From 17af45b984d348505527140470c7fff204748ea6 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 12 Sep 2025 22:16:13 +0200 Subject: Facilitate centering covariates The motivation for this is to obtain confidence intervals for covariate dependent parameters that are valid for a median/mean value of the covariate. Implementation by adding an argument to the 'saem' function, and adapting the relevant functions working with 'saem' objects. Vignettes, the template and tests were updated to use the new functionality. --- DESCRIPTION | 4 +- NEWS.md | 6 +- R/endpoints.R | 1 + R/plot.mixed.mmkin.R | 2 +- R/saem.R | 42 +- README.md | 8 +- docs/404.html | 6 +- docs/articles/index.html | 6 +- docs/articles/web_only/mesotrione_parent_2023.html | 707 ++++++++--------- .../figure-html/unnamed-chunk-14-1.png | Bin 78165 -> 83449 bytes .../figure-html/unnamed-chunk-19-1.png | Bin 77391 -> 82150 bytes .../figure-html/unnamed-chunk-25-1.png | Bin 77786 -> 82704 bytes .../figure-html/unnamed-chunk-30-1.png | Bin 77683 -> 82968 bytes .../figure-html/unnamed-chunk-8-1.png | Bin 76004 -> 80875 bytes docs/authors.html | 10 +- docs/index.html | 8 +- docs/news/index.html | 10 +- docs/reference/index.html | 6 +- docs/reference/saem-3.png | Bin 128590 -> 128574 bytes docs/reference/saem.html | 29 +- docs/search.json | 2 +- .../hierarchical_kinetics/skeleton/skeleton.Rmd | 14 +- log/build.log | 2 +- log/check.log | 14 +- log/test.log | 24 +- man/saem.Rd | 5 + tests/testthat/test_mixed.R | 20 + vignettes/web_only/mesotrione_parent_2023.html | 856 ++++++++++----------- vignettes/web_only/mesotrione_parent_2023.rmd | 25 +- .../figure-html/unnamed-chunk-14-1.png | Bin 78165 -> 83449 bytes .../figure-html/unnamed-chunk-19-1.png | Bin 77391 -> 82150 bytes .../figure-html/unnamed-chunk-25-1.png | Bin 77786 -> 82704 bytes .../figure-html/unnamed-chunk-30-1.png | Bin 77683 -> 82968 bytes .../figure-html/unnamed-chunk-8-1.png | Bin 76004 -> 80875 bytes 34 files changed, 946 insertions(+), 861 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index f9cb67be..065c000c 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,8 +1,8 @@ Package: mkin Type: Package Title: Kinetic Evaluation of Chemical Degradation Data -Version: 1.2.10 -Date: 2025-05-13 +Version: 1.2.11 +Date: 2025-09-12 Authors@R: c( person("Johannes", "Ranke", role = c("aut", "cre", "cph"), email = "johannes.ranke@jrwb.de", diff --git a/NEWS.md b/NEWS.md index d3ca5b78..82f6aa4d 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,5 +1,9 @@ # mkin 1.2.10 (unreleased) +## New features + +- 'R/{saem,endpoints,plot.mixed.mmkin}.R': The function 'saem()' gains an argument 'center_covariates'. The functions 'parms', 'endpoints' and 'plot.mixed.mmkin' were adapted, so the user can still specify covariate values on the original, uncentered scale even if a covariate is centered. + ## Bug fixes - 'inst/rmarkdown/templates/hierarchical_kinetics/skeleton/skeleton.Rmd': Make parent model selection more robust @@ -8,7 +12,7 @@ # mkin 1.2.9 (2024-02-13) -## New features +## New features - 'R/plot.mixed.R': Support more than 25 datasets diff --git a/R/endpoints.R b/R/endpoints.R index c3e0a0d3..70a9eef3 100644 --- a/R/endpoints.R +++ b/R/endpoints.R @@ -45,6 +45,7 @@ endpoints <- function(fit, covariates = NULL, covariate_quantile = 0.5) { if (!is.null(fit$covariate_models)) { if (is.null(covariates)) { + # Use covariate quantiles if no explicit covariates are given covariates = as.data.frame( apply(fit$covariates, 2, quantile, covariate_quantile, simplify = FALSE)) diff --git a/R/plot.mixed.mmkin.R b/R/plot.mixed.mmkin.R index f05f1110..058e01a8 100644 --- a/R/plot.mixed.mmkin.R +++ b/R/plot.mixed.mmkin.R @@ -157,7 +157,7 @@ plot.mixed.mmkin <- function(x, ifelse(length(x$covariate_models) == 1, "Covariate", "Covariates"), rownames(covariates)) - } + } degparms_pop <- parms(x, covariates = covariates) pop_curves <- TRUE } diff --git a/R/saem.R b/R/saem.R index a9f97d23..45a7f8e9 100644 --- a/R/saem.R +++ b/R/saem.R @@ -50,6 +50,9 @@ utils::globalVariables(c("predicted", "std")) #' initialisation of [saemix::saemixModel] is used for omega.init. #' @param covariates A data frame with covariate data for use in #' 'covariate_models', with dataset names as row names. +#' @param center_covariates Either NA, for no centering, or your +#' preferred function for calculating the center, currently either +#' median or mean. #' @param covariate_models A list containing linear model formulas with one explanatory #' variable, i.e. of the type 'parameter ~ covariate'. Covariates must be available #' in the 'covariates' data frame. @@ -148,6 +151,7 @@ saem.mmkin <- function(object, omega.init = "auto", covariates = NULL, covariate_models = NULL, + center_covariates = c(NA, "median", "mean"), no_random_effect = NULL, error.init = c(1, 1), nbiter.saemix = c(300, 100), @@ -158,6 +162,18 @@ saem.mmkin <- function(object, { call <- match.call() transformations <- match.arg(transformations) + center_covariates <- match.arg(center_covariates) + if (is.na(center_covariates)) { + covariate_centers <- NA + centered_covariates <- NA + } else { + center_covariate_func <- get(center_covariates) + centered_covariates <- data.frame(lapply(covariates, + function(x) x - center_covariate_func(x))) + rownames(centered_covariates) <- rownames(covariates) + covariate_centers <- sapply(covariates, center_covariate_func) + } + m_saemix <- saemix_model(object, verbose = verbose, error_model = error_model, degparms_start = degparms_start, @@ -166,12 +182,14 @@ saem.mmkin <- function(object, transformations = transformations, covariance.model = covariance.model, omega.init = omega.init, - covariates = covariates, + covariates = if (is.na(center_covariates)) covariates else centered_covariates, covariate_models = covariate_models, error.init = error.init, no_random_effect = no_random_effect, ...) - d_saemix <- saemix_data(object, covariates = covariates, verbose = verbose) + d_saemix <- saemix_data(object, + covariates = if (is.na(center_covariates)) covariates else centered_covariates, + verbose = verbose) fit_failed <- FALSE FIM_failed <- NULL @@ -227,6 +245,8 @@ saem.mmkin <- function(object, transform_rates = object[[1]]$transform_rates, transform_fractions = object[[1]]$transform_fractions, covariates = covariates, + centered_covariates = centered_covariates, + covariate_centers = covariate_centers, covariate_models = covariate_models, sm = m_saemix, so = f_saemix, @@ -817,7 +837,8 @@ update.saem.mmkin <- function(object, ..., evaluate = TRUE) { #' each column corresponding to a row of the data frame holding the covariates #' @param covariates A data frame holding covariate values for which to #' return parameter values. Only has an effect if 'ci' is FALSE. -parms.saem.mmkin <- function(object, ci = FALSE, covariates = NULL, ...) { +parms.saem.mmkin <- function(object, ci = FALSE, covariates = NULL, ...) +{ cov.mod <- object$sm@covariance.model n_cov_mod_parms <- sum(cov.mod[upper.tri(cov.mod, diag = TRUE)]) n_parms <- length(object$sm@name.modpar) + @@ -839,12 +860,25 @@ parms.saem.mmkin <- function(object, ci = FALSE, covariates = NULL, ...) { names(estimate) <- rownames(conf.int) + # If confidence intervals are requested, we do not care about covariates if (ci) { return(conf.int) } else { if (is.null(covariates)) { return(estimate) } else { + # If there are covariates in the model, calculate parameter + # estimates for the corresponding covariate values passed + # in 'covariates'. + covariate_centers <- object$covariate_centers + centered_covariates <- covariates + if (!is.na(covariate_centers[1])) { + # If covariates were centered by the saem function, we need to center + # user specified covariates as well + for (i in names(covariates)) { + centered_covariates[i] <- covariates[i] - object$covariate_centers[i] + } + } est_for_cov <- matrix(NA, nrow = length(object$sm@name.modpar), ncol = nrow(covariates), dimnames = (list(object$sm@name.modpar, rownames(covariates)))) @@ -856,7 +890,7 @@ parms.saem.mmkin <- function(object, ci = FALSE, covariates = NULL, ...) { beta_degparm_name <- paste0("beta_", covariate, "(", deg_parm_name, ")") est_for_cov[deg_parm_name, ] <- estimate[deg_parm_name] + - covariates[[covariate]] * estimate[beta_degparm_name] + centered_covariates[[covariate]] * estimate[beta_degparm_name] } else { est_for_cov[deg_parm_name, ] <- estimate[deg_parm_name] } diff --git a/README.md b/README.md index 2d3720ca..a7ecf758 100644 --- a/README.md +++ b/README.md @@ -47,7 +47,7 @@ at the package vignettes The HTML documentation of the latest version released to CRAN is available at [jrwb.de](https://pkgdown.jrwb.de/mkin/) and -[github](https://jranke.github.io/mkin/). +[github](https://jranke.github.io/mkin/). Documentation of the development version is found in the ['dev' subdirectory](https://pkgdown.jrwb.de/mkin/dev/). @@ -238,13 +238,13 @@ saemix for the evaluation of chemical degradation data. Regarding the application of nonlinear mixed-effects models to degradation data, von Götz et al (1999) have already proposed to use this technique in the context of environmental risk assessments of pesticides. However, this work was -apparently not followed up, which is why we had to independently arrive at the +apparently not followed up, which is why we had to independently arrive at the idea and missed to cite this previous work on the topic in our first publications. ## References - - +
Ranke J (2023) Application of nonlinear hierarchical models to the +
Ranke J (2023) Application of nonlinear hierarchical models to the kinetic evaluation of chemical degradation data - Guidance for the use of an R markdown template file. Umweltbundesamt TEXTE 151/2023 @@ -270,7 +270,7 @@ idea and missed to cite this previous work on the topic in our first publication 30 17 doi:10.1186/s12302-018-0145-1
Von Götz N, Nörtersheuser P, Richter O (1999) Population based analysis of pesticide kinetics Chemosphere diff --git a/docs/404.html b/docs/404.html index 39613c3e..4a18a694 100644 --- a/docs/404.html +++ b/docs/404.html @@ -1,5 +1,5 @@ - + @@ -20,7 +20,7 @@ mkin - 1.2.10 + 1.2.11

