Probabilistic Bias Analysis for an Unmeasured Confounder
Description
Monte Carlo version of deterministic_bias_analysis(): instead of a single set of assumptions, the bias parameters are drawn repeatedly from prior distributions and combined with the sampling uncertainty in the observed risk difference, yielding a simulation interval for the bias-adjusted effect. This ports the probabilistic unmeasured-confounding sensitivity analysis of García-Albéniz et al. (supplementary analysis).
Usage
probabilistic_bias_analysis(
rd,
prev_continue,
prev_stopbase,
confounder_effect,
rd_se = 0,
n_sim = 1000L,
conf_level = 0.95,
seed = NULL
)
Arguments
rd
|
Observed arm risk difference (CONTINUE minus STOPBASE).
|
prev_continue, prev_stopbase, confounder_effect
|
Either a single value (fixed) or a length-2 c(min, max) uniform range, as described above.
|
rd_se
|
Standard error of the observed risk difference. Default: 0 (ignore sampling uncertainty, propagate only the bias parameters).
|
n_sim
|
Number of Monte Carlo iterations. Default: 1000L.
|
conf_level
|
Width of the reported simulation interval. Default: 0.95.
|
seed
|
Optional integer seed. The caller’s RNG state is restored on exit. Default: NULL.
|
Details
On each of n_sim iterations the function draws the observed risk difference from a normal distribution (rd, rd_se), draws each bias parameter, and computes the bias-adjusted risk difference rd_draw - (prev_continue - prev_stopbase) * confounder_effect. The reported interval is the central conf_level percentile range of those draws.
Each bias parameter (prev_continue, prev_stopbase, confounder_effect) may be given as a single number (held fixed) or as a length-2 vector c(min, max) (drawn from a uniform distribution on that range). Set rd_se to 0 to propagate only the bias-parameter uncertainty.
Value
A named list with estimate (median adjusted risk difference), conf_low and conf_high (the simulation-interval bounds), draws (the n_sim adjusted risk differences), n_sim, and conf_level.
References
García-Albéniz X, Uno H, Bhatt DL, McArdle PH, Joffe MM, Hernán MA. Continuation of Annual Screening Mammography and Breast Cancer Mortality in Women Older Than 70 Years: A Prospective Observational Study. Ann Intern Med. 2020;172(6):381-389. doi:10.7326/M18-1199
Examples
Code
$estimate
[1] -0.0122241
$conf_low
[1] -0.0202571
$conf_high
[1] -0.004001624
$draws
[1] -1.412347e-02 -1.134877e-02 -1.478847e-02 -5.647437e-03 -1.152106e-02
[6] -1.524205e-02 -1.023671e-02 -9.207823e-03 -9.714303e-03 -1.297946e-02
[11] -6.441358e-03 -1.024163e-02 -1.461969e-02 -2.100805e-02 -7.117834e-03
[16] -1.239369e-02 -1.131225e-02 -7.813182e-03 -8.668842e-03 -9.300315e-03
[21] -8.231016e-03 -8.653851e-03 -1.129757e-02 -2.008124e-02 -9.648644e-03
[26] -1.235879e-02 -1.250153e-02 -1.834798e-02 -1.436913e-02 -1.096348e-02
[31] -7.045500e-03 -1.292745e-02 -1.031326e-02 -1.251865e-02 -1.739314e-02
[36] -1.307338e-02 -1.368454e-02 -1.217665e-02 -7.912250e-03 -9.007405e-03
[41] -1.219278e-02 -1.313671e-02 -8.794417e-03 -9.761533e-03 -1.442862e-02
[46] -1.559437e-02 -1.064153e-02 -9.376370e-03 -1.310379e-02 -8.818844e-03
[51] -1.032714e-02 -1.407958e-02 -1.058001e-02 -1.600358e-02 -6.021354e-03
[56] -4.638462e-03 -1.330323e-02 -1.552877e-02 -9.943100e-03 -1.222915e-02
[61] -2.029932e-03 -1.255950e-02 -9.175329e-03 -1.204982e-02 -1.486430e-02
[66] -1.093256e-02 -1.925509e-02 -5.847213e-03 -1.191690e-02 -2.986778e-03
[71] -1.059995e-02 -1.554600e-02 -1.005419e-02 -1.521150e-02 -1.657368e-02
[76] -1.083484e-02 -1.356040e-02 -1.239331e-02 -1.240247e-02 -1.438197e-02
[81] -1.418813e-02 -1.251937e-02 -7.449260e-03 -1.807228e-02 -9.317511e-03
[86] -1.150378e-02 -7.518261e-03 -1.303636e-02 -1.015834e-02 -1.069683e-02
[91] -1.481996e-02 -7.662621e-03 -7.287372e-03 -9.226735e-03 -6.133115e-03
[96] -1.055295e-02 -1.775492e-02 -1.458939e-02 -1.711942e-02 -1.425404e-02
[101] -1.480994e-02 -1.252064e-02 -1.494900e-02 -1.125463e-02 -1.437333e-02
[106] -5.185444e-03 -9.073002e-03 -8.172661e-03 -1.028055e-02 -5.311970e-03
[111] -1.448023e-02 -1.336579e-02 -5.737990e-03 -1.476842e-02 -1.262012e-02
