Lists model equations, initial parameter values, optimised parameters for fixed effects (population), random effects (deviations from the population mean) and residual error model, as well as the resulting endpoints such as formation fractions and DT50 values. Optionally (default is FALSE), the data are listed in full.

# S3 method for saem.mmkin
summary(object, data = FALSE, verbose = FALSE, distimes = TRUE, ...)

# S3 method for summary.saem.mmkin
print(x, digits = max(3, getOption("digits") - 3), verbose = x$verbose, ...)

Arguments

object

an object of class saem.mmkin

data

logical, indicating whether the full data should be included in the summary.

verbose

Should the summary be verbose?

distimes

logical, indicating whether DT50 and DT90 values should be included.

...

optional arguments passed to methods like print.

x

an object of class summary.saem.mmkin

digits

Number of digits to use for printing

Value

The summary function returns a list based on the saemix::SaemixObject obtained in the fit, with at least the following additional components

saemixversion, mkinversion, Rversion

The saemix, mkin and R versions used

date.fit, date.summary

The dates where the fit and the summary were produced

diffs

The differential equations used in the degradation model

use_of_ff

Was maximum or minimum use made of formation fractions

data

The data

confint_trans

Transformed parameters as used in the optimisation, with confidence intervals

confint_back

Backtransformed parameters, with confidence intervals if available

confint_errmod

Error model parameters with confidence intervals

ff

The estimated formation fractions derived from the fitted model.

distimes

The DT50 and DT90 values for each observed variable.

SFORB

If applicable, eigenvalues of SFORB components of the model.

The print method is called for its side effect, i.e. printing the summary.

Author

Johannes Ranke for the mkin specific parts saemix authors for the parts inherited from saemix.

