tests/testthat/test-steady-state.R

In nlmixr2/rxode2: Facilities for Simulating from ODE-Based Models

rxTest({
  ms <- c("liblsoda", "lsoda", "dop853")
  for (m in ms) {
    
    et <- eventTable() %>%
      add.dosing(dose = 3, nbr.doses = 6, dosing.interval = 8) %>%
      add.sampling(seq(0, 48, length.out = 200))

    ode.1c <- rxode2({
      V <- 20
      Cl <- 1
      fc <- 1
      C2 <- center / V
      d / dt(center) ~ -Cl * C2
      f(center) <- fc
    })

    ode.1cR <- rxode2({
      V <- 20
      Cl <- 1
      C2 <- center / V
      fc <- 1
      d / dt(center) ~ -Cl * C2
      rate(center) <- rateIn
      f(center) <- fc
    })

    ode.1cD <- rxode2({
      V <- 20
      Cl <- 1
      C2 <- center / V
      fc <- 1
      d / dt(center) ~ -Cl * C2
      dur(center) <- durIn
      f(center) <- fc
    })

    d <- 3
    et2 <- eventTable() %>%
      add.dosing(dose = d, nbr.doses = 2, dosing.interval = 8) %>%
      add.sampling(seq(0, 48, length.out = 200))

    x2 <- solve(ode.1c, et2, method = m)

    c0 <- setNames(d / rxInits(ode.1c)["V"], NULL)

    ke <- with(as.list(rxInits(ode.1c)), {
      Cl / V
    })

    # context(sprintf("Steady state IV Bolus (%s)", m))

    test_that(paste0("Non steady state dose makes sense; meth=",m), {
      expect_equal(x2$C2[1], c0)
    })

    tol <- 1e-3

    for (ii in seq(2, 24, by = 2)) {
      ## now setup bolus steady state evid
      et3 <- et() %>%
        et(amt = d, ss = 1, ii = ii) %>%
        et(amt = d, time = ii) %>%
        et(seq(0, 48, length.out = 200))
      x2 <- solve(ode.1c, et3, method = m)
      test_that(paste("Steady State dose makes sense for ii=", ii,"; meth=", m), {
        expect_equal(x2$C2[1], c0 / (1 - exp(-ke * ii)), tolerance = tol)
      })
    }

    # context(sprintf("Steady state Infusions (%s)", m))

    ## Need to test:
    ## - Fixed Infusion w/rate (check)
    ## - Fixed Infusion w/rate + bioavailability change (check)
    ## - Fixed Infusion w/dur (check)
    ## - Fixed Infusion w/dur + bioavailability change
    ## - Modeled rate (check)
    ## - Modeled rate + bioavailability change (check)
    ## - Modeled duration (check)
    ## - Modeled duration + bioavailability change
    for (dur in c(0.5, 1)) {
      for (ii in seq(2, 24, by = 2)) {
        ## Fixed rate
        et3 <- et() %>%
          et(amt = d, ss = 1, ii = ii, rate = d / dur) %>%
          et(time = ii, amt = d, ii = ii, addl = floor(24 / ii), rate = d / dur) %>%
          et(c(dur, seq(0, 24, length.out = 200)))
        x2 <- solve(ode.1c, et3, method = m, maxsteps = 10000)
        infMax <- with(
          as.list(rxInit(ode.1c)),
          d / (Cl * dur) * (1 - exp(-ke * dur)) / (1 - exp(-ke * ii))
        )
        inf0 <- with(
          as.list(rxInit(ode.1c)),
          infMax * exp(-ke * (ii - dur))
        )
        
        test_that(paste("Infusion Steady State dose makes sense for ii=", ii, " dur=", dur, "(rate); meth=", m), {
          expect_equal(x2$C2[x2$time == dur], infMax, tolerance = tol)
          expect_equal(x2$C2[1], inf0, tolerance = tol)
        })
        
