(rectime, censrec) ~ group,
data = bc
|>
) define_surv_fit()
plot(km_cov)
```

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

```
<- set_covariates(km_cov, group = "Good")
km_good <- set_covariates(km_cov, group = "Medium")
km_medium <- set_covariates(km_cov, group = "Poor") km_poor
```

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()`

.

```
<- apply_hr(km_poor, hr = 0.5)
km_poor_ph <- apply_af(km_medium, af = 1.2) km_medium_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()`

.

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

`compute_surv(surv_dist_2, time = 1:5)`

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

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

pipe 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.

```
<- define_parameters(
param 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
)
)
<- define_transition(
tm - p2, p2,
C, p1 0, C, p2,
0, 0, C
)
```

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

`plot(tm)`

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

`plot(resTM)`

A partitioned survival model can also be computed:

```
<- define_part_surv(
ps 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.`

```
<- define_strategy(
stratPS transition = ps,
A = sA, B = sB, C = sC
)
<- run_model(
resPS
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.
```

`plot(resPS)`