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##dr4pl

The package dr4pl (Dose Response 4 Parameter Logisitic model) specializes in applying the 4 Parameter Logistic (4PL) model. The 4PL model has been recognized as a major tool to analyze the relationship between a dose and a response in pharmacological experiments. The package dr4pl may be used to model increasing and decreasing curves. The goal of dr4pl is to bring a statistical method which is capable of handeling specific error cases of which other statistical packages produce errors. Examples of Dose Response datasets that will produce errors in other packages may be accessed by name once dr4pl is loaded and these data sets are under the names of drc_error_1, drc_error_2, drc_error_3, and drc_error_4. Along with these error data sets, this package also supplies 13 standard example data sets for the 4PL model under the name sample_data_1, sampel_data_2, etc. The package dr4pl also alows for the user to decide how their theta variable is approximated. The user may choose the default logistic model or use Mead’s Method. Additionally, the user may decide between four loss functions to minimize: Squared, Absolute, Huber, or Tukey’s biweight. Please attempt each of the loss functions and choose the best fit from plotting the dr4pl object.

You can install dr4pl from github with:

This is a basic example which shows you how to solve a common problem. This example may be used with drc_error_1, drc_error_2, drc_error_3, and drc_error_4:

```
## basic example code, datasets
## example requires the drc and dr4pl package to be loaded
library(dr4pl)
library(drc)
#> Loading required package: MASS
#>
#> 'drc' has been loaded.
#> Please cite R and 'drc' if used for a publication,
#> for references type 'citation()' and 'citation('drc')'.
#>
#> Attaching package: 'drc'
#> The following objects are masked from 'package:stats':
#>
#> gaussian, getInitial
a <- drc::drm(drc_error_1$Response~drc_error_1$Dose, fct = LL.4())
#> Error in optim(startVec, opfct, hessian = TRUE, method = optMethod, control = list(maxit = maxIt, :
#> non-finite finite-difference value [4]
#> Error in drmOpt(opfct, opdfct1, startVecSc, optMethod, constrained, warnVal, : Convergence failed
plot(a)
#> Error in plot(a): object 'a' not found
```

```
## basic example code
## example requires the dr4pl package to be loaded
b <- dr4pl(drc_error_1$Response~drc_error_1$Dose, method.init = "logistic", method.robust = "Tukey")
plot(b)
#> Warning: Transformation introduced infinite values in continuous x-axis
#> Warning: Transformation introduced infinite values in continuous x-axis
```

```
summary(b)
#> Call:
#> dr4pl.formula(formula = drc_error_1$Response ~ drc_error_1$Dose,
#> method.init = "logistic", method.robust = "Tukey")
#>
#> Estimate StdErr 2.5 % 97.5 %
#> UpperLimit 7.9134e+04 6.5396e+01 7.9004e+04 79262.7084
#> Log10(IC50) -1.2371e+01 2.5194e+00 -1.7347e+01 -7.3946
#> Slope -7.3707e-02 2.2747e-02 -1.1864e-01 -0.0288
#> LowerLimit -8.3931e+03 6.5427e+01 -8.5223e+03 -8263.8406
```

With the release of `dr4pl (>= 2.0.0)`

, `dr4pl`

is getting a few quality improvements as well as more accurate confidence intervals. First and foremost, prior to `dr4pl (>= 2.0.0)`

, `dr4pl`

possessed an error in the second derivative of the model function with respects to `(theta_3)^2`

. This has been corrected and a new vignette “dr4pl_derivatives” exists showing how each derivative was calculated for this package.

The `parameters`

field of the `dr4pl`

object has changed. This field will now have an object inheriting from `dr4pl_param`

S3 class. This is likely the biggest change as a lot of internals now dispatch on this object. The primary function of this object is to track if the `theta_2`

parameter is in the log10 space. Users were often confused as to which parameter estimate they were looking at, to remedy this, when printing the object, it will explicitly tell you the type.

```
obj <- dr4pl(Response~Dose, sample_data_3)
coef(obj)
#> UpperLimit IC50 Slope LowerLimit
#> 59858.0700194411 5.07949182697285 -0.611737121034004 980.820568608382
```

For backwards compatibility, `dr4pl`

always stores the `dr4pl_theta`

version of the `dr4pl_param`

object. The user can change the state of the parameter with the `ParmToLog()`

and `LogToParm()`

functions.

```
ParmToLog(coef(obj))
#> UpperLimit Log10(IC50) Slope LowerLimit
#> 59858.0700194411 0.705820265870361 -0.611737121034004 980.820568608382
```

