Apply SER module
Yunqi Yang
2/5/2023
Last updated: 2023-02-21
Checks: 6 1
Knit directory: survival-susie/
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Description:
I simulated data in 4 different scenarios, and apply both coxph model and susie procedure. The data simulation procedure is available at https://yunqiyang0215.github.io/survival-susie/sim_survival.html
Susie works in 1,2,4 scenarios, but not scenario 3.
The Wakefield approximation:
\[ ABF(H_1/H_0)=\sqrt\frac{V}{V+W}\exp\{\frac{z^2}{2}\frac{W}{V+W}\}, \] where \(V\) is the variance of estimated regression coefficient, and \(W\) is variance in the normal prior, \(N(0,W)\).
# Function to calculate approximate BF based on Wakefield approximation
# @param z: zscore of the regression coefficient
# @param s: standard deviation of the estimated coefficient
compute_abf <- function(z, s, prior_variance){
abf <- sqrt(s^2/(s^2+prior_variance))*exp(z^2/2*(prior_variance/(s^2+prior_variance)))
return(abf)
}
compute_approx_post_var <- function(z, s, prior_variance){
post_var <- 1/(1/s^2 + 1/prior_variance)
return(post_var)
}
# @param post_var: posterior variance
# @param s: standard deviation of the estimated coefficient
# @param bhat: estimated beta effect
compute_approx_post_mean <- function(post_var, s, bhat){
mu <- post_var/(s^2)*bhat
return(mu)
}dat = readRDS("./data/sim_dat_simple.rds")
library(survival)
# Modified Karl's code for intercept part
devtools::load_all("/Users/nicholeyang/Desktop/logisticsusie")ℹ Loading logisticsusiesurv_uni_fun <- function(x, y, o, prior_variance, estimate_intercept = 0, ...){
fit <- coxph(y~ x + offset(o))
bhat <- summary(fit)$coefficients[1, 1] # bhat = -alphahat
sd <- summary(fit)$coefficients[1, 3]
zscore <- bhat/sd
bf <- compute_abf(zscore, sd, prior_variance)
var <- compute_approx_post_var(zscore, sd, prior_variance)
mu <- compute_approx_post_mean(var, sd, bhat)
lbf <- log(bf)
return(list(mu = mu, var=var, lbf=lbf, intercept=0))
}
fit_coxph <- ser_from_univariate(surv_uni_fun)Data 1: simulated from null model:
\(\log T_i =\beta_0+\epsilon_i\) and \(\beta_0 = 1\).
## Create survival object. status == 2 is death
dat[[1]]$y <- with(dat[[1]], Surv(surT, status == 2))
# Fit cox ph. Cox ph model with select multiple significant predictors..
cox1 <- coxph(y ~ .-status - surT, data = dat[[1]])Run IBSS on data from null model with L=1.
p = 50
X = as.matrix(dat[[1]][, c(2:(p+1))])
y = dat[[1]]$y# IBSS of susie
set.seed(1)
fit1 <- ibss_from_ser(X, y, L = 1, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)0.602 sec elapsedpar(mfrow = c(1,2))
hist(fit1$alpha, breaks = 20)
hist(fit1$mu* fit1$alpha, breaks = 20)
Run IBSS on data from null model, L = 5.