For obtaining fits with only well-defined random effects, we update -the set of fits, excluding random effects that were ill-defined -according to the illparms function.

+the set of fits, excluding random effects for degradation parameters +that were ill-defined according to the illparms +function.

 f_saem_2 <- update(f_saem_1, no_random_effect = illparms(f_saem_1))
 status(f_saem_2) |> kable()
@@ -1432,7 +1433,8 @@ according to the illparms function.

-

The updated fits terminate without errors.

+

The updated fits terminate without errors, and the only +ill-defined

 illparms(f_saem_2) |> kable()
@@ -1487,7 +1489,7 @@ significant pH effect could be found.

 sfo_pH <- saem(f_sep_const["SFO", ], no_random_effect = "meso_0", covariates = pH,
-  covariate_models = list(log_k_meso ~ pH))
+ covariate_models = list(log_k_meso ~ pH), center_covariates = "median")
 summary(sfo_pH)$confint_trans |> kable(digits = 2)
@@ -1506,9 +1508,9 @@ significant pH effect could be found.

- - - + + + @@ -1585,7 +1587,7 @@ meso 8.89035 29.5331
 fomc_pH <- saem(f_sep_const["FOMC", ], no_random_effect = "meso_0", covariates = pH,
-  covariate_models = list(log_alpha ~ pH))
+ covariate_models = list(log_alpha ~ pH), center_covariates = "median")
 summary(fomc_pH)$confint_trans |> kable(digits = 2)
log_k_meso-6.66-7.97-5.35-3.29-3.46-3.11
beta_pH(log_k_meso)
@@ -1604,9 +1606,9 @@ meso 8.89035 29.5331 - - - + + + @@ -1661,7 +1663,7 @@ ill-defined parameters remain.

npar AIC BIC Lik Chisq Df Pr(>Chisq) f_saem_2[["FOMC", "const"]] 5 783.25 787.71 -386.63 -fomc_pH_2 6 767.49 772.83 -377.75 17.762 1 2.503e-05 *** +fomc_pH_2 6 766.50 771.84 -377.25 18.753 1 1.488e-05 *** fomc_pH 7 770.07 776.30 -378.04 0.000 1 1 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 @@ -1680,39 +1682,39 @@ results in the most preferable FOMC fit.

- - - + + + - - - + + + - - - + + + - - - + + + - - - + + + - - - + + +
log_alpha-2.21-3.49-0.921.110.481.75
beta_pH(log_alpha)
meso_093.0590.9895.1393.2091.1095.29
log_alpha-2.91-4.18-1.630.810.331.30
beta_pH(log_alpha)0.660.440.870.550.350.75
log_beta3.953.294.623.853.224.47
a.14.984.285.685.004.305.70
SD.log_beta0.400.260.540.380.250.52
@@ -1727,7 +1729,7 @@ results in the most preferable FOMC fit.

$distimes DT50 DT90 DT50back -meso 17.30248 82.91343 24.95943 +meso 16.86448 83.26704 25.06588 
 endpoints(fomc_pH_2, covariates = c(pH = 7))
$covariates
@@ -1736,7 +1738,7 @@ User  7
 
 $distimes
          DT50     DT90 DT50back
-meso 6.986239 27.02927 8.136621
+meso 7.835768 31.46451 9.47176

DFOP @@ -1805,7 +1807,9 @@ identifiable parameters k2 and g.

 dfop_pH <- saem(f_sep_const["DFOP", ], no_random_effect = c("meso_0", "log_k1"),
   covariates = pH,
-  covariate_models = list(log_k2 ~ pH, g_qlogis ~ pH))
+ covariate_models = list(log_k2 ~ pH, g_qlogis ~ pH), + center_covariates = "median" +)

The corresponding parameters for the influence of soil pH are beta_pH(log_k2) for the influence of soil pH on k2, and beta_pH(g_qlogis) for its influence on @@ -1834,9 +1838,9 @@ identifiable parameters k2 and g.

log_k2 --11.48 --15.32 --7.64 +-3.96 +-4.47 +-3.44 beta_pH(log_k2) @@ -1846,9 +1850,9 @@ identifiable parameters k2 and g.

g_qlogis -3.13 -0.47 -5.80 +-0.12 +-0.57 +0.33 beta_pH(g_qlogis) @@ -1894,7 +1898,8 @@ corresponding covariate model.

 dfop_pH_3 <- saem(f_sep_const["DFOP", ], no_random_effect = c("meso_0", "log_k1"),
   covariates = pH,
-  covariate_models = list(log_k2 ~ pH))
+  covariate_models = list(log_k2 ~ pH),
+  center_covariates = "median")
 illparms(dfop_pH_3)
[1] "sd(g_qlogis)"

As the random effect for g is again ill-defined, the fit @@ -1913,7 +1918,7 @@ on the likelihood ratio test.

npar AIC BIC Lik f_saem_2[["DFOP", "const"]] 7 782.94 789.18 -384.47 dfop_pH_4 7 767.35 773.58 -376.68 -dfop_pH_2 8 765.14 772.26 -374.57 +dfop_pH_2 8 765.06 772.18 -374.53 dfop_pH_3 8 769.00 776.12 -376.50 dfop_pH 9 769.10 777.11 -375.55 
@@ -1922,7 +1927,7 @@ dfop_pH                        9 769.10 777.11 -375.55
npar AIC BIC Lik Chisq Df Pr(>Chisq) dfop_pH_4 7 767.35 773.58 -376.68 -dfop_pH_2 8 765.14 772.26 -374.57 4.2153 1 0.04006 * +dfop_pH_2 8 765.06 772.18 -374.53 4.2909 1 0.03832 * --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

When focussing on parameter identifiability using the test if the @@ -1944,7 +1949,7 @@ most preferable model.

