Examples

library(rPBK)

Single Compartment and Single Exposure : Male Gammarus Single

data("dataMaleGammarusSingle")
# work only when replicate have the same length !!!
data_MGS <- dataMaleGammarusSingle[dataMaleGammarusSingle$replicate == 1,]
modelData_MGS <- dataPBK(
  object = data_MGS,
  col_time = "time",
  col_replicate = "replicate",
  col_exposure = "expw",
  col_compartment = "conc",
  time_accumulation = 4,
  nested_model = NA)
fitPBK_MGS <- fitPBK(modelData_MGS)
#> 
#> SAMPLING FOR MODEL 'PBK_AD' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 9e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.9 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.568 seconds (Warm-up)
#> Chain 1:                0.426 seconds (Sampling)
#> Chain 1:                0.994 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'PBK_AD' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 7.8e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.78 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 2: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 2: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 2: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.558 seconds (Warm-up)
#> Chain 2:                0.5 seconds (Sampling)
#> Chain 2:                1.058 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'PBK_AD' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 5.1e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.51 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3: 
#> Chain 3: 
#> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.504 seconds (Warm-up)
#> Chain 3:                0.267 seconds (Sampling)
#> Chain 3:                0.771 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'PBK_AD' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 4.7e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.47 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
#> Chain 4: 
#> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.517 seconds (Warm-up)
#> Chain 4:                0.54 seconds (Sampling)
#> Chain 4:                1.057 seconds (Total)
#> Chain 4:
#> Warning: There were 2394 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
plot(fitPBK_MGS)
#> Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
#> ℹ Please use tidy evaluation idioms with `aes()`.
#> ℹ See also `vignette("ggplot2-in-packages")` for more information.
#> ℹ The deprecated feature was likely used in the rPBK package.
#>   Please report the issue at
#>   <https://gitlab.in2p3.fr/mosaic-software/rPBK/-/issues>.
#> This warning is displayed once per session.
#> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
#> generated.

library(loo)
#> This is loo version 2.9.0
#> - Online documentation and vignettes at mc-stan.org/loo
#> - As of v2.0.0 loo defaults to 1 core but we recommend using as many as possible. Use the 'cores' argument or set options(mc.cores = NUM_CORES) for an entire session.
log_lik_MGS <- loo::extract_log_lik(fitPBK_MGS$stanfit, merge_chains = FALSE)
WAIC_MGS <- waic(log_lik_MGS)
#> Warning: 
#> 1 (12.5%) p_waic estimates greater than 0.4. We recommend trying loo instead.

Multiple Compartiment, Single Exposure - Default interaction

data("dataCompartment4")
data_C4 <- dataCompartment4
modelData_C4 <- dataPBK(
  object = data_C4,
  col_time = "temps",
  col_replicate = "replicat",
  col_exposure = "condition",
  col_compartment = c("intestin", "reste", "caecum", "cephalon"),
  time_accumulation = 7)

You can have a look at the assumption on the interaction

nested_model(modelData_C4)
#> $ku_nest
#> uptake intestin    uptake reste   uptake caecum uptake cephalon 
#>               1               1               1               1 
#> 
#> $ke_nest
#> excretion intestin    excretion reste   excretion caecum excretion cephalon 
#>                  1                  1                  1                  1 
#> 
#> $k_nest
#>          intestin reste caecum cephalon
#> intestin        0     1      1        1
#> reste           1     0      1        1
#> caecum          1     1      0        1
#> cephalon        1     1      1        0
fitPBK_C4 <- fitPBK(modelData_C4, chains = 1, iter = 1000)
#> 
#> SAMPLING FOR MODEL 'PBK_AD' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 0.000539 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 5.39 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:   1 / 1000 [  0%]  (Warmup)
#> Chain 1: Iteration: 100 / 1000 [ 10%]  (Warmup)
#> Chain 1: Iteration: 200 / 1000 [ 20%]  (Warmup)
#> Chain 1: Iteration: 300 / 1000 [ 30%]  (Warmup)
#> Chain 1: Iteration: 400 / 1000 [ 40%]  (Warmup)
#> Chain 1: Iteration: 500 / 1000 [ 50%]  (Warmup)
#> Chain 1: Iteration: 501 / 1000 [ 50%]  (Sampling)
#> Chain 1: Iteration: 600 / 1000 [ 60%]  (Sampling)
#> Chain 1: Iteration: 700 / 1000 [ 70%]  (Sampling)
#> Chain 1: Iteration: 800 / 1000 [ 80%]  (Sampling)
#> Chain 1: Iteration: 900 / 1000 [ 90%]  (Sampling)
#> Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 21.546 seconds (Warm-up)
#> Chain 1:                11.91 seconds (Sampling)
#> Chain 1:                33.456 seconds (Total)
#> Chain 1:
#> Warning: There were 500 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
plot(fitPBK_C4)

Compute WAIC with loo library:

library(loo)
log_lik_C4 <- loo::extract_log_lik(fitPBK_C4$stanfit, merge_chains = FALSE)
WAIC_C4 <- waic(log_lik_C4)
#> Warning: 
#> 6 (7.1%) p_waic estimates greater than 0.4. We recommend trying loo instead.
print(WAIC_C4)
#> 
#> Computed from 500 by 84 log-likelihood matrix.
#> 
#>           Estimate   SE
#> elpd_waic   -236.8 17.9
#> p_waic         9.0  1.6
#> waic         473.7 35.8
#> 
#> 6 (7.1%) p_waic estimates greater than 0.4. We recommend trying loo instead.