[116] -1.386771e-02 -1.358401e-02 -1.282908e-02 -1.023759e-02 -1.248696e-02
[121] -1.464930e-02 -6.780311e-03 -1.281245e-02 -1.269423e-02 -1.223436e-02
[126] -8.702467e-03 -1.222534e-02 -1.202373e-02 -1.438810e-02 -1.357074e-02
[131] -1.200759e-02 -1.417968e-02 -9.494366e-03 -1.817075e-02 -1.119216e-02
[136] -1.786821e-02 -1.317703e-02 -1.480044e-02 -1.515374e-02 -1.246547e-02
[141] -2.036865e-02 -7.696256e-03 -1.859049e-02 -1.467703e-02 -1.627108e-02
[146] -1.546113e-02 -3.692087e-03 -1.191132e-02 -1.689159e-02 -1.847788e-02
[151] -1.079394e-02 -1.226686e-02 -1.330336e-02 -1.558935e-02 -1.859424e-02
[156] -1.693069e-02 -8.359705e-03 -1.499618e-02 -1.788068e-02 -4.664430e-03
[161] -1.027498e-02 -1.307193e-02 -7.270244e-03 -8.697524e-03 -1.464731e-02
[166] -3.211614e-03 -1.259793e-02 -1.799130e-02 -1.292866e-02 -1.128568e-02
[171] -2.298231e-03 -1.134361e-02 -1.018493e-02 -1.213522e-02 -1.309053e-02
[176] -1.197758e-02 -8.784783e-03 -3.893962e-03 -7.693575e-03 -7.419161e-03
[181] -1.675905e-02 -8.322660e-03 -1.125236e-02 -1.836020e-02 -9.338758e-03
[186] -1.238233e-02 -6.057673e-03 -1.500941e-02 -1.363168e-02 -1.501572e-02
[191] -1.262562e-02 -1.074477e-02 -1.551070e-02 -8.485635e-03 -1.623817e-02
[196] -1.605782e-02 -6.277730e-03 -1.638588e-02 -1.006137e-02 -1.389453e-02
[201] -9.904301e-03 -4.941522e-03 -5.698920e-03 -1.347641e-02 -2.199157e-02
[206] -1.776646e-03 -9.835892e-03 -9.996117e-03 -1.219465e-02 -1.036791e-02
[211] -1.235524e-02 -1.125383e-02 -1.421902e-02 -1.771952e-02 -8.026919e-03
[216] -6.096600e-03 -1.305420e-02 -1.683558e-02 -8.894095e-03 -1.205554e-02
[221] -1.868543e-02 -1.182492e-02 -1.526973e-02 -1.396009e-02 -1.721049e-02
[226] -4.217887e-03 -1.375860e-02 -1.827717e-02 -1.085845e-02 -1.179767e-02
[231] -1.585627e-02 -2.367125e-02 -1.480107e-02 -9.140818e-03 -1.213753e-02
[236] -1.265813e-02 -9.576140e-03 -1.659049e-02 -7.725557e-03 -1.262005e-02
[241] -8.952528e-03 -7.622596e-03 -1.103338e-02 -1.573959e-02 -7.978183e-03
[246] -2.008340e-02 -1.452068e-02 -1.372902e-02 -1.316931e-02 -7.846699e-03
[251] -1.153193e-02 -1.051254e-02 -1.219431e-02 -1.280404e-02 -9.711432e-03
[256] -7.599242e-03 -2.118026e-02 -9.683114e-03 -1.111389e-02 -1.362917e-02
[261] -8.141918e-03 -1.401728e-02 -1.236616e-02 -8.793383e-03 -4.688363e-03
[266] -1.037620e-02 -1.358856e-02 -1.626924e-02 -1.409967e-02 -1.610604e-02
[271] -1.307742e-02 -1.019710e-02 -1.519094e-02 -1.742498e-03 -1.134348e-02
[276] -7.556366e-03 -2.084598e-02 -9.045056e-03 -1.694640e-02 -7.969111e-03
[281] -1.006484e-02 -1.332425e-02 -6.018602e-03 -1.531508e-02 -1.457359e-02
[286] -1.648725e-02 -1.475770e-02 -7.831091e-03 -1.070836e-02 -8.388023e-03
[291] -1.313609e-02 -1.107245e-02 -1.183772e-02 -1.739554e-02 -5.201873e-03
[296] -1.133637e-02 -8.462728e-03 -8.296988e-03 -1.220838e-02 -1.312707e-02
[301] -8.361148e-03 -1.585785e-02 -4.668824e-03 -1.388796e-02 -5.375187e-03
[306] -6.204812e-03 -1.197415e-02 -1.051649e-02 -1.629503e-02 -1.049751e-02
[311] -7.772930e-03 -1.165485e-02 -1.383546e-02 -1.414460e-02 -1.194635e-02
[316] -7.419335e-03 -1.372548e-02 -1.242808e-02 -1.690462e-02 -1.020482e-02
[321] -6.598805e-03 -6.618195e-03 -8.628363e-03 -1.939550e-02 -1.003086e-02
[326] -9.988359e-03 -1.367257e-02 -1.145451e-02 -1.551136e-02 -9.830324e-03
[331] -1.285834e-02 -1.854858e-02 -1.413184e-02 -6.607320e-03 -1.324655e-02
[336] -8.641634e-03 -8.720261e-03 -1.183521e-02 -1.353730e-02 -1.474021e-02
[341] -9.569428e-03 -1.678074e-02 -1.106967e-02 -1.256409e-02 -2.080103e-02
[346] -1.778082e-02 -8.659296e-03 -1.260846e-02 -8.411592e-03 -5.194322e-03
[351] -6.261032e-03 -9.489575e-03 -1.024330e-02 -1.258007e-02 -5.916786e-03
[356] -9.894765e-03 -1.696318e-02 -1.246449e-02 -1.950107e-02 -1.273250e-02
[361] -2.227055e-02 -6.641933e-03 -1.489855e-02 -1.414357e-02 -1.224507e-02
[366] -9.137186e-03 -8.906958e-03 -1.039882e-02 -1.462847e-02 -1.786180e-02
[371] -1.405300e-02 -1.032270e-02 -1.461271e-02 -1.208373e-02 -1.675865e-02
[376] -1.208378e-02 -1.113353e-02 -1.254391e-02 -1.236751e-02 -5.091090e-03
[381] -9.328832e-03 -7.819831e-03 -1.628101e-02 -1.112956e-02 -7.355912e-03
