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 2.5e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.25 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)
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#> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.368 seconds (Warm-up)
#> Chain 1:                0.292 seconds (Sampling)
#> Chain 1:                0.66 seconds (Total)
#> Chain 1: 
#> $info
#>                    mean      se_mean          sd          2.5%           25%
#> est_se     9.580822e-01 0.0001677009 0.005291766  9.474431e-01  9.546114e-01
#> est_sp     8.074432e-01 0.0002727824 0.010293202  7.879326e-01  8.003633e-01
#> theta[1]   1.665906e-02 0.0004114001 0.014915046  4.470735e-04  5.027980e-03
#> theta[2]   4.446571e-02 0.0008003960 0.032307490  2.946000e-03  2.031588e-02
#> theta[3]   4.033849e-02 0.0008822391 0.029878917  1.446891e-03  1.699614e-02
#> theta[4]   1.460278e-01 0.0011752978 0.042118190  6.516402e-02  1.178951e-01
#> theta[5]   3.163587e-01 0.0010950553 0.044710676  2.282073e-01  2.868205e-01
#> theta[6]   4.461688e-01 0.0009682181 0.047028068  3.522789e-01  4.136844e-01
#> theta[7]   4.624928e-01 0.0010882358 0.051244607  3.588082e-01  4.279892e-01
#> theta[8]   6.102896e-01 0.0009369177 0.048987343  5.148583e-01  5.780589e-01
#> theta[9]   7.169041e-01 0.0009088274 0.044192481  6.267072e-01  6.853081e-01
#> theta[10]  6.441565e-01 0.0010869773 0.053649351  5.305130e-01  6.095803e-01
#> theta[11]  7.241735e-01 0.0009225447 0.047654990  6.286940e-01  6.921916e-01
#> theta[12]  8.224332e-01 0.0008361334 0.039776184  7.370909e-01  7.990787e-01
#> theta[13]  7.645448e-01 0.0009357397 0.040334238  6.831493e-01  7.396098e-01
#> theta[14]  8.602990e-01 0.0008224877 0.036694751  7.822392e-01  8.365051e-01
#> theta[15]  7.696229e-01 0.0014413184 0.066191371  6.432757e-01  7.262503e-01
#> theta[16]  8.382780e-01 0.0012817349 0.059233712  7.010630e-01  8.004274e-01
#> theta[17]  9.125376e-01 0.0012039606 0.044762969  8.175760e-01  8.871747e-01
#> theta[18]  8.767165e-01 0.0011510410 0.048709425  7.708718e-01  8.440557e-01
#> theta[19]  8.821519e-01 0.0008613922 0.039283011  8.007685e-01  8.578043e-01
#> theta[20]  8.531544e-01 0.0011158580 0.053455664  7.393866e-01  8.181030e-01
#> theta[21]  9.120147e-01 0.0010323369 0.041036862  8.237412e-01  8.865657e-01
#> theta[22]  8.269462e-01 0.0009323689 0.045833384  7.292499e-01  7.995566e-01
#> theta[23]  9.472939e-01 0.0009469101 0.035552854  8.658989e-01  9.261789e-01
#> theta[24]  9.445664e-01 0.0010044896 0.035162878  8.622421e-01  9.240897e-01
#> theta[25]  9.701647e-01 0.0006227046 0.025261812  9.113874e-01  9.566521e-01
#> theta[26]  9.391715e-01 0.0008478956 0.035030943  8.582779e-01  9.188163e-01
#> theta[27]  9.243407e-01 0.0011262384 0.039888793  8.343587e-01  8.988866e-01
#> theta[28]  9.589846e-01 0.0007236672 0.031158433  8.763660e-01  9.425749e-01
#> theta[29]  9.096108e-01 0.0013232844 0.044875733  8.113606e-01  8.835232e-01
#> theta[30]  9.165345e-01 0.0011586078 0.049047010  8.026214e-01  8.875614e-01
#> theta[31]  8.599559e-01 0.0015387598 0.065212290  7.144827e-01  8.214934e-01
#> theta[32]  9.372633e-01 0.0012014984 0.046203975  8.242861e-01  9.098596e-01
#> theta[33]  9.359540e-01 0.0010341964 0.049270000  8.184358e-01  9.097596e-01