Examples

# Generate five datasets following DFOP-SFO kinetics sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120) dfop_sfo <- mkinmod(parent = mkinsub("DFOP", "m1"), m1 = mkinsub("SFO"), quiet = TRUE) set.seed(1234) k1_in <- rlnorm(5, log(0.1), 0.3) k2_in <- rlnorm(5, log(0.02), 0.3) g_in <- plogis(rnorm(5, qlogis(0.5), 0.3)) f_parent_to_m1_in <- plogis(rnorm(5, qlogis(0.3), 0.3)) k_m1_in <- rlnorm(5, log(0.02), 0.3) pred_dfop_sfo <- function(k1, k2, g, f_parent_to_m1, k_m1) { mkinpredict(dfop_sfo, c(k1 = k1, k2 = k2, g = g, f_parent_to_m1 = f_parent_to_m1, k_m1 = k_m1), c(parent = 100, m1 = 0), sampling_times) } ds_mean_dfop_sfo <- lapply(1:5, function(i) { mkinpredict(dfop_sfo, c(k1 = k1_in[i], k2 = k2_in[i], g = g_in[i], f_parent_to_m1 = f_parent_to_m1_in[i], k_m1 = k_m1_in[i]), c(parent = 100, m1 = 0), sampling_times) }) names(ds_mean_dfop_sfo) <- paste("ds", 1:5) ds_syn_dfop_sfo <- lapply(ds_mean_dfop_sfo, function(ds) { add_err(ds, sdfunc = function(value) sqrt(1^2 + value^2 * 0.07^2), n = 1)[[1]] }) # \dontrun{ # Evaluate using mmkin and saem f_mmkin_dfop_sfo <- mmkin(list(dfop_sfo), ds_syn_dfop_sfo, quiet = TRUE, error_model = "tc", cores = 5) f_saem_dfop_sfo <- saem(f_mmkin_dfop_sfo)
#> Running main SAEM algorithm #> [1] "Sat Feb 6 18:30:00 2021" #> .... #> Minimisation finished #> [1] "Sat Feb 6 18:30:11 2021"
summary(f_saem_dfop_sfo, data = TRUE)
#> saemix version used for fitting: 3.1.9000 #> mkin version used for pre-fitting: 1.0.1.9000 #> R version used for fitting: 4.0.3 #> Date of fit: Sat Feb 6 18:30:12 2021 #> Date of summary: Sat Feb 6 18:30:12 2021 #> #> Equations: #> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * #> time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) #> * parent #> d_m1/dt = + f_parent_to_m1 * ((k1 * g * exp(-k1 * time) + k2 * (1 - g) #> * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * #> exp(-k2 * time))) * parent - k_m1 * m1 #> #> Data: #> 171 observations of 2 variable(s) grouped in 5 datasets #> #> Model predictions using solution type analytical #> #> Fitted in 11.769 s using 300, 100 iterations #> #> Variance model: Two-component variance function #> #> Mean of starting values for individual parameters: #> parent_0 log_k_m1 f_parent_qlogis log_k1 log_k2 #> 101.65645 -4.05368 -0.94311 -2.35943 -4.07006 #> g_qlogis #> -0.01132 #> #> Fixed degradation parameter values: #> None #> #> Results: #> #> Likelihood computed by importance sampling #> AIC BIC logLik #> 829.3 823.9 -400.7 #> #> Optimised parameters: #> est. lower upper #> parent_0 101.29457 97.855 104.7344 #> log_k_m1 -4.06337 -4.182 -3.9445 #> f_parent_qlogis -0.94546 -1.307 -0.5841 #> log_k1 -2.98794 -3.844 -2.1321 #> log_k2 -3.47891 -4.253 -2.7050 #> g_qlogis -0.03211 -1.157 1.0931 #> #> Correlation: #> prnt_0 lg_k_1 f_prn_ log_k1 log_k2 #> log_k_m1 -0.202 #> f_parent_qlogis -0.145 0.195 #> log_k1 0.094 -0.099 -0.049 #> log_k2 -0.042 0.056 0.024 -0.097 #> g_qlogis -0.005 0.000 0.007 -0.160 -0.113 #> #> Random effects: #> est. lower upper #> SD.parent_0 2.70085 -0.64980 6.0515 #> SD.log_k_m1 0.08408 -0.04023 0.2084 #> SD.f_parent_qlogis 0.39215 0.13695 0.6473 #> SD.log_k1 0.89280 0.27466 1.5109 #> SD.log_k2 0.82387 0.26388 1.3838 #> SD.g_qlogis 0.36468 -0.86978 1.5991 #> #> Variance model: #> est. lower upper #> a.1 0.65724 0.49361 0.82086 #> b.1 0.06434 0.05034 0.07835 #> #> Backtransformed parameters: #> est. lower upper #> parent_0 101.29457 97.85477 104.73437 #> k_m1 0.01719 0.01526 0.01936 #> f_parent_to_m1 0.27980 0.21302 0.35798 #> k1 0.05039 0.02141 0.11859 #> k2 0.03084 0.01422 0.06687 #> g 0.49197 0.23916 0.74896 #> #> Resulting formation fractions: #> ff #> parent_m1 0.2798 #> parent_sink 0.7202 #> #> Estimated disappearance times: #> DT50 DT90 DT50back DT50_k1 DT50_k2 #> parent 17.49 61.05 18.38 13.76 22.47 #> m1 40.32 133.94 NA NA NA #> #> Data: #> ds name time observed predicted residual std standardized #> ds 1 parent 0 89.8 9.878e+01 8.98039 6.3899 1.40541 #> ds 1 parent 0 104.1 9.878e+01 -5.31961 6.3899 -0.83251 #> ds 1 parent 1 88.7 9.422e+01 5.52084 6.0981 0.90533 #> ds 1 parent 1 95.5 9.422e+01 -1.27916 6.0981 -0.20976 #> ds 1 parent 3 81.8 8.587e+01 4.06752 5.5641 0.73103 #> ds 1 parent 3 94.5 8.587e+01 -8.63248 5.5641 -1.55147 #> ds 1 parent 7 71.5 7.180e+01 0.29615 4.6662 0.06347 #> ds 1 parent 7 70.3 7.180e+01 1.49615 4.6662 0.32063 #> ds 1 parent 14 54.2 5.360e+01 -0.59602 3.5112 -0.16975 #> ds 1 parent 14 49.6 5.360e+01 4.00398 3.5112 1.14035 #> ds 1 parent 28 31.5 3.213e+01 0.62529 2.1691 0.28828 #> ds 1 parent 28 28.8 3.213e+01 3.32529 2.1691 1.53306 #> ds 1 parent 60 12.1 1.271e+01 0.60718 1.0490 0.57879 #> ds 1 parent 60 13.6 1.271e+01 -0.89282 1.0490 -0.85108 #> ds 1 parent 90 6.2 6.080e+00 -0.12020 0.7649 -0.15716 #> ds 1 parent 90 8.3 6.080e+00 -2.22020 0.7649 -2.90279 #> ds 1 parent 120 2.2 3.011e+00 0.81059 0.6852 1.18302 #> ds 1 parent 120 2.4 3.011e+00 0.61059 0.6852 0.89113 #> ds 1 m1 1 0.3 1.131e+00 0.83071 0.6613 1.25628 #> ds 1 m1 1 0.2 1.131e+00 0.93071 0.6613 1.40750 #> ds 1 m1 3 2.2 3.147e+00 0.94691 0.6877 1.37688 #> ds 1 m1 3 3.0 3.147e+00 0.14691 0.6877 0.21361 #> ds 1 m1 7 6.5 6.341e+00 -0.15949 0.7736 -0.20618 #> ds 1 m1 7 5.0 6.341e+00 1.34051 0.7736 1.73290 #> ds 1 m1 14 10.2 9.910e+00 -0.28991 0.9157 -0.31659 #> ds 1 