Global Sensitivity Analysis on Voriconazole model

2021-04-26
using Pumas, CairoMakie, PumasPlots, GlobalSensitivity

Introduction

In this tutorial, we will cover running global sensitivity analysis on the Voriconazole model published here https://github.com/metrumresearchgroup/Voriconazole-PBPK/

Model Code

model = @model begin
    @param begin
        Fup  RealDomain(init = 0.42)
        fumic  RealDomain(init = 0.711)
        WEIGHT  RealDomain(init = 73)
        MPPGL  RealDomain(init = 30.3)
        MPPGI  RealDomain(init = 0)
        C_OUTPUT  RealDomain(init = 6.5)
        VmaxH  RealDomain(init = 40)
        VmaxG  RealDomain(init = 40)
        KmH  RealDomain(init = 9.3)
        KmG  RealDomain(init = 9.3)
        bp  RealDomain(init = 1)
        kpad  RealDomain(init = 9.89)
        kpbo  RealDomain(init = 7.91)
        kpbr  RealDomain(init = 7.35)
        kpgu  RealDomain(init = 5.82)
        kphe  RealDomain(init = 1.95)
        kpki  RealDomain(init = 2.9)
        kpli  RealDomain(init = 4.66)
        kplu  RealDomain(init = 0.83)
        kpmu  RealDomain(init = 2.94)
        kpsp  RealDomain(init = 2.96)
        kpre  RealDomain(init = 4)
        MW  RealDomain(init = 349.317)
        logP  RealDomain(init = 2.56)
        s_lumen  RealDomain(init = 0.39*1000)
        L  RealDomain(init = 280)
        d  RealDomain(init = 2.5)
        PF  RealDomain(init = 1.57)
        VF  RealDomain(init = 6.5)
        MF  RealDomain(init = 13)
        ITT  RealDomain(init = 3.32)
        A  RealDomain(init = 7440)
        B  RealDomain(init = 1e7)
        alpha  RealDomain(init = 0.6)
        beta  RealDomain(init = 4.395)
        fabs  RealDomain(init = 1)
        fdis  RealDomain(init = 1)
        fperm  RealDomain(init = 1)
        vad  RealDomain(init = 18.2)
        vbo  RealDomain(init =10.5)
        vbr  RealDomain(init =1.45)
        vguWall  RealDomain(init =0.65)
        vgulumen  RealDomain(init =0.35)
        vhe  RealDomain(init =0.33)
        vki  RealDomain(init =0.31)
        vli  RealDomain(init =1.8)
        vlu  RealDomain(init =0.5)
        vmu  RealDomain(init =29)
        vsp  RealDomain(init =0.15)
        vbl  RealDomain(init =5.6)
        FQad  RealDomain(lower = 0.0, init = 0.05, upper = 1.0) #add bounds to parameters for estimation
        FQbo  RealDomain(lower = 0.0, init = 0.05, upper = 1.0)
        FQbr  RealDomain(lower = 0.0, init = 0.12, upper = 1.0)
        FQgu  RealDomain(lower = 0.0, init = 0.16, upper = 1.0)
        FQhe  RealDomain(lower = 0.0, init = 0.04, upper = 1.0)
        FQki  RealDomain(lower = 0.0, init = 0.19, upper = 1.0)
        FQli  RealDomain(lower = 0.0, init = 0.255, upper = 1.0)
        FQmu  RealDomain(lower = 0.0, init = 0.17, upper = 1.0)
        FQsp  RealDomain(lower = 0.0, init = 0.03, upper = 1.0)
    end
    @pre begin
        Vgu = vguWall + vgulumen
        Vve = 0.705*vbl
        Var = 0.295*vbl
        Vre = WEIGHT - (vli+vki+vsp+vhe+vlu+vbo+vbr+vmu+vad+vguWall+vbl)
        CO = C_OUTPUT*60
        Qad = FQad*CO
        Qbo = FQbo*CO
        Qbr = FQbr*CO
        Qgu = FQgu*CO
        Qhe = FQhe*CO
        Qki = FQki*CO
        Qli = FQli*CO
        Qmu = FQmu*CO
        Qsp = FQsp*CO
        Qha = Qli - (Qgu+Qsp)
        Qtot = Qli+Qki+Qbo+Qhe+Qmu+Qad+Qbr
        Qre = CO - Qtot
        Qlu = CO
        Vgulumen = vgulumen
        S_lumen = s_lumen
        VguWall = vguWall
        Kpgu = kpgu
        BP = bp
        Vad = vad
        Kpad = kpad
        Vbr = vbr
        Kpbr = kpbr
        Vhe = vhe
        Kphe = kphe
        Vki = vki
        Kpki = kpki
        fup = Fup
        Vsp = vsp
        Kpsp = kpsp
        Vli = vli
        Kpli = kpli
        Vlu = vlu
        Kplu = kplu
        Kpmu = kpmu
        Kpre = kpre
        Vmu = vmu
        Vbl = vbl
        Vbo = vbo
        Kpbo = kpbo
        SA_abs = pi*L*d*PF*VF*MF*1e-4
        SA_basal = pi*L*d*PF*VF*1e-4
        MA = 10^logP
        MW_eff = MW - (3*17)
        Peff = fperm*A*(((MW_eff^(-alpha-beta))*MA)/((MW_eff^(-alpha)) + B*(MW_eff^(-beta))*MA) * 1e-2 * 3600)
        kd = fdis*Peff*SA_abs*1000/vgulumen
        ka = fabs*Peff*SA_basal*1000/VguWall
        kt = 1/ITT
        scale_factor_H = MPPGL*Vli*1000
        scale_factor_G = MPPGI*VguWall*1000
        CLintHep = ((VmaxH/KmH)*scale_factor_H*60*1e-6)/fumic
        CLintGut = ((VmaxG/KmG)*scale_factor_G*60*1e-6)/fumic
        #CLintHep = CLintHep/fumic
        #CLintGut = CLintGut/fumic
        CLrenal = 0.096
        f = 1
    end
    @dynamics begin
        GUTLUMEN' = -kd*Vgulumen*(f*(GUTLUMEN/Vgulumen) + (1-f)*S_lumen) -
            kt*GUTLUMEN
        GUTWALL' = kd*Vgulumen*(f*(GUTLUMEN/Vgulumen) + (1-f)*S_lumen) -
            ka*GUTWALL - CLintGut*(GUTWALL/VguWall)
        GUT' = ka*GUTWALL + Qgu*((ART/Var) - (GUT/VguWall)/(Kpgu/BP))
        ADIPOSE' = Qad*((ART/Var) - (ADIPOSE/Vad)/(Kpad/BP))
        BRAIN' = Qbr*((ART/Var) - (BRAIN/Vbr)/(Kpbr/BP))
        HEART' = Qhe*((ART/Var) - (HEART/Vhe)/(Kphe/BP))
        KIDNEY' = Qki*((ART/Var) - (KIDNEY/Vki)/(Kpki/BP)) -
            CLrenal*(((KIDNEY/Vki)*fup)/(Kpki/BP))
        LIVER' = Qgu*((GUT/VguWall)/(Kpgu/BP)) + Qsp*((SPLEEN/Vsp)/(Kpsp/BP)) +
            Qha*(ART/Var) - Qli*((LIVER/Vli)/(Kpli/BP)) -
            CLintHep*(((LIVER/Vli)*fup)/(Kpli/BP))
        LUNG' = Qlu*((VEN/Vve) - (LUNG/Vlu)/(Kplu/BP))
        MUSCLE' = Qmu*((ART/Var) - (MUSCLE/Vmu)/(Kpmu/BP))
        SPLEEN' = Qsp*((ART/Var) - (SPLEEN/Vsp)/(Kpsp/BP))
        BONE' = Qbo*((ART/Var) - (BONE/Vbo)/(Kpbo/BP))
        REST' = Qre*((ART/Var) - (REST/Vre)/(Kpre/BP))
        VEN' = Qad*((ADIPOSE/Vad)/(Kpad/BP)) + Qbr*((BRAIN/Vbr)/(Kpbr/BP)) +
            Qhe*((HEART/Vhe)/(Kphe/BP)) + Qki*((KIDNEY/Vki)/(Kpki/BP)) +
            Qli*((LIVER/Vli)/(Kpli/BP)) + Qmu*((MUSCLE/Vmu)/(Kpmu/BP)) +
            Qbo*((BONE/Vbo)/(Kpbo/BP)) + Qre*((REST/Vre)/(Kpre/BP)) -
            Qlu*(VEN/Vve)
        ART' = Qlu*((LUNG/Vlu)/(Kplu/BP) - (ART/Var))
    end
    @derived begin
        Cvenn = VEN./Vve
        cp ~ @. Normal(Cvenn, 0.1) #for estimation
    end
end
PumasModel
  Parameters: Fup, fumic, WEIGHT, MPPGL, MPPGI, C_OUTPUT, VmaxH, VmaxG, KmH
, KmG, bp, kpad, kpbo, kpbr, kpgu, kphe, kpki, kpli, kplu, kpmu, kpsp, kpre
, MW, logP, s_lumen, L, d, PF, VF, MF, ITT, A, B, alpha, beta, fabs, fdis, 
fperm, vad, vbo, vbr, vguWall, vgulumen, vhe, vki, vli, vlu, vmu, vsp, vbl,
 FQad, FQbo, FQbr, FQgu, FQhe, FQki, FQli, FQmu, FQsp
  Random effects: 
  Covariates: 
  Dynamical variables: GUTLUMEN, GUTWALL, GUT, ADIPOSE, BRAIN, HEART, KIDNE
Y, LIVER, LUNG, MUSCLE, SPLEEN, BONE, REST, VEN, ART
  Derived: Cvenn, cp
  Observed: Cvenn, cp

Let's create a subject to study the model

regimen_s = DosageRegimen(200, time=0, addl=13, ii=12, cmt=1, ss=1)
sub_s = Subject(id=1, events=regimen_s)
Subject
  ID: 1
  Events: 14

Below are setting the initial estimates of the parameters in the model

p = (Fup = 0.42, fumic = 0.711, WEIGHT = 73, MPPGL = 30.3, MPPGI = 0,
    C_OUTPUT = 6.5, VmaxH = 40, VmaxG = 40, KmH = 9.3, KmG = 9.3, bp = 1,
    kpad = 9.89, kpbo = 7.91, kpbr = 7.35, kpgu = 5.82, kphe = 1.95, kpki = 2.9,
    kpli = 4.66, kplu = 0.83, kpmu = 2.94, kpsp = 2.96, kpre = 4, MW = 349.317,
    logP = 2.56, s_lumen = 0.39*1000, L = 280, d = 2.5, PF = 1.57, VF = 6.5,
    MF = 13, ITT = 3.32, A = 7440, B = 1e7, alpha = 0.6, beta = 4.395, fabs = 1,
    fdis = 1, fperm = 1, vad = 18.2, vbo = 10.5, vbr = 1.45, vguWall = 0.65,
    vgulumen = 0.35, vhe = 0.33, vki = 0.31, vli = 1.8, vlu = 0.5, vmu = 29,
    vsp = 0.15, vbl = 5.6, FQad = 0.05, FQbo = 0.05, FQbr = 0.12, FQgu = 0.16,
    FQhe = 0.04, FQki = 0.19, FQli = 0.255, FQmu = 0.17, FQsp = 0.03)
(Fup = 0.42, fumic = 0.711, WEIGHT = 73, MPPGL = 30.3, MPPGI = 0, C_OUTPUT 
= 6.5, VmaxH = 40, VmaxG = 40, KmH = 9.3, KmG = 9.3, bp = 1, kpad = 9.89, k
pbo = 7.91, kpbr = 7.35, kpgu = 5.82, kphe = 1.95, kpki = 2.9, kpli = 4.66,
 kplu = 0.83, kpmu = 2.94, kpsp = 2.96, kpre = 4, MW = 349.317, logP = 2.56
, s_lumen = 390.0, L = 280, d = 2.5, PF = 1.57, VF = 6.5, MF = 13, ITT = 3.
32, A = 7440, B = 1.0e7, alpha = 0.6, beta = 4.395, fabs = 1, fdis = 1, fpe
rm = 1, vad = 18.2, vbo = 10.5, vbr = 1.45, vguWall = 0.65, vgulumen = 0.35
, vhe = 0.33, vki = 0.31, vli = 1.8, vlu = 0.5, vmu = 29, vsp = 0.15, vbl =
 5.6, FQad = 0.05, FQbo = 0.05, FQbr = 0.12, FQgu = 0.16, FQhe = 0.04, FQki
 = 0.19, FQli = 0.255, FQmu = 0.17, FQsp = 0.03)

Let's take a look at the simulation of the model to ensure everything is working as expected.

simdata = simobs(model, [sub_s], p)
sim_plot(model, simdata, observations=[:Cvenn])

We can run parameter estimation on the PBPK model with the fit function, we'll use the simulated data to run the estimation here FQad, FQbo, FQbr, FQgu, FQhe, FQki, FQli, FQmu and FQsp will be estimated within the bounds specified and the other parameters will be fixed.

data = read_pumas(DataFrame(simdata), observations = [:cp])
ft = fit(model, data, p, Pumas.NaivePooled(),
    constantcoef = (
        Fup = 0.42, fumic = 0.711, WEIGHT = 73, MPPGL = 30.3, MPPGI = 0,
        C_OUTPUT = 6.5, VmaxH = 40, VmaxG = 40, KmH = 9.3, KmG = 9.3, bp = 1,
        kpad = 9.89, kpbo = 7.91, kpbr = 7.35, kpgu = 5.82, kphe = 1.95,
        kpki = 2.9, kpli = 4.66, kplu = 0.83, kpmu = 2.94, kpsp = 2.96,
        kpre = 4, MW = 349.317, logP = 2.56, s_lumen = 0.39*1000, L = 280,
        d = 2.5, PF = 1.57, VF = 6.5, MF = 13, ITT = 3.32, A = 7440, B = 1e7,
        alpha = 0.6, beta = 4.395, fabs = 1, fdis = 1, fperm = 1, vad = 18.2,
        vbo = 10.5, vbr = 1.45, vguWall = 0.65, vgulumen = 0.35, vhe = 0.33,
        vki = 0.31, vli = 1.8, vlu = 0.5, vmu = 29, vsp = 0.15, vbl = 5.6),
    ensemblealg=EnsembleThreads())
Iter     Function value   Gradient norm 
     0     3.657192e+03     2.607035e+02
 * time: 0.025118112564086914
     1     3.241209e+03     4.455011e+02
 * time: 1.5972142219543457
     2     2.295659e+03     5.026841e+02
 * time: 1.98335599899292
     3     1.743439e+03     1.027871e+02
 * time: 2.3764491081237793
     4     1.691397e+03     5.985337e+01
 * time: 2.7760300636291504
     5     1.614438e+03     4.339930e+01
 * time: 3.1652421951293945
     6     1.601321e+03     4.281688e+01
 * time: 3.6293580532073975
     7     1.593131e+03     4.829028e+01
 * time: 4.215947151184082
     8     1.584966e+03     5.518827e+01
 * time: 4.8891921043396
     9     1.576472e+03     6.340342e+01
 * time: 5.43677020072937
    10     1.562828e+03     7.779079e+01
 * time: 5.982057094573975
    11     1.550757e+03     9.102401e+01
 * time: 6.658033132553101
    12     1.448763e+03     3.642408e+04
 * time: 7.252338171005249
    13     1.351485e+03     8.106431e+04
 * time: 8.105850219726562
    14     1.298978e+03     2.213366e+04
 * time: 8.991234064102173
    15     1.298507e+03     7.324496e+04
 * time: 9.522240161895752
    16     1.293128e+03     1.016642e+05
 * time: 9.983633041381836
    17     1.274054e+03     6.031992e+04
 * time: 10.446171998977661
    18     1.251007e+03     4.464959e+04
 * time: 11.070340156555176
    19     1.236457e+03     4.228087e+04
 * time: 11.578341007232666
    20     1.233424e+03     5.243328e+04
 * time: 12.037075996398926
    21     1.215738e+03     8.184257e+04
 * time: 12.425692081451416
    22     1.182985e+03     1.796932e+04
 * time: 12.88393521308899
    23     1.180575e+03     7.046725e+04
 * time: 13.342640161514282
    24     1.170711e+03     5.518235e+04
 * time: 13.734888076782227
    25     1.165515e+03     4.103303e+04
 * time: 14.129729986190796
    26     1.163332e+03     9.593253e+04
 * time: 14.522889137268066
    27     1.153391e+03     1.967176e+04
 * time: 14.916717052459717
    28     1.148724e+03     7.305954e+04
 * time: 15.310567140579224
    29     1.139033e+03     3.621172e+04
 * time: 15.706979990005493
    30     1.132120e+03     6.610451e+04
 * time: 16.16630506515503
    31     1.116956e+03     9.382807e+04
 * time: 16.559526205062866
    32     1.102737e+03     9.549517e+03
 * time: 16.955154180526733
    33     1.096125e+03     1.535296e+04
 * time: 17.419313192367554
    34     1.092804e+03     3.346137e+04
 * time: 17.948216199874878
    35     1.087481e+03     7.204119e+04
 * time: 18.412342071533203
    36     1.079593e+03     9.888147e+04
 * time: 18.804563999176025
    37     1.061438e+03     8.833039e+04
 * time: 19.196150064468384
    38     1.056181e+03     6.742429e+03
 * time: 19.585251092910767
    39     1.052269e+03     3.097171e+04
 * time: 19.978493213653564
    40     1.051246e+03     1.401920e+05
 * time: 20.37032413482666
    41     1.043074e+03     3.068286e+04
 * time: 20.770151138305664
    42     1.038125e+03     3.111973e+04
 * time: 21.16218400001526
    43     1.030768e+03     5.471411e+04
 * time: 21.626190185546875
    44     1.024288e+03     1.052098e+05
 * time: 22.021958112716675
    45     1.014740e+03     2.440580e+04
 * time: 22.41450810432434
    46     1.007542e+03     4.797757e+04
 * time: 22.808723211288452
    47     1.002041e+03     7.075238e+04
 * time: 23.205604076385498
    48     9.939096e+02     1.258856e+04
 * time: 23.598764181137085
    49     9.919840e+02     8.510299e+04
 * time: 23.992838144302368
    50     9.875815e+02     1.073070e+04
 * time: 24.38602113723755
    51     9.846835e+02     1.101316e+04
 * time: 24.835902214050293
    52     9.823051e+02     2.451084e+04
 * time: 25.29187512397766
    53     9.805571e+02     5.726252e+04
 * time: 25.68031406402588
    54     9.777365e+02     1.528257e+04
 * time: 26.06947112083435
    55     9.755156e+02     1.139442e+04
 * time: 26.459115028381348
    56     9.745592e+02     4.845227e+04
 * time: 26.848570108413696
    57     9.727153e+02     4.629180e+03
 * time: 27.238020181655884
    58     9.716272e+02     5.462276e+03
 * time: 27.628557205200195
    59     9.708752e+02     1.124922e+04
 * time: 28.087642192840576
    60     9.707767e+02     4.360281e+04
 * time: 28.479709148406982
    61     9.694370e+02     5.410729e+03
 * time: 28.87162208557129
    62     9.688697e+02     4.756832e+03
 * time: 29.263514041900635
    63     9.683101e+02     8.575984e+03
 * time: 29.724399089813232
    64     9.678049e+02     1.458830e+04
 * time: 30.18381404876709
    65     9.671923e+02     2.216617e+04
 * time: 30.580212116241455
    66     9.662454e+02     9.431309e+03
 * time: 30.97350001335144
    67     9.656690e+02     2.508778e+04
 * time: 31.370419025421143
    68     9.647154e+02     3.271200e+03
 * time: 31.819563150405884
    69     9.638406e+02     1.638602e+04
 * time: 32.21011805534363
    70     9.632485e+02     1.544362e+04
 * time: 32.60400319099426
    71     9.622788e+02     1.187724e+04
 * time: 32.99617409706116
    72     9.616636e+02     7.115173e+03
 * time: 33.45523810386658
    73     9.610727e+02     1.985221e+03
 * time: 33.91469407081604
    74     9.608545e+02     6.324628e+03
 * time: 34.374094009399414
    75     9.605423e+02     1.475327e+04
 * time: 34.83284521102905
    76     9.602192e+02     2.170793e+04
 * time: 35.22576904296875
    77     9.593409e+02     2.506721e+04
 * time: 35.62064504623413
    78     9.569314e+02     4.243640e+04
 * time: 36.01368999481201
    79     9.529442e+02     5.722420e+03
 * time: 36.40583920478821
    80     9.517232e+02     4.796529e+03
 * time: 36.86394715309143
    81     9.510395e+02     1.299780e+04
 * time: 37.31966018676758
    82     9.501967e+02     2.841467e+04
 * time: 37.711342096328735
    83     9.491520e+02     1.145158e+04
 * time: 38.10966420173645
    84     9.480868e+02     1.131265e+04
 * time: 38.50284004211426
    85     9.473795e+02     8.661365e+03
 * time: 38.94040513038635
    86     9.467840e+02     4.150579e+03
 * time: 39.33058714866638
    87     9.465877e+02     1.027156e+04
 * time: 39.785086154937744
    88     9.460418e+02     1.297354e+04
 * time: 40.17449712753296
    89     9.458964e+02     8.739627e+03
 * time: 40.56657814979553
    90     9.455687e+02     3.383459e+03
 * time: 40.96258211135864
    91     9.455209e+02     7.147025e+03
 * time: 41.418596029281616
    92     9.454247e+02     7.312736e+03
 * time: 41.80994200706482
    93     9.451991e+02     4.857973e+03
 * time: 42.20412802696228
    94     9.450417e+02     4.419519e+03
 * time: 42.59780812263489
    95     9.448356e+02     5.375114e+01
 * time: 42.99150204658508
    96     9.447825e+02     5.465711e+03
 * time: 43.471973180770874
    97     9.446931e+02     6.228662e+03
 * time: 43.87731409072876
    98     9.445161e+02     2.199833e+03
 * time: 44.270167112350464
    99     9.444775e+02     4.235756e+03
 * time: 44.73040199279785
   100     9.444249e+02     1.145766e+04
 * time: 45.123032093048096
   101     9.442922e+02     2.869223e+02
 * time: 45.51614999771118
   102     9.442141e+02     1.155613e+03
 * time: 45.98071599006653
   103     9.441646e+02     3.641592e+03
 * time: 46.43804621696472
   104     9.441434e+02     9.029391e+03
 * time: 46.825929164886475
   105     9.440720e+02     3.417675e+03
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   826     9.388262e+02     9.352200e+02
 * time: 351.90537905693054
   827     9.388153e+02     6.298657e+02
 * time: 352.31986021995544
   828     9.388079e+02     8.437740e+02
 * time: 352.7992961406708
   829     9.388013e+02     1.087630e+03
 * time: 353.28058409690857
   830     9.387919e+02     1.541422e+03
 * time: 353.7598600387573
   831     9.387898e+02     4.473401e+03
 * time: 354.17170214653015
   832     9.387681e+02     8.028229e+02
 * time: 354.58347511291504
   833     9.387569e+02     5.840657e+02
 * time: 354.99406599998474
   834     9.387489e+02     8.682025e+02
 * time: 355.5222361087799
   835     9.387425e+02     1.126911e+03
 * time: 355.9861800670624
   836     9.387327e+02     1.640334e+03
 * time: 356.4471261501312
   837     9.387268e+02     4.048240e+03
 * time: 356.8345220088959
   838     9.387070e+02     9.911250e+02
 * time: 357.2223060131073
   839     9.386932e+02     5.444877e+02
 * time: 357.6105110645294
   840     9.386861e+02     7.875711e+02
 * time: 358.0625071525574
   841     9.386789e+02     1.082263e+03
 * time: 358.5137400627136
   842     9.386700e+02     1.548768e+03
 * time: 358.96644711494446
   843     9.386676e+02     4.416063e+03
 * time: 359.3561761379242
   844     9.386469e+02     9.383699e+02
 * time: 359.7459101676941
   845     9.386358e+02     6.382706e+02
 * time: 360.1354880332947
   846     9.386283e+02     8.513481e+02
 * time: 360.59360218048096
   847     9.386214e+02     1.096685e+03
 * time: 361.05092310905457
   848     9.386118e+02     1.551623e+03
 * time: 361.51149106025696
   849     9.386100e+02     4.556137e+03
 * time: 361.90260314941406
   850     9.385875e+02     7.999225e+02
 * time: 362.3477191925049
   851     9.385761e+02     5.927011e+02
 * time: 362.73694705963135
   852     9.385679e+02     8.836139e+02
 * time: 363.19387912750244
   853     9.385614e+02     1.142887e+03
 * time: 363.6502470970154
   854     9.385512e+02     1.666812e+03
 * time: 364.10598516464233
   855     9.385448e+02     4.058371e+03
 * time: 364.5043201446533
   856     9.385246e+02     1.011683e+03
 * time: 364.8967881202698
   857     9.385102e+02     5.471217e+02
 * time: 365.29087805747986
   858     9.385029e+02     7.969858e+02
 * time: 365.7521290779114
   859     9.384955e+02     1.094109e+03
 * time: 366.2171721458435
   860     9.384864e+02     1.566947e+03
 * time: 366.6863000392914
   861     9.384838e+02     4.454082e+03
 * time: 367.0889141559601
   862     9.384626e+02     9.524098e+02
 * time: 367.48913311958313
   863     9.384512e+02     6.442085e+02
 * time: 367.8926820755005
   864     9.384434e+02     8.615177e+02
 * time: 368.36272501945496
   865     9.384364e+02     1.109804e+03
 * time: 368.8349461555481
   866     9.384265e+02     1.571919e+03
 * time: 369.356831073761
   867     9.384245e+02     4.582057e+03
 * time: 369.77164602279663
   868     9.384015e+02     8.150521e+02
 * time: 370.1848430633545
   869     9.383898e+02     5.970954e+02
 * time: 370.60179018974304
   870     9.383814e+02     8.886415e+02
 * time: 371.09275102615356
   871     9.383747e+02     1.151826e+03
 * time: 371.5906400680542
   872     9.383643e+02     1.677838e+03
 * time: 372.09760999679565
   873     9.383579e+02     4.121884e+03
 * time: 372.5546250343323
   874     9.383371e+02     1.015151e+03
 * time: 373.00675320625305
   875     9.383226e+02     5.547200e+02
 * time: 373.46762108802795
   876     9.383151e+02     8.040418e+02
 * time: 374.00419521331787
   877     9.383075e+02     1.104309e+03
 * time: 374.54356598854065
   878     9.382982e+02     1.580583e+03
 * time: 375.08097219467163
   879     9.382956e+02     4.507870e+03
 * time: 375.54271817207336
   880     9.382738e+02     9.576397e+02
 * time: 376.00430607795715
   881     9.382621e+02     6.514429e+02
 * time: 376.4663870334625
   882     9.382542e+02     8.690983e+02
 * time: 377.0016140937805
   883     9.382470e+02     1.119026e+03
 * time: 377.60564613342285
   884     9.382369e+02     1.583551e+03
 * time: 378.138943195343
   885     9.382350e+02     4.646009e+03
 * time: 378.5747950077057
   886     9.382114e+02     8.163165e+02
 * time: 379.01111221313477
   887     9.381994e+02     6.040697e+02
 * time: 379.4472281932831
   888     9.381908e+02     9.005090e+02
 * time: 379.95031213760376
   889     9.381839e+02     1.164971e+03
 * time: 380.45406317710876
   890     9.381733e+02     1.698928e+03
 * time: 380.9600582122803
   891     9.381666e+02     4.142377e+03
 * time: 381.37450408935547
   892     9.381453e+02     1.030640e+03
 * time: 381.80883717536926
   893     9.381302e+02     5.583480e+02
 * time: 382.25474214553833
   894     9.381225e+02     8.122532e+02
 * time: 382.7431890964508
   895     9.381148e+02     1.114729e+03
 * time: 383.21660804748535
   896     9.381052e+02     1.596028e+03
 * time: 383.68693804740906
   897     9.381026e+02     4.547462e+03
 * time: 384.0833320617676
   898     9.380803e+02     9.678983e+02
 * time: 384.4764380455017
   899     9.380683e+02     6.572018e+02
 * time: 384.92799615859985
   900     9.380602e+02     8.776040e+02
 * time: 385.3788421154022
   901     9.380528e+02     1.129860e+03
 * time: 385.8324520587921
   902     9.380425e+02     1.599555e+03
 * time: 386.2825860977173