Compute LOO:

r_eff_C4 <- relative_eff(exp(log_lik_C4))
LOO_C4 <- loo(log_lik_C4, r_eff = r_eff_C4, cores = 2)
print(LOO_C4)
#> 
#> Computed from 500 by 84 log-likelihood matrix.
#> 
#>          Estimate   SE
#> elpd_loo   -237.0 17.9
#> p_loo         9.2  1.6
#> looic       474.0 35.8
#> ------
#> MCSE of elpd_loo is 1.6.
#> MCSE and ESS estimates assume MCMC draws (r_eff in [0.0, 0.2]).
#> 
#> All Pareto k estimates are good (k < 0.63).
#> See help('pareto-k-diagnostic') for details.

Multiple Compartiment, Single Exposure : Change nesting

You can have a look at the assumption on the interaction

nm_C4 = nested_model(modelData_C4)

We want to change the interaction between organs. For now, all organs interact with each other but not with themselve, the the interaction matrix look like:

nm_C4$k_nest
#>          intestin reste caecum cephalon
#> intestin        0     1      1        1
#> reste           1     0      1        1
#> caecum          1     1      0        1
#> cephalon        1     1      1        0

which can be written like:

matrix(c(
  c(0,1,1,1),
  c(1,0,1,1),
  c(1,1,0,0),
  c(1,1,1,0)),
  ncol=4,nrow=4,byrow=TRUE)
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    1
#> [2,]    1    0    1    1
#> [3,]    1    1    0    0
#> [4,]    1    1    1    0

Let assume interaction are only one way, so a triangular matrix:

matrix(c(
  c(0,1,1,1),
  c(0,0,1,1),
  c(0,0,0,0),
  c(0,0,0,0)),
  ncol=4,nrow=4,byrow=TRUE)
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    1
#> [2,]    0    0    1    1
#> [3,]    0    0    0    0
#> [4,]    0    0    0    0
modelData_C42 <- dataPBK(
  object = data_C4,
  col_time = "temps",
  col_replicate = "replicat",
  col_exposure = "condition",
  col_compartment = c("intestin", "reste", "caecum", "cephalon"),
  time_accumulation = 7,
  ku_nest = c(1,1,1,1), # No Change here
  ke_nest = c(1,1,1,1), # No Change here
  k_nest = matrix(c(
            c(0,1,1,1),
            c(0,0,1,1),
            c(0,0,0,0),
            c(0,0,0,0)),
            ncol=4,nrow=4,byrow=TRUE) # Remove 
  )
nested_model(modelData_C42)
#> $ku_nest
#> uptake intestin    uptake reste   uptake caecum uptake cephalon 
#>               1               1               1               1 
#> 
#> $ke_nest
#> excretion intestin    excretion reste   excretion caecum excretion cephalon 
#>                  1                  1                  1                  1 
#> 
#> $k_nest
#>          intestin reste caecum cephalon
#> intestin        0     1      1        1
#> reste           0     0      1        1
#> caecum          0     0      0        0
#> cephalon        0     0      0        0
fitPBK_C42 <- fitPBK(modelData_C42, chains = 1, iter = 1000)
#> 
#> SAMPLING FOR MODEL 'PBK_AD' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 0.000831 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 8.31 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:   1 / 1000 [  0%]  (Warmup)
#> Chain 1: Iteration: 100 / 1000 [ 10%]  (Warmup)
#> Chain 1: Iteration: 200 / 1000 [ 20%]  (Warmup)
#> Chain 1: Iteration: 300 / 1000 [ 30%]  (Warmup)
#> Chain 1: Iteration: 400 / 1000 [ 40%]  (Warmup)
#> Chain 1: Iteration: 500 / 1000 [ 50%]  (Warmup)
#> Chain 1: Iteration: 501 / 1000 [ 50%]  (Sampling)
#> Chain 1: Iteration: 600 / 1000 [ 60%]  (Sampling)
#> Chain 1: Iteration: 700 / 1000 [ 70%]  (Sampling)
#> Chain 1: Iteration: 800 / 1000 [ 80%]  (Sampling)
#> Chain 1: Iteration: 900 / 1000 [ 90%]  (Sampling)
#> Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 6.875 seconds (Warm-up)
#> Chain 1:                99.329 seconds (Sampling)
#> Chain 1:                106.204 seconds (Total)
#> Chain 1:
#> Warning: There were 473 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: There were 27 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
#> https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
#> Warning: There were 1 chains where the estimated Bayesian Fraction of Missing Information was low. See
#> https://mc-stan.org/misc/warnings.html#bfmi-low
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
plot(fitPBK_C42)

log_lik_C42 <- loo::extract_log_lik(fitPBK_C42$stanfit, merge_chains = FALSE)
WAIC_C42 <- waic(log_lik_C42)
#> Warning: 
#> 8 (9.5%) p_waic estimates greater than 0.4. We recommend trying loo instead.
print(WAIC_C42)
#> 
#> Computed from 500 by 84 log-likelihood matrix.
#> 
#>           Estimate   SE
#> elpd_waic   -262.5 12.4
#> p_waic        12.9  1.4
#> waic         525.0 24.8
#> 
#> 8 (9.5%) p_waic estimates greater than 0.4. We recommend trying loo instead.

Compare WAIC with previous model

comp_C4_C42 <- loo_compare(WAIC_C4, WAIC_C42)
print(comp_C4_C42)
#>        elpd_diff se_diff
#> model1   0.0       0.0  
#> model2 -25.7      10.3

The first column shows the difference in ELPD relative to the model with the largest ELPD. In this case, the difference in elpd and its scale relative to the approximate standard error of the difference) indicates a preference for the second model (model2).