m1 14 9.5 9.910e+00 0.41009 0.9157 0.44783 #> ds 1 m1 28 12.2 1.255e+01 0.34690 1.0410 0.33323 #> ds 1 m1 28 13.4 1.255e+01 -0.85310 1.0410 -0.81949 #> ds 1 m1 60 11.8 1.087e+01 -0.92713 0.9599 -0.96586 #> ds 1 m1 60 13.2 1.087e+01 -2.32713 0.9599 -2.42434 #> ds 1 m1 90 6.6 7.813e+00 1.21254 0.8274 1.46541 #> ds 1 m1 90 9.3 7.813e+00 -1.48746 0.8274 -1.79766 #> ds 1 m1 120 3.5 5.295e+00 1.79489 0.7403 2.42457 #> ds 1 m1 120 5.4 5.295e+00 -0.10511 0.7403 -0.14198 #> ds 2 parent 0 118.0 1.074e+02 -10.63436 6.9396 -1.53242 #> ds 2 parent 0 99.8 1.074e+02 7.56564 6.9396 1.09021 #> ds 2 parent 1 90.2 1.012e+02 10.96486 6.5425 1.67594 #> ds 2 parent 1 94.6 1.012e+02 6.56486 6.5425 1.00342 #> ds 2 parent 3 96.1 9.054e+01 -5.56014 5.8627 -0.94839 #> ds 2 parent 3 78.4 9.054e+01 12.13986 5.8627 2.07069 #> ds 2 parent 7 77.9 7.468e+01 -3.21805 4.8501 -0.66350 #> ds 2 parent 7 77.7 7.468e+01 -3.01805 4.8501 -0.62226 #> ds 2 parent 14 56.0 5.748e+01 1.47774 3.7563 0.39340 #> ds 2 parent 14 54.7 5.748e+01 2.77774 3.7563 0.73948 #> ds 2 parent 28 36.6 3.996e+01 3.36317 2.6541 1.26717 #> ds 2 parent 28 36.8 3.996e+01 3.16317 2.6541 1.19182 #> ds 2 parent 60 22.1 2.132e+01 -0.78225 1.5210 -0.51430 #> ds 2 parent 60 24.7 2.132e+01 -3.38225 1.5210 -2.22369 #> ds 2 parent 90 12.4 1.215e+01 -0.25010 1.0213 -0.24487 #> ds 2 parent 90 10.8 1.215e+01 1.34990 1.0213 1.32169 #> ds 2 parent 120 6.8 6.931e+00 0.13105 0.7943 0.16500 #> ds 2 parent 120 7.9 6.931e+00 -0.96895 0.7943 -1.21994 #> ds 2 m1 1 1.3 1.519e+00 0.21924 0.6645 0.32995 #> ds 2 m1 3 3.7 4.049e+00 0.34891 0.7070 0.49351 #> ds 2 m1 3 4.7 4.049e+00 -0.65109 0.7070 -0.92094 #> ds 2 m1 7 8.1 7.565e+00 -0.53526 0.8179 -0.65448 #> ds 2 m1 7 7.9 7.565e+00 -0.33526 0.8179 -0.40993 #> ds 2 m1 14 10.1 1.071e+01 0.60614 0.9521 0.63663 #> ds 2 m1 14 10.3 1.071e+01 0.40614 0.9521 0.42657 #> ds 2 m1 28 10.7 1.224e+01 1.54440 1.0260 1.50526 #> ds 2 m1 28 12.2 1.224e+01 0.04440 1.0260 0.04327 #> ds 2 m1 60 10.7 1.056e+01 -0.14005 0.9453 -0.14815 #> ds 2 m1 60 12.5 1.056e+01 -1.94005 0.9453 -2.05226 #> ds 2 m1 90 9.1 8.089e+00 -1.01088 0.8384 -1.20577 #> ds 2 m1 90 7.4 8.089e+00 0.68912 0.8384 0.82197 #> ds 2 m1 120 6.1 5.855e+00 -0.24463 0.7576 -0.32292 #> ds 2 m1 120 4.5 5.855e+00 1.35537 0.7576 1.78911 #> ds 3 parent 0 106.2 1.095e+02 3.30335 7.0765 0.46680 #> ds 3 parent 0 106.9 1.095e+02 2.60335 7.0765 0.36788 #> ds 3 parent 1 107.4 9.939e+01 -8.01282 6.4287 -1.24641 #> ds 3 parent 1 96.1 9.939e+01 3.28718 6.4287 0.51133 #> ds 3 parent 3 79.4 8.365e+01 4.24698 5.4222 0.78326 #> ds 3 parent 3 82.6 8.365e+01 1.04698 5.4222 0.19309 #> ds 3 parent 7 63.9 6.405e+01 0.14704 4.1732 