[386] -1.274197e-02 -2.008770e-02 -1.052967e-02 -1.970740e-02 -1.522572e-02
[391] -7.352663e-03 -1.021601e-02 -8.227738e-03 -1.156296e-02 -1.273817e-02
[396] -1.562532e-02 -5.773993e-03 -1.190746e-02 -1.530633e-02 -8.212461e-03
[401] -8.102337e-03 -4.288003e-03 -1.494388e-02 -1.392569e-02 -1.345351e-02
[406] -1.397260e-02 -1.271858e-02 -1.333028e-02 -5.950345e-03 -1.468563e-02
[411] -1.393562e-02 -9.910645e-03 -7.488236e-03 -1.555648e-02 -1.372645e-02
[416] -1.004582e-02 -7.301741e-03 -1.296330e-02 -1.746568e-02 -4.874712e-03
[421] -6.100949e-03 -1.442685e-02 -1.205088e-02 -1.857268e-02 -9.865847e-03
[426] -5.326697e-03 -1.851457e-02 -1.550835e-02 -1.515459e-02 -1.463476e-02
[431] -1.995432e-02 -1.035641e-02 -1.750867e-02 -1.224922e-02 -9.455191e-03
[436] -1.243087e-02 -8.455085e-03 -1.224093e-02 -1.549359e-02 -9.548486e-03
[441] -1.443527e-02 -4.708060e-03 -1.199648e-02 -8.975414e-03 -1.097445e-02
[446] -2.431854e-02 -1.816578e-02 -1.360345e-02 -1.133771e-02 -2.174118e-02
[451] -8.036215e-03 -1.473329e-02 -1.504351e-02 -1.826070e-02 -1.821652e-02
[456] -1.180286e-02 -9.980745e-03 -2.002276e-02 -1.615656e-02 -9.898784e-03
[461] -1.403733e-02 -3.472166e-03 -6.913033e-03 -9.301923e-03 -1.150963e-02
[466] -1.097335e-02 -1.487613e-02 -9.249772e-03 -6.464486e-03 -7.929139e-03
[471] -1.523922e-02 -1.855702e-02 -1.280928e-02 -1.020885e-02 -6.384768e-03
[476] -1.752302e-02 -1.008232e-02 -1.090792e-02 -7.626702e-03 -1.198504e-02
[481] -1.329773e-02 -1.688250e-02 -1.431915e-02 -1.325426e-02 -3.169964e-03
[486] -2.578904e-03 -1.260285e-02 -1.600591e-02 -2.005526e-02 -1.003522e-02
[491] -1.663277e-02 -3.164982e-03 -1.616509e-02 -1.116840e-02 3.415225e-03
[496] -1.676838e-02 -1.057817e-02 -1.676091e-02 -1.053169e-02 -1.546755e-02
[501] -1.233149e-02 -1.300080e-02 -1.635373e-02 -1.180458e-02 -7.900675e-03
[506] -6.034125e-03 -1.742646e-02 -1.291456e-02 -6.780204e-03 -1.616869e-02
[511] -2.202138e-02 -1.650285e-02 -1.572989e-02 -1.205570e-02 -1.370115e-02
[516] -1.065574e-02 -1.405354e-02 -1.025475e-02 -1.426808e-02 -6.908885e-03
[521] -1.531106e-02 -1.131131e-02 -1.518266e-02 -1.140670e-02 -1.264209e-02
[526] -1.833420e-02 -1.282515e-02 -7.218131e-03 -9.312620e-03 -1.160835e-02
[531] -1.712776e-02 -7.528283e-03 -1.213835e-02 -1.391651e-02 -5.425725e-03
[536] -1.543384e-02 -1.069033e-02 -7.454588e-03 -9.896980e-03 -1.321897e-02
[541] -1.343186e-02 -1.129373e-02 -9.942843e-03 -1.167462e-02 -6.234619e-03
[546] -1.178561e-02 -1.439094e-02 -9.754133e-03 -2.101737e-02 -1.007957e-02
[551] -1.001593e-02 -1.275575e-02 -1.623565e-02 -1.353114e-02 -5.755673e-03
[556] -1.433541e-02 -2.148836e-02 -8.637461e-03 -1.420825e-02 -1.494722e-02
[561] -1.705256e-02 -1.245867e-02 -9.701030e-03 -1.431235e-02 -1.457837e-02
[566] -7.899488e-03 -1.308532e-02 -1.291053e-02 -1.452145e-02 -9.006590e-03
[571] -1.549399e-02 -8.657001e-03 -9.055012e-03 -1.395640e-02 -8.982479e-03
[576] -8.592989e-03 -1.066282e-02 -3.688515e-03 -1.970576e-02 -1.658748e-02
[581] -1.756201e-02 -1.143364e-02 -5.352173e-03 -5.259951e-03 -9.920895e-03
[586] -8.641724e-03 -1.330917e-02 -1.071208e-02 -1.042030e-02 -1.544720e-02
[591] -1.361450e-02 -1.223970e-02 -6.872168e-03 -1.624867e-02 -2.010810e-02
[596] -8.746551e-03 -1.534258e-02 -1.389497e-02 -8.642084e-03 -1.503213e-02
[601] -1.330463e-02 -6.266512e-03 -9.994594e-03 -9.976374e-03 -1.229482e-02
[606] -1.678522e-02 -1.772210e-02 -1.319573e-02 -4.143690e-03 -1.062089e-02
[611] -1.167404e-02 -1.081120e-02 -1.371755e-02 -1.774989e-02 -1.346229e-03
[616] -1.349101e-02 -1.309081e-02 -1.854090e-02 -1.329319e-02 -1.284869e-02
[621] -1.353428e-02 -1.863809e-02 -5.703641e-03 -5.249242e-03 -9.730745e-03
[626] -1.694246e-02 -9.398481e-03 -1.354420e-02 -1.358458e-02 -6.626569e-03
[631] -1.717466e-02 -1.401186e-02 -1.439346e-02 -1.177912e-02 -1.884288e-02
[636] -1.474252e-02 -8.901339e-03 -1.066431e-02 -1.626957e-02 -1.007068e-02
[641] -2.154500e-02 -1.334888e-02 -8.748550e-03 -1.461618e-02 -1.192631e-02
[646] -1.839993e-02 -8.456472e-03 -1.995076e-02 -1.331211e-02 -1.292766e-02
[651] -1.142889e-02 -1.497869e-02 -4.868810e-03 -1.795371e-02 -1.168926e-02
[656] -2.396129e-02 -1.219240e-02 -1.041280e-02 -1.603747e-02 -8.846879e-03
