Add nlmixr tests, reorganize, test intervals()

6 files changed, 236 insertions, 176 deletions

diff --git a/test.log b/test.log
index e6ab6d6d..5a9e0034 100644
--- a/test.log
+++ b/test.log
@@ -7,38 +7,41 @@ Loading required package: parallel
 ✔ |         5 | Calculation of Akaike weights
 ✔ |         2 | Export dataset for reading into CAKE
 ✔ |        12 | Confidence intervals and p-values [1.0s]
-✔ |        14 | Error model fitting [4.8s]
+⠋ |         1 | Dimethenamid data from 2018, parent fits                        
+✔ |        24 | Dimethenamid data from 2018, parent fits [36.7s]
+✔ |        14 | Error model fitting [6.8s]
 ✔ |         5 | Time step normalisation
-✔ |         4 | Calculation of FOCUS chi2 error levels [0.6s]
-✔ |        14 | Results for FOCUS D established in expertise for UBA (Ranke 2014) [0.8s]
-✔ |         4 | Test fitting the decline of metabolites from their maximum [0.4s]
-✔ |         1 | Fitting the logistic model [0.2s]
-✔ |     1  35 | Nonlinear mixed-effects models [26.8s]
+✔ |         4 | Calculation of FOCUS chi2 error levels [0.8s]
+✔ |        14 | Results for FOCUS D established in expertise for UBA (Ranke 2014) [1.1s]
+✔ |         4 | Test fitting the decline of metabolites from their maximum [0.5s]
+✔ |         1 | Fitting the logistic model [0.3s]
+✔ |     1  12 | Nonlinear mixed-effects models [0.2s]
 ────────────────────────────────────────────────────────────────────────────────
-Skip (test_mixed.R:161:3): saem results are reproducible for biphasic fits
+Skip (test_mixed.R:67:3): saemix results are reproducible for biphasic fits
 Reason: Fitting with saemix takes around 10 minutes when using deSolve
 ────────────────────────────────────────────────────────────────────────────────
 ✔ |         2 | Test dataset classes mkinds and mkindsg
-✔ |        10 | Special cases of mkinfit calls [0.4s]
-✔ |         1 | mkinfit features [0.3s]
+✔ |        10 | Special cases of mkinfit calls [0.6s]
+✔ |         1 | mkinfit features [0.5s]
 ✔ |         8 | mkinmod model generation and printing [0.2s]
-✔ |         3 | Model predictions with mkinpredict [0.4s]
-✔ |        16 | Evaluations according to 2015 NAFTA guidance [1.5s]
-✔ |         9 | Nonlinear mixed-effects models with nlme [8.3s]
-✔ |        16 | Plotting [1.3s]
+✔ |         3 | Model predictions with mkinpredict [0.3s]
+✔ |        16 | Evaluations according to 2015 NAFTA guidance [2.1s]
+✔ |         9 | Nonlinear mixed-effects models with nlme [9.4s]
+✔ |        16 | Plotting [1.5s]
 ✔ |         4 | Residuals extracted from mkinfit models
-✔ |         2 | Complex test case from Schaefer et al. (2007) Piacenza paper [1.5s]
-✔ |         7 | Fitting the SFORB model [3.9s]
+✔ |        23 | saemix_parent [29.2s]
+✔ |         2 | Complex test case from Schaefer et al. (2007) Piacenza paper [1.7s]
+✔ |         7 | Fitting the SFORB model [4.4s]
 ✔ |         1 | Summaries of old mkinfit objects
 ✔ |         4 | Summary [0.1s]
-✔ |         4 | Results for synthetic data established in expertise for UBA (Ranke 2014) [2.3s]
-✔ |         9 | Hypothesis tests [8.6s]
+✔ |         4 | Results for synthetic data established in expertise for UBA (Ranke 2014) [2.5s]
+✔ |         9 | Hypothesis tests [9.5s]