        ## Fixed duration
        et3 <- et() %>%
          et(amt = d, ss = 1, ii = ii, dur = dur) %>%
          et(c(dur, seq(0, 24, length.out = 19)))
        x2 <- solve(ode.1c, et3, method = m, maxsteps = 10000)
        test_that(paste("Infusion Steady State dose makes sense for ii=", ii, " dur=", dur, "(dur); met=", m), {
          expect_equal(x2$C2[x2 == dur], infMax, tolerance = tol)
          expect_equal(x2$C2[1], inf0, tolerance = tol)
        })
        ## rate modeled
        et3 <- et() %>%
          et(amt = d, ss = 1, ii = ii, rate = -1) %>%
          et(c(dur, seq(0, 24, length.out = 19)))
        x2 <- rxSolve(ode.1cR, et3, c(rateIn = d / dur), method = m, maxsteps = 10000)
        test_that(paste("Infusion Steady State dose makes sense for ii=", ii, " dur=", dur, "(rate modeled); meth=", m), {
          expect_equal(x2$C2[x2 == dur], infMax, tolerance = tol)
          expect_equal(x2$C2[1], inf0, tolerance = tol)
        })
        ## duration modeled
        et3 <- et() %>%
          et(amt = d, ss = 1, ii = ii, rate = -2) %>%
          et(c(dur, seq(0, 24, length.out = 19)))
        x2 <- rxSolve(ode.1cD, et3, c(durIn = dur), method = m, maxsteps = 10000)
        test_that(paste("Infusion Steady State dose makes sense for ii=", ii, " dur=", dur, "(dur modeled); meth=", m), {
          expect_equal(x2$C2[x2 == dur], infMax, tolerance = tol)
          expect_equal(x2$C2[1], inf0, tolerance = tol)
        })
        for (f in c(0.5, 1)) {
          if (dur * f < ii) {
            ## Now add modeled bioavailability change
            ## That changes duration
            infMax <- with(
              as.list(rxInit(ode.1c)),
              f * d / (Cl * dur * f) * (1 - exp(-ke * dur * f)) / (1 - exp(-ke * ii))
            )
            inf0 <- with(
              as.list(rxInit(ode.1c)),
              infMax * exp(-ke * (ii - dur * f))
            )
            et3 <- et() %>%
              et(amt = d, ss = 1, ii = ii, rate = d / dur) %>%
              et(time = ii, amt = d, ii = ii, addl = floor(24 / ii), rate = d / dur) %>%
              et(c(dur * f, seq(0, 24, length.out = 400)))
            x2 <- solve(ode.1c, et3, c(fc = f), method = m, maxsteps = 10000)
            test_that(paste("Infusion Steady State dose makes sense for f= ", f, "ii=", ii, " dur=", dur, "(rate); meth=", m), {
              expect_equal(x2$C2[x2 == dur * f], infMax, tolerance = tol)
              expect_equal(x2$C2[1], inf0, tolerance = tol)
            })
            ## rate modeled
            et3 <- et() %>%
              et(amt = d, ss = 1, ii = ii, rate = -1) %>%
              et(c(dur * f, seq(0, 24, length.out = 19)))
            x2 <- rxSolve(ode.1cR, et3, c(fc = f, rateIn = d / dur), method = m, maxsteps = 10000)
            test_that(paste("Infusion Steady State dose makes sense for f= ", f, " ii=", ii, " dur=", dur, "(rate modeled); meth=", m), {
              expect_equal(x2$C2[x2 == dur * f], infMax, tolerance = tol)
              expect_equal(x2$C2[1], inf0, tolerance = tol)
            })
          }
          ## Add modeled bioavailability change
          ## That changes rate
          infMax <- with(
            as.list(rxInit(ode.1c)),
            f * d / (Cl * dur) * (1 - exp(-ke * dur)) / (1 - exp(-ke * ii))
          )
          inf0 <- with(
            as.list(rxInit(ode.1c)),
            infMax * exp(-ke * (ii - dur))
          )
          et3 <- et() %>%
            et(amt = d, ss = 1, ii = ii, dur = dur) %>%
            et(time = ii, amt = d, ii = ii, addl = floor(24 / ii), dur = dur) %>%
            et(unique(c(dur, seq(0, 24, length.out = 200))))
          x2 <- solve(ode.1c, et3, c(fc = f), method = m, maxsteps = 10000)
          test_that(paste("Infusion Steady State dose makes sense for f= ", f, "ii=", ii, " dur=", dur, "(dur); meth=", m), {
            expect_equal(x2$C2[x2 == dur], infMax, tolerance = tol)
            expect_equal(x2$C2[1], inf0, tolerance = tol)
          })
          et3 <- et() %>%
            et(amt = d, ss = 1, ii = ii, rate = -2) %>%
            et(c(dur, seq(0, 24, length.out = 19)))
          x2 <- rxSolve(ode.1cD, et3, c(fc = f, durIn = dur), method = m, maxsteps = 10000)
          test_that(paste("Infusion Steady State dose makes sense for f=", f, "ii=", ii, " dur=", dur, "(dur modeled); meth=", m), {
            expect_equal(x2$C2[x2 == dur], infMax, tolerance = tol)
            expect_equal(x2$C2[1], inf0, tolerance = tol)
          })
        }
      }
    }