$distimes DT50 DT90 DT50back DT50_k1 DT50_k2 -meso 18.36876 73.51841 22.13125 4.191901 23.98672 +meso 18.46687 74.91602 22.55197 4.568623 24.64483 
 endpoints(dfop_pH_2, covariates = c(pH = 7))
$covariates
@@ -1953,7 +1958,7 @@ User  7
 
 $distimes
          DT50     DT90 DT50back  DT50_k1  DT50_k2
-meso 8.346428 28.34437 8.532507 4.191901 8.753618
+meso 8.370528 28.37824 8.542701 4.568623 8.785409

SFORB @@ -1961,7 +1966,8 @@ meso 8.346428 28.34437 8.532507 4.191901 8.753618 
 sforb_pH <- saem(f_sep_const["SFORB", ], no_random_effect = c("meso_free_0", "log_k_meso_free_bound"),
   covariates = pH,
-  covariate_models = list(log_k_meso_free ~ pH, log_k_meso_bound_free ~ pH))
+ covariate_models = list(log_k_meso_free ~ pH, log_k_meso_bound_free ~ pH), + center_covariates = "median")

 summary(sforb_pH)$confint_trans |> kable(digits = 2)
@@ -1980,9 +1986,9 @@ meso 8.346428 28.34437 8.532507 4.191901 8.753618 - - - + + + @@ -1998,9 +2004,9 @@ meso 8.346428 28.34437 8.532507 4.191901 8.753618 - - - + + + @@ -2075,14 +2081,14 @@ not fully identifiable, the second model is selected.

- - + + - - - + + + @@ -2093,19 +2099,19 @@ not fully identifiable, the second model is selected.

- - + + - - + + - + @@ -2160,7 +2166,8 @@ meso 7.932495 36.93311 11.11797 5.205671 18.26
 hs_pH <- saem(f_sep_const["HS", ], no_random_effect = c("meso_0"),
   covariates = pH,
-  covariate_models = list(log_k1 ~ pH, log_k2 ~ pH, log_tb ~ pH))
+ covariate_models = list(log_k1 ~ pH, log_k2 ~ pH, log_tb ~ pH), + center_covariates = "median")
 summary(hs_pH)$confint_trans |> kable(digits = 2)
log_k_meso_free-5.37-6.94-3.81-2.94-3.23-2.65
beta_pH(log_k_meso_free)
log_k_meso_bound_free-9.98-19.22-0.74-2.91-4.30-1.52
beta_pH(log_k_meso_bound_free)
meso_free_0 93.3291.1695.4891.1795.47
log_k_meso_free-6.15-7.43-4.86-3.02-3.27-2.78
beta_pH(log_k_meso_free)
log_k_meso_free_bound -3.80-5.20-2.40-5.18-2.42
log_k_meso_bound_free -2.95-4.26-1.64-4.24-1.65
a.1 5.084.384.37 5.79
@@ -2179,9 +2186,9 @@ meso 7.932495 36.93311 11.11797 5.205671 18.26 - - - + + + @@ -2191,9 +2198,9 @@ meso 7.932495 36.93311 11.11797 5.205671 18.26 - - - + + + @@ -2203,9 +2210,9 @@ meso 7.932495 36.93311 11.11797 5.205671 18.26 - - - + + + @@ -2281,9 +2288,9 @@ Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 - - - + + + @@ -2293,9 +2300,9 @@ Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 - - - + + + @@ -2368,10 +2375,10 @@ compared with each other.

npar AIC BIC Lik sfo_pH 5 783.09 787.54 -386.54 -fomc_pH_2 6 767.49 772.83 -377.75 +fomc_pH_2 6 766.50 771.84 -377.25 dfop_pH_4 7 767.35 773.58 -376.68 sforb_pH_2 7 770.94 777.17 -378.47 -dfop_pH_2 8 765.14 772.26 -374.57 +dfop_pH_2 8 765.06 772.18 -374.53 hs_pH_2 10 766.47 775.37 -373.23

The DFOP model with pH influence on k2 and g and a random effect only on k2 is finally @@ -2386,7 +2393,7 @@ refer to the Appendix for a detailed listing.

$distimes DT50 DT90 DT50back DT50_k1 DT50_k2 -meso 18.36876 73.51841 22.13125 4.191901 23.98672 +meso 18.46687 74.91602 22.55197 4.568623 24.64483
 endpoints(dfop_pH_2, covariates = c(pH = 7))
$covariates
@@ -2395,7 +2402,7 @@ User  7
 
 $distimes
          DT50     DT90 DT50back  DT50_k1  DT50_k2
-meso 8.346428 28.34437 8.532507 4.191901 8.753618
+meso 8.370528 28.37824 8.542701 4.568623 8.785409
@@ -2418,11 +2425,11 @@ further refined to make them fully identifiable.

Hierarchical SFO fit with constant variance 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:12:46 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:01 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - k_meso * meso
@@ -2432,7 +2439,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 0.71 s
+Fitted in 0.602 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -2495,11 +2502,11 @@ meso 16.41 54.5
 Hierarchical FOMC fit with constant variance
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:12:46 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:02 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso
@@ -2509,7 +2516,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 0.842 s
+Fitted in 0.983 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -2578,11 +2585,11 @@ meso 14.8 74.64    22.47
 Hierarchical DFOP fit with constant variance
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:12:47 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:02 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -2594,7 +2601,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 1.168 s
+Fitted in 1.202 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -2669,11 +2676,11 @@ meso 16.04 63.75    19.19   3.931    20.8
 Hierarchical SFORB fit with constant variance
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:12:47 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:02 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound *
@@ -2686,7 +2693,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 1.256 s
+Fitted in 1.557 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -2776,11 +2783,11 @@ meso 14.79 60.81     18.3        4.521        20.37
 Hierarchical HS fit with constant variance
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:12:48 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:03 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - ifelse(time <= tb, k1, k2) * meso
@@ -2790,7 +2797,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 1.653 s
+Fitted in 1.61 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -2869,11 +2876,11 @@ meso   16   76    22.88    11.1   25.84
 Hierarchichal SFO fit with pH influence
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:13:00 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:15 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - k_meso * meso
@@ -2883,7 +2890,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 1.343 s
+Fitted in 0.924 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -2913,15 +2920,15 @@ Likelihood computed by importance sampling
 Optimised parameters:
                        est.   lower   upper
 meso_0              91.3481 89.2688 93.4275
-log_k_meso          -6.6614 -7.9715 -5.3514
+log_k_meso          -3.2854 -3.4590 -3.1118
 beta_pH(log_k_meso)  0.5871  0.3684  0.8059
 a.1                  5.4750  4.7085  6.2415
 SD.log_k_meso        0.3471  0.2258  0.4684
 
 Correlation: 
                     meso_0  lg_k_ms
-log_k_meso           0.0414        
-beta_pH(log_k_meso) -0.0183 -0.9917
+log_k_meso           0.1797        
+beta_pH(log_k_meso) -0.0183 -0.2379
 