#> theta[34]  9.439138e-01 0.0011298579 0.043857617  8.416949e-01  9.201564e-01
#> theta[35]  8.949250e-01 0.0014343679 0.065221257  7.350569e-01  8.560160e-01
#> theta[36]  9.570296e-01 0.0009469318 0.038216763  8.531427e-01  9.414531e-01
#> theta[37]  9.424748e-01 0.0009861636 0.046008427  8.347117e-01  9.172013e-01
#> theta[38]  9.016027e-01 0.0015786867 0.058449543  7.616728e-01  8.681172e-01
#> theta[39]  9.198288e-01 0.0014622409 0.062854455  7.592456e-01  8.878378e-01
#> theta[40]  9.382487e-01 0.0013360424 0.052923971  8.031185e-01  9.123606e-01
#> theta[41]  9.524841e-01 0.0012642555 0.046850860  8.344275e-01  9.334619e-01
#> theta[42]  9.203959e-01 0.0014741926 0.064005751  7.538865e-01  8.870096e-01
#> theta[43]  9.054694e-01 0.0018592371 0.079995055  7.053635e-01  8.640245e-01
#> theta[44]  9.398381e-01 0.0015168301 0.059400498  7.935919e-01  9.152837e-01
#> lp__      -2.762763e+03 0.3723095862 5.980963874 -2.775599e+03 -2.766236e+03
#>                     50%           75%         97.5%     n_eff      Rhat
#> est_se     9.582065e-01  9.617356e-01  9.674997e-01  995.7041 0.9990116
#> est_sp     8.075349e-01  8.141697e-01  8.293521e-01 1423.8631 0.9990033
#> theta[1]   1.319507e-02  2.347917e-02  5.530626e-02 1314.3784 0.9993005
#> theta[2]   3.760763e-02  6.107277e-02  1.243571e-01 1629.2836 0.9992908
#> theta[3]   3.377140e-02  5.937305e-02  1.092119e-01 1146.9833 1.0000724
#> theta[4]   1.448780e-01  1.750683e-01  2.260392e-01 1284.2322 0.9991804
#> theta[5]   3.164987e-01  3.465573e-01  4.008304e-01 1667.0568 0.9990138
#> theta[6]   4.475848e-01  4.790213e-01  5.362937e-01 2359.2168 0.9990800
#> theta[7]   4.654187e-01  4.961354e-01  5.609067e-01 2217.4320 0.9998677
#> theta[8]   6.087411e-01  6.444279e-01  7.048676e-01 2733.7885 1.0006807
#> theta[9]   7.167308e-01  7.481016e-01  8.007058e-01 2364.4707 0.9993092
#> theta[10]  6.454541e-01  6.802877e-01  7.441940e-01 2436.0601 0.9991624
#> theta[11]  7.243507e-01  7.582121e-01  8.108004e-01 2668.3444 1.0000274
#> theta[12]  8.236176e-01  8.482542e-01  8.975830e-01 2263.0551 0.9990002
#> theta[13]  7.654113e-01  7.909668e-01  8.378039e-01 1857.9655 1.0012950
#> theta[14]  8.624993e-01  8.856324e-01  9.265868e-01 1990.4399 0.9992797
#> theta[15]  7.723260e-01  8.176870e-01  8.900496e-01 2109.0306 1.0012365
#> theta[16]  8.418818e-01  8.785714e-01  9.423628e-01 2135.7060 0.9990384
#> theta[17]  9.160096e-01  9.455393e-01  9.854278e-01 1382.3348 0.9990387
#> theta[18]  8.803974e-01  9.123397e-01  9.569319e-01 1790.7890 0.9990391
#> theta[19]  8.835304e-01  9.095966e-01  9.545395e-01 2079.7337 0.9991114
#> theta[20]  8.574111e-01  8.910876e-01  9.459229e-01 2294.9309 0.9994774
#> theta[21]  9.158318e-01  9.412503e-01  9.795411e-01 1580.1758 0.9990402
#> theta[22]  8.307917e-01  8.579621e-01  9.098851e-01 2416.5084 0.9990325
#> theta[23]  9.539527e-01  9.741822e-01  9.971524e-01 1409.7155 0.9991723
#> theta[24]  9.500680e-01  9.705381e-01  9.959156e-01 1225.4001 0.9993520
#> theta[25]  9.767115e-01  9.889895e-01  9.989495e-01 1645.7539 1.0002200
#> theta[26]  9.415557e-01  9.646443e-01  9.921506e-01 1706.9424 0.9995324
#> theta[27]  9.300208e-01  9.524267e-01  9.894799e-01 1254.4148 0.9991461
#> theta[28]  9.649456e-01  9.825285e-01  9.980265e-01 1853.8449 0.9995199