    ## steady-state = 2 for bolus
    # context(sprintf("Bolus SS=2 (%s)", m))
    test_that(paste0("bolus SS=2; meth=", m), {
      e2 <- et(amt = 20, ii = 24, ss = 2, time = 12) %>%
        et(seq(0, 24, length.out = 100))
      s2 <- rxSolve(ode.1c, e2)
      e3 <- et(amt = 20, ii = 24, ss = 1, time = 12) %>%
        et(seq(0, 24, length.out = 100))
      s3 <- rxSolve(ode.1c, e3)
      expect_equal(as.data.frame(s2), as.data.frame(s3))
      e1 <- et(amt = 10, ii = 24, ss = 1, time = 0) %>%
        et(seq(0, 24, length.out = 100))
      s1 <- rxSolve(ode.1c, e1)
      e2 <- et(amt = 20, ii = 24, ss = 2, time = 12) %>%
        et(seq(0, 24, length.out = 100))
      s2 <- rxSolve(ode.1c, e2)
      e3 <- c(e1, e2, ii = 0) %>%
        et(seq(0, 24, length.out = 100))
      s3 <- rxSolve(ode.1c, e3)
      expect_equal(s1$C2 + s2$C2, s3$C2)
      for (f in c(0.5, 2)) {
        s1 <- rxSolve(ode.1c, e1, c(fc = f))
        s2 <- rxSolve(ode.1c, e2, c(fc = f))
        s3 <- rxSolve(ode.1c, e3, c(fc = f))
        expect_equal(s1$C2 + s2$C2, s3$C2)
      }
    })
    # context(sprintf("IV Infusion SS=2 (%s)", m))
    d <- 10
    ## Changing Bioavailability causes changes in these results...
    for (f in c(0.5, 1, 2)) {
      for (dur in c(1, 2)) {
        ## Fixed rate
        e1 <- et() %>%
          et(amt = d, ss = 1, ii = 24, rate = d / dur) %>%
          et(seq(0, 24, length.out = 200))
        s1 <- solve(ode.1c, e1, c(fc = f), method = m, maxsteps = 1000000)
        e2 <- et() %>%
          et(time = 12, amt = 2 * d, ss = 2, ii = 24, rate = d * 2 / dur) %>%
          et(seq(0, 24, length.out = 200))
        if (f == 1) {
          s2 <- solve(ode.1c, e2, c(fc = f), method = m, maxsteps = 1000000)
          e3 <- et() %>%
            et(amt = d, ss = 1, ii = 24, rate = d / dur) %>%
            et(time = 12, amt = 2 * d, ss = 2, ii = 24, rate = d * 2 / dur) %>%
            et(seq(0, 24, length.out = 200))
          s3 <- solve(ode.1c, e3, c(fc = f), method = m, maxsteps = 1000000)
          test_that(paste("Infusion SS=2 dose makes sense for f=", f, " dur=", dur, "(rate); meth=", m), {
            expect_equal(s1$C2 + s2$C2, s3$C2, tolerance = 1e-4)
          })
        } else {
          test_that(paste("Infusion SS=2 dose makes sense for f=", f, " dur=", dur, "(dur); meth=", m), {
            expect_error(solve(ode.1c, e2, c(fc = f), method = m, maxsteps = 1000000))
          })
        }
        ## Fixed duration
        e1 <- et() %>%
          et(amt = d, ss = 1, ii = 24, dur = dur) %>%
          et(seq(0, 24, length.out = 200))
        s1 <- solve(ode.1c, e1, c(fc = f), method = m, maxsteps = 1000000)
        e2 <- et() %>%
          et(time = 12, amt = 2 * d, ss = 2, ii = 24, dur = dur) %>%
          et(seq(0, 24, length.out = 200))
        if (f == 1) {
          s2 <- solve(ode.1c, e2, c(fc = f), method = m, maxsteps = 1000000)
          e3 <- et() %>%
            et(amt = d, ss = 1, ii = 24, rate = d / dur) %>%
            et(time = 12, amt = 2 * d, ss = 2, ii = 24, rate = d * 2 / dur) %>%
            et(seq(0, 24, length.out = 200))
          s3 <- solve(ode.1c, e3, c(fc = f), method = m, maxsteps = 1000000)
          test_that(paste("Infusion SS=2 dose makes sense for f=", f, " dur=", dur, "(dur); meth=", m), {
            expect_equal(s1$C2 + s2$C2, s3$C2, tolerance = 1e-4)
          })
        } else {
          test_that(paste("Infusion SS=2 dose makes sense for f=", f, " dur=", dur, "(dur); meth=", m), {
            expect_error(solve(ode.1c, e2, c(fc = f), method = m, maxsteps = 1000000))
          })
        }
        ## Modeled rate when used with SS=2
        e1 <- et() %>%
          et(amt = d, ss = 1, ii = 24, rate = d / dur) %>%
          et(seq(0, 24, length.out = 200))
        s1 <- solve(ode.1cR, e1, c(fc = f, rateIn = 2 * d / dur), method = m, maxsteps = 1000000)
        e2 <- et() %>%
          et(time = 12, amt = 2 * d, ss = 2, ii = 24, rate = -1) %>%
          et(seq(0, 24, length.out = 200))
        if (f == 1) {
          s2 <- solve(ode.1cR, e2, c(fc = f, rateIn = 2 * d / dur), method = m, maxsteps = 1000000)
          e3 <- et() %>%
            et(amt = d, ss = 1, ii = 24, rate = d / dur) %>%
            et(time = 12, amt = 2 * d, ss = 2, ii = 24, rate = -1) %>%
            et(seq(0, 24, length.out = 200))
          s3 <- solve(ode.1cR, e3, c(fc = f, rateIn = 2 * d / dur), method = m, maxsteps = 1000000)
          test_that(paste("Infusion SS=2 dose makes sense for f=", f, " dur=", dur, "(modeled rate); meth=", m), {
            expect_equal(s1$C2 + s2$C2, s3$C2, tolerance = 1e-4)
          })
        } else {
          test_that(paste("Infusion SS=2 dose makes sense for f=", f, " dur=", dur, "(modeled rate); meth=", m), {
            expect_error(solve(ode.1cR, e2, c(fc = f, rateIn = 2 * d / dur), method = m, maxsteps = 1000000))
          })
        }
        ## Modeled duration when used with SS=2
        e1 <- et() %>%
          et(amt = d, ss = 1, ii = 24, dur = dur) %>%
          et(seq(0, 24, length.out = 200))
        s1 <- solve(ode.1cD, e1, c(fc = f, durIn = dur), method = m, maxsteps = 1000000)
        e2 <- et() %>%
          et(time = 12, amt = 2 * d, ss = 2, ii = 24, rate = -2) %>%
          et(seq(0, 24, length.out = 200))
        if (f == 1) {
          s2 <- solve(ode.1cD, e2, c(fc = f, durIn = dur), method = m, maxsteps = 1000000)
          e3 <- et() %>%
            et(amt = d, ss = 1, ii = 24, dur = dur) %>%
            et(time = 12, amt = 2 * d, ss = 2, ii = 24, rate = -2) %>%
            et(seq(0, 24, length.out = 200))
          s3 <- solve(ode.1cD, e3, c(fc = f, durIn = dur), method = m, maxsteps = 1000000)
          test_that(paste("Infusion SS=2 dose makes sense for f=", f, " dur=", dur, "(modeled duration); meth=", m), {
            expect_equal(s1$C2 + s2$C2, s3$C2, tolerance = 1e-4)
          })
        } else {
          test_that(paste("Infusion SS=2 dose makes sense for f=", f, " dur=", dur, "(modeled duration); meth=", m), {
            expect_error(solve(ode.1cD, e2, c(fc = f, durIn = dur), method = m, maxsteps = 1000000))
          })
        }
      }
    }

    # context("Constant Infusion steady state")

    test_that(paste0("constant infusion steady state; meth=", m), {
      ode.1cR <- rxode2({
        V <- 20
        Cl <- 1
        C2 <- center / V
        fc <- 1
        d / dt(center) ~ -Cl * C2
        rate(center) <- rateIn
        f(center) <- fc
      })

      s <- rxSolve(ode.1cR, c(rateIn = 3), et(amt = 0, rate = 10, ss = 1))

      expect_equal(s$C2[1], 10, tolerance = 1e-5)

      s <- rxSolve(ode.1cR, c(rateIn = 3), et(amt = 0, rate = -1, ss = 1))

      expect_equal(s$C2[1], 3, tolerance = 1e-5)
    })
  }
})