 Random effects:
                 est.  lower  upper
@@ -2932,9 +2939,9 @@ Variance model:
 a.1 5.475 4.709 6.242
 
 Backtransformed parameters:
-            est.     lower     upper
-meso_0 91.348139 8.927e+01 93.427476
-k_meso  0.001279 3.452e-04  0.004741
+           est.    lower    upper
+meso_0 91.34814 89.26880 93.42748
+k_meso  0.03743  0.03146  0.04452
 
 Covariates used for endpoints below:
       pH
@@ -2950,11 +2957,11 @@ meso 18.52 61.52
 Hierarchichal FOMC fit with pH influence
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:13:03 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:18 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso
@@ -2964,7 +2971,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 1.897 s
+Fitted in 1.901 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -2995,7 +3002,7 @@ Likelihood computed by importance sampling
 Optimised parameters:
                         est.      lower   upper
 meso_0             92.840646  90.750461 94.9308
-log_alpha          -2.206602  -3.494546 -0.9187
+log_alpha           1.114051   0.475668  1.7524
 beta_pH(log_alpha)  0.577505   0.369805  0.7852
 log_beta            4.214099   3.438851  4.9893
 a.1                 5.027768   4.322028  5.7335
@@ -3004,9 +3011,9 @@ SD.log_beta         0.374640   0.009252  0.7400
 
 Correlation: 
                    meso_0  log_lph bt_H(_)
-log_alpha          -0.0865                
-beta_pH(log_alpha) -0.0789 -0.8704        
-log_beta           -0.3544  0.3302  0.1628
+log_alpha          -0.3220                
+beta_pH(log_alpha) -0.0789  0.1148        
+log_beta           -0.3544  0.9709  0.1628
 
 Random effects:
                  est.      lower upper
@@ -3018,10 +3025,10 @@ Variance model:
 a.1 5.028 4.322 5.734
 
 Backtransformed parameters:
-          est.    lower    upper
-meso_0 92.8406 90.75046  94.9308
-alpha   0.1101  0.03036   0.3991
-beta   67.6332 31.15113 146.8404
+         est.  lower   upper
+meso_0 92.841 90.750  94.931
+alpha   3.047  1.609   5.769
+beta   67.633 31.151 146.840
 
 Covariates used for endpoints below:
       pH
@@ -3037,11 +3044,11 @@ meso 17.28 76.37    22.99
 Refined hierarchichal FOMC fit with pH influence
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:13:08 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:21 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - (alpha/beta) * 1/((time/beta) + 1) * meso
@@ -3051,7 +3058,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 4.184 s
+Fitted in 3.35 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -3077,44 +3084,44 @@ Results:
 
 Likelihood computed by importance sampling
     AIC   BIC logLik
-  767.5 772.8 -377.7
+  766.5 771.8 -377.3
 
 Optimised parameters:
                       est.   lower   upper
-meso_0             93.0536 90.9771 95.1300
-log_alpha          -2.9054 -4.1803 -1.6304
-beta_pH(log_alpha)  0.6590  0.4437  0.8744
-log_beta            3.9549  3.2860  4.6239
-a.1                 4.9784  4.2815  5.6754
-SD.log_beta         0.4019  0.2632  0.5406
+meso_0             93.1950 91.1047 95.2853
+log_alpha           0.8125  0.3292  1.2957
+beta_pH(log_alpha)  0.5497  0.3490  0.7504
+log_beta            3.8464  3.2179  4.4750
+a.1                 4.9972  4.2976  5.6968
+SD.log_beta         0.3829  0.2499  0.5159
 
 Correlation: 
                    meso_0  log_lph bt_H(_)
-log_alpha          -0.0397                
-beta_pH(log_alpha) -0.0899 -0.9146        
-log_beta           -0.3473  0.2038  0.1919
+log_alpha          -0.3094                
+beta_pH(log_alpha) -0.0779  0.0841        
+log_beta           -0.3493  0.9533  0.1434
 
 Random effects:
               est.  lower  upper
-SD.log_beta 0.4019 0.2632 0.5406
+SD.log_beta 0.3829 0.2499 0.5159
 
 Variance model:
      est. lower upper
-a.1 4.978 4.281 5.675
+a.1 4.997 4.298 5.697
 
 Backtransformed parameters:
-           est.    lower    upper
-meso_0 93.05359 90.97713  95.1300
-alpha   0.05473  0.01529   0.1958
-beta   52.19251 26.73597 101.8874
+         est. lower  upper
+meso_0 93.195 91.10 95.285
+alpha   2.253  1.39  3.654
+beta   46.826 24.98 87.793
 
 Covariates used for endpoints below:
       pH
 50% 5.75
 
 Estimated disappearance times:
-     DT50  DT90 DT50back
-meso 17.3 82.91    24.96
+      DT50  DT90 DT50back
+meso 16.86 83.27    25.07
 
 

 

@@ -3122,11 +3129,11 @@ meso 17.3 82.91    24.96
 Hierarchichal DFOP fit with pH influence
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:13:11 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:25 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -3138,7 +3145,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 2.18 s
+Fitted in 2.592 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -3168,24 +3175,24 @@ Likelihood computed by importance sampling
   769.1 777.1 -375.5
 
 Optimised parameters:
-                        est.    lower    upper
-meso_0             92.843344  90.8464 94.84028
-log_k1             -2.815685  -3.0888 -2.54261
-log_k2            -11.479779 -15.3203 -7.63923
-beta_pH(log_k2)     1.308417   0.6948  1.92203
-g_qlogis            3.133036   0.4657  5.80035
-beta_pH(g_qlogis)  -0.565988  -1.0394 -0.09262
-a.1                 4.955518   4.2597  5.65135
-SD.log_k2           0.758963   0.4685  1.04943
-SD.g_qlogis         0.005215  -9.9561  9.96656
+                       est.   lower    upper
+meso_0            92.843344 90.8464 94.84028
+log_k1            -2.815685 -3.0888 -2.54261
+log_k2            -3.956384 -4.4741 -3.43868
+beta_pH(log_k2)    1.308417  0.6948  1.92203
+g_qlogis          -0.121394 -0.5691  0.32627
+beta_pH(g_qlogis) -0.565988 -1.0394 -0.09262
+a.1                4.955518  4.2597  5.65135
+SD.log_k2          0.758963  0.4685  1.04943
+SD.g_qlogis        0.005215 -9.9561  9.96656
 
 Correlation: 
                   meso_0  log_k1  log_k2  b_H(_2) g_qlogs
 log_k1             0.2706                                
-log_k2            -0.0571  0.1096                        
-beta_pH(log_k2)    0.0554 -0.1291 -0.9937                
-g_qlogis          -0.1125 -0.5062 -0.1305  0.1294        
-beta_pH(g_qlogis)  0.1267  0.4226  0.0419 -0.0438 -0.9864
+log_k2            -0.0457 -0.0667                        
+beta_pH(log_k2)    0.0554 -0.1291 -0.5566                
+g_qlogis           0.1004 -0.4462 -0.4397  0.5042        
+beta_pH(g_qlogis)  0.1267  0.4226  0.0123 -0.0438  0.2029
 
 Random effects:
                 est.   lower upper
@@ -3197,11 +3204,11 @@ Variance model:
 a.1 4.956  4.26 5.651
 
 Backtransformed parameters:
-            est.     lower     upper
-meso_0 9.284e+01 9.085e+01 9.484e+01
-k1     5.986e-02 4.556e-02 7.866e-02
-k2     1.034e-05 2.221e-07 4.812e-04
-g      9.582e-01 6.144e-01 9.970e-01
+           est.    lower    upper
+meso_0 92.84334 90.84641 94.84028
+k1      0.05986  0.04556  0.07866
+k2      0.01913  0.01140  0.03211
+g       0.46969  0.36145  0.58085
 