[661] -1.110618e-02 -8.327940e-03 -1.551826e-02 -1.588537e-02 -1.977224e-02
[666] -1.305933e-02 -1.762076e-02 -8.751228e-03 -1.166394e-02 -2.808653e-03
[671] -1.611584e-02 -7.349380e-03 -1.418432e-02 -1.753188e-02 -1.007896e-02
[676] -1.769464e-02 -1.596739e-02 -1.472098e-02 -1.090287e-02 -1.635195e-02
[681] -8.308072e-03 -1.709603e-02 -1.130968e-02 -1.110407e-02 -1.615997e-02
[686] -1.420923e-02 -1.446412e-02 -7.769150e-03 -5.706569e-03 -1.687104e-02
[691] -8.888730e-03 -1.250785e-02 -1.993164e-02 -1.492952e-02 -1.025428e-02
[696] -1.119943e-02 -2.210332e-02 -1.026808e-02 -9.893644e-03 -1.378005e-02
[701] -1.547149e-02 -3.848569e-03 -1.266912e-02 -1.244256e-02 -1.642156e-02
[706] -1.775320e-02 -1.810071e-02 -1.333884e-02 -6.718348e-03 -4.523025e-03
[711] -5.926044e-03 -6.808639e-03 -1.285010e-02 -1.676292e-02 -1.349609e-02
[716] -2.154862e-02 -1.292127e-02 -5.808731e-03 -1.157523e-02 -7.660806e-03
[721] -9.806805e-03 -1.534597e-02 -4.961739e-03 -1.236429e-02 -1.657194e-02
[726] -1.193752e-02 -1.793248e-02 -9.042007e-03 -9.880952e-03 -1.388066e-02
[731] -1.428753e-02 -7.910266e-03 -1.594228e-02 -1.625915e-02 -1.046095e-02
[736] -1.412256e-02 -8.530271e-03 -1.284512e-02 -7.965643e-03 -1.047567e-02
[741] -2.070790e-02 -1.776439e-02 -6.501599e-03 -8.931213e-03 -1.616803e-02
[746] -1.782586e-02 -8.061068e-03 -1.536140e-02 -4.877892e-03 -4.877242e-03
[751] -1.793545e-02 -1.546595e-02 -1.685015e-02 -9.414366e-03 -1.686590e-02
[756] -2.031561e-02 -4.217520e-03 -8.094633e-03 -8.788899e-03 -1.467701e-02
[761] -1.206644e-02 -9.816693e-03 -1.668014e-02 -1.307723e-02 -1.096736e-02
[766] -5.173742e-03 -9.749506e-03 -6.974242e-03 -1.106614e-02 -1.669551e-02
[771] -1.370335e-02 -1.874545e-02 -8.642888e-03 -6.206475e-03 -1.286224e-02
[776] -1.641094e-02 -7.082093e-03 -1.215419e-02 -1.366883e-02 -7.853073e-03
[781] -1.509764e-02 -7.586160e-03 -1.580442e-02 -1.014009e-02 -8.757227e-03
[786] -1.733311e-02 -1.010854e-02 -1.206176e-02 -9.179612e-03 -1.527454e-02
[791] -1.297613e-02 -6.029964e-03 -1.150756e-02 -9.039242e-03 -1.329246e-02
[796] -1.641704e-02 -1.187804e-02 -1.682650e-02 -2.206888e-02 -7.818869e-03
[801] -1.628900e-02 -1.924527e-02 -8.376076e-03 -1.159657e-02 -1.449471e-02
[806] -1.280078e-02 -1.450282e-02 -8.308381e-03 -9.465025e-03 -1.839941e-02
[811] -1.070724e-02 -8.805167e-03 -9.729629e-03 -2.233259e-02 -1.329260e-02
[816] -3.816426e-03 -9.144919e-03 -1.948012e-02 -1.868514e-02 -1.043240e-02
[821] -1.268054e-02 -8.419484e-03 -1.053808e-02 -1.154050e-02 -1.095734e-02
[826] -1.115737e-02 -1.703896e-02 -2.691836e-03 -1.769829e-02 -1.228687e-02
[831] -1.510149e-02 -5.132148e-03 -8.471813e-03 -1.445414e-02 -1.103708e-02
[836] -7.992256e-03 -3.694425e-03 -1.115407e-02 -1.593430e-02 -1.536492e-02
[841] -4.057736e-03 -2.009667e-02 -7.823526e-05 -1.325171e-02 -1.344800e-02
[846] -1.112187e-02 -8.978371e-03 -1.131082e-02 -1.958277e-02 -1.052928e-02
[851] -9.629565e-03 -9.653779e-03 -1.595624e-02 -2.150196e-02 -1.296673e-02
[856] -1.578611e-02 -1.493088e-02 -1.568653e-02 -1.406621e-02 -1.294473e-02
[861] -8.709147e-03 -8.104347e-03 -1.479687e-02 -1.340483e-02 -1.048435e-02
[866] -7.062468e-03 -1.231230e-02 -1.828210e-02 -1.126879e-02 -1.214962e-02
[871] -5.169727e-03 -9.998559e-03 -1.442552e-02 -1.442000e-02 -1.404724e-02
[876] -1.136310e-02 -1.179206e-02 -8.832158e-03 -1.128477e-02 -1.436480e-02
[881] -1.547242e-02 -9.867647e-03 -1.258542e-02 -1.151426e-02 -7.682733e-03
[886] -4.886180e-03 -1.641272e-02 -6.099437e-03 -1.594003e-02 -1.052592e-02
[891] -1.155283e-02 -1.320957e-02 -6.321908e-03 -1.511804e-02 -9.938404e-03
[896] -1.259024e-02 -1.602888e-02 -6.785902e-03 -1.990222e-02 -1.406602e-02
[901] -1.796362e-02 -1.172250e-02 -1.137606e-02 -1.619551e-02 -9.339716e-03
[906] -1.635655e-02 -9.709148e-03 -1.136141e-02 -9.549295e-03 -1.604061e-02
[911] -1.108040e-02 -1.390264e-02 -1.780405e-02 -1.110253e-02 -4.484815e-03
[916] -1.467182e-02 -1.289794e-02 -9.010195e-03 -1.140567e-02 -3.978850e-03
[921] -9.713663e-03 -3.290906e-03 -1.071728e-02 -1.671625e-02 -1.055234e-02
[926] -1.576472e-02 -1.599234e-02 -1.324555e-02 -8.522360e-03 -1.070730e-02
