In survival analysis, events sometimes only start to occur after a
certain delay since entry time and this delay period might vary for
different treatments or groups. While parametric delay models, like the
three-parameter Weibull distribution, might adequately describe this
process the estimation of delay via standard maximum likelihood is
severely biased in small samples. The R-package `incubate`

employs an
alternative estimation method called *maximum product of spacings
estimation (MPSE)* to estimate and test delay and other parameters in a
one or two group setting. Concretely, building on MPSE, `incubate`

can

- fit parameter estimates where certain parameters can be constrained to be shared between both groups
- calculate bootstrap confidence intervals for these model parameters
*and* - compare the survival experience of two groups within this statistical model with respect to model parameters.

The `incubate`

-package provides the delayed exponential distribution as
special case of the delayed Weibull distribution. We draw random samples
corresponding to two groups with different model parameters.

```
library("incubate")
# simulate data from exponential distribution with delay
x <- rexp_delayed(n = 13, delay = 1.0, rate = 0.8)
y <- rexp_delayed(n = 11, delay = 1.5, rate = 1.2)
```

We use the model function `delay_model`

to fit a exponential model with
delay to both groups and show the model fit.

```
fm <- delay_model(x, y)
plot(fm)
```

Inference on the model parameters is possible through `confint`

for
bootstrap confidence intervals and `delay_test`

for parameter
comparisons in a two group setting.

```
# confidence interval for delay-parameters
confint(fm, parm = c('delay.x', 'delay.y'))
#> 2.5% 97.5%
#> delay.x 0.80601 1.0943
#> delay.y 1.35051 1.7531
# test on difference in delay
# for real applications use R>=1000 bootrap draws
delay_test <- test_diff(x, y, R = 100)
plot(delay_test)
```

To switch on parallel computation, e.g. for bootstrap parameter tests or
power simulations, simply set up a suitable computation plan via the
Future-API. For instance, do the following to activate four R-sessions
in the background of your local computer for computer-intensive tasks in
`incubate`

:

```
library("future")
plan(multisession, workers = 4)
```

That’s it. You do *not* have to change any function calls. `incubate`

is
`future`

-aware. Consult the `future`

-package on
CRAN for more information
about futures and about supported computation plans.

When you are done with the heavy computing, it is best practice to
release the parallel connections via `plan(sequential)`

.

The `incubate`

package is found on
CRAN and development
happens at Gitlab.

Use `install.packages`

to install `incubate`

from CRAN as usual, i.e.,
`install.packages('incubate')`

should do.

To install its **latest version** from the main branch on Gitlab use the
following R-code:

```
remotes::install_gitlab("imb-dev/incubate")
```

To install a specific version, add the version tag after the name,
separated by a `@`

, e.g. to install `incubate`

in version `v1.1.9`

use

```
remotes::install_gitlab("imb-dev/incubate@v1.1.9")
```

The suffix `@develop`

points to the latest **development version** on
Gitlab.

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