 Covariates used for endpoints below:
       pH
@@ -3217,11 +3224,11 @@ meso 20.23 88.45    26.62   11.58   36.23
 Refined hierarchical DFOP fit with pH influence
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:13:14 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:30 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -3233,7 +3240,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 2.424 s
+Fitted in 4.483 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -3260,41 +3267,41 @@ Results:
 
 Likelihood computed by importance sampling
     AIC   BIC logLik
-  765.1 772.3 -374.6
+  765.1 772.2 -374.5
 
 Optimised parameters:
-                     est.    lower    upper
-meso_0            93.3333  91.2427 95.42394
-log_k1            -1.7997  -2.9124 -0.68698
-log_k2            -8.1810 -10.1819 -6.18008
-beta_pH(log_k2)    0.8064   0.4903  1.12257
-g_qlogis           3.3513  -1.1792  7.88182
-beta_pH(g_qlogis) -0.8672  -1.7661  0.03177
-a.1                4.9158   4.2277  5.60390
-SD.log_k2          0.3946   0.2565  0.53281
+                     est.   lower    upper
+meso_0            93.1612 91.0766 95.24580
+log_k1            -1.8857 -2.8975 -0.87395
+log_k2            -3.5711 -3.8859 -3.25622
+beta_pH(log_k2)    0.8252  0.4952  1.15513
+g_qlogis          -1.5326 -2.6994 -0.36574
+beta_pH(g_qlogis) -0.8365 -1.7163  0.04333
+a.1                4.9218  4.2328  5.61070
+SD.log_k2          0.4011  0.2604  0.54184
 
 Correlation: 
                   meso_0  log_k1  log_k2  b_H(_2) g_qlogs
-log_k1             0.1730                                
-log_k2             0.0442  0.5370                        
-beta_pH(log_k2)   -0.0392 -0.4880 -0.9923                
-g_qlogis          -0.1536  0.1431 -0.1129  0.1432        
-beta_pH(g_qlogis)  0.1504 -0.3151 -0.0196 -0.0212 -0.9798
+log_k1             0.1734                                
+log_k2             0.0553  0.6421                        
+beta_pH(log_k2)   -0.0382 -0.5121 -0.5860                
+g_qlogis           0.0616 -0.8501 -0.7251  0.4941        
+beta_pH(g_qlogis)  0.1408 -0.3240 -0.2716 -0.0041  0.6264
 
 Random effects:
             est.  lower  upper
-SD.log_k2 0.3946 0.2565 0.5328
+SD.log_k2 0.4011 0.2604 0.5418
 
 Variance model:
      est. lower upper
-a.1 4.916 4.228 5.604
+a.1 4.922 4.233 5.611
 
 Backtransformed parameters:
-            est.     lower    upper
-meso_0 9.333e+01 9.124e+01 95.42394
-k1     1.654e-01 5.435e-02  0.50309
-k2     2.799e-04 3.785e-05  0.00207
-g      9.661e-01 2.352e-01  0.99962
+           est.    lower    upper
+meso_0 93.16118 91.07655 95.24580
+k1      0.15172  0.05516  0.41730
+k2      0.02813  0.02053  0.03853
+g       0.17762  0.06301  0.40957
 
 Covariates used for endpoints below:
       pH
@@ -3302,7 +3309,7 @@ Covariates used for endpoints below:
 
 Estimated disappearance times:
       DT50  DT90 DT50back DT50_k1 DT50_k2
-meso 18.37 73.52    22.13   4.192   23.99
+meso 18.47 74.92    22.55   4.569   24.64
 
 

 

@@ -3310,11 +3317,11 @@ meso 18.37 73.52    22.13   4.192   23.99
 Further refined hierarchical DFOP fit with pH influence
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:13:23 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:37 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -3326,7 +3333,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 3.211 s
+Fitted in 3.213 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -3356,21 +3363,21 @@ Likelihood computed by importance sampling
   767.4 773.6 -376.7
 
 Optimised parameters:
-                   est.    lower   upper
-meso_0          93.3011  91.1905 95.4118
-log_k1          -2.1487  -2.7607 -1.5367
-log_k2          -8.1039 -10.4225 -5.7853
-beta_pH(log_k2)  0.7821   0.4126  1.1517
-g_qlogis        -1.0373  -1.9337 -0.1409
-a.1              5.0095   4.3082  5.7108
-SD.log_k2        0.4622   0.3009  0.6235
+                   est.   lower   upper
+meso_0          93.3011 91.1905 95.4118
+log_k1          -2.1487 -2.7607 -1.5367
+log_k2          -3.6066 -3.9305 -3.2828
+beta_pH(log_k2)  0.7821  0.4126  1.1517
+g_qlogis        -1.0373 -1.9337 -0.1409
+a.1              5.0095  4.3082  5.7108
+SD.log_k2        0.4622  0.3009  0.6235
 
 Correlation: 
                 meso_0  log_k1  log_k2  b_H(_2)
 log_k1           0.2179                        
-log_k2           0.0337  0.5791                
-beta_pH(log_k2) -0.0326 -0.5546 -0.9932        
-g_qlogis         0.0237 -0.8479 -0.6571  0.6123
+log_k2           0.0271  0.5067                
+beta_pH(log_k2) -0.0326 -0.5546 -0.5485        
+g_qlogis         0.0237 -0.8479 -0.6866  0.6123
 
 Random effects:
             est.  lower  upper
@@ -3381,11 +3388,11 @@ Variance model:
 a.1 5.009 4.308 5.711
 
 Backtransformed parameters:
-            est.     lower     upper
-meso_0 9.330e+01 9.119e+01 95.411751
-k1     1.166e-01 6.325e-02  0.215084
-k2     3.024e-04 2.975e-05  0.003072
-g      2.617e-01 1.263e-01  0.464832
+           est.    lower    upper
+meso_0 93.30113 91.19050 95.41175
+k1      0.11664  0.06325  0.21508
+k2      0.02714  0.01963  0.03752
+g       0.26168  0.12635  0.46483
 
 Covariates used for endpoints below:
       pH
@@ -3401,11 +3408,11 @@ meso 17.09 73.67    22.18   5.943   25.54
 Hierarchichal SFORB fit with pH influence
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:13:26 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:41 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound *
@@ -3418,7 +3425,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 2.649 s
+Fitted in 2.758 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -3455,24 +3462,24 @@ Likelihood computed by importance sampling
   768.8 776.8 -375.4
 
 Optimised parameters:
-                                  est.    lower   upper
-meso_free_0                    93.4204  91.3213 95.5195
-log_k_meso_free                -5.3742  -6.9366 -3.8117
-beta_pH(log_k_meso_free)        0.4232   0.1769  0.6695
-log_k_meso_free_bound          -3.4889  -4.9243 -2.0535
-log_k_meso_bound_free          -9.9797 -19.2232 -0.7362
-beta_pH(log_k_meso_bound_free)  1.2290  -0.2107  2.6687
-a.1                             4.9031   4.1795  5.6268
-SD.log_k_meso_free              0.3454   0.2252  0.4656
-SD.log_k_meso_bound_free        0.1277  -1.9459  2.2012
+                                  est.   lower   upper
+meso_free_0                    93.4204 91.3213 95.5195
+log_k_meso_free                -2.9408 -3.2344 -2.6471
+beta_pH(log_k_meso_free)        0.4232  0.1769  0.6695
+log_k_meso_free_bound          -3.4889 -4.9243 -2.0535
+log_k_meso_bound_free          -2.9130 -4.3047 -1.5212
+beta_pH(log_k_meso_bound_free)  1.2290 -0.2107  2.6687
+a.1                             4.9031  4.1795  5.6268
+SD.log_k_meso_free              0.3454  0.2252  0.4656
+SD.log_k_meso_bound_free        0.1277 -1.9459  2.2012
 