[931] -8.812061e-03 -8.049340e-03 -1.242832e-02 -2.194333e-02 -8.838917e-03
[936] -2.628085e-03 -1.196150e-02 -1.718375e-02 -1.323667e-02 -1.577637e-02
[941] -1.219781e-02 -9.051510e-03 -8.403553e-03 -1.118153e-02 -1.508995e-02
[946] -8.530021e-03 -6.862940e-03 -3.329874e-03 -1.405598e-02 -9.698763e-03
[951] -7.542522e-03 -1.247928e-02 -9.968472e-03 -1.190817e-02 -1.214674e-02
[956] -1.123076e-02 -8.202138e-03 -9.695696e-03 -1.454511e-02 -2.139018e-02
[961] -1.582107e-02 -1.220444e-02 -2.184287e-02 -3.121930e-03 -1.860148e-02
[966] -1.619491e-02 -7.036392e-03 -2.063933e-02 -9.421752e-03 -1.404043e-02
[971] -1.080256e-02 -8.416593e-03 -1.604816e-02 -1.526147e-02 -2.423054e-02
[976] -1.576035e-02 -9.821913e-03 -1.076890e-02 -4.254089e-03 -1.161396e-02
[981] -1.029504e-02 -1.251838e-02 -1.351679e-02 -8.693641e-03 -1.014000e-02
[986] -1.169636e-02 -1.512511e-02 -1.234596e-02 -9.596344e-03 -9.568963e-03
[991] -1.390835e-02 -1.523356e-02 -9.385663e-03 -7.485349e-03 -1.162889e-02
[996] -1.327260e-02 -1.509419e-02 -1.365226e-02 -1.745168e-02 -1.465287e-02
[1001] -6.890392e-03 -7.457861e-03 -1.522425e-02 -1.171294e-02 -1.162002e-02
[1006] -1.844068e-02 -9.092573e-03 -1.954942e-02 -1.676849e-02 -8.676164e-03
[1011] -1.449804e-02 -1.268079e-02 -1.799554e-02 -1.749312e-02 -1.023342e-02
[1016] -1.272369e-02 -1.410380e-02 -1.750388e-02 -1.601274e-02 -4.589355e-03
[1021] -1.311608e-02 -8.340252e-03 -8.877040e-03 -9.019208e-03 -1.066449e-02
[1026] -1.767426e-02 -1.608556e-02 -8.954555e-03 -1.791689e-02 -1.048207e-02
[1031] -1.433970e-02 -1.349062e-02 -1.450524e-02 -1.316178e-02 -8.581837e-03
[1036] -9.772885e-03 -1.249269e-02 -8.986140e-03 -5.359942e-03 -1.216538e-02
[1041] -1.018340e-02 -1.103671e-02 -1.578047e-02 -1.513643e-02 -4.008296e-03
[1046] -8.491911e-03 -9.082862e-03 -1.169403e-02 -1.015511e-02 -1.153791e-02
[1051] -1.148083e-02 -1.096115e-02 -1.559847e-02 -2.460940e-03 -9.577161e-03
[1056] -1.321689e-02 -7.020728e-03 -1.438347e-02 -5.419674e-03 -1.346840e-02
[1061] -2.125995e-02 -6.818090e-03 -7.150587e-03 -1.458056e-02 -1.778917e-02
[1066] -1.921139e-02 -1.327990e-02 -1.934027e-02 -1.558453e-02 -1.123316e-02
[1071] -8.537164e-03 -1.532045e-02 -1.210865e-02 -1.129798e-02 -4.522995e-03
[1076] -1.555834e-02 -1.810844e-02 -1.981445e-02 -1.023922e-02 -1.292401e-02
[1081] -9.007703e-03 -1.276345e-02 -1.107951e-02 -1.091277e-02 -1.181735e-02
[1086] -1.405750e-02 -7.213022e-03 -1.401114e-02 -9.596073e-03 -1.175756e-02
[1091] -4.625565e-03 -9.619979e-03 -1.339604e-02 -1.204279e-02 -1.281335e-02
[1096] -2.039233e-02 -4.872028e-03 -7.741185e-03 -1.519778e-02 -1.064726e-02
[1101] -1.128025e-02 -1.699213e-02 -6.022270e-03 -1.310398e-02 -1.171859e-02
[1106] -1.059928e-02 -1.633884e-02 -1.591180e-02 -1.185579e-02 -9.557287e-03
[1111] -1.186199e-02 -9.334093e-03 -1.063459e-02 -9.966874e-03 -1.802558e-02
[1116] -9.222819e-03 -1.473606e-02 -1.374458e-02 -1.243621e-02 -1.856308e-02
[1121] -1.244416e-02 -1.318997e-02 -1.511500e-02 -1.450741e-02 -7.113500e-03
[1126] -1.754832e-02 -1.249042e-02 -2.230085e-02 -1.440294e-02 -1.420108e-02
[1131] -5.652770e-03 -1.560359e-02 -1.498379e-02 -1.756098e-02 -1.186340e-02
[1136] -7.346896e-03 -1.686690e-02 -1.419074e-02 -6.461745e-03 -1.456319e-02
[1141] -9.236541e-03 -1.135303e-02 -1.713687e-02 -7.247496e-03 -8.850296e-03
[1146] -1.425637e-02 -1.559114e-02 -1.355743e-02 -8.586793e-03 -1.400418e-02
[1151] -1.937649e-02 -1.254811e-02 -8.730145e-03 -1.712826e-02 -1.253488e-02
[1156] -1.718091e-02 -1.169742e-02 -1.282376e-02 -1.198188e-02 -1.478615e-02
[1161] -1.560963e-02 -8.518074e-03 -1.166461e-02 -1.305979e-02 -2.522415e-02
[1166] -1.689277e-02 -8.776897e-03 -1.371249e-02 -1.654839e-02 -1.439025e-02
[1171] -1.360027e-02 -1.463396e-02 -1.023516e-02 -5.882596e-03 -8.073135e-03
[1176] -6.709464e-03 -1.325970e-02 -8.957845e-03 -1.603866e-02 -1.333265e-02
[1181] -3.366968e-03 -1.273813e-02 -1.294858e-02 -1.413924e-02 -9.811541e-03
[1186] -3.715120e-03 -1.031804e-02 -1.376408e-02 -3.385325e-03 -1.505473e-02
[1191] -7.172382e-03 -1.410291e-02 -1.646665e-02 -6.897699e-03 -1.952347e-02
[1196] -1.298100e-02 -1.259445e-02 -1.382092e-02 -1.859072e-02 -1.465740e-02