# IBSS of susie
t1 <- proc.time()
fit2 <- ibss_from_ser(X, y, L = 5, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 50, estimate_intercept = TRUE, ser_function = fit_coxph)6.5 sec elapsedt2 <- proc.time()
t(apply(fit2$alpha, 1, function(x) sort(x, decreasing = TRUE))) [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.05609322 0.04032955 0.03492124 0.03336796 0.03314579 0.03097663
[2,] 0.02896932 0.02623430 0.02481716 0.02286828 0.02282500 0.02269597
[3,] 0.02745036 0.02469365 0.02337122 0.02308924 0.02272713 0.02198974
[4,] 0.02796014 0.02430599 0.02331861 0.02310070 0.02252764 0.02223497
[5,] 0.02799527 0.02427965 0.02333430 0.02308225 0.02251404 0.02225175
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 0.03080564 0.03034312 0.03024764 0.02753592 0.02542502 0.02455909
[2,] 0.02266410 0.02265191 0.02216320 0.02197107 0.02131879 0.02120126
[3,] 0.02126563 0.02118921 0.02104036 0.02098470 0.02094191 0.02087132
[4,] 0.02156076 0.02124952 0.02111598 0.02102838 0.02077182 0.02068683
[5,] 0.02158102 0.02126382 0.02112493 0.02101741 0.02076020 0.02067426
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] 0.02370002 0.02311701 0.02208584 0.02195033 0.02169923 0.02162388
[2,] 0.02095127 0.02078628 0.02065878 0.02038459 0.02014915 0.02011939
[3,] 0.02051121 0.02044395 0.02033894 0.02032515 0.02028252 0.02012283
[4,] 0.02046062 0.02040317 0.02031091 0.02030855 0.02027867 0.02015906
[5,] 0.02046893 0.02041141 0.02030988 0.02029474 0.02026738 0.02016380
[,19] [,20] [,21] [,22] [,23] [,24]
[1,] 0.02106625 0.01894784 0.01883752 0.01854216 0.01823958 0.01783465
[2,] 0.01992669 0.01978913 0.01961306 0.01954943 0.01945667 0.01931688
[3,] 0.02008913 0.02006092 0.01998112 0.01993821 0.01980109 0.01952122
[4,] 0.02001577 0.01990919 0.01987853 0.01983631 0.01965239 0.01957681
[5,] 0.02000845 0.01990424 0.01986610 0.01982932 0.01964224 0.01958364
[,25] [,26] [,27] [,28] [,29] [,30]
[1,] 0.01775138 0.01741396 0.01672260 0.01639646 0.01609113 0.01517470
[2,] 0.01931072 0.01928345 0.01925305 0.01909494 0.01909311 0.01907063
[3,] 0.01947655 0.01943566 0.01941398 0.01936334 0.01934717 0.01929358
[4,] 0.01955838 0.01944712 0.01943737 0.01943675 0.01936155 0.01931401
[5,] 0.01956089 0.01944788 0.01944720 0.01944172 0.01935795 0.01931977
[,31] [,32] [,33] [,34] [,35] [,36]
[1,] 0.01499459 0.01499112 0.01466262 0.01432951 0.01419841 0.01383754
[2,] 0.01902290 0.01894060 0.01865592 0.01854349 0.01842011 0.01840300
[3,] 0.01922937 0.01920149 0.01909674 0.01903267 0.01900058 0.01890968
[4,] 0.01926617 0.01919231 0.01909377 0.01901204 0.01899055 0.01896307
[5,] 0.01926059 0.01919166 0.01909792 0.01901901 0.01898327 0.01896540
[,37] [,38] [,39] [,40] [,41] [,42]
[1,] 0.01371178 0.01339826 0.01338319 0.01334452 0.01326245 0.01324939
[2,] 0.01836541 0.01835444 0.01832318 0.01831466 0.01821466 0.01819967
[3,] 0.01889245 0.01885691 0.01880577 0.01874234 0.01856491 0.01851308
[4,] 0.01896075 0.01891510 0.01873787 0.01863618 0.01858348 0.01854783
[5,] 0.01896046 0.01891904 0.01873321 0.01862890 0.01858471 0.01855017
[,43] [,44] [,45] [,46] [,47] [,48]
[1,] 0.01239763 0.01239286 0.01189832 0.01171859 0.01082499 0.01053711
[2,] 0.01816079 0.01810006 0.01794403 0.01793372 0.01782749 0.01781656
[3,] 0.01850820 0.01848166 0.01845963 0.01831789 0.01817668 0.01805154
[4,] 0.01851871 0.01850763 0.01845904 0.01828050 0.01823954 0.01803063
[5,] 0.01851940 0.01851089 0.01845746 0.01828759 0.01823417 0.01802917
[,49] [,50]
[1,] 0.009008596 0.008913122
[2,] 0.017161011 0.017110724
[3,] 0.017917187 0.017880153
[4,] 0.017988391 0.017869995
[5,] 0.017993240 0.017869278
Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.
beta <- colSums(fit2$alpha * fit2$mu)
hist(beta, breaks = 20)
Data 2: simulated from \(\log T_i=\beta_0 + \beta_1x_{i1}\). Predictors are independent.