 ✔ |         4 | Calculation of maximum time weighted average concentrations (TWAs) [2.2s]
 
 ══ Results ═════════════════════════════════════════════════════════════════════
-Duration: 69.5 s
+Duration: 115.5 s
 
 ── Skipped tests  ──────────────────────────────────────────────────────────────
 • Fitting with saemix takes around 10 minutes when using deSolve (1)
 
-[ FAIL 0 | WARN 0 | SKIP 1 | PASS 206 ]
+[ FAIL 0 | WARN 0 | SKIP 1 | PASS 230 ]
diff --git a/tests/testthat/summary_saem_biphasic_s.txt b/tests/testthat/summary_saem_biphasic_s.txt
index 995e81c8..4569099f 100644
--- a/tests/testthat/summary_saem_biphasic_s.txt
+++ b/tests/testthat/summary_saem_biphasic_s.txt
@@ -17,7 +17,8 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in test time 0 s using 300, 100 iterations
+Fitted in test time 0 s
+Using 300, 100 iterations and 4 chains
 
 Variance model: Constant variance 
 
diff --git a/tests/testthat/test-dmta.R b/tests/testthat/test-dmta.R
deleted file mode 100644
index 12bbcb8e..00000000
--- a/tests/testthat/test-dmta.R
+++ /dev/null
@@ -1,64 +0,0 @@
-local_edition(3)
-
-# Data
-dmta_ds <- lapply(1:7, function(i) {
-  ds_i <- dimethenamid_2018$ds[[i]]$data
-  ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"
-  ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i]
-  ds_i
-})
-names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
-dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])
-dmta_ds[["Elliot 1"]] <- dmta_ds[["Elliot 2"]] <- NULL
-
-# mkin
-nlm_dfop <- mmkin("DFOP", dmta_ds)
-nlm_dfop_tc <- mmkin("DFOP", dmta_ds, error_model = "tc")
-parms(nlm_dfop_tc)
-
-# nlme
-nlme_dfop_tc <- nlme(nlm_dfop_tc)
-summary(nlme_dfop_tc)
-intervals(nlme_dfop_tc)
-
-# saemix
-saem_saemix_dfop_tc <- saem(nlm_dfop_tc)
-saem_saemix_dfop_tc$so <- saemix::llgq.saemix(saem_saemix_dfop_tc$so)
-summary(saem_saemix_dfop_tc)
-intervals(saem_saemix_dfop_tc)
-AIC(saem_saemix_dfop_tc$so)
-AIC(saem_saemix_dfop_tc$so, "gq")
-AIC(saem_saemix_dfop_tc$so, "lin")
-saemix::plot(saem_saemix_dfop_tc$so, plot.type = "likelihood")
-saemix::plot(saem_saemix_dfop_tc$so, plot.type = "convergence")
-
-saem_saemix_dfop_tc_1k <- saem(nlm_dfop_tc, nbiter.saemix = c(1000, 100))
-AIC(saem_saemix_dfop_tc_1k$so)
-saemix::plot(saem_saemix_dfop_tc_1k$so, plot.type = "convergence")
-saemix::plot(saem_saemix_dfop_tc_1k$so, plot.type = "likelihood")
-intervals(saem_saemix_dfop_tc_1k)
-
-saem_saemix_dfop_tc_1.5k <- saem(nlm_dfop_tc, nbiter.saemix = c(1500, 100))
-saem_saemix_dfop_tc_1.5k$so <- saemix::llgq.saemix(saem_saemix_dfop_tc_1.5k$so)
-saemix::plot(saem_saemix_dfop_tc_1.5k$so, plot.type = "convergence")
-AIC(saem_saemix_dfop_tc_1.5k$so)
-AIC(saem_saemix_dfop_tc_1.5k$so, "gq")
-intervals(saem_saemix_dfop_tc_1.5k)
-
-# nlmixr saem
-saem_nlmixr_dfop_tc <- nlmixr(nlm_dfop_tc, est = "saem",
-  control = nlmixr::saemControl(nBurn = 300, nEm = 100, nmc = 9, print = 0))
-intervals(saem_nlmixr_dfop_tc)
-summary(saem_nlmixr_dfop_tc)
-AIC(saem_nlmixr_dfop_tc$nm)
-
-saem_nlmixr_dfop_tc_1k <- nlmixr(nlm_dfop_tc, est = "saem",
-  control = nlmixr::saemControl(nBurn = 1000, nEm = 300, nmc = 9, print = 0))
-intervals(saem_nlmixr_dfop_tc_1k)
-summary(saem_nlmixr_dfop_tc_1k)
-AIC(saem_nlmixr_dfop_tc_1k$nm)
-
-focei_nlmixr_dfop_tc <- nlmixr(nlm_dfop_tc, est = "focei")
-intervals(focei_nlmixr_dfop_tc)
