# mkin v1.0.3

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## Kinetic Evaluation of Chemical Degradation Data

Calculation routines based on the FOCUS Kinetics Report (2006, 2014). Includes a function for conveniently defining differential equation models, model solution based on eigenvalues if possible or using numerical solvers. If a C compiler (on windows: 'Rtools') is installed, differential equation models are solved using automatically generated C functions. Please note that no warranty is implied for correctness of results or fitness for a particular purpose.

# mkin

The R package mkin provides calculation routines for the analysis of chemical degradation data, including multicompartment kinetics as needed for modelling the formation and decline of transformation products, or if several degradation compartments are involved.

## Installation

You can install the latest released version from CRAN from within R:

install.packages("mkin")


## Background

In the regulatory evaluation of chemical substances like plant protection products (pesticides), biocides and other chemicals, degradation data play an important role. For the evaluation of pesticide degradation experiments, detailed guidance and helpful tools have been developed as detailed in 'Credits and historical remarks' below.

## Usage

For a start, have a look at the code examples provided for plot.mkinfit and plot.mmkin, and at the package vignettes FOCUS L and FOCUS D.

## Documentation

The HTML documentation of the latest version released to CRAN is available at jrwb.de and github. Documentation of the development version is found in the 'dev' subdirectory.

## Features

### General

• Highly flexible model specification using mkinmod, including equilibrium reactions and using the single first-order reversible binding (SFORB) model, which will automatically create two latent state variables for the observed variable.
• Model solution (forward modelling) in the function mkinpredict is performed either using the analytical solution for the case of parent only degradation, an eigenvalue based solution if only simple first-order (SFO) or SFORB kinetics are used in the model, or using a numeric solver from the deSolve package (default is lsoda).
• The usual one-sided t-test for significant difference from zero is nevertheless shown based on estimators for the untransformed parameters.
• Summary and plotting functions. The summary of an mkinfit object is in fact a full report that should give enough information to be able to approximately reproduce the fit with other tools.
• The chi-squared error level as defined in the FOCUS kinetics guidance (see below) is calculated for each observed variable.
• The 'variance by variable' error model which is often fitted using Iteratively Reweighted Least Squares (IRLS) should now be specified as error_model = "obs".

### Unique in mkin

• Three different error models can be selected using the argument error_model to the mkinfit function. A two-component error model similar to the one proposed by Rocke and Lorenzato can be selected using the argument error_model = "tc".
• Model comparisons using the Akaike Information Criterion (AIC) are supported which can also be used for non-constant variance. In such cases the FOCUS chi-squared error level is not meaningful.
• By default, kinetic rate constants and kinetic formation fractions are transformed internally using transform_odeparms so their estimators can more reasonably be expected to follow a normal distribution.
• When parameter estimates are backtransformed to match the model definition, confidence intervals calculated from standard errors are also backtransformed to the correct scale, and will not include meaningless values like negative rate constants or formation fractions adding up to more than 1, which cannot occur in a single experiment with a single defined radiolabel position.
• When a metabolite decline phase is not described well by SFO kinetics, SFORB kinetics can be used for the metabolite. Mathematically, the SFORB model is equivalent to the DFOP model used by other tools for biphasic metabolite curves. However, the SFORB model has the advantage that there is a mechanistic interpretation of the model parameters.
• Nonlinear mixed-effects models can be created from fits of the same degradation model to different datasets for the same compound by using the nlme.mmkin method. Note that the convergence of the nlme fits depends on the quality of the data. Convergence is better for simple models and data for many groups (e.g. soils).

## GUI

There is a graphical user interface that may be useful. Please refer to its documentation page for installation instructions and a manual.

## News

There is a list of changes for the latest CRAN release and one for each github branch, e.g. the main branch.

## Credits and historical remarks

mkin would not be possible without the underlying software stack consisting of, among others, R and the package deSolve. In previous version, mkin was also using the functionality of the FME package. Please refer to the package page on CRAN for the full list of imported and suggested R packages. Also, Debian Linux, the vim editor and the Nvim-R plugin have been invaluable in its development.

mkin could not have been written without me being introduced to regulatory fate modelling of pesticides by Adrian Gurney during my time at Harlan Laboratories Ltd (formerly RCC Ltd). mkin greatly profits from and largely follows the work done by the FOCUS Degradation Kinetics Workgroup, as detailed in their guidance document from 2006, slightly updated in 2011 and in 2014.

