This small package performs simple sigmoidal Emax model fit using
Stan, without the need of (1) writing Stan model code and (2) setting up
an environment to compile Stan model, inspired by
**rstanarm** package.

**rstanarm** package (link) is a very
flexible, general purpose tool to perform various Bayesian modeling with
formula notations, such as generalized mixed effect models or joint
models. One small gap it has is in nonlinear model fitting, where it
only accepts nonlinear functions defined in stats package with
`SS`

prefixes (link).
Unfortunately the (sigmoidal) Emax model, one of the most commonly used
nonlinear functions in the field of pharmacometrics, is not among the
available functions. The **rstanarm** package also seems to
be assuming that we fit nonlinear mixed effect models, but not simple
nonlinear models without mixed effects. **brms** is another
great general purpose package that allows formula notation, but it
requires users to compile generated Stan models. The need for setting up
an environment for compiling Stan code can be daunting for beginners,
especially with Windows.

I hope this **rstanemax** package will fill the niche
gap, allow for easier implementation of Emax model in Bayesian
framework, and enable routine uses in the
pharmacokinetic/pharmacodynamic field.

This package was build using **rstantools** (link) following a very
helpful step-by-step guide (link)
on creating a package that depends on RStan.

You can install the released version of rstanemax from CRAN with:

`install.packages("rstanemax")`

You can alternatively install the package from source.

Before doing so, you first have to install RStan and C++
Toolchain.

RStan
Getting Started

Also, you have to follow the instruction below if you are using Windows
PC.

Installing
RStan from source on Windows

After this step you should be able to install the package from GitHub
using **devtools**.

```
install.packages("devtools")
library(devtools)
::install_github("yoshidk6/rstanemax") devtools
```

This GitHub pages contains function references and vignette.

```
# Load rstanemax
library(rstanemax)
#> Loading required package: Rcpp
# Run model with a sample dataset
set.seed(12345)
data(exposure.response.sample)
<- stan_emax(response ~ exposure, data = exposure.response.sample,
fit.emax # the next line is only to make the output short
chains = 1, iter = 500, seed = 12345)
#>
#> SAMPLING FOR MODEL 'emax' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.00014 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 1.4 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 500 [ 0%] (Warmup)
#> Chain 1: Iteration: 50 / 500 [ 10%] (Warmup)
#> Chain 1: Iteration: 100 / 500 [ 20%] (Warmup)
#> Chain 1: Iteration: 150 / 500 [ 30%] (Warmup)
#> Chain 1: Iteration: 200 / 500 [ 40%] (Warmup)
#> Chain 1: Iteration: 250 / 500 [ 50%] (Warmup)
#> Chain 1: Iteration: 251 / 500 [ 50%] (Sampling)
#> Chain 1: Iteration: 300 / 500 [ 60%] (Sampling)
#> Chain 1: Iteration: 350 / 500 [ 70%] (Sampling)
#> Chain 1: Iteration: 400 / 500 [ 80%] (Sampling)
#> Chain 1: Iteration: 450 / 500 [ 90%] (Sampling)
#> Chain 1: Iteration: 500 / 500 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 0.121053 seconds (Warm-up)
#> Chain 1: 0.046308 seconds (Sampling)
#> Chain 1: 0.167361 seconds (Total)
#> Chain 1:
#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> http://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> http://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> http://mc-stan.org/misc/warnings.html#tail-ess
```

```
fit.emax#> ---- Emax model fit with rstanemax ----
#>
#> mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
#> emax 92.01 0.47 6.49 79.08 87.94 92.11 96.35 103.43 188.95 1
#> e0 5.69 0.35 4.92 -2.87 2.13 5.90 9.07 15.00 192.44 1
#> ec50 75.78 1.23 19.37 44.51 62.88 72.26 85.34 124.31 246.47 1
#> gamma 1.00 NaN 0.00 1.00 1.00 1.00 1.00 1.00 NaN NaN
#> sigma 16.65 0.13 1.66 13.77 15.47 16.55 17.55 20.20 157.45 1
#>
#> * Use `extract_stanfit()` function to extract raw stanfit object
#> * Use `plot()` function to visualize model fit
#> * Use `posterior_predict()` or `posterior_predict_quantile()` function to get
#> raw predictions or make predictions on new data
#> * Use `extract_obs_mod_frame()` function to extract raw data
#> in a processed format (useful for plotting)
```

`plot(fit.emax)`

Fitting the
Emax Model in R has nice intro on Emax (with kindly introducing this
package). **brms** implementation of the same model can be
found here.