\(\beta_0 = 1, \beta_1 = 3\)
dat[[2]]$y <- with(dat[[2]], Surv(surT, status == 2))
X = as.matrix(dat[[2]][, c(2:(p+1))])
y = dat[[2]]$y
# IBSS of susie
t1 <- proc.time()
fit2 <- ibss_from_ser(X, y, L = 5, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)5.843 sec elapsedt2 <- proc.time()
t2 - t1 user system elapsed
5.579 0.101 5.900
Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.
fit2$alpha [,1] [,2] [,3] [,4] [,5]
[1,] 1.00000000 2.307716e-25 7.411530e-25 1.364349e-25 1.378772e-25
[2,] 0.04292694 1.186338e-02 2.799609e-02 1.203703e-02 1.555158e-02
[3,] 0.04292983 1.186381e-02 2.799437e-02 1.203744e-02 1.555229e-02
[4,] 0.04293056 1.186391e-02 2.799435e-02 1.203752e-02 1.555240e-02
[5,] 0.04292941 1.186371e-02 2.799521e-02 1.203733e-02 1.555207e-02
[,6] [,7] [,8] [,9] [,10]
[1,] 1.274855e-25 1.394375e-25 1.440577e-25 2.041674e-25 1.271053e-25
[2,] 1.231117e-02 2.285562e-02 2.032461e-02 2.102240e-02 1.836279e-02
[3,] 1.231149e-02 2.285620e-02 2.032511e-02 2.102288e-02 1.836289e-02
[4,] 1.231157e-02 2.285623e-02 2.032525e-02 2.102311e-02 1.836299e-02
[5,] 1.231143e-02 2.285592e-02 2.032503e-02 2.102291e-02 1.836296e-02
[,11] [,12] [,13] [,14] [,15]
[1,] 1.270159e-25 1.282280e-25 1.315745e-25 1.133932e-25 1.193168e-25
[2,] 7.315552e-02 1.591384e-02 1.347406e-02 4.542299e-02 1.040702e-02
[3,] 7.314127e-02 1.591454e-02 1.347450e-02 4.543055e-02 1.040733e-02
[4,] 7.313721e-02 1.591463e-02 1.347458e-02 4.543086e-02 1.040740e-02
[5,] 7.314364e-02 1.591430e-02 1.347439e-02 4.542696e-02 1.040726e-02
[,16] [,17] [,18] [,19] [,20]
[1,] 1.268907e-25 2.277648e-25 3.677275e-25 1.637013e-25 1.343948e-25
[2,] 1.495222e-02 1.127507e-02 1.213458e-02 1.553421e-02 1.255682e-02
[3,] 1.495291e-02 1.127545e-02 1.213500e-02 1.553447e-02 1.255730e-02
[4,] 1.495300e-02 1.127553e-02 1.213507e-02 1.553453e-02 1.255739e-02
[5,] 1.495267e-02 1.127536e-02 1.213489e-02 1.553442e-02 1.255717e-02
[,21] [,22] [,23] [,24] [,25]
[1,] 1.567569e-25 1.655280e-25 1.442488e-25 1.158482e-25 2.546165e-25
[2,] 1.473564e-02 1.400340e-02 1.576270e-02 1.254437e-02 1.556932e-02
[3,] 1.473622e-02 1.400388e-02 1.576297e-02 1.254491e-02 1.556980e-02
[4,] 1.473639e-02 1.400398e-02 1.576308e-02 1.254505e-02 1.556989e-02
[5,] 1.473612e-02 1.400376e-02 1.576296e-02 1.254481e-02 1.556968e-02
[,26] [,27] [,28] [,29] [,30]
[1,] 1.629070e-25 1.160590e-25 1.728822e-25 1.318097e-25 1.442441e-25
[2,] 1.671226e-02 1.151320e-02 1.592331e-02 1.909934e-02 1.350350e-02
[3,] 1.671323e-02 1.151358e-02 1.592358e-02 1.909905e-02 1.350396e-02
[4,] 1.671339e-02 1.151366e-02 1.592362e-02 1.909903e-02 1.350404e-02
[5,] 1.671294e-02 1.151349e-02 1.592350e-02 1.909917e-02 1.350383e-02
[,31] [,32] [,33] [,34] [,35]
[1,] 1.248397e-25 2.453707e-25 3.780222e-25 1.546542e-25 1.318572e-25
[2,] 1.268569e-02 2.897596e-02 1.361216e-02 1.530646e-02 2.093614e-02
[3,] 1.268614e-02 2.897633e-02 1.361263e-02 1.530710e-02 2.093680e-02
[4,] 1.268623e-02 2.897630e-02 1.361266e-02 1.530726e-02 2.093680e-02
[5,] 1.268603e-02 2.897610e-02 1.361242e-02 1.530697e-02 2.093646e-02