-
-AIC(saem_nlmixr_dfop_tc$nm)
diff --git a/tests/testthat/test_dmta.R b/tests/testthat/test_dmta.R
new file mode 100644
index 00000000..3437966f
--- /dev/null
+++ b/tests/testthat/test_dmta.R
@@ -0,0 +1,120 @@
+context("Dimethenamid data from 2018, parent fits")
+
+# Data
+dmta_ds <- lapply(1:7, function(i) {
+  ds_i <- dimethenamid_2018$ds[[i]]$data
+  ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"
+  ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i]
+  ds_i
+})
+names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
+dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])
+dmta_ds[["Elliot 1"]] <- dmta_ds[["Elliot 2"]] <- NULL
+
+# mkin
+dmta_dfop <- mmkin("DFOP", dmta_ds, quiet = TRUE)
+dmta_dfop_tc <- mmkin("DFOP", dmta_ds, error_model = "tc", quiet = TRUE)
+
+test_that("Different backends get consistent results for DFOP tc, dimethenamid data", {
+
+  # nlme
+  expect_warning(
+    nlme_dfop_tc <- nlme(dmta_dfop_tc),
+    "Iteration 3, .* false convergence")
+  ints_nlme <- intervals(nlme_dfop_tc)
+
+  # saemix
+  saem_saemix_dfop_tc <- saem(dmta_dfop_tc)
+  ints_saemix <- intervals(saem_saemix_dfop_tc)
+
+  # saemix mkin transformations
+  saem_saemix_dfop_tc_mkin <- saem(dmta_dfop_tc, transformations = "mkin")
+  ints_saemix_mkin <- intervals(saem_saemix_dfop_tc_mkin)
+
+  # nlmixr saem
+  saem_nlmixr_dfop_tc <- nlmixr(dmta_dfop_tc, est = "saem",
+    control = nlmixr::saemControl(nBurn = 300, nEm = 100, nmc = 9, print = 0))
+  ints_nlmixr_saem <- intervals(saem_nlmixr_dfop_tc)
+
+  # nlmixr focei
+  # We get three warnings about nudged etas, the initial optimization and
+  # gradient problems with initial estimate and covariance
+  # We need to capture output, otherwise it pops up in testthat output
+  expect_warning(tmp <- capture_output(focei_nlmixr_dfop_tc <- nlmixr(
+      dmta_dfop_tc, est = "focei",
+      control = nlmixr::foceiControl(print = 0), all = TRUE)))
+  ints_nlmixr_focei <- intervals(focei_nlmixr_dfop_tc)
+
+  # Fixed effects
+  ## saemix vs. nlme
+  expect_true(all(ints_saemix$fixed[, "est."] >
+      backtransform_odeparms(ints_nlme$fixed[, "lower"], dmta_dfop$mkinmod)))
+  expect_true(all(ints_saemix$fixed[, "est."] <
+      backtransform_odeparms(ints_nlme$fixed[, "upper"], dmta_dfop$mkinmod)))
+
+  ## saemix mkin vs. nlme
+  expect_true(all(ints_saemix_mkin$fixed[, "est."] >
+      backtransform_odeparms(ints_nlme$fixed[, "lower"], dmta_dfop$mkinmod)))
+  expect_true(all(ints_saemix_mkin$fixed[, "est."] <
+      backtransform_odeparms(ints_nlme$fixed[, "upper"], dmta_dfop$mkinmod)))
+
+  ## nlmixr saem vs. nlme
+  expect_true(all(ints_nlmixr_saem$fixed[, "est."] >
+      backtransform_odeparms(ints_nlme$fixed[, "lower"], dmta_dfop$mkinmod)))
+  expect_true(all(ints_nlmixr_saem$fixed[, "est."] <
+      backtransform_odeparms(ints_nlme$fixed[, "upper"], dmta_dfop$mkinmod)))
+
+  ## nlmixr focei vs. nlme
+  expect_true(all(ints_nlmixr_focei$fixed[, "est."] >
+      backtransform_odeparms(ints_nlme$fixed[, "lower"], dmta_dfop$mkinmod)))
+  expect_true(all(ints_nlmixr_focei$fixed[, "est."] <
+      backtransform_odeparms(ints_nlme$fixed[, "upper"], dmta_dfop$mkinmod)))
+
+  # Random effects
+  ## for saemix with saemix transformations, the comparison would be complicated...