[1201] -1.889419e-02 -4.652533e-03 -1.967570e-02 -2.077834e-02 -9.255534e-03
[1206] -9.117111e-03 -1.290120e-02 -1.244869e-02 -9.830374e-03 -5.768109e-03
[1211] -1.806698e-02 -6.508396e-03 -1.128988e-02 -1.321234e-02 -6.825827e-03
[1216] -7.876592e-03 -6.292748e-03 -1.290769e-02 -8.696133e-03 -1.108117e-02
[1221] -1.406882e-02 -5.827989e-03 -1.120751e-02 -1.246155e-02 -1.043383e-02
[1226] -1.133126e-02 -1.501246e-02 -1.232023e-02 -1.017017e-03 -1.263513e-02
[1231] -1.333506e-02 -9.192816e-03 -1.058573e-02 -1.458384e-02 -1.600319e-02
[1236] -8.539363e-03 -1.147929e-02 -1.030044e-02 -1.378953e-02 -1.917006e-02
[1241] -1.196768e-02 -2.759814e-03 -1.824589e-02 -1.581913e-02 -1.786578e-02
[1246] -1.332023e-02 -6.632958e-03 -1.254580e-02 -1.318940e-02 -1.693724e-02
[1251] -1.215035e-02 -7.851716e-03 -2.989768e-03 -7.070079e-03 -1.558328e-02
[1256] -1.340315e-02 -9.434734e-03 -1.173936e-02 -1.073478e-02 -1.765862e-02
[1261] -1.372468e-02 -1.534162e-02 -1.563493e-02 -1.472182e-02 -1.416312e-02
[1266] -1.223303e-02 -9.246588e-03 -1.461793e-02 -1.512647e-02 -5.726078e-03
[1271] -7.889543e-03 -9.173094e-03 -5.539220e-03 -1.582455e-02 -3.703604e-03
[1276] -7.082055e-03 -1.064072e-02 -9.195009e-03 -1.176161e-02 -1.261909e-02
[1281] -1.819471e-02 -9.031138e-03 -4.292045e-03 -3.719402e-03 -1.175235e-02
[1286] -1.262839e-02 -1.107466e-02 -7.264707e-03 -6.325618e-03 -1.008591e-02
[1291] -7.685889e-03 -1.225834e-02 -1.069299e-02 -7.703987e-03 2.664271e-03
[1296] -1.240058e-02 -1.500052e-02 -1.051351e-02 -1.405613e-02 -9.851516e-03
[1301] -1.158866e-02 -6.822016e-03 -1.588724e-02 -1.696035e-02 -5.785621e-03
[1306] -1.111349e-02 -1.627347e-02 -1.579053e-02 -1.440299e-02 -9.307387e-03
[1311] -1.417370e-02 -6.845241e-03 -1.163639e-02 -1.081621e-02 -1.265868e-02
[1316] -1.348532e-02 -1.272806e-02 -7.558424e-03 -1.670254e-02 -8.163758e-03
[1321] -1.342132e-02 -9.618183e-03 -1.292030e-02 -1.747460e-02 -1.045757e-02
[1326] -1.455299e-02 -6.991955e-03 -1.518631e-02 -1.929224e-02 -1.545539e-02
[1331] -1.401210e-02 -1.530978e-02 -1.296062e-02 -1.427092e-02 -1.366094e-02
[1336] -1.068023e-02 -1.636104e-02 -9.260747e-03 -1.199882e-02 -1.235022e-02
[1341] -2.003836e-02 -1.332621e-02 -1.418473e-02 -7.990822e-03 -6.199014e-03
[1346] -7.313632e-03 -1.626024e-02 -1.509133e-02 -1.212387e-02 -1.600528e-02
[1351] -1.866004e-02 -8.577450e-03 -1.214231e-02 -9.979511e-03 -1.711237e-02
[1356] -1.327780e-02 -1.734822e-02 -1.511009e-02 -1.096663e-02 -1.514917e-02
[1361] -1.634234e-02 -1.747090e-02 -1.750175e-02 -1.556590e-02 -5.041498e-03
[1366] -1.524732e-02 -1.662746e-02 -1.788301e-02 -1.246786e-02 -1.353539e-02
[1371] -1.083549e-02 -1.355619e-02 -8.806273e-03 -9.773497e-03 -8.382181e-03
[1376] -1.151667e-02 -7.363109e-03 -1.255538e-02 -8.322531e-03 -1.274921e-02
[1381] -1.496188e-02 -1.684985e-02 -1.416637e-02 -1.513124e-02 -9.564747e-03
[1386] -1.259461e-02 -1.469312e-02 -1.591250e-02 -6.088412e-03 -1.343207e-02
[1391] -1.693123e-02 -1.376181e-02 -1.125080e-02 -8.729382e-03 -1.283355e-02
[1396] -1.206811e-02 -1.699012e-02 -8.512943e-03 -1.125282e-02 -8.578666e-03
[1401] -5.655664e-03 -1.157943e-02 -1.341763e-02 -1.536706e-02 -1.452671e-02
[1406] -1.610505e-02 -1.050067e-02 -1.789778e-02 -1.858026e-02 -1.549012e-02
[1411] -7.610562e-03 -1.186157e-02 -1.456387e-02 -9.114229e-03 -1.361756e-02
[1416] -1.233423e-02 -1.159277e-02 -7.939455e-03 -6.676175e-03 -7.086391e-03
[1421] -8.092592e-03 -1.065219e-02 -4.126566e-03 -4.045604e-03 -6.938595e-03
[1426] -1.263090e-02 -1.657224e-02 -1.187095e-02 -1.471886e-02 -1.083911e-02
[1431] -1.436868e-02 -8.016003e-03 -3.117471e-03 -8.356230e-03 -9.696891e-03
[1436] -1.203060e-02 -3.036148e-03 -1.216541e-02 -6.788935e-03 -5.396042e-03
[1441] -1.149152e-02 -2.525783e-02 -1.385972e-02 -9.828227e-03 -1.790810e-02
[1446] -1.670703e-02 -8.419376e-03 -2.342584e-02 -1.128351e-02 -1.318501e-02
[1451] -1.443328e-02 -1.218116e-02 -1.177522e-02 -1.081327e-02 -1.209429e-02
[1456] -1.435862e-02 -1.189679e-02 -6.317913e-03 -8.841641e-03 -6.353404e-03
[1461] -1.327611e-02 -1.005462e-02 -1.006622e-02 -1.504986e-02 -1.567613e-02