#> theta[29]  9.134935e-01  9.411331e-01  9.853984e-01 1150.0500 0.9991689
#> theta[30]  9.219956e-01  9.529422e-01  9.909736e-01 1792.0586 0.9997941
#> theta[31]  8.666501e-01  9.089361e-01  9.660925e-01 1796.0451 0.9994872
#> theta[32]  9.475452e-01  9.737303e-01  9.967317e-01 1478.8096 0.9990261
#> theta[33]  9.448753e-01  9.755974e-01  9.971338e-01 2269.6511 0.9995909
#> theta[34]  9.551519e-01  9.766556e-01  9.968077e-01 1506.7542 0.9996925
#> theta[35]  9.046023e-01  9.430230e-01  9.903739e-01 2067.5556 0.9990049
#> theta[36]  9.657940e-01  9.860136e-01  9.984955e-01 1628.8100 0.9990131
#> theta[37]  9.526012e-01  9.778939e-01  9.981827e-01 2176.5909 1.0000563
#> theta[38]  9.093435e-01  9.444921e-01  9.894880e-01 1370.7882 0.9989998
#> theta[39]  9.338862e-01  9.695528e-01  9.964630e-01 1847.7119 0.9991342
#> theta[40]  9.518235e-01  9.790494e-01  9.983187e-01 1569.1496 0.9990092
#> theta[41]  9.667780e-01  9.858340e-01  9.982205e-01 1373.3000 0.9993270
#> theta[42]  9.367858e-01  9.669280e-01  9.959764e-01 1885.0789 0.9990012
#> theta[43]  9.266005e-01  9.652812e-01  9.974887e-01 1851.2145 0.9990077
#> theta[44]  9.577977e-01  9.831545e-01  9.989427e-01 1533.5795 0.9990006
#> lp__      -2.762367e+03 -2.758555e+03 -2.752517e+03  258.0679 1.0044855
#> 
#> $corrected_se
#>            age       sero        pos tot
#> theta[1]   1.5 0.01665906   3.431767 206
#> theta[2]   2.5 0.04446571   6.491993 146
#> theta[3]   3.5 0.04033849   6.776867 168
#> theta[4]   4.5 0.14602776  27.599246 189
#> theta[5]   5.5 0.31635871  69.282557 219
#> theta[6]   6.5 0.44616879  87.002913 195
#> theta[7]   7.5 0.46249280  75.848818 164
#> theta[8]   8.5 0.61028960  88.491992 145
#> theta[9]   9.5 0.71690405 129.042729 180
#> theta[10] 10.5 0.64415648 103.065037 160
#> theta[11] 11.5 0.72417345 107.177671 148
#> theta[12] 12.5 0.82243321 146.393111 178
#> theta[13] 13.5 0.76454476 135.324422 177
#> theta[14] 14.5 0.86029897 141.949330 165
#> theta[15] 15.5 0.76962286  51.564732  67
#> theta[16] 16.5 0.83827804  48.620126  58
#> theta[17] 17.5 0.91253760  73.915546  81
#> theta[18] 18.5 0.87671652  69.260605  79
#> theta[19] 19.5 0.88215195  97.918866 111
#> theta[20] 20.5 0.85315445  64.839738  76
#> theta[21] 21.5 0.91201471  74.785206  82
#> theta[22] 22.5 0.82694622  83.521568 101
#> theta[23] 23.5 0.94729391  83.361864  88
#> theta[24] 24.5 0.94456641  80.288145  85
#> theta[25] 25.5 0.97016474  91.195486  94
#> theta[26] 26.5 0.93917148  85.464604  91
#> theta[27] 27.5 0.92434068  82.266320  89
#> theta[28] 28.5 0.95898458  72.882828  76
#> theta[29] 29.5 0.90961080  71.859253  79
#> theta[30] 30.5 0.91653450  51.325932  56
#> theta[31] 31.5 0.85995587  44.717705  52
#> theta[32] 32.5 0.93726332  44.988639  48
#> theta[33] 33.5 0.93595396  34.630297  37
#> theta[34] 34.5 0.94391377  38.700464  41
#> theta[35] 35.5 0.89492502  35.797001  40
#> theta[36] 36.5 0.95702955  36.367123  38
#> theta[37] 37.5 0.94247483  36.756518  39
#> theta[38] 38.5 0.90160269  36.965710  41
#> theta[39] 39.5 0.91982884  27.594865  30
#> theta[40] 40.5 0.93824871  25.332715  27
#> theta[41] 41.5 0.95248410  23.812102  25
#> theta[42] 42.5 0.92039595  20.248711  22
#> theta[43] 43.5 0.90546939  17.203918  19
#> theta[44] 44.5 0.93983807  16.917085  18
#>