+  ## saemix mkin vs. nlme
+  expect_true(all(ints_saemix$random[, "est."] >
+      backtransform_odeparms(ints_nlme$reStruct$ds[, "lower"], dmta_dfop$mkinmod)))
+  expect_true(all(ints_saemix$fixed[, "est."] <
+      backtransform_odeparms(ints_nlme$fixed[, "upper"], dmta_dfop$mkinmod)))
+
+  ## nlmixr saem vs. nlme
+  expect_true(all(ints_nlmixr_saem$random[, "est."] >
+      backtransform_odeparms(ints_nlme$reStruct$ds[, "lower"], dmta_dfop$mkinmod)))
+  expect_true(all(ints_nlmixr_saem$random[, "est."] <
+      backtransform_odeparms(ints_nlme$reStruct$ds[, "upper"], dmta_dfop$mkinmod)))
+
+  ## nlmixr focei vs. nlme
+  expect_true(all(ints_nlmixr_focei$random[, "est."] >
+      backtransform_odeparms(ints_nlme$reStruct$ds[, "lower"], dmta_dfop$mkinmod)))
+  expect_true(all(ints_nlmixr_focei$random[, "est."] <
+      backtransform_odeparms(ints_nlme$reStruct$ds[, "upper"], dmta_dfop$mkinmod)))
+
+  # Variance function
+  # saemix vs. nlme
+  expect_true(all(ints_saemix[[3]][, "est."] >
+      ints_nlme$varStruct[, "lower"]))
+  expect_true(all(ints_saemix[[3]][, "est."] <
+      ints_nlme$varStruct[, "upper"]))
+
+  # saemix with mkin transformations vs. nlme
+  expect_true(all(ints_saemix_mkin[[3]][, "est."] >
+      ints_nlme$varStruct[, "lower"]))
+  expect_true(all(ints_saemix_mkin[[3]][, "est."] <
+      ints_nlme$varStruct[, "upper"]))
+
+  # nlmixr saem vs. nlme
+  expect_true(all(ints_nlmixr_saem[[3]][, "est."] >
+      ints_nlme$varStruct[, "lower"]))
+  expect_true(all(ints_nlmixr_saem[[3]][, "est."] <
+      ints_nlme$varStruct[, "upper"]))
+
+  # nlmixr focei vs. nlme
+  # We only test for the proportional part (rsd_high), as the 
+  # constant part (sigma_low) obtained with nlmixr/FOCEI is below the lower
+  # bound of the confidence interval obtained with nlme
+  expect_true(ints_nlmixr_focei[[3]]["rsd_high", "est."] >
+      ints_nlme$varStruct["prop", "lower"])
+  expect_true(ints_nlmixr_focei[[3]]["rsd_high", "est."] <
+      ints_nlme$varStruct["prop", "upper"])
+})
diff --git a/tests/testthat/test_mixed.R b/tests/testthat/test_mixed.R
index 40bd3fdf..dbcc66ce 100644
--- a/tests/testthat/test_mixed.R
+++ b/tests/testthat/test_mixed.R
@@ -1,96 +1,5 @@
 context("Nonlinear mixed-effects models")
 
-test_that("Parent fits using saemix are correctly implemented", {
-
-  expect_error(saem(fits), "Only row objects")
-  # Some fits were done in the setup script
-  mmkin_sfo_2 <- update(mmkin_sfo_1, fixed_initials = c(parent = 100))
-  expect_error(update(mmkin_sfo_1, models = c("SFOOO")), "Please supply models.*")
-
-  sfo_saem_2 <- saem(mmkin_sfo_1, quiet = TRUE, transformations = "mkin")
-  sfo_saem_3 <- expect_error(saem(mmkin_sfo_2, quiet = TRUE), "at least two parameters")
-  s_sfo_s1 <- summary(sfo_saem_1)
-  s_sfo_s2 <- summary(sfo_saem_2)
-
-  sfo_nlme_1 <- expect_warning(nlme(mmkin_sfo_1), "not converge")
-  s_sfo_n <- summary(sfo_nlme_1)
-