 Correlation: 
                                ms_fr_0 lg_k_m_ b_H(___) lg_k_ms_f_ lg_k_ms_b_
-log_k_meso_free                 0.1493                                       
-beta_pH(log_k_meso_free)       -0.0930 -0.9854                               
-log_k_meso_free_bound           0.2439  0.4621 -0.3492                       
-log_k_meso_bound_free           0.2188  0.1292 -0.0339   0.7287              
-beta_pH(log_k_meso_bound_free) -0.2216 -0.0797 -0.0111  -0.6566    -0.9934   
+log_k_meso_free                 0.3460                                       
+beta_pH(log_k_meso_free)       -0.0930 -0.4206                               
+log_k_meso_free_bound           0.2439  0.7749 -0.3492                       
+log_k_meso_bound_free           0.1350  0.6400 -0.2912   0.9346              
+beta_pH(log_k_meso_bound_free) -0.2216 -0.4778 -0.0111  -0.6566    -0.6498   
 
 Random effects:
                            est.   lower  upper
@@ -3484,11 +3491,11 @@ Variance model:
 a.1 4.903  4.18 5.627
 
 Backtransformed parameters:
-                       est.     lower    upper
-meso_free_0       9.342e+01 9.132e+01 95.51946
-k_meso_free       4.635e-03 9.716e-04  0.02211
-k_meso_free_bound 3.054e-02 7.268e-03  0.12829
-k_meso_bound_free 4.633e-05 4.482e-09  0.47894
+                      est.     lower    upper
+meso_free_0       93.42040 91.321340 95.51946
+k_meso_free        0.05282  0.039384  0.07085
+k_meso_free_bound  0.03054  0.007268  0.12829
+k_meso_bound_free  0.05431  0.013505  0.21845
 
 Covariates used for endpoints below:
       pH
@@ -3512,11 +3519,11 @@ meso 16.42 75.2    22.64        6.185        27.08
 Refined hierarchichal SFORB fit with pH influence
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:13:30 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:44 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso_free/dt = - k_meso_free * meso_free - k_meso_free_bound *
@@ -3529,7 +3536,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 3.186 s
+Fitted in 2.971 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -3567,20 +3574,20 @@ Likelihood computed by importance sampling
 
 Optimised parameters:
                             est.   lower   upper
-meso_free_0              93.3196 91.1633 95.4760
-log_k_meso_free          -6.1460 -7.4306 -4.8614
+meso_free_0              93.3196 91.1650 95.4743
+log_k_meso_free          -3.0207 -3.2655 -2.7759
 beta_pH(log_k_meso_free)  0.5435  0.3329  0.7542
-log_k_meso_free_bound    -3.8001 -5.2027 -2.3975
-log_k_meso_bound_free    -2.9462 -4.2565 -1.6359
-a.1                       5.0825  4.3793  5.7856
+log_k_meso_free_bound    -3.8001 -5.1809 -2.4193
+log_k_meso_bound_free    -2.9462 -4.2411 -1.6513
+a.1                       5.0825  4.3709  5.7940
 SD.log_k_meso_free        0.3338  0.2175  0.4502
 
 Correlation: 
                          ms_fr_0 lg_k_m_ b_H(___ lg_k_ms_f_
-log_k_meso_free           0.1086                           
-beta_pH(log_k_meso_free) -0.0426 -0.9821                   
-log_k_meso_free_bound     0.2513  0.1717 -0.0409           
-log_k_meso_bound_free     0.1297  0.1171 -0.0139  0.9224   
+log_k_meso_free           0.3556                           
+beta_pH(log_k_meso_free) -0.0422 -0.2041                   
+log_k_meso_free_bound     0.2513  0.6866 -0.0400           
+log_k_meso_bound_free     0.1292  0.5341 -0.0129  0.9214   
 
 Random effects:
                      est.  lower  upper
@@ -3588,14 +3595,14 @@ SD.log_k_meso_free 0.3338 0.2175 0.4502
 
 Variance model:
      est. lower upper
-a.1 5.082 4.379 5.786
+a.1 5.082 4.371 5.794
 
 Backtransformed parameters:
-                       est.     lower    upper
-meso_free_0       93.319649 9.116e+01 95.47601
-k_meso_free        0.002142 5.928e-04  0.00774
-k_meso_free_bound  0.022369 5.502e-03  0.09095
-k_meso_bound_free  0.052539 1.417e-02  0.19478
+                      est.     lower    upper
+meso_free_0       93.31965 91.165044 95.47425
+k_meso_free        0.04877  0.038177  0.06230
+k_meso_free_bound  0.02237  0.005623  0.08898
+k_meso_bound_free  0.05254  0.014392  0.19179
 
 Covariates used for endpoints below:
       pH
@@ -3619,11 +3626,11 @@ meso 16.87 73.16    22.02         7.12        26.34
 Hierarchichal HS fit with pH influence
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:13:32 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:48 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - ifelse(time <= tb, k1, k2) * meso
@@ -3633,7 +3640,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 1.833 s
+Fitted in 2.254 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -3665,11 +3672,11 @@ Likelihood computed by importance sampling
 Optimised parameters:
                     est.   lower   upper
 meso_0          93.32599 91.4658 95.1862
-log_k1          -5.81463 -7.2710 -4.3583
+log_k1          -3.08497 -3.2830 -2.8870
 beta_pH(log_k1)  0.47472  0.2334  0.7160
-log_k2          -6.79633 -8.7605 -4.8322
+log_k2          -3.68267 -3.9077 -3.4577
 beta_pH(log_k2)  0.54151  0.2124  0.8706
-log_tb           3.24674  1.2470  5.2465
+log_tb           2.67815  2.3846  2.9717
 beta_pH(log_tb) -0.09889 -0.4258  0.2280
 a.1              4.49487  3.7766  5.2132
 SD.log_k1        0.37191  0.2370  0.5068
@@ -3678,12 +3685,12 @@ SD.log_tb        0.25353 -0.0664  0.5735
 
 Correlation: 
                 meso_0  log_k1  b_H(_1) log_k2  b_H(_2) log_tb 
-log_k1           0.0744                                        
-beta_pH(log_k1) -0.0452 -0.9915                                
-log_k2           0.0066 -0.0363  0.0376                        
-beta_pH(log_k2) -0.0071  0.0372 -0.0391 -0.9939                
-log_tb          -0.0238 -0.1483  0.1362 -0.3836  0.3696        
-beta_pH(log_tb)  0.0097  0.1359 -0.1265  0.3736 -0.3653 -0.9905
+log_k1           0.2301                                        
+beta_pH(log_k1) -0.0452 -0.2842                                
+log_k2          -0.0029 -0.0322 -0.0008                        
+beta_pH(log_k2) -0.0071  0.0000 -0.0391 -0.2655                
+log_tb          -0.1003 -0.2052  0.1180 -0.4197  0.1794        
+beta_pH(log_tb)  0.0097  0.1125 -0.1265  0.1894 -0.3653 -0.3449
 
 Random effects:
             est.   lower  upper
@@ -3696,11 +3703,11 @@ Variance model:
 a.1 4.495 3.777 5.213
 
 Backtransformed parameters:
-            est.     lower     upper
-meso_0 93.325994 9.147e+01 9.519e+01
-k1      0.002984 6.954e-04 1.280e-02
-k2      0.001118 1.568e-04 7.969e-03
-tb     25.706437 3.480e+00 1.899e+02
+           est.    lower    upper
+meso_0 93.32599 91.46575 95.18624
+k1      0.04573  0.03752  0.05574
+k2      0.02516  0.02009  0.03150
+tb     14.55810 10.85502 19.52445
 
 Covariates used for endpoints below:
       pH
@@ -3716,11 +3723,11 @@ meso 15.65 79.63    23.97   15.16   27.55
 Refined hierarchichal HS fit with pH influence
 
 

-saemix version used for fitting:      3.3 
-mkin version used for pre-fitting:  1.2.10 
-R version used for fitting:         4.5.0 
-Date of fit:     Wed May 14 05:13:35 2025 
-Date of summary: Wed May 14 05:13:35 2025 
+saemix version used for fitting:      3.4 
+mkin version used for pre-fitting:  1.2.11 
+R version used for fitting:         4.5.1 
+Date of fit:     Fri Sep 12 22:15:50 2025 
+Date of summary: Fri Sep 12 22:15:50 2025 
 
 Equations:
 d_meso/dt = - ifelse(time <= tb, k1, k2) * meso
@@ -3730,7 +3737,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 1.852 s
+Fitted in 1.425 s
 Using 300, 100 iterations and 3 chains
 
 Variance model: Constant variance 
@@ -3762,9 +3769,9 @@ Likelihood computed by importance sampling
 Optimised parameters:
                    est.    lower   upper
 meso_0          93.3251 91.49823 95.1520
-log_k1          -5.6796 -7.08789 -4.2714
+log_k1          -3.0535 -3.24879 -2.8582
 beta_pH(log_k1)  0.4567  0.22400  0.6894
-log_k2          -6.6083 -8.33839 -4.8781
+log_k2          -3.7439 -3.94307 -3.5447
 beta_pH(log_k2)  0.4982  0.20644  0.7899
 log_tb           2.7040  2.33033  3.0777
 a.1              4.4452  3.73537  5.1551
@@ -3774,11 +3781,11 @@ SD.log_tb        0.5488  0.24560  0.8521
 
 Correlation: 
                 meso_0  log_k1  b_H(_1) log_k2  b_H(_2)
-log_k1           0.0740                                
-beta_pH(log_k1) -0.0453 -0.9912                        
-log_k2           0.0115 -0.0650  0.0661                
-beta_pH(log_k2) -0.0116  0.0649 -0.0667 -0.9936        
-log_tb          -0.0658 -0.1135  0.0913 -0.1500  0.1210
+log_k1           0.2233                                
+beta_pH(log_k1) -0.0453 -0.2955                        
+log_k2           0.0028 -0.0420  0.0126                
+beta_pH(log_k2) -0.0116  0.0112 -0.0667 -0.2097        
+log_tb          -0.0658 -0.1928  0.0913 -0.2843  0.1210
 
 Random effects:
             est.   lower  upper
@@ -3791,11 +3798,11 @@ Variance model:
 a.1 4.445 3.735 5.155
 
 Backtransformed parameters:
-            est.     lower     upper
-meso_0 93.325134 9.150e+01 95.152036
-k1      0.003415 8.352e-04  0.013962
-k2      0.001349 2.392e-04  0.007611
-tb     14.939247 1.028e+01 21.707445
+           est.    lower    upper
+meso_0 93.32513 91.49823 95.15204
+k1      0.04719  0.03882  0.05737
+k2      0.02366  0.01939  0.02888
+tb     14.93925 10.28132 21.70744
 
 Covariates used for endpoints below:
       pH
@@ -3812,13 +3819,13 @@ meso 14.69 82.45    24.82   14.69   29.29
 

 
Session info
 

-
R version 4.5.0 (2025-04-11)
+
R version 4.5.1 (2025-06-13)
 Platform: x86_64-pc-linux-gnu
-Running under: Debian GNU/Linux 12 (bookworm)
+Running under: Debian GNU/Linux 13 (trixie)
 
 Matrix products: default
-BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
-LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0  LAPACK version 3.11.0
+BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.12.1 
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.1;  LAPACK version 3.12.0
 
 locale:
  [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
@@ -3836,29 +3843,29 @@ attached base packages:
 [8] base     
 
 other attached packages:
-[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.3      npde_3.5       
-[5] knitr_1.49      mkin_1.2.10    
+[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.4      npde_3.5       
+[5] knitr_1.50      mkin_1.2.11    
 
 loaded via a namespace (and not attached):
- [1] gtable_0.3.6      jsonlite_1.9.0    dplyr_1.1.4       compiler_4.5.0   
- [5] tidyselect_1.2.1  gridExtra_2.3     jquerylib_0.1.4   systemfonts_1.2.1
- [9] scales_1.3.0      textshaping_1.0.0 readxl_1.4.4      yaml_2.3.10      
-[13] fastmap_1.2.0     lattice_0.22-6    ggplot2_3.5.1     R6_2.6.1         
-[17] generics_0.1.3    lmtest_0.9-40     MASS_7.3-65       htmlwidgets_1.6.4
-[21] tibble_3.2.1      desc_1.4.3        munsell_0.5.1     bslib_0.9.0      
-[25] pillar_1.10.1     rlang_1.1.5       cachem_1.1.0      xfun_0.51        
-[29] fs_1.6.5          sass_0.4.9        cli_3.6.4         pkgdown_2.1.1    
-[33] magrittr_2.0.3    digest_0.6.37     grid_4.5.0        mclust_6.1.1     
-[37] lifecycle_1.0.4   nlme_3.1-168      vctrs_0.6.5       evaluate_1.0.3   
-[41] glue_1.8.0        cellranger_1.1.0  codetools_0.2-20  ragg_1.3.3       
-[45] zoo_1.8-13        colorspace_2.1-1  tools_4.5.0       pkgconfig_2.0.3  
-[49] htmltools_0.5.8.1

+ [1] gtable_0.3.6       jsonlite_2.0.0     dplyr_1.1.4        compiler_4.5.1    
+ [5] tidyselect_1.2.1   dichromat_2.0-0.1  gridExtra_2.3      jquerylib_0.1.4   
+ [9] systemfonts_1.2.3  scales_1.4.0       textshaping_1.0.1  readxl_1.4.5      
+[13] yaml_2.3.10        fastmap_1.2.0      lattice_0.22-7     ggplot2_3.5.2     
+[17] R6_2.6.1           generics_0.1.4     lmtest_0.9-40      MASS_7.3-65       
+[21] htmlwidgets_1.6.4  tibble_3.3.0       desc_1.4.3         bslib_0.9.0       
+[25] pillar_1.10.2      RColorBrewer_1.1-3 rlang_1.1.6        cachem_1.1.0      
+[29] xfun_0.52          fs_1.6.6           sass_0.4.10        cli_3.6.5         
+[33] pkgdown_2.1.3      magrittr_2.0.3     digest_0.6.37      grid_4.5.1        
+[37] mclust_6.1.1       lifecycle_1.0.4    nlme_3.1-168       vctrs_0.6.5       
+[41] evaluate_1.0.3     glue_1.8.0         cellranger_1.1.0   farver_2.1.2      
+[45] codetools_0.2-20   ragg_1.4.0         zoo_1.8-14         colorspace_2.1-1  
+[49] tools_4.5.1        pkgconfig_2.0.3    htmltools_0.5.8.1 

 

 

 
Hardware info
 

 
CPU model: AMD Ryzen 9 7950X 16-Core Processor

-
MemTotal:       64927780 kB

+
MemTotal:       64933716 kB
log_k1-5.81-7.27-4.36-3.08-3.28-2.89
beta_pH(log_k1)
log_k2-6.80-8.76-4.83-3.68-3.91-3.46
beta_pH(log_k2)
log_tb3.251.255.252.682.382.97
beta_pH(log_tb)
log_k1-5.68-7.09-4.27-3.05-3.25-2.86
beta_pH(log_k1)
log_k2-6.61-8.34-4.88-3.74-3.94-3.54
beta_pH(log_k2)
","
"],col:[2,"","
"],tr:[2,"","
"],td:[3,"","
"],_default:[0,"",""]};function ve(e,t){var n;return n="undefined"!=typeof e.getElementsByTagName?e.getElementsByTagName(t||"*"):"undefined"!=typeof e.querySelectorAll?e.querySelectorAll(t||"*"):[],void 0===t||t&&A(e,t)?S.merge([e],n):n}function ye(e,t){for(var n=0,r=e.length;n",""]);var me=/<|&#?\w+;/;function xe(e,t,n,r,i){for(var o,a,s,u,l,c,f=t.createDocumentFragment(),p=[],d=0,h=e.length;d\s*$/g;function je(e,t){return A(e,"table")&&A(11!==t.nodeType?t:t.firstChild,"tr")&&S(e).children("tbody")[0]||e}function De(e){return e.type=(null!==e.getAttribute("type"))+"/"+e.type,e}function qe(e){return"true/"===(e.type||"").slice(0,5)?e.type=e.type.slice(5):e.removeAttribute("type"),e}function Le(e,t){var n,r,i,o,a,s;if(1===t.nodeType){if(Y.hasData(e)&&(s=Y.get(e).events))for(i in Y.remove(t,"handle events"),s)for(n=0,r=s[i].length;n").attr(n.scriptAttrs||{}).prop({charset:n.scriptCharset,src:n.url}).on("load error",i=function(e){r.remove(),i=null,e&&t("error"===e.type?404:200,e.type)}),E.head.appendChild(r[0])},abort:function(){i&&i()}}});var _t,zt=[],Ut=/(=)\?(?=&|$)|\?\?/;S.ajaxSetup({jsonp:"callback",jsonpCallback:function(){var e=zt.pop()||S.expando+"_"+wt.guid++;return this[e]=!0,e}}),S.ajaxPrefilter("json jsonp",function(e,t,n){var r,i,o,a=!1!==e.jsonp&&(Ut.test(e.url)?"url":"string"==typeof e.data&&0===(e.contentType||"").indexOf("application/x-www-form-urlencoded")&&Ut.test(e.data)&&"data");if(a||"jsonp"===e.dataTypes[0])return r=e.jsonpCallback=m(e.jsonpCallback)?e.jsonpCallback():e.jsonpCallback,a?e[a]=e[a].replace(Ut,"$1"+r):!1!==e.jsonp&&(e.url+=(Tt.test(e.url)?"&":"?")+e.jsonp+"="+r),e.converters["script json"]=function(){return o||S.error(r+" was not called"),o[0]},e.dataTypes[0]="json",i=C[r],C[r]=function(){o=arguments},n.always(function(){void 0===i?S(C).removeProp(r):C[r]=i,e[r]&&(e.jsonpCallback=t.jsonpCallback,zt.push(r)),o&&m(i)&&i(o[0]),o=i=void 0}),"script"}),y.createHTMLDocument=((_t=E.implementation.createHTMLDocument("").body).innerHTML="
",2===_t.childNodes.length),S.parseHTML=function(e,t,n){return"string"!=typeof e?[]:("boolean"==typeof t&&(n=t,t=!1),t||(y.createHTMLDocument?((r=(t=E.implementation.createHTMLDocument("")).createElement("base")).href=E.location.href,t.head.appendChild(r)):t=E),o=!n&&[],(i=N.exec(e))?[t.createElement(i[1])]:(i=xe([e],t,o),o&&o.length&&S(o).remove(),S.merge([],i.childNodes)));var r,i,o},S.fn.load=function(e,t,n){var r,i,o,a=this,s=e.indexOf(" ");return-1").append(S.parseHTML(e)).find(r):e)}).always(n&&function(e,t){a.each(function(){n.apply(this,o||[e.responseText,t,e])})}),this},S.expr.pseudos.animated=function(t){return S.grep(S.timers,function(e){return t===e.elem}).length},S.offset={setOffset:function(e,t,n){var r,i,o,a,s,u,l=S.css(e,"position"),c=S(e),f={};"static"===l&&(e.style.position="relative"),s=c.offset(),o=S.css(e,"top"),u=S.css(e,"left"),("absolute"===l||"fixed"===l)&&-1<(o+u).indexOf("auto")?(a=(r=c.position()).top,i=r.left):(a=parseFloat(o)||0,i=parseFloat(u)||0),m(t)&&(t=t.call(e,n,S.extend({},s))),null!=t.top&&(f.top=t.top-s.top+a),null!=t.left&&(f.left=t.left-s.left+i),"using"in t?t.using.call(e,f):c.css(f)}},S.fn.extend({offset:function(t){if(arguments.length)return void 0===t?this:this.each(function(e){S.offset.setOffset(this,t,e)});var e,n,r=this[0];return r?r.getClientRects().length?(e=r.getBoundingClientRect(),n=r.ownerDocument.defaultView,{top:e.top+n.pageYOffset,left:e.left+n.pageXOffset}):{top:0,left:0}:void 0},position:function(){if(this[0]){var e,t,n,r=this[0],i={top:0,left:0};if("fixed"===S.css(r,"position"))t=r.getBoundingClientRect();else{t=this.offset(),n=r.ownerDocument,e=r.offsetParent||n.documentElement;while(e&&(e===n.body||e===n.documentElement)&&"static"===S.css(e,"position"))e=e.parentNode;e&&e!==r&&1===e.nodeType&&((i=S(e).offset()).top+=S.css(e,"borderTopWidth",!0),i.left+=S.css(e,"borderLeftWidth",!0))}return{top:t.top-i.top-S.css(r,"marginTop",!0),left:t.left-i.left-S.css(r,"marginLeft",!0)}}},offsetParent:function(){return this.map(function(){var e=this.offsetParent;while(e&&"static"===S.css(e,"position"))e=e.offsetParent;return e||re})}}),S.each({scrollLeft:"pageXOffset",scrollTop:"pageYOffset"},function(t,i){var o="pageYOffset"===i;S.fn[t]=function(e){return $(this,function(e,t,n){var r;if(x(e)?r=e:9===e.nodeType&&(r=e.defaultView),void 0===n)return r?r[i]:e[t];r?r.scrollTo(o?r.pageXOffset:n,o?n:r.pageYOffset):e[t]=n},t,e,arguments.length)}}),S.each(["top","left"],function(e,n){S.cssHooks[n]=Fe(y.pixelPosition,function(e,t){if(t)return t=We(e,n),Pe.test(t)?S(e).position()[n]+"px":t})}),S.each({Height:"height",Width:"width"},function(a,s){S.each({padding:"inner"+a,content:s,"":"outer"+a},function(r,o){S.fn[o]=function(e,t){var n=arguments.length&&(r||"boolean"!=typeof e),i=r||(!0===e||!0===t?"margin":"border");return $(this,function(e,t,n){var r;return x(e)?0===o.indexOf("outer")?e["inner"+a]:e.document.documentElement["client"+a]:9===e.nodeType?(r=e.documentElement,Math.max(e.body["scroll"+a],r["scroll"+a],e.body["offset"+a],r["offset"+a],r["client"+a])):void 0===n?S.css(e,t,i):S.style(e,t,n,i)},s,n?e:void 0,n)}})}),S.each(["ajaxStart","ajaxStop","ajaxComplete","ajaxError","ajaxSuccess","ajaxSend"],function(e,t){S.fn[t]=function(e){return this.on(t,e)}}),S.fn.extend({bind:function(e,t,n){return this.on(e,null,t,n)},unbind:function(e,t){return this.off(e,null,t)},delegate:function(e,t,n,r){return this.on(t,e,n,r)},undelegate:function(e,t,n){return 1===arguments.length?this.off(e,"**"):this.off(t,e||"**",n)},hover:function(e,t){return this.mouseenter(e).mouseleave(t||e)}}),S.each("blur focus focusin focusout resize scroll click dblclick mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave change select submit keydown keypress keyup contextmenu".split(" "),function(e,n){S.fn[n]=function(e,t){return 0 - +h1.title {font-size: 38px;} +h2 {font-size: 30px;} +h3 {font-size: 24px;} +h4 {font-size: 18px;} +h5 {font-size: 16px;} +h6 {font-size: 12px;} +code {color: inherit; background-color: rgba(0, 0, 0, 0.04);} +pre:not([class]) { background-color: white } +code{white-space: pre-wrap;} +span.smallcaps{font-variant: small-caps;} +span.underline{text-decoration: underline;} +div.column{display: inline-block; vertical-align: top; width: 50%;} +div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;} +ul.task-list{list-style: none;} +