0.03523 #> ds 3 parent 7 62.4 6.405e+01 1.64704 4.1732 0.39467 #> ds 3 parent 14 51.0 4.795e+01 -3.04985 3.1546 -0.96681 #> ds 3 parent 14 47.1 4.795e+01 0.85015 3.1546 0.26950 #> ds 3 parent 28 36.1 3.501e+01 -1.09227 2.3465 -0.46549 #> ds 3 parent 28 36.6 3.501e+01 -1.59227 2.3465 -0.67858 #> ds 3 parent 60 20.1 2.012e+01 0.02116 1.4520 0.01457 #> ds 3 parent 60 19.8 2.012e+01 0.32116 1.4520 0.22119 #> ds 3 parent 90 11.3 1.206e+01 0.76096 1.0170 0.74826 #> ds 3 parent 90 10.7 1.206e+01 1.36096 1.0170 1.33825 #> ds 3 parent 120 8.2 7.230e+00 -0.97022 0.8052 -1.20493 #> ds 3 parent 120 7.3 7.230e+00 -0.07022 0.8052 -0.08721 #> ds 3 m1 0 0.8 -5.684e-13 -0.80000 0.6572 -1.21722 #> ds 3 m1 1 1.8 2.045e+00 0.24538 0.6703 0.36608 #> ds 3 m1 1 2.3 2.045e+00 -0.25462 0.6703 -0.37987 #> ds 3 m1 3 4.2 5.136e+00 0.93594 0.7356 1.27228 #> ds 3 m1 3 4.1 5.136e+00 1.03594 0.7356 1.40822 #> ds 3 m1 7 6.8 8.674e+00 1.87438 0.8623 2.17381 #> ds 3 m1 7 10.1 8.674e+00 -1.42562 0.8623 -1.65335 #> ds 3 m1 14 11.4 1.083e+01 -0.56746 0.9580 -0.59233 #> ds 3 m1 14 12.8 1.083e+01 -1.96746 0.9580 -2.05369 #> ds 3 m1 28 11.5 1.098e+01 -0.51762 0.9651 -0.53637 #> ds 3 m1 28 10.6 1.098e+01 0.38238 0.9651 0.39623 #> ds 3 m1 60 7.5 8.889e+00 1.38911 0.8713 1.59436 #> ds 3 m1 60 8.6 8.889e+00 0.28911 0.8713 0.33183 #> ds 3 m1 90 7.3 6.774e+00 -0.52608 0.7886 -0.66708 #> ds 3 m1 90 8.1 6.774e+00 -1.32608 0.7886 -1.68150 #> ds 3 m1 120 5.3 4.954e+00 -0.34584 0.7305 -0.47345 #> ds 3 m1 120 3.8 4.954e+00 1.15416 0.7305 1.58004 #> ds 4 parent 0 104.7 9.957e+01 -5.13169 6.4403 -0.79681 #> ds 4 parent 0 88.3 9.957e+01 11.26831 6.4403 1.74966 #> ds 4 parent 1 94.2 9.644e+01 2.23888 6.2400 0.35879 #> ds 4 parent 1 94.6 9.644e+01 1.83888 6.2400 0.29469 #> ds 4 parent 3 78.1 9.054e+01 12.43946 5.8627 2.12180 #> ds 4 parent 3 96.5 9.054e+01 -5.96054 5.8627 -1.01669 #> ds 4 parent 7 76.2 8.004e+01 3.83771 5.1918 0.73919 #> ds 4 parent 7 77.8 8.004e+01 2.23771 5.1918 0.43101 #> ds 4 parent 14 70.8 6.511e+01 -5.69246 4.2406 -1.34238 #> ds 4 parent 14 67.3 6.511e+01 -2.19246 4.2406 -0.51702 #> ds 4 parent 28 43.1 4.454e+01 1.43744 2.9401 0.48890 #> ds 4 parent 28 45.1 4.454e+01 -0.56256 2.9401 -0.19134 #> ds 4 parent 60 21.3 2.132e+01 0.02005 1.5211 0.01318 #> ds 4 parent 60 23.5 2.132e+01 -2.17995 1.5211 -1.43310 #> ds 4 parent 90 11.8 1.182e+01 0.02167 1.0053 0.02156 #> ds 4 parent 90 12.1 1.182e+01 -0.27833 1.0053 -0.27687 #> ds 4 parent 120 7.0 6.852e+00 -0.14780 0.7914 -0.18675 #> ds 4 parent 120 6.2 6.852e+00 0.65220 0.7914 0.82408 #> ds 4 m1 0 1.6 -5.684e-14 -1.60000 0.6572 -2.43444 #> ds 4 m1 1 0.9 6.918e-01 -0.20821 0.6587 -0.31607 #> ds 4 m1 3 3.7 1.959e+00 -1.74131 0.6692 -2.60204 #> ds 4 m1 3 2.0 1.959e+00 -0.04131 0.6692 -0.06173 #> ds 4 m1 7 3.6 4.076e+00 0.47590 0.7076 0.67252 #> ds 4 m1 7 3.8 4.076e+00 0.27590 0.7076 0.38989 #> ds 4 m1 14 7.1 6.698e+00 -0.40189 0.7859 -0.51135 #> ds 4 m1 14 6.6 6.698e+00 0.09811 0.7859 0.12483 #> ds 4 m1 28 9.5 9.175e+00 -0.32492 0.8835 -0.36779 #> ds 4 m1 28 9.3 9.175e+00 -0.12492 0.8835 -0.14141 #> ds 4 m1 60 8.3 8.818e+00 0.51810 0.8683 0.59671 #> ds 4 m1 60 9.0 8.818e+00 -0.18190 0.8683 -0.20949 #> ds 4 m1 90 6.6 6.645e+00 0.04480 0.7841 0.05713 #> ds 4 m1 90 7.7 6.645e+00 -1.05520 0.7841 -1.34581 #> ds 4 m1 120 3.7 4.648e+00 0.94805 0.7221 1.31293 #> ds 4 m1 120 3.5 4.648e+00 1.14805 0.7221 1.58991 #> ds 5 parent 0 110.4 1.026e+02 -7.81752 6.6333 -1.17853 #> ds 5 parent 0 112.1 1.026e+02 -9.51752 6.6333 -1.43482 #> ds 5 parent 1 93.5 9.560e+01 2.10274 6.1865 0.33989 #> ds 5 parent 1 91.0 9.560e+01 4.60274 6.1865 0.74399 #> ds 5 parent 3 71.0 8.356e+01 12.55799 5.4165 2.31846 #> ds 5 parent 3 89.7 8.356e+01 -6.14201 5.4165 -1.13394 #> ds 5 parent 7 60.4 6.550e+01 5.09732 4.2653 1.19506 #> ds 5 parent 7 59.1 6.550e+01 6.39732 4.2653 1.49984 #> ds 5 parent 14 56.5 4.641e+01 -10.09145 3.0576 -3.30044 #> ds 5 parent 14 47.0 4.641e+01 -0.59145 3.0576 -0.19344 #> ds 5 parent 28 30.2 2.982e+01 -0.37647 2.0284 -0.18560 #> ds 5 parent 28 23.9 2.982e+01 5.92353 2.0284 2.92028 #> ds 5 parent 60 17.0 1.754e+01 0.53981 1.3060 0.41332 #> ds 5 parent 60 18.7 1.754e+01 -1.16019 1.3060 -0.88834 #> ds 5 parent 90 11.3 1.175e+01 0.45050 1.0018 0.44969 #> ds 5 parent 90 11.9 1.175e+01 -0.14950 1.0018 -0.14923 #> ds 5 parent 120 9.0 7.915e+00 -1.08476 0.8315 -1.30462 #> ds 5 parent 120 8.1 7.915e+00 -0.18476 0.8315 -0.22220 #> ds 5 m1 0 0.7 0.000e+00 -0.70000 0.6572 -1.06507 #> ds 5 m1 1 3.0 3.062e+00 0.06170 0.6861 0.08992 #> ds 5 m1 1 2.6 3.062e+00 0.46170 0.6861 0.67290 #> ds 5 m1 3 5.1 8.209e+00 3.10938 0.8432 3.68760 #> ds 5 m1 3 7.5 8.209e+00 0.70938 0.8432 0.84130 #> ds 5 m1 7 16.5 1.544e+01 -1.05567 1.1914 -0.88605 #> ds 5 m1 7 19.0 1.544e+01 -3.55567 1.1914 -2.98436 #> ds 5 m1 14 22.9 2.181e+01 -1.08765 1.5498 -0.70181 #> ds 5 m1 14 23.2 2.181e+01 -1.38765 1.5498 -0.89539 #> ds 5 m1 28 22.2 2.404e+01 1.83624 1.6805 1.09270 #> ds 5 m1 28 24.4 2.404e+01 -0.36376 1.6805 -0.21647 #> ds 5 m1 60 15.5 1.875e+01 3.25390 1.3741 2.36805 #> ds 5 m1 60 19.8 1.875e+01 -1.04610 1.3741 -0.76131 #> ds 5 m1 90 14.9 1.380e+01 -1.09507 1.1050 -0.99102 #> ds 5 m1 90 14.2 1.380e+01 -0.39507 1.1050 -0.35753 #> ds 5 m1 120 10.9 1.002e+01 -0.88429 0.9205 -0.96069 #> ds 5 m1 120 10.4 1.002e+01 -0.38429 0.9205 -0.41749
# }