[1466] -5.102198e-03 -1.528321e-02 -8.076155e-03 -1.310838e-02 -1.674687e-02
[1471] -1.784745e-02 -1.746694e-02 -1.982650e-02 -1.562088e-02 -7.786732e-03
[1476] -1.478714e-02 -5.040796e-03 -1.283223e-02 -1.563977e-02 -1.331207e-02
[1481] -1.435053e-02 -1.393308e-02 -1.159956e-02 -1.195273e-02 -9.775046e-03
[1486] -9.859552e-03 -8.777185e-03 -1.141436e-02 -1.529783e-02 -1.038579e-02
[1491] -1.029135e-02 -1.347818e-02 -1.385731e-02 -7.064715e-03 -7.006817e-03
[1496] -1.203953e-02 -1.349895e-02 -5.902496e-03 -1.673076e-02 -1.603491e-02
[1501] -8.696682e-03 -1.636743e-02 -8.574297e-03 -1.592184e-02 -9.718045e-03
[1506] -1.216668e-02 -8.964256e-03 -6.625256e-03 -1.250524e-02 -9.776265e-03
[1511] -1.888860e-02 -1.291129e-02 -1.698888e-02 -1.120438e-02 -1.179328e-02
[1516] -1.274385e-02 -1.336169e-02 -8.519134e-03 -1.276534e-02 -4.656451e-03
[1521] -2.025560e-02 -1.058351e-02 -3.560448e-03 -1.699259e-02 -1.498499e-02
[1526] -1.395006e-02 -1.139098e-02 -1.277965e-02 -1.407622e-02 -4.385783e-03
[1531] -1.140329e-02 -8.323199e-03 -2.340479e-02 -8.156395e-03 -6.882008e-03
[1536] -1.432628e-02 -1.286299e-02 -5.473740e-03 -1.163122e-02 -8.421951e-03
[1541] -8.994452e-03 -1.270057e-02 -1.299497e-02 -1.811591e-02 -2.087703e-02
[1546] -1.267716e-02 -1.079265e-02 -1.374483e-02 -9.474553e-03 -9.634394e-03
[1551] -1.319401e-02 -1.221778e-02 -7.018769e-03 -1.111085e-02 -9.334305e-03
[1556] -9.995291e-03 -5.678264e-03 -1.156527e-02 -1.545962e-02 -1.401265e-02
[1561] -1.116941e-02 -1.331887e-02 -1.262529e-02 -9.516457e-03 -1.574518e-02
[1566] -2.009037e-02 -4.849420e-03 -1.057727e-02 -7.878332e-03 -1.359933e-02
[1571] -1.193514e-02 -2.080321e-02 -1.114834e-02 -1.041654e-02 -1.622104e-02
[1576] -1.426601e-02 -7.028144e-03 -1.060107e-02 -1.251739e-02 -1.132147e-02
[1581] -1.719290e-02 -7.478858e-03 -1.957557e-02 -1.603792e-02 -1.005864e-02
[1586] -7.032085e-03 -1.909196e-02 -9.418704e-03 -1.071576e-02 -1.225761e-02
[1591] -1.461950e-02 -1.527979e-02 -1.163276e-02 -7.496375e-03 -1.823899e-02
[1596] -1.602259e-02 -5.804031e-03 -1.673050e-02 -2.229852e-02 -1.187300e-02
[1601] -1.029679e-02 -1.151046e-02 -1.551557e-02 -1.120685e-02 -1.297889e-02
[1606] -7.989644e-03 -1.033866e-02 -9.534183e-03 -1.093051e-02 -1.079928e-02
[1611] -8.463807e-03 -2.058081e-02 -1.010881e-02 -1.784959e-02 -1.058725e-02
[1616] -6.509002e-03 -1.356259e-02 -1.500146e-02 -1.264997e-02 -5.592683e-03
[1621] -1.180271e-02 -1.104194e-02 -1.502934e-02 -1.403187e-02 -1.278904e-02
[1626] -1.824855e-02 -7.029022e-03 -1.312087e-02 -2.000950e-02 -1.211959e-02
[1631] -1.274611e-02 -1.949780e-02 -3.234932e-03 -1.691427e-02 -1.701433e-02
[1636] -1.105334e-02 -7.949329e-03 -1.278581e-02 -1.166684e-02 -1.637122e-02
[1641] -8.275238e-03 -1.098145e-02 -1.148696e-02 -8.992176e-03 -8.242691e-03
[1646] -1.427342e-02 -1.030960e-02 -1.551198e-02 -3.540190e-03 -1.092432e-02
[1651] -1.256384e-02 -1.429865e-02 -1.286099e-02 -1.695685e-02 -1.224910e-02
[1656] -1.018451e-02 -1.421555e-02 -1.481366e-02 -1.831888e-02 -9.985075e-03
[1661] -1.107722e-02 -1.302790e-02 -1.461456e-02 -1.059633e-02 -1.779530e-02
[1666] -1.785874e-02 -1.839714e-02 -1.315758e-02 -9.074881e-03 -8.649164e-03
[1671] -1.467800e-02 -6.062985e-03 -1.655404e-02 -1.393217e-02 -1.417042e-02
[1676] -1.083077e-02 -1.869772e-02 -7.564942e-03 -7.153158e-03 -8.362337e-03
[1681] -1.208669e-02 -6.890051e-03 -9.554146e-03 -8.702507e-03 -1.134538e-02
[1686] -1.095688e-02 -2.036216e-02 -1.434246e-02 -8.555766e-03 -1.177324e-02
[1691] -1.701689e-02 -1.607221e-02 -1.437416e-02 -3.731249e-03 -1.311360e-02
[1696] -1.449222e-02 -2.044489e-02 -1.968439e-02 -7.589009e-03 -1.595798e-02
[1701] -5.871190e-03 -1.343616e-02 -2.149826e-02 -2.936248e-03 -1.697005e-02
[1706] -1.429353e-02 -1.199733e-02 -1.247245e-02 -1.821167e-02 -1.760957e-02
[1711] -6.167028e-03 -1.481093e-02 -7.941049e-03 -4.842124e-03 -1.504157e-02
[1716] -1.493730e-02 -1.943330e-02 -5.096401e-03 -1.490743e-02 -1.368365e-02
[1721] -1.741905e-02 -9.475644e-03 -5.752645e-03 -1.096850e-02 -1.393455e-02
[1726] -1.819460e-02 -6.852245e-03 -8.926920e-03 -1.273330e-02 -7.094457e-03
[1731] -6.922486e-03 -1.412665e-02 -1.717691e-02 -8.470325e-03 -9.291256e-03
[1736] -1.409285e-02 1.041667e-03 -2.226866e-02 -1.238850e-02 -7.814660e-03
[1741] -6.757596e-03 -8.051009e-03 -1.194144e-02 -8.911895e-03 -9.678817e-03
[1746] -1.233491e-02 -1.581867e-02 -7.114667e-03 -1.353610e-02 -1.315232e-02
[1751] -1.068335e-02 -1.200239e-02 -1.989470e-02 -1.373309e-02 -9.775079e-03
[1756] -7.072926e-03 -1.717911e-02 -1.485204e-02 -2.150893e-02 -8.780728e-03
[1761] -1.276068e-02 -8.472149e-03 -1.457927e-02 -1.114930e-02 -8.433660e-03
[1766] -1.329781e-02 -8.423605e-03 -9.499174e-03 -1.820206e-02 -1.071429e-02
[1771] -2.157221e-02 -1.321353e-02 -1.388326e-02 -9.098625e-03 -1.058503e-02
[1776] -1.461227e-02 -1.299616e-02 -1.137578e-02 -1.553816e-02 -1.500022e-02
[1781] -1.681253e-02 -1.865024e-02 -1.426960e-02 -1.210232e-02 -1.860563e-02
[1786] -1.069514e-02 -1.499500e-02 -1.064347e-02 -1.157726e-02 -1.364041e-02
[1791] -1.982953e-02 -1.807964e-02 -2.237030e-02 -7.181908e-03 -1.296132e-02
[1796] -4.460579e-03 -1.792439e-02 -6.253420e-03 -7.904901e-03 -1.549753e-02
[1801] -9.571254e-03 -9.853775e-03 -1.263067e-02 -6.052263e-03 -1.326111e-02
[1806] -4.219574e-03 -1.623943e-02 -6.340379e-03 -1.443913e-02 -1.019279e-02
[1811] -1.161521e-02 -1.222286e-02 -1.254738e-02 -8.134102e-03 -1.216991e-02
[1816] -6.928278e-03 -1.197049e-02 -1.110295e-02 -1.280297e-02 -1.334731e-02
[1821] -1.153484e-02 -7.916907e-03 -8.448133e-03 -8.356054e-03 -5.645026e-03
[1826] -1.059471e-02 -1.124866e-02 -5.724450e-03 -1.264247e-02 -1.620827e-02
[1831] -1.541650e-02 -1.478019e-02 -1.746167e-02 -6.572737e-03 -1.458141e-02
[1836] -7.194133e-03 -2.517925e-03 -1.379453e-02 -1.076900e-02 -1.379583e-02
[1841] -2.511596e-04 -1.603907e-02 -7.139327e-03 -8.323244e-03 -8.652919e-03
[1846] -8.310262e-03 -9.497258e-03 -9.221392e-03 -1.601301e-02 -9.894486e-03
[1851] -1.376896e-02 -5.675662e-04 -9.008835e-03 -8.664044e-03 -2.096283e-02
[1856] -1.740360e-02 -1.621574e-02 -1.438344e-02 -1.392436e-02 -9.330847e-03
[1861] -1.279290e-02 -1.345012e-02 -7.338053e-03 -2.011792e-02 -1.283873e-02
[1866] -8.460963e-03 -8.201767e-03 -1.319253e-02 -1.386991e-02 -1.240164e-02
[1871] -1.399020e-02 -1.373099e-02 -1.769142e-02 -1.302822e-02 -1.077136e-02
[1876] -1.429055e-02 -1.680147e-02 -1.823135e-02 -1.322851e-02 -5.193791e-03
[1881] -1.390051e-02 -1.451125e-02 -1.055049e-03 -1.954746e-02 -1.221614e-02
[1886] -9.618119e-03 -1.363780e-02 -7.384940e-03 -9.286042e-03 -1.169263e-02
[1891] -1.664750e-02 -1.008690e-02 -1.352205e-02 -1.485557e-02 -1.082444e-02
[1896] -9.749510e-03 -1.189296e-02 -8.192714e-03 -2.268753e-02 -9.440518e-03
[1901] -1.439505e-02 -1.075177e-02 -7.518676e-03 -1.107845e-02 -1.124109e-02
[1906] -2.211718e-02 -1.725872e-02 -8.891412e-03 -1.766620e-02 -1.276252e-02
[1911] -1.102023e-02 -1.345689e-02 -1.564544e-02 -1.768190e-02 -1.125972e-02
[1916] -2.013028e-02 -1.556690e-02 -1.253992e-02 -1.664412e-02 -1.281259e-02
[1921] -8.666716e-03 -1.244357e-02 -1.143828e-02 -5.422215e-03 -1.321648e-02
[1926] -1.116743e-02 -1.988143e-02 -1.205941e-02 -1.446997e-02 -1.709868e-02
[1931] -7.228652e-03 -1.246256e-02 -8.232519e-03 -1.500286e-02 -2.134235e-02
[1936] -1.174574e-02 -8.180098e-03 -1.727276e-03 -8.552068e-03 -7.385426e-03
[1941] -1.489363e-02 -1.062721e-02 -1.406924e-02 -1.025971e-02 -1.670340e-02
[1946] -1.362805e-02 -1.835224e-02 -1.199339e-02 -1.014740e-02 -1.223056e-02
[1951] -1.468765e-02 -1.295921e-02 -1.888020e-02 -1.285040e-02 -1.913085e-02
[1956] -1.155712e-02 -4.720846e-03 -9.724164e-03 -5.935432e-03 -6.382537e-03
[1961] -1.406346e-02 -1.046951e-02 -1.929741e-02 -8.058587e-03 -1.542174e-02
[1966] -8.080189e-03 -1.974457e-02 -7.625541e-03 -1.405312e-02 -7.123971e-03
[1971] -1.175247e-02 -1.494214e-02 -1.028378e-02 -1.282329e-02 -1.437047e-02
[1976] -1.568407e-02 -2.284864e-03 -1.592642e-02 -9.605418e-03 -1.310946e-02
[1981] -1.686458e-02 -1.774139e-02 -1.760737e-02 -1.744837e-02 -1.762097e-02
[1986] -9.246228e-03 -1.333126e-02 -4.002208e-03 -9.998200e-03 -4.843748e-03
[1991] -9.969705e-03 -8.924845e-03 -1.007693e-02 -1.404516e-02 -8.866975e-03
[1996] -1.174005e-02 -7.442462e-03 -1.476689e-02 -7.772260e-03 -1.302246e-02
$n_sim
[1] 2000
$conf_level
[1] 0.95