`dr4pl`

’s convention was to always report the values in linear space (even if the Confidence Intervals reflected the log10 parameter), but this understandably so only increased confusion around how the values were calculated. To remedy this, various S3 functions that dispatch with `dr4pl`

have an optional `theta`

argument in which you can force a calculation on a parameter set. To stay somewhat backwards compatible, `dr4pl`

will use the `log10`

space by default since parameters are always estimated in that space.

```
summary(obj) #uses log10 space by default
#> Call:
#> dr4pl.formula(formula = Response ~ Dose, data = sample_data_3)
#>
#> Estimate StdErr 2.5 % 97.5 %
#> UpperLimit 5.9858e+04 6.1255e+02 5.8616e+04 61100.3693
#> Log10(IC50) 7.0582e-01 8.1390e-02 5.4075e-01 0.8709
#> Slope -6.1174e-01 6.4982e-02 -7.4353e-01 -0.4799
#> LowerLimit 9.8082e+02 6.2518e+02 -2.8710e+02 2248.7443
summary(obj, theta = coef(obj)) #grab linear space of dr4pl_param
#> Call:
#> dr4pl.formula(formula = Response ~ Dose, data = sample_data_3)
#>
#> Estimate StdErr 2.5 % 97.5 %
#> UpperLimit 5.9858e+04 6.1255e+02 5.8616e+04 61100.3693
#> Log10(IC50) 7.0582e-01 8.1390e-02 5.4075e-01 0.8709
#> Slope -6.1174e-01 6.4982e-02 -7.4353e-01 -0.4799
#> LowerLimit 9.8082e+02 6.2518e+02 -2.8710e+02 2248.7443
```

Since the `dr4pl_param`

object’s displayed names may change, the user is able to programmatically select elements with theta_1, theta_2, theta_3, theta_4 or by integer index.

`dr4pl`

now imports the `rlang`

package to allow for tidy evaluation when using `dr4pl.data.frame`

. This is not a major dependency as `dr4pl`

already imports `ggplot2`

which imports `rlang`

.

```
dr4pl(sample_data_3, dose = Dose, response = Response)
#> Call:
#> dr4pl.data.frame(data = sample_data_3, dose = Dose, response = Response)
#>
#> Coefficients:
#> UpperLimit IC50 Slope LowerLimit
#> 59858.0700194411 5.07949182697285 -0.611737121034004 980.820568608382
dr4pl(sample_data_3, dose = Dose/100000, response = Response)
#> Call:
#> dr4pl.data.frame(data = sample_data_3, dose = Dose/1e+05, response = Response)
#>
#> Coefficients:
#> UpperLimit IC50 Slope LowerLimit
#> 56553.5168965252 0.000167802698462147 -0.880333688166774 -753.724715235523
```

Prior to `dr4pl (>= 2.0.0)`

, users were required to specify a limit for each parameter even if they wanted to only constrain one. Now the users can supply a named numeric vector for ease of use.

```
dr4pl(sample_data_1, dose = Dose, response = Response, lowerl = c(theta_4 = 0)) #make lowerlimit positive
#> Call:
#> dr4pl.data.frame(data = sample_data_1, dose = Dose, response = Response,
#> lowerl = c(theta_4 = 0))
#>
#> Coefficients:
#> UpperLimit IC50 Slope LowerLimit
#> 112247.294407694 17.2973238818617 -0.384948923142149 0.00189050905753972
```

In addition, users will receive a more helpful error message if they ever attempt to constrain the fit with `upperl`

and `lowerl`

.

```
dr4pl(Response~Dose, sample_data_4, lowerl = c(theta_4 = 0)) #make lowerlimit positive
#> Error: Initial parameter values are not in the interior of the feasible region.
#> Estimated Parameters:
#> UpperLimit Log10(IC50) Slope LowerLimit
#> 31295.0216027415 4.67986724187866 -8.2357409544985 -57.218
#> Failed Constraints:
#> theta_4 = - 57.218 >= 0
```

You may also pass a named numeric vector to `init.parm`

, but you will also receive a warning message as `init.parm`

expects a `dr4pl_param`

object constructed from `dr4pl_theta()`

. This warning will only appear every 8 hours though.

```
dr4pl(Response~Dose, sample_data_4, init.parm = c(theta_4 = 0.1),lowerl = c(theta_4 = 0))
#> Warning: A numeric object is being coerced to a "dr4pl_param" object.`theta_2` is assumed to be in linear space. Please use `dr4pl_theta()` to construct the theta parameter.
#> This warning is displayed once every 8 hours.
#> Call:
#> dr4pl.formula(formula = Response ~ Dose, data = sample_data_4,
#> init.parm = c(theta_4 = 0.1), lowerl = c(theta_4 = 0))
#>
#> Coefficients:
#> UpperLimit IC50 Slope LowerLimit
#> 30599.6079444198 1020.20601140621 -8.03521868073897 3716.67380596223
```

`dr4pl_theta()`

function allows the user to specify if the object is in log10 space or not: