Estimate the true sero prevalence using Bayesian estimation

Usage

correct_prevalence(
  age,
  pos = NULL,
  tot = NULL,
  status = NULL,
  init_se = 0.95,
  init_sp = 0.8,
  study_size_se = 1000,
  study_size_sp = 1000,
  chains = 1,
  warmup = 1000,
  iter = 2000
)

Arguments

age: the age vector
pos: the positive count vector (optional if status is provided).
tot: the total count vector (optional if status is provided).
status: the serostatus vector (optional if pos & tot are provided).
init_se: sensitivity of the serological test
init_sp: specificity of the serological test
study_size_se: study size for sensitivity validation study (i.e., number of confirmed infected patients in the study)
study_size_sp: study size for specificity validation study (i.e., number of confirmed non-infected patients in the study)
chains: number of Markov chains
warmup: number of warm up runs
iter: number of iterations

Value

a list of 2 items

info: estimated parameters
corrected_sero: data.frame containing age, the corresponding estimated seroprevalance, adjusted tot and pos

Examples

data <- rubella_uk_1986_1987
correct_prevalence(data$age, pos = data$pos, tot = data$tot)
#> 
#> SAMPLING FOR MODEL 'prevalence_correction' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 0.000251 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 2.51 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 1: 
#> Chain 1:  Elapsed Time: 1.796 seconds (Warm-up)
#> Chain 1:                1.343 seconds (Sampling)
#> Chain 1:                3.139 seconds (Total)
#> Chain 1: 
#> $info
#>                    mean      se_mean          sd          2.5%           25%
#> est_se     9.581929e-01 0.0001609135 0.005230293  9.479660e-01  9.547228e-01
#> est_sp     8.069757e-01 0.0002828964 0.011044871  7.854039e-01  7.996085e-01
#> theta[1]   1.706464e-02 0.0003758854 0.014989311  3.690544e-04  5.921739e-03
#> theta[2]   4.384368e-02 0.0009200557 0.031159439  2.121645e-03  2.001407e-02
#> theta[3]   3.850694e-02 0.0008826740 0.029991391  1.972698e-03  1.513077e-02
#> theta[4]   1.431935e-01 0.0012414607 0.045817055  5.786349e-02  1.125689e-01
#> theta[5]   3.165637e-01 0.0012872042 0.045617903  2.288035e-01  2.846881e-01
#> theta[6]   4.444701e-01 0.0009451693 0.045250540  3.599190e-01  4.125157e-01
#> theta[7]   4.626891e-01 0.0013201546 0.048348387  3.614287e-01  4.320284e-01
#> theta[8]   6.106122e-01 0.0011822001 0.050639289  5.022235e-01  5.767448e-01
#> theta[9]   7.175997e-01 0.0011008843 0.044719614  6.230635e-01  6.873996e-01
#> theta[10]  6.419766e-01 0.0012393796 0.048736983  5.461536e-01  6.081532e-01
#> theta[11]  7.220485e-01 0.0012029224 0.047430010  6.271027e-01  6.869883e-01
#> theta[12]  8.227953e-01 0.0009076172 0.036852851  7.482824e-01  7.975976e-01
#> theta[13]  7.627398e-01 0.0010626785 0.041669972  6.753443e-01  7.362022e-01
#> theta[14]  8.587556e-01 0.0007333958 0.037123956  7.792670e-01  8.357116e-01
#> theta[15]  7.731065e-01 0.0016930107 0.063281557  6.296218e-01  7.332235e-01
#> theta[16]  8.355733e-01 0.0014522080 0.061611408  7.059238e-01  7.936201e-01
#> theta[17]  9.129714e-01 0.0011670213 0.043390142  8.209613e-01  8.833520e-01
#> theta[18]  8.774053e-01 0.0012095021 0.049055119  7.736844e-01  8.467484e-01
#> theta[19]  8.809649e-01 0.0010927956 0.039403502  7.980845e-01  8.579858e-01
#> theta[20]  8.529601e-01 0.0016385553 0.057174064  7.312159e-01  8.165787e-01
#> theta[21]  9.138139e-01 0.0012630170 0.041859407  8.244294e-01  8.863258e-01
#> theta[22]  8.259165e-01 0.0011436089 0.045601968  7.285091e-01  7.944683e-01
#> theta[23]  9.467582e-01 0.0009523828 0.032369969  8.707946e-01  9.287364e-01
#> theta[24]  9.445504e-01 0.0011926430 0.037324845  8.608275e-01  9.213222e-01
#> theta[25]  9.711767e-01 0.0006479416 0.023911199  9.087006e-01  9.593204e-01
#> theta[26]  9.389326e-01 0.0010738197 0.035526856  8.598293e-01  9.175298e-01
#> theta[27]  9.225048e-01 0.0011609875 0.037619498  8.388538e-01  8.993849e-01
#> theta[28]  9.572464e-01 0.0007611328 0.031613624  8.734294e-01  9.417387e-01
#> theta[29]  9.094723e-01 0.0012455871 0.045441053  8.093298e-01  8.818336e-01
#> theta[30]  9.172450e-01 0.0015495416 0.049401780  8.019122e-01  8.886713e-01
#> theta[31]  8.592529e-01 0.0015215384 0.059760216  7.247602e-01  8.216484e-01
#> theta[32]  9.402675e-01 0.0012045051 0.047141758  8.193893e-01  9.149402e-01
#> theta[33]  9.380364e-01 0.0012494314 0.049443567  8.147240e-01  9.118179e-01
#> theta[34]  9.459028e-01 0.0012373057 0.043407912  8.408670e-01  9.244129e-01
#> theta[35]  8.926621e-01 0.0014595882 0.069482239  7.300403e-01  8.516782e-01
#> theta[36]  9.566368e-01 0.0009100621 0.037218304  8.524151e-01  9.398737e-01
#> theta[37]  9.402055e-01 0.0012889185 0.049025151  8.190774e-01  9.158457e-01
#> theta[38]  8.972827e-01 0.0016245163 0.061436648  7.584656e-01  8.581675e-01
#> theta[39]  9.211567e-01 0.0016407994 0.058707430  7.744334e-01  8.893928e-01
#> theta[40]  9.356209e-01 0.0014752568 0.054909867  7.951714e-01  9.050129e-01
#> theta[41]  9.533126e-01 0.0010332280 0.045038095  8.376966e-01  9.334340e-01
#> theta[42]  9.198561e-01 0.0017652536 0.060365376  7.740165e-01  8.866775e-01
#> theta[43]  9.078516e-01 0.0017433479 0.067439029  7.451051e-01  8.692745e-01
#> theta[44]  9.380297e-01 0.0015528750 0.063675966  7.669778e-01  9.133157e-01
#> lp__      -2.762598e+03 0.2749034942 5.360660152 -2.774227e+03 -2.766007e+03
#>                     50%           75%         97.5%     n_eff      Rhat
#> est_se     9.584447e-01  9.619761e-01  9.678106e-01 1056.4936 0.9991695
#> est_sp     8.071410e-01  8.149658e-01  8.271894e-01 1524.2856 0.9991034
#> theta[1]   1.352593e-02  2.376979e-02  5.650053e-02 1590.2027 0.9991373
#> theta[2]   3.755705e-02  6.215776e-02  1.134722e-01 1146.9674 0.9996657
#> theta[3]   3.145086e-02  5.565008e-02  1.094077e-01 1154.4965 0.9992727
#> theta[4]   1.417909e-01  1.728511e-01  2.383082e-01 1362.0354 0.9993613
#> theta[5]   3.164776e-01  3.466235e-01  4.045569e-01 1255.9597 1.0003572
#> theta[6]   4.445659e-01  4.749955e-01  5.303761e-01 2292.0723 1.0010897
#> theta[7]   4.620885e-01  4.952945e-01  5.543290e-01 1341.2644 0.9997882
#> theta[8]   6.118090e-01  6.456523e-01  7.084200e-01 1834.8188 0.9993449
#> theta[9]   7.198536e-01  7.483989e-01  7.985096e-01 1650.1096 0.9995444
#> theta[10]  6.432274e-01  6.749764e-01  7.378660e-01 1546.3529 0.9990159
#> theta[11]  7.255408e-01  7.561061e-01  8.119058e-01 1554.6448 0.9990106
#> theta[12]  8.249793e-01  8.473920e-01  8.917033e-01 1648.6814 0.9990383
#> theta[13]  7.645160e-01  7.923548e-01  8.382969e-01 1537.5972 1.0000083
#> theta[14]  8.590567e-01  8.849603e-01  9.248671e-01 2562.3100 0.9999734
#> theta[15]  7.756140e-01  8.165988e-01  8.883877e-01 1397.1238 0.9999912
#> theta[16]  8.413271e-01  8.815836e-01  9.387800e-01 1799.9673 0.9990116
#> theta[17]  9.171108e-01  9.465813e-01  9.850605e-01 1382.3708 1.0025188
#> theta[18]  8.811083e-01  9.135804e-01  9.610183e-01 1644.9601 0.9997443
#> theta[19]  8.837311e-01  9.088757e-01  9.482833e-01 1300.1449 0.9995279
#> theta[20]  8.556595e-01  8.959927e-01  9.531399e-01 1217.5194 1.0001435
#> theta[21]  9.187279e-01  9.435835e-01  9.833824e-01 1098.4182 0.9993065
#> theta[22]  8.277229e-01  8.569425e-01  9.096893e-01 1590.0549 0.9990819
#> theta[23]  9.507876e-01  9.707137e-01  9.942870e-01 1155.2115 1.0018554
#> theta[24]  9.493524e-01  9.729901e-01  9.976023e-01  979.4339 0.9990053
#> theta[25]  9.769145e-01  9.884179e-01  9.991942e-01 1361.8555 1.0003647
#> theta[26]  9.432770e-01  9.652616e-01  9.929998e-01 1094.5883 0.9994120
#> theta[27]  9.254389e-01  9.486743e-01  9.859532e-01 1049.9555 0.9990119
#> theta[28]  9.627506e-01  9.808278e-01  9.982050e-01 1725.1534 1.0001250
#> theta[29]  9.124451e-01  9.432541e-01  9.840203e-01 1330.9098 0.9990845
#> theta[30]  9.235671e-01  9.524745e-01  9.913246e-01 1016.4329 0.9990045
#> theta[31]  8.668765e-01  9.022011e-01  9.551086e-01 1542.6183 0.9991644
#> theta[32]  9.497947e-01  9.767184e-01  9.970982e-01 1531.7726 1.0000293
#> theta[33]  9.500388e-01  9.752579e-01  9.980635e-01 1566.0108 0.9998868
#> theta[34]  9.559917e-01  9.783305e-01  9.969428e-01 1230.7894 0.9990017
#> theta[35]  9.048680e-01  9.455510e-01  9.909934e-01 2266.1410 0.9990055
#> theta[36]  9.677596e-01  9.849612e-01  9.981735e-01 1672.5193 0.9994178
#> theta[37]  9.515684e-01  9.783618e-01  9.979456e-01 1446.7284 0.9998791
#> theta[38]  9.082948e-01  9.460790e-01  9.867077e-01 1430.2333 0.9990185
#> theta[39]  9.329785e-01  9.659220e-01  9.960304e-01 1280.1922 0.9990404
#> theta[40]  9.526373e-01  9.780353e-01  9.973468e-01 1385.3693 0.9990002
#> theta[41]  9.669428e-01  9.871043e-01  9.986769e-01 1900.0616 0.9992308
#> theta[42]  9.334860e-01  9.675611e-01  9.962890e-01 1169.3961 0.9993389
#> theta[43]  9.246035e-01  9.588806e-01  9.940502e-01 1496.4234 0.9989997
#> theta[44]  9.580634e-01  9.846834e-01  9.988281e-01 1681.4273 0.9991492
#> lp__      -2.762095e+03 -2.758919e+03 -2.753363e+03  380.2560 0.9997653
#> 
#> $corrected_se
#>            age       sero        pos tot
#> theta[1]   1.5 0.01706464   3.515315 206
#> theta[2]   2.5 0.04384368   6.401178 146
#> theta[3]   3.5 0.03850694   6.469165 168
#> theta[4]   4.5 0.14319346  27.063563 189
#> theta[5]   5.5 0.31656368  69.327445 219
#> theta[6]   6.5 0.44447008  86.671666 195
#> theta[7]   7.5 0.46268911  75.881014 164
#> theta[8]   8.5 0.61061222  88.538772 145
#> theta[9]   9.5 0.71759969 129.167944 180
#> theta[10] 10.5 0.64197659 102.716254 160
#> theta[11] 11.5 0.72204847 106.863174 148
#> theta[12] 12.5 0.82279530 146.457563 178
#> theta[13] 13.5 0.76273979 135.004942 177
#> theta[14] 14.5 0.85875564 141.694681 165
#> theta[15] 15.5 0.77310653  51.798138  67
#> theta[16] 16.5 0.83557326  48.463249  58
#> theta[17] 17.5 0.91297138  73.950682  81
#> theta[18] 18.5 0.87740525  69.315015  79
#> theta[19] 19.5 0.88096489  97.787103 111
#> theta[20] 20.5 0.85296012  64.824969  76
#> theta[21] 21.5 0.91381393  74.932742  82
#> theta[22] 22.5 0.82591646  83.417563 101
#> theta[23] 23.5 0.94675817  83.314719  88
#> theta[24] 24.5 0.94455038  80.286783  85
#> theta[25] 25.5 0.97117667  91.290607  94
#> theta[26] 26.5 0.93893261  85.442867  91
#> theta[27] 27.5 0.92250475  82.102923  89
#> theta[28] 28.5 0.95724644  72.750729  76
#> theta[29] 29.5 0.90947233  71.848314  79
#> theta[30] 30.5 0.91724503  51.365722  56
#> theta[31] 31.5 0.85925291  44.681151  52
#> theta[32] 32.5 0.94026753  45.132841  48
#> theta[33] 33.5 0.93803638  34.707346  37
#> theta[34] 34.5 0.94590280  38.782015  41
#> theta[35] 35.5 0.89266213  35.706485  40
#> theta[36] 36.5 0.95663683  36.352200  38
#> theta[37] 37.5 0.94020554  36.668016  39
#> theta[38] 38.5 0.89728275  36.788593  41
#> theta[39] 39.5 0.92115665  27.634700  30
#> theta[40] 40.5 0.93562086  25.261763  27
#> theta[41] 41.5 0.95331258  23.832814  25
#> theta[42] 42.5 0.91985610  20.236834  22
#> theta[43] 43.5 0.90785161  17.249181  19
#> theta[44] 44.5 0.93802974  16.884535  18
#>