-  # Compare with input
-  expect_equal(round(s_sfo_s2$confint_ranef["SD.log_k_parent", "est."], 1), 0.3)
-  # k_parent is a bit different from input 0.03 here
-  expect_equal(round(s_sfo_s1$confint_back["k_parent", "est."], 3), 0.035)
-  expect_equal(round(s_sfo_s2$confint_back["k_parent", "est."], 3), 0.035)
-
-  # But the result is pretty unanimous between methods
-  expect_equal(round(s_sfo_s1$confint_back["k_parent", "est."], 3),
-    round(s_sfo_s2$confint_back["k_parent", "est."], 3))
-  expect_equal(round(s_sfo_s1$confint_back["k_parent", "est."], 3),
-    round(s_sfo_n$confint_back["k_parent", "est."], 3))
-
-  mmkin_fomc_1 <- mmkin("FOMC", ds_fomc, quiet = TRUE, error_model = "tc", cores = n_cores)
-  fomc_saem_1 <- saem(mmkin_fomc_1, quiet = TRUE)
-  ci_fomc_s1 <- summary(fomc_saem_1)$confint_back
-
-  fomc_pop <- as.numeric(fomc_pop)
-  expect_true(all(ci_fomc_s1[, "lower"] < fomc_pop))
-  expect_true(all(ci_fomc_s1[, "upper"] > fomc_pop))
-
-  mmkin_fomc_2 <- update(mmkin_fomc_1, state.ini = 100, fixed_initials = "parent")
-  fomc_saem_2 <- saem(mmkin_fomc_2, quiet = TRUE, transformations = "mkin")
-  ci_fomc_s2 <- summary(fomc_saem_2)$confint_back
-
-  expect_true(all(ci_fomc_s2[, "lower"] < fomc_pop[2:3]))
-  expect_true(all(ci_fomc_s2[, "upper"] > fomc_pop[2:3]))
-
-  s_dfop_s1 <- summary(dfop_saemix_1)
-  s_dfop_s2 <- summary(dfop_saemix_2)
-  s_dfop_n <- summary(dfop_nlme_1)
-
-  dfop_pop <- as.numeric(dfop_pop)
-  expect_true(all(s_dfop_s1$confint_back[, "lower"] < dfop_pop))
-  expect_true(all(s_dfop_s1$confint_back[, "upper"] > dfop_pop))
-  expect_true(all(s_dfop_s2$confint_back[, "lower"] < dfop_pop))
-  expect_true(all(s_dfop_s2$confint_back[, "upper"] > dfop_pop))
-
-  dfop_mmkin_means_trans_tested <- mean_degparms(mmkin_dfop_1, test_log_parms = TRUE)
-  dfop_mmkin_means_trans <- apply(parms(mmkin_dfop_1, transformed = TRUE), 1, mean)
-
-  dfop_mmkin_means_tested <- backtransform_odeparms(dfop_mmkin_means_trans_tested, mmkin_dfop_1$mkinmod)
-  dfop_mmkin_means <- backtransform_odeparms(dfop_mmkin_means_trans, mmkin_dfop_1$mkinmod)
-
-  # We get < 20% deviations for parent_0 and k1 by averaging the transformed parameters
-  # If we average only parameters passing the t-test, the deviation for k2 is also < 20%
-  rel_diff_mmkin <- (dfop_mmkin_means - dfop_pop) / dfop_pop
-  rel_diff_mmkin_tested <- (dfop_mmkin_means_tested - dfop_pop) / dfop_pop
-  expect_true(all(rel_diff_mmkin[c("parent_0", "k1")] < 0.20))
-  expect_true(all(rel_diff_mmkin_tested[c("parent_0", "k1", "k2")] < 0.20))
-
-  # We get < 15% deviations with transformations made in mkin
-  rel_diff_1 <- (s_dfop_s1$confint_back[, "est."] - dfop_pop) / dfop_pop
-  expect_true(all(rel_diff_1 < 0.15))
-
-  # We get < 20% deviations with transformations made in saemix
-  rel_diff_2 <- (s_dfop_s2$confint_back[, "est."] - dfop_pop) / dfop_pop
-  expect_true(all(rel_diff_2 < 0.2))
-