   903     9.380404e+02     4.680997e+03
 * time: 386.668240070343
   904     9.380163e+02     8.261191e+02
 * time: 387.05666518211365
   905     9.380040e+02     6.088980e+02
 * time: 387.44654512405396
   906     9.379952e+02     9.070808e+02
 * time: 387.89852714538574
   907     9.379882e+02     1.174286e+03
 * time: 388.35124707221985
   908     9.379773e+02     1.711740e+03
 * time: 388.80669021606445
   909     9.379705e+02     4.188475e+03
 * time: 389.1976091861725
   910     9.379487e+02     1.036953e+03
 * time: 389.58826518058777
   911     9.379333e+02     5.641297e+02
 * time: 389.9774811267853
   912     9.379255e+02     8.189797e+02
 * time: 390.4333071708679
   913     9.379176e+02     1.124039e+03
 * time: 390.8929510116577
   914     9.379078e+02     1.608977e+03
 * time: 391.35013818740845
   915     9.379051e+02     4.591938e+03
 * time: 391.8150911331177
   916     9.378823e+02     9.741289e+02
 * time: 392.20040822029114
   917     9.378700e+02     6.632561e+02
 * time: 392.58830213546753
   918     9.378618e+02     8.847021e+02
 * time: 393.0379400253296
   919     9.378542e+02     1.138648e+03
 * time: 393.4884731769562
   920     9.378436e+02     1.611376e+03
 * time: 393.93959522247314
   921     9.378416e+02     4.730008e+03
 * time: 394.32542610168457
   922     9.378169e+02     8.299093e+02
 * time: 394.71249318122864
   923     9.378044e+02     6.145337e+02
 * time: 395.09951305389404
   924     9.377954e+02     9.161080e+02
 * time: 395.55349922180176
   925     9.377882e+02     1.184877e+03
 * time: 396.0091199874878
   926     9.377770e+02     1.728055e+03
 * time: 396.4672441482544
   927     9.377700e+02     4.215158e+03
 * time: 396.8568642139435
   928     9.377477e+02     1.047965e+03
 * time: 397.247670173645
   929     9.377320e+02     5.681553e+02
 * time: 397.6372480392456
   930     9.377240e+02     8.259365e+02
 * time: 398.0928750038147
   931     9.377159e+02     1.132960e+03
 * time: 398.54879212379456
   932     9.377059e+02     1.621872e+03
 * time: 399.04938101768494
   933     9.377032e+02     4.629658e+03
 * time: 399.4431040287018
   934     9.376798e+02     9.816178e+02
 * time: 399.8281600475311
   935     9.376673e+02     6.685031e+02
 * time: 400.213171005249
   936     9.376589e+02     8.917313e+02
 * time: 400.6658470630646
   937     9.376512e+02     1.147488e+03
 * time: 401.11904406547546
   938     9.376403e+02     1.624019e+03
 * time: 401.57257318496704
   939     9.376383e+02     4.766918e+03
 * time: 401.960871219635
   940     9.376130e+02     8.362903e+02
 * time: 402.34787011146545
   941     9.376002e+02     6.191771e+02
 * time: 402.74171900749207
   942     9.375910e+02     9.228704e+02
 * time: 403.1998391151428
   943     9.375837e+02     1.193603e+03
 * time: 403.6887512207031
   944     9.375723e+02     1.740763e+03
 * time: 404.14480113983154
   945     9.375651e+02     4.248694e+03
 * time: 404.5359961986542
   946     9.375424e+02     1.055299e+03
 * time: 404.9256122112274
   947     9.375263e+02     5.726050e+02
 * time: 405.31950211524963
   948     9.375182e+02     8.319626e+02
 * time: 405.837562084198
   949     9.375099e+02     1.140989e+03
 * time: 406.2926821708679
   950     9.374997e+02     1.633242e+03
 * time: 406.74381709098816
   951     9.374969e+02     4.666420e+03
 * time: 407.1286270618439
   952     9.374731e+02     9.874911e+02
 * time: 407.5138611793518
   953     9.374603e+02     6.734980e+02
 * time: 407.8999800682068
   954     9.374517e+02     8.979344e+02
 * time: 408.35046005249023
   955     9.374438e+02     1.155193e+03
 * time: 408.8026111125946
   956     9.374328e+02     1.634689e+03
 * time: 409.25479006767273
   957     9.374308e+02     4.805172e+03
 * time: 409.64393401145935
   958     9.374050e+02     8.405823e+02
 * time: 410.03370809555054
   959     9.373919e+02     6.236977e+02
 * time: 410.4257290363312
   960     9.373825e+02     9.298179e+02
 * time: 410.8816590309143
   961     9.373750e+02     1.202049e+03
 * time: 411.3367991447449
   962     9.373634e+02     1.753535e+03
 * time: 411.79293298721313
   963     9.373561e+02     4.274602e+03
 * time: 412.1815860271454
   964     9.373329e+02     1.063417e+03
 * time: 412.61955308914185
   965     9.373164e+02     5.762898e+02
 * time: 413.004545211792
   966     9.373081e+02     8.376256e+02
 * time: 413.45770502090454
   967     9.372997e+02     1.148270e+03
 * time: 413.9082942008972
   968     9.372893e+02     1.643666e+03
 * time: 414.35897517204285
   969     9.372865e+02     4.699050e+03
 * time: 414.7441551685333
   970     9.372622e+02     9.930421e+02
 * time: 415.1312041282654
   971     9.372492e+02     6.779175e+02
 * time: 415.51741218566895
   972     9.372404e+02     9.035955e+02
 * time: 415.9711470603943
   973     9.372324e+02     1.162219e+03
 * time: 416.4253041744232
   974     9.372211e+02     1.644583e+03
 * time: 416.88101720809937
   975     9.372191e+02     4.837805e+03
 * time: 417.27207612991333
   976     9.371928e+02     8.449547e+02
 * time: 417.6629731655121
   977     9.371795e+02     6.276119e+02
 * time: 418.0569500923157
   978     9.371699e+02     9.357073e+02
 * time: 418.51430106163025
   979     9.371623e+02     1.209341e+03
 * time: 418.9717102050781
   980     9.371504e+02     1.764407e+03
 * time: 419.5687870979309
   981     9.371430e+02     4.299511e+03
 * time: 420.0529839992523
   982     9.371194e+02     1.070038e+03
 * time: 420.5413341522217
   983     9.371026e+02     5.797146e+02
 * time: 420.9610261917114
   984     9.370941e+02     8.425393e+02
 * time: 421.41899013519287
   985     9.370855e+02     1.154624e+03
 * time: 421.87152004241943
   986     9.370749e+02     1.652702e+03
 * time: 422.322802066803
   987     9.370721e+02     4.728681e+03
 * time: 422.70869421958923
   988     9.370474e+02     9.975638e+02
 * time: 423.09693217277527
   989     9.370341e+02     6.818658e+02
 * time: 423.48443818092346
   990     9.370252e+02     9.085326e+02
 * time: 423.93975806236267
   991     9.370171e+02     1.168271e+03
 * time: 424.39653420448303
   992     9.370056e+02     1.653094e+03
 * time: 424.85426115989685
   993     9.370035e+02     4.867134e+03
 * time: 425.2475640773773
   994     9.369767e+02     8.484818e+02
 * time: 425.6377260684967
   995     9.369632e+02     6.310357e+02
 * time: 426.0274600982666
   996     9.369535e+02     9.408984e+02
 * time: 426.48434019088745
   997     9.369457e+02     1.215693e+03
 * time: 426.984078168869
   998     9.369336e+02     1.774044e+03
 * time: 427.4396970272064
   999     9.369260e+02     4.320207e+03
 * time: 427.82569003105164
  1000     9.369020e+02     1.076058e+03
 * time: 428.2111761569977
FittedPumasModel

Successful minimization:                     false

Likelihood approximation:        Pumas.NaivePooled
Log-likelihood value:                   -936.90202
Number of subjects:                              1
Number of parameters:         Fixed      Optimized
                                 50              9
Observation records:         Active        Missing
    cp:                         181              0
    Total:                      181              0

-------------------------------------------------
                        Estimate
-------------------------------------------------
Fup                      0.42
fumic                    0.711
WEIGHT                  73.0
MPPGL                   30.3
MPPGI                    0.0
C_OUTPUT                 6.5
VmaxH                   40.0
VmaxG                   40.0
KmH                      9.3
KmG                      9.3
bp                       1.0
kpad                     9.89
kpbo                     7.91
kpbr                     7.35
kpgu                     5.82
kphe                     1.95
kpki                     2.9
kpli                     4.66
kplu                     0.83
kpmu                     2.94
kpsp                     2.96
kpre                     4.0
MW                     349.32
logP                     2.56
s_lumen                390.0
L                      280.0
d                        2.5
PF                       1.57
VF                       6.5
MF                      13.0
ITT                      3.32
A                     7440.0
B                        1.0e7
alpha                    0.6
beta                     4.395
fabs                     1.0
fdis                     1.0
fperm                    1.0
vad                     18.2
vbo                     10.5
vbr                      1.45
vguWall                  0.65
vgulumen                 0.35
vhe                      0.33
vki                      0.31
vli                      1.8
vlu                      0.5
vmu                     29.0
vsp                      0.15
vbl                      5.6
FQad                     3.3396000000000004e-219
FQbo                     6.2867e-5
FQbr                     0.17136
FQgu                     1.0
FQhe                     0.072327
FQki                     0.14744
FQli                     0.27682
FQmu                     0.33244
FQsp                     0.0016579
-------------------------------------------------

GSA

We'll run the GSA on the AUC and Cmax output of the Cvenn variable and therefore redefine the model to include the NCA calculation.

model = @model begin
    @param begin
        Fup  RealDomain(init = 0.42)
        fumic  RealDomain(init = 0.711)
        WEIGHT  RealDomain(init = 73)
        MPPGL  RealDomain(init = 30.3)
        MPPGI  RealDomain(init = 0)
        C_OUTPUT  RealDomain(init = 6.5)
        VmaxH  RealDomain(init = 40)
        VmaxG  RealDomain(init = 40)
        KmH  RealDomain(init = 9.3)
        KmG  RealDomain(init = 9.3)
        bp  RealDomain(init = 1)
        kpad  RealDomain(init = 9.89)
        kpbo  RealDomain(init = 7.91)
        kpbr  RealDomain(init = 7.35)
        kpgu  RealDomain(init = 5.82)
        kphe  RealDomain(init = 1.95)
        kpki  RealDomain(init = 2.9)
        kpli  RealDomain(init = 4.66)
        kplu  RealDomain(init = 0.83)
        kpmu  RealDomain(init = 2.94)
        kpsp  RealDomain(init = 2.96)
        kpre  RealDomain(init = 4)
        MW  RealDomain(init = 349.317)
        logP  RealDomain(init = 2.56)
        s_lumen  RealDomain(init = 0.39*1000)
        L  RealDomain(init = 280)
        d  RealDomain(init = 2.5)
        PF  RealDomain(init = 1.57)
        VF  RealDomain(init = 6.5)
        MF  RealDomain(init = 13)
        ITT  RealDomain(init = 3.32)
        A  RealDomain(init = 7440)
        B  RealDomain(init = 1e7)
        alpha  RealDomain(init = 0.6)
        beta  RealDomain(init = 4.395)
        fabs  RealDomain(init = 1)
        fdis  RealDomain(init = 1)
        fperm  RealDomain(init = 1)
        vad  RealDomain(init = 18.2)
        vbo  RealDomain(init =10.5)
        vbr  RealDomain(init =1.45)
        vguWall  RealDomain(init =0.65)
        vgulumen  RealDomain(init =0.35)
        vhe  RealDomain(init =0.33)
        vki  RealDomain(init =0.31)
        vli  RealDomain(init =1.8)
        vlu  RealDomain(init =0.5)
        vmu  RealDomain(init =29)
        vsp  RealDomain(init =0.15)
        vbl  RealDomain(init =5.6)
        FQad  RealDomain(lower = 0.0, init = 0.05, upper = 1.0)
        FQbo  RealDomain(lower = 0.0, init = 0.05, upper = 1.0)
        FQbr  RealDomain(lower = 0.0, init = 0.12, upper = 1.0)
        FQgu  RealDomain(lower = 0.0, init = 0.16, upper = 1.0)
        FQhe  RealDomain(lower = 0.0, init = 0.04, upper = 1.0)
        FQki  RealDomain(lower = 0.0, init = 0.19, upper = 1.0)
        FQli  RealDomain(lower = 0.0, init = 0.255, upper = 1.0)
        FQmu  RealDomain(lower = 0.0, init = 0.17, upper = 1.0)
        FQsp  RealDomain(lower = 0.0, init = 0.03, upper = 1.0)
    end
    @pre begin
        Vgu = vguWall + vgulumen
        Vve = 0.705*vbl
        Var = 0.295*vbl
        Vre = WEIGHT - (vli+vki+vsp+vhe+vlu+vbo+vbr+vmu+vad+vguWall+vbl)
        CO = C_OUTPUT*60
        Qad = FQad*CO
        Qbo = FQbo*CO
        Qbr = FQbr*CO
        Qgu = FQgu*CO
        Qhe = FQhe*CO
        Qki = FQki*CO
        Qli = FQli*CO
        Qmu = FQmu*CO
        Qsp = FQsp*CO
        Qha = Qli - (Qgu+Qsp)
        Qtot = Qli+Qki+Qbo+Qhe+Qmu+Qad+Qbr
        Qre = CO - Qtot
        Qlu = CO
        Vgulumen = vgulumen
        S_lumen = s_lumen
        VguWall = vguWall
        Kpgu = kpgu
        BP = bp
        Vad = vad
        Kpad = kpad
        Vbr = vbr
        Kpbr = kpbr
        Vhe = vhe
        Kphe = kphe
        Vki = vki
        Kpki = kpki
        fup = Fup
        Vsp = vsp
        Kpsp = kpsp
        Vli = vli
        Kpli = kpli
        Vlu = vlu
        Kplu = kplu
        Kpmu = kpmu
        Kpre = kpre
        Vmu = vmu
        Vbl = vbl
        Vbo = vbo
        Kpbo = kpbo
        SA_abs = pi*L*d*PF*VF*MF*1e-4
        SA_basal = pi*L*d*PF*VF*1e-4
        MA = 10^logP
        MW_eff = MW - (3*17)
        Peff = fperm*A*(((MW_eff^(-alpha-beta))*MA)/((MW_eff^(-alpha)) + B*(MW_eff^(-beta))*MA) * 1e-2 * 3600)
        kd = fdis*Peff*SA_abs*1000/vgulumen
        ka = fabs*Peff*SA_basal*1000/VguWall
        kt = 1/ITT
        scale_factor_H = MPPGL*Vli*1000
        scale_factor_G = MPPGI*VguWall*1000
        CLintHep = ((VmaxH/KmH)*scale_factor_H*60*1e-6)/fumic
        CLintGut = ((VmaxG/KmG)*scale_factor_G*60*1e-6)/fumic
        #CLintHep = CLintHep/fumic
        #CLintGut = CLintGut/fumic
        CLrenal = 0.096
        f = 1
    end
    @dynamics begin
        GUTLUMEN' = -kd*Vgulumen*(f*(GUTLUMEN/Vgulumen) + (1-f)*S_lumen) -
            kt*GUTLUMEN
        GUTWALL' = kd*Vgulumen*(f*(GUTLUMEN/Vgulumen) + (1-f)*S_lumen) -
            ka*GUTWALL - CLintGut*(GUTWALL/VguWall)
        GUT' = ka*GUTWALL + Qgu*((ART/Var) - (GUT/VguWall)/(Kpgu/BP))
        ADIPOSE' = Qad*((ART/Var) - (ADIPOSE/Vad)/(Kpad/BP))
        BRAIN' = Qbr*((ART/Var) - (BRAIN/Vbr)/(Kpbr/BP))
        HEART' = Qhe*((ART/Var) - (HEART/Vhe)/(Kphe/BP))
        KIDNEY' = Qki*((ART/Var) - (KIDNEY/Vki)/(Kpki/BP)) -
            CLrenal*(((KIDNEY/Vki)*fup)/(Kpki/BP))
        LIVER' = Qgu*((GUT/VguWall)/(Kpgu/BP)) + Qsp*((SPLEEN/Vsp)/(Kpsp/BP)) +
            Qha*(ART/Var) - Qli*((LIVER/Vli)/(Kpli/BP)) -
            CLintHep*(((LIVER/Vli)*fup)/(Kpli/BP))
        LUNG' = Qlu*((VEN/Vve) - (LUNG/Vlu)/(Kplu/BP))
        MUSCLE' = Qmu*((ART/Var) - (MUSCLE/Vmu)/(Kpmu/BP))
        SPLEEN' = Qsp*((ART/Var) - (SPLEEN/Vsp)/(Kpsp/BP))
        BONE' = Qbo*((ART/Var) - (BONE/Vbo)/(Kpbo/BP))
        REST' = Qre*((ART/Var) - (REST/Vre)/(Kpre/BP))
        VEN' = Qad*((ADIPOSE/Vad)/(Kpad/BP)) + Qbr*((BRAIN/Vbr)/(Kpbr/BP)) +
            Qhe*((HEART/Vhe)/(Kphe/BP)) + Qki*((KIDNEY/Vki)/(Kpki/BP)) +
            Qli*((LIVER/Vli)/(Kpli/BP)) + Qmu*((MUSCLE/Vmu)/(Kpmu/BP)) +
            Qbo*((BONE/Vbo)/(Kpbo/BP)) + Qre*((REST/Vre)/(Kpre/BP)) -
            Qlu*(VEN/Vve)
        ART' = Qlu*((LUNG/Vlu)/(Kplu/BP) - (ART/Var))
    end
    @derived begin
        Cvenn = VEN./Vve
        #capturing NCA metrics for evaluations
        nca := @nca Cvenn
        auc =  last(NCA.auc(nca))
        cmax = last(NCA.cmax(nca))
    end
end
PumasModel
  Parameters: Fup, fumic, WEIGHT, MPPGL, MPPGI, C_OUTPUT, VmaxH, VmaxG, KmH
, KmG, bp, kpad, kpbo, kpbr, kpgu, kphe, kpki, kpli, kplu, kpmu, kpsp, kpre
, MW, logP, s_lumen, L, d, PF, VF, MF, ITT, A, B, alpha, beta, fabs, fdis, 
fperm, vad, vbo, vbr, vguWall, vgulumen, vhe, vki, vli, vlu, vmu, vsp, vbl,
 FQad, FQbo, FQbr, FQgu, FQhe, FQki, FQli, FQmu, FQsp
  Random effects: 
  Covariates: 
  Dynamical variables: GUTLUMEN, GUTWALL, GUT, ADIPOSE, BRAIN, HEART, KIDNE
Y, LIVER, LUNG, MUSCLE, SPLEEN, BONE, REST, VEN, ART
  Derived: Cvenn, auc, cmax
  Observed: Cvenn, auc, cmax

To run the GSA we'll define the parameter ranges for our parameters of interest.

p_range_low = (fperm=1/3, s_lumen=390/3, ITT = 3.32/3, MPPGI=1.44/3, )

p_range_high = (fperm=1*3, s_lumen=390*3, ITT = 3.32*3, MPPGI=1.44*3, )
(fperm = 3, s_lumen = 1170, ITT = 9.959999999999999, MPPGI = 4.32)

Now, we are ready to run GSA on our model.

The Sobol Method

We will run the Sobol method for 1000 iterations, please note that this takes a couple of hours to finish because of the complexity of the model.

regimen_s = DosageRegimen(200, time=0, addl=13, ii=12, cmt=1, ss=1, route = Pumas.NCA.IVInfusion)
sub_s = Subject(id=1, events=regimen_s)
sobol_ = Pumas.gsa(model, sub_s, p, GlobalSensitivity.Sobol(), [:cmax,:auc], p_range_low,p_range_high, N=1000, obstimes=0.0:1.0:30.0)
Sobol Sensitivity Analysis

First Order Indices
2×5 DataFrame
 Row │ dv_name  fperm     s_lumen  ITT         MPPGI
     │ Any      Float64   Float64  Float64     Float64
─────┼──────────────────────────────────────────────────
   1 │ cmax     0.505844      0.0  0.00157097  0.444075
   2 │ auc      0.550181      0.0  0.0014958   0.388602

Total Order Indices
2×5 DataFrame
 Row │ dv_name  fperm     s_lumen  ITT          MPPGI
     │ Any      Float64   Float64  Float64      Float64
─────┼───────────────────────────────────────────────────
   1 │ cmax     0.561158      0.0  -0.00111054  0.468542
   2 │ auc      0.611066      0.0  -0.00114236  0.430997

We can use scatter plot the result to visualize the result.

keys_ = keys(p_range_low)
cmax_s1 = [sobol_.first_order[1,:][key] for key in keys_]
cmax_st = [sobol_.total_order[1,:][key] for key in keys_]

fig = Figure(resolution = (1200, 800))
plot_cmax_s1 = scatter(fig[1,1], 1:4, cmax_s1, axis = (yticks = 0:1, xticks = (1:4, [string.(keys_)...]), label = "First Order", title="Cmax"))
plot_cmax_st = scatter(fig[1,2], 1:4, cmax_st, axis = (yticks = 0:1, xticks = (1:4, [string.(keys_)...]), label = "Total Order"), marker=:utriangle)

auc_s1 = [sobol_.first_order[2,:][key] for key in keys_]
auc_st = [sobol_.total_order[2,:][key] for key in keys_]

plot_auc_s1 = scatter(fig[2,1], 1:4, auc_s1, axis = (yticks = 0:1, xticks = (1:4, [string.(keys_)...]), label = "First Order", title="AUC"))
plot_auc_st = scatter(fig[2,2], 1:4, auc_st, axis = (yticks = 0:1, xticks = (1:4, [string.(keys_)...]), label = "Total Order"), marker=:utriangle)
display(fig)

The eFAST method

eFAST method allows the estimation of first order and total Sobol indices in a more computationaly efficient way.

eFAST_ = Pumas.gsa(model, sub_s, p, GlobalSensitivity.eFAST(), [:cmax,:auc], p_range_low, p_range_high, n=1000, obstimes=0.0:1.0:30.0)
eFAST Sensitivity Analysis

First Order Indices
2×5 DataFrame
 Row │ dv_name  fperm     s_lumen     ITT          MPPGI
     │ Any      Float64   Float64     Float64      Float64
─────┼──────────────────────────────────────────────────────
   1 │ cmax     0.514258  8.01551e-8  0.000239631  0.444768
   2 │ auc      0.560856  1.68315e-7  0.000214603  0.395028

Total Order Indices
2×5 DataFrame
 Row │ dv_name  fperm     s_lumen     ITT         MPPGI
     │ Any      Float64   Float64     Float64     Float64
─────┼─────────────────────────────────────────────────────
   1 │ cmax     0.553115  0.00154969  0.00183721  0.470198
   2 │ auc      0.603238  0.00160792  0.00187704  0.427326

We can use scatter plot the result to visualize the result.

keys_ = keys(p_range_low)
cmax_s1 = [eFAST_.first_order[1,:][key] for key in keys_]
cmax_st = [eFAST_.total_order[1,:][key] for key in keys_]

fig = Figure(resolution = (1200,800))
plot_cmax_s1 = scatter(fig[1,1], 1:4, cmax_s1, axis = (yticks = 0:1, xticks = (1:4, [string.(keys_)...]), label = "First Order", title="Cmax"))
plot_cmax_st = scatter(fig[1,2], 1:4, cmax_st, axis = (yticks = 0:1, xticks = (1:4, [string.(keys_)...]), label = "Total Order"), marker=:utriangle)

auc_s1 = [eFAST_.first_order[2,:][key] for key in keys_]
auc_st = [eFAST_.total_order[2,:][key] for key in keys_]

plot_auc_s1 = scatter(fig[2,1], 1:4, auc_s1, axis = (yticks = 0:1, xticks = (1:4, [string.(keys_)...]), label = "First Order", title="AUC"))
plot_auc_st = scatter(fig[2,2], 1:4, auc_st, axis = (yticks = 0:1, xticks = (1:4, [string.(keys_)...]), label = "Total Order"), marker=:utriangle)
display(fig)

Conclusion

We observe for both AUC and Cmax fperm and MPPGI show high values for both First and Total Order indices of Sobol whereas s_lumen and ITT have no effect at all and show a value of zero for the indices.