Also, it was inspired by the first version of KinGUI developed by BayerCropScience, which is based on the MatLab runtime environment.

The companion package kinfit (now deprecated) was started in 2008 and first published on CRAN on 01 May 2010.

The first mkin code was published on 11 May 2010 and the first CRAN version on 18 May 2010.

In 2011, Bayer Crop Science started to distribute an R based successor to KinGUI named KinGUII whose R code is based on mkin, but which added, among other refinements, a closed source graphical user interface (GUI), iteratively reweighted least squares (IRLS) optimisation of the variance for each of the observed variables, and Markov Chain Monte Carlo (MCMC) simulation functionality, similar to what is available e.g. in the FME package.

Somewhat in parallel, Syngenta has sponsored the development of an mkin and KinGUII based GUI application called CAKE, which also adds IRLS and MCMC, is more limited in the model formulation, but puts more weight on usability. CAKE is available for download from the CAKE website, where you can also find a zip archive of the R scripts derived from mkin, published under the GPL license.

Finally, there is KineticEval, which contains a further development of the scripts used for KinGUII, so the different tools will hopefully be able to learn from each other in the future as well.

Thanks to René Lehmann, formerly working at the Umweltbundesamt, for the nice cooperation cooperation on parameter transformations, especially the isometric log-ratio transformation that is now used for formation fractions in case there are more than two transformation targets.

Many inspirations for improvements of mkin resulted from doing kinetic evaluations of degradation data for my clients while working at Harlan Laboratories and at Eurofins Regulatory AG, and now as an independent consultant.

Funding was received from the Umweltbundesamt in the course of the projects

• Grant Number 112407 (Testing and validation of modelling software as an alternative to ModelMaker 4.0, 2014-2015)
• Project Number 56703 (Optimization of gmkin for routine use in the Umweltbundesamt, 2015)
• Project Number 112407 (Testing the feasibility of using an error model according to Rocke and Lorenzato for more realistic parameter estimates in the kinetic evaluation of degradation data, 2018-2019)
• Project Number 120667 (Development of objective criteria for the evaluation of the visual fit in the kinetic evaluation of degradation data, 2019-2020)
• Project 146839 (Checking the feasibility of using mixed-effects models for the derivation of kinetic modelling parameters from degradation studies, 2020-2021)

## References

 Ranke J, Meinecke S (2019) Error Models for the Kinetic Evaluation of Chemical Degradation Data Environments 6 (12) 124 doi:10.3390/environments6120124 Ranke J, Wöltjen J, Meinecke S (2018) Comparison of software tools for kinetic evaluation of chemical degradation data Environmental Sciences Europe 30 17 doi:10.1186/s12302-018-0145-1

## Development

Contributions are welcome!