-  mmkin_hs_1 <- mmkin("HS", ds_hs, quiet = TRUE, error_model = "const", cores = n_cores)
-  hs_saem_1 <- saem(mmkin_hs_1, quiet = TRUE)
-  ci_hs_s1 <- summary(hs_saem_1)$confint_back
-
-  hs_pop <- as.numeric(hs_pop)
-  # expect_true(all(ci_hs_s1[, "lower"] < hs_pop)) # k1 is overestimated
-  expect_true(all(ci_hs_s1[, "upper"] > hs_pop))
-
-  mmkin_hs_2 <- update(mmkin_hs_1, state.ini = 100, fixed_initials = "parent")
-  hs_saem_2 <- saem(mmkin_hs_2, quiet = TRUE)
-  ci_hs_s2 <- summary(hs_saem_2)$confint_back
-
-  #expect_true(all(ci_hs_s2[, "lower"] < hs_pop[2:4])) # k1 again overestimated
-  expect_true(all(ci_hs_s2[, "upper"] > hs_pop[2:4]))
-
-  # HS would likely benefit from implemenation of transformations = "saemix"
-})
-
 test_that("Print methods work", {
   expect_known_output(print(fits[, 2:3], digits = 2), "print_mmkin_parent.txt")
   expect_known_output(print(mmkin_biphasic_mixed, digits = 2), "print_mmkin_biphasic_mixed.txt")
@@ -122,7 +31,7 @@ test_that("nlme results are reproducible to some degree", {
   expect_true(all(ci_dfop_sfo_n[, "upper"] > dfop_sfo_pop))
 })
 
-test_that("saem results are reproducible for biphasic fits", {
+test_that("saemix results are reproducible for biphasic fits", {
 
   test_summary <- summary(saem_biphasic_s)
   test_summary$saemixversion <- "Dummy 0.0 for testing"
diff --git a/tests/testthat/test_saemix_parent.R b/tests/testthat/test_saemix_parent.R
new file mode 100644
index 00000000..2f05c175
--- /dev/null
+++ b/tests/testthat/test_saemix_parent.R
@@ -0,0 +1,91 @@
+test_that("Parent fits using saemix are correctly implemented", {
+
+  expect_error(saem(fits), "Only row objects")
+  # Some fits were done in the setup script
+  mmkin_sfo_2 <- update(mmkin_sfo_1, fixed_initials = c(parent = 100))
+  expect_error(update(mmkin_sfo_1, models = c("SFOOO")), "Please supply models.*")
+
+  sfo_saem_2 <- saem(mmkin_sfo_1, quiet = TRUE, transformations = "mkin")
+  sfo_saem_3 <- expect_error(saem(mmkin_sfo_2, quiet = TRUE), "at least two parameters")
+  s_sfo_s1 <- summary(sfo_saem_1)
+  s_sfo_s2 <- summary(sfo_saem_2)
+
+  sfo_nlme_1 <- expect_warning(nlme(mmkin_sfo_1), "not converge")
+  s_sfo_n <- summary(sfo_nlme_1)
+
+  # Compare with input
+  expect_equal(round(s_sfo_s2$confint_ranef["SD.log_k_parent", "est."], 1), 0.3)
+  # k_parent is a bit different from input 0.03 here
+  expect_equal(round(s_sfo_s1$confint_back["k_parent", "est."], 3), 0.035)
+  expect_equal(round(s_sfo_s2$confint_back["k_parent", "est."], 3), 0.035)
+
+  # But the result is pretty unanimous between methods
+  expect_equal(round(s_sfo_s1$confint_back["k_parent", "est."], 3),
+    round(s_sfo_s2$confint_back["k_parent", "est."], 3))
+  expect_equal(round(s_sfo_s1$confint_back["k_parent", "est."], 3),
+    round(s_sfo_n$confint_back["k_parent", "est."], 3))
+
+  mmkin_fomc_1 <- mmkin("FOMC", ds_fomc, quiet = TRUE, error_model = "tc", cores = n_cores)
+  fomc_saem_1 <- saem(mmkin_fomc_1, quiet = TRUE)
+  ci_fomc_s1 <- summary(fomc_saem_1)$confint_back
+
+  fomc_pop <- as.numeric(fomc_pop)
+  expect_true(all(ci_fomc_s1[, "lower"] < fomc_pop))
+  expect_true(all(ci_fomc_s1[, "upper"] > fomc_pop))
+
+  mmkin_fomc_2 <- update(mmkin_fomc_1, state.ini = 100, fixed_initials = "parent")
+  fomc_saem_2 <- saem(mmkin_fomc_2, quiet = TRUE, transformations = "mkin")
+  ci_fomc_s2 <- summary(fomc_saem_2)$confint_back
+
+  expect_true(all(ci_fomc_s2[, "lower"] < fomc_pop[2:3]))
+  expect_true(all(ci_fomc_s2[, "upper"] > fomc_pop[2:3]))
+
+  s_dfop_s1 <- summary(dfop_saemix_1)
+  s_dfop_s2 <- summary(dfop_saemix_2)
+  s_dfop_n <- summary(dfop_nlme_1)
+
+  dfop_pop <- as.numeric(dfop_pop)
+  expect_true(all(s_dfop_s1$confint_back[, "lower"] < dfop_pop))
+  expect_true(all(s_dfop_s1$confint_back[, "upper"] > dfop_pop))
+  expect_true(all(s_dfop_s2$confint_back[, "lower"] < dfop_pop))
+  expect_true(all(s_dfop_s2$confint_back[, "upper"] > dfop_pop))
+
+  dfop_mmkin_means_trans_tested <- mean_degparms(mmkin_dfop_1, test_log_parms = TRUE)
+  dfop_mmkin_means_trans <- apply(parms(mmkin_dfop_1, transformed = TRUE), 1, mean)
+
+  dfop_mmkin_means_tested <- backtransform_odeparms(dfop_mmkin_means_trans_tested, mmkin_dfop_1$mkinmod)
+  dfop_mmkin_means <- backtransform_odeparms(dfop_mmkin_means_trans, mmkin_dfop_1$mkinmod)
+
+  # We get < 20% deviations for parent_0 and k1 by averaging the transformed parameters
+  # If we average only parameters passing the t-test, the deviation for k2 is also < 20%
+  rel_diff_mmkin <- (dfop_mmkin_means - dfop_pop) / dfop_pop
+  rel_diff_mmkin_tested <- (dfop_mmkin_means_tested - dfop_pop) / dfop_pop
+  expect_true(all(rel_diff_mmkin[c("parent_0", "k1")] < 0.20))
+  expect_true(all(rel_diff_mmkin_tested[c("parent_0", "k1", "k2")] < 0.20))
+
+  # We get < 15% deviations with transformations made in mkin
+  rel_diff_1 <- (s_dfop_s1$confint_back[, "est."] - dfop_pop) / dfop_pop
+  expect_true(all(rel_diff_1 < 0.15))
+
+  # We get < 20% deviations with transformations made in saemix
+  rel_diff_2 <- (s_dfop_s2$confint_back[, "est."] - dfop_pop) / dfop_pop
+  expect_true(all(rel_diff_2 < 0.2))
+
+  mmkin_hs_1 <- mmkin("HS", ds_hs, quiet = TRUE, error_model = "const", cores = n_cores)
+  hs_saem_1 <- saem(mmkin_hs_1, quiet = TRUE)
+  ci_hs_s1 <- summary(hs_saem_1)$confint_back
+
+  hs_pop <- as.numeric(hs_pop)
+  # expect_true(all(ci_hs_s1[, "lower"] < hs_pop)) # k1 is overestimated
+  expect_true(all(ci_hs_s1[, "upper"] > hs_pop))
+
+  mmkin_hs_2 <- update(mmkin_hs_1, state.ini = 100, fixed_initials = "parent")
+  hs_saem_2 <- saem(mmkin_hs_2, quiet = TRUE)
+  ci_hs_s2 <- summary(hs_saem_2)$confint_back
+
+  #expect_true(all(ci_hs_s2[, "lower"] < hs_pop[2:4])) # k1 again overestimated
+  expect_true(all(ci_hs_s2[, "upper"] > hs_pop[2:4]))
+
+  # HS would likely benefit from implemenation of transformations = "saemix"
+})
+