## Functions in mkin

 Name Description AIC.mmkin Calculate the AIC for a column of an mmkin object D24_2014 Aerobic soil degradation data on 2,4-D from the EU assessment in 2014 DFOP.solution Double First-Order in Parallel kinetics [.mmkin Subsetting method for mmkin objects CAKE_export Export a list of datasets format to a CAKE study file FOCUS_2006_HS_ref_A_to_F Results of fitting the HS model to Datasets A to F of FOCUS (2006) FOCUS_2006_SFO_ref_A_to_F Results of fitting the SFO model to Datasets A to F of FOCUS (2006) FOCUS_2006_FOMC_ref_A_to_F Results of fitting the FOMC model to Datasets A to F of FOCUS (2006) NAFTA_SOP_Attachment Example datasets from Attachment 1 to the NAFTA SOP published 2015 FOCUS_2006_DFOP_ref_A_to_B Results of fitting the DFOP model to Datasets A to B of FOCUS (2006) aw Calculate Akaike weights for model averaging loftest Lack-of-fit test for models fitted to data with replicates SFO.solution Single First-Order kinetics logLik.mkinfit Calculated the log-likelihood of a fitted mkinfit object mixed Create a mixed effects model from an mmkin row object create_deg_func Create degradation functions for known analytical solutions confint.mkinfit Confidence intervals for parameters of mkinfit objects dimethenamid_2018 Aerobic soil degradation data on dimethenamid and dimethenamid-P from the EU assessment in 2018 get_deg_func Retrieve a degradation function from the mmkin namespace FOCUS_2006_datasets Datasets A to F from the FOCUS Kinetics report from 2006 add_err Add normally distributed errors to simulated kinetic degradation data endpoints Function to calculate endpoints for further use from kinetic models fitted with mkinfit SFORB.solution Single First-Order Reversible Binding kinetics ilr Function to perform isometric log-ratio transformation IORE.solution Indeterminate order rate equation kinetics logistic.solution Logistic kinetics mkin_wide_to_long Convert a dataframe with observations over time into long format NAFTA_SOP_2015 Example datasets from the NAFTA SOP published 2015 experimental_data_for_UBA_2019 Experimental datasets used for development and testing of error models nafta Evaluate parent kinetics using the NAFTA guidance nlme.mmkin Create an nlme model for an mmkin row object mkin_long_to_wide Convert a dataframe from long to wide format nlme_function Helper functions to create nlme models from mmkin row objects nobs.mkinfit Number of observations on which an mkinfit object was fitted test_data_from_UBA_2014 Three experimental datasets from two water sediment systems and one soil mkindsg A class for dataset groups for mkin mkinds A dataset class for mkin mkinresplot Function to plot residuals stored in an mkin object mkinerrmin Calculate the minimum error to assume in order to pass the variance test lrtest.mkinfit Likelihood ratio test for mkinfit models mccall81_245T Datasets on aerobic soil metabolism of 2,4,5-T in six soils max_twa_parent Function to calculate maximum time weighted average concentrations from kinetic models fitted with mkinfit mkinparplot Function to plot the confidence intervals obtained using mkinfit mkinmod Function to set up a kinetic model with one or more state variables f_time_norm_focus Normalisation factors for aerobic soil degradation according to FOCUS guidance FOMC.solution First-Order Multi-Compartment kinetics HS.solution Hockey-Stick kinetics plot.nafta Plot the results of the three models used in the NAFTA scheme. reexports Objects exported from other packages focus_soil_moisture FOCUS default values for soil moisture contents at field capacity, MWHC and 1/3 bar mkinerrplot Function to plot squared residuals and the error model for an mkin object update.mkinfit Update an mkinfit model with different arguments parms Extract model parameters from mkinfit models mmkin Fit one or more kinetic models with one or more state variables to one or more datasets plot.mkinfit Plot the observed data and the fitted model of an mkinfit object plot.mmkin Plot model fits (observed and fitted) and the residuals for a row or column of an mmkin object synthetic_data_for_UBA_2014 Synthetic datasets for one parent compound with two metabolites mkinfit Fit a kinetic model to data with one or more state variables summary.nlme.mmkin Summary method for class "nlme.mmkin" transform_odeparms Functions to transform and backtransform kinetic parameters for fitting schaefer07_complex_case Metabolism data set used for checking the software quality of KinGUI summary.mkinfit Summary method for class "mkinfit" sigma_twocomp Two-component error model residuals.mkinfit Extract residuals from an mkinfit model mkinplot Plot the observed data and the fitted model of an mkinfit object mkinpredict Produce predictions from a kinetic model using specific parameters plot.mixed.mmkin Plot predictions from a fitted nonlinear mixed model obtained via an mmkin row object No Results!

## Vignettes of mkin

 Name web_only/FOCUS_Z.html web_only/FOCUS_Z.rmd web_only/NAFTA_examples.html web_only/NAFTA_examples.rmd web_only/benchmarks.html web_only/benchmarks.rmd web_only/compiled_models.html web_only/compiled_models.rmd FOCUS_D.rmd FOCUS_L.rmd mkin.rmd mkin_vignettes.css references.bib twa.rmd No Results!