[,36] [,37] [,38] [,39] [,40]
[1,] 6.916937e-25 9.750268e-26 1.307822e-25 2.011690e-25 1.501407e-25
[2,] 2.134703e-02 1.161268e-02 1.756904e-02 1.390547e-02 1.632848e-02
[3,] 2.134732e-02 1.161312e-02 1.757048e-02 1.390593e-02 1.632902e-02
[4,] 2.134741e-02 1.161318e-02 1.757071e-02 1.390602e-02 1.632913e-02
[5,] 2.134731e-02 1.161298e-02 1.757003e-02 1.390581e-02 1.632889e-02
[,41] [,42] [,43] [,44] [,45]
[1,] 1.222045e-25 1.801522e-25 1.440586e-25 1.505744e-25 1.226334e-25
[2,] 1.618001e-02 1.313164e-02 6.208979e-02 1.230718e-02 3.292905e-02
[3,] 1.618063e-02 1.313214e-02 6.207667e-02 1.230761e-02 3.293183e-02
[4,] 1.618072e-02 1.313225e-02 6.207589e-02 1.230769e-02 3.293201e-02
[5,] 1.618042e-02 1.313204e-02 6.208229e-02 1.230749e-02 3.293060e-02
[,46] [,47] [,48] [,49] [,50]
[1,] 1.893290e-25 1.236505e-25 1.410184e-25 7.540486e-25 2.087607e-25
[2,] 4.334369e-02 1.297647e-02 1.982894e-02 2.130821e-02 1.418095e-02
[3,] 4.333981e-02 1.297698e-02 1.982963e-02 2.130754e-02 1.418150e-02
[4,] 4.333966e-02 1.297707e-02 1.982971e-02 2.130749e-02 1.418160e-02
[5,] 4.334149e-02 1.297684e-02 1.982936e-02 2.130783e-02 1.418135e-02beta <- colSums(fit2$alpha * fit2$mu)
hist(beta, breaks = 20)
Data 3: simulated from \(\log T_i=\beta_0 + \beta_1x_{i1}\). Predictors have high correlation.
dat[[3]]$y <- with(dat[[3]], Surv(surT, status == 2))
X = as.matrix(dat[[3]][, c(2:(p+1))])
y = dat[[3]]$y
# IBSS of susie
t1 <- proc.time()
fit3 <- ibss_from_ser(X, y, L = 5, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)15.182 sec elapsedt2 <- proc.time()
t2 - t1 user system elapsed
12.794 0.264 15.198 t(apply(fit3$alpha, 1, function(x) sort(x, decreasing = TRUE))) [,1] [,2] [,3] [,4] [,5]
[1,] 0.99986965 4.136298e-05 4.104706e-05 1.915872e-05 8.894234e-06
[2,] 0.04011044 3.005711e-02 2.690318e-02 2.654547e-02 2.556933e-02
[3,] 0.04157315 2.930629e-02 2.703757e-02 2.603876e-02 2.600848e-02
[4,] 0.03696112 3.178081e-02 2.925385e-02 2.544157e-02 2.452026e-02
[5,] 0.03425956 3.288860e-02 3.287825e-02 2.464801e-02 2.391154e-02
[,6] [,7] [,8] [,9] [,10]
[1,] 6.642297e-06 5.494192e-06 1.702179e-06 1.002326e-06 7.036141e-07
[2,] 2.549146e-02 2.508731e-02 2.405777e-02 2.338434e-02 2.226460e-02
[3,] 2.592096e-02 2.556921e-02 2.451164e-02 2.380416e-02 2.265399e-02
[4,] 2.433410e-02 2.400936e-02 2.303727e-02 2.270160e-02 2.244892e-02
[5,] 2.307498e-02 2.273596e-02 2.252341e-02 2.252128e-02 2.161827e-02
[,11] [,12] [,13] [,14] [,15]
[1,] 6.766364e-07 5.960689e-07 5.140254e-07 3.959313e-07 3.826679e-07
[2,] 2.140634e-02 2.138452e-02 2.055655e-02 2.009172e-02 1.999360e-02
[3,] 2.161356e-02 2.081940e-02 2.081786e-02 2.019267e-02 1.962927e-02
[4,] 2.138739e-02 2.103059e-02 2.091528e-02 1.995622e-02 1.985105e-02
[5,] 2.116558e-02 2.112074e-02 2.083334e-02 2.021565e-02 2.017466e-02
[,16] [,17] [,18] [,19] [,20]
[1,] 2.934595e-07 2.444224e-07 1.713643e-07 1.517155e-07 1.397109e-07
[2,] 1.954806e-02 1.952036e-02 1.942617e-02 1.930895e-02 1.912646e-02
[3,] 1.961999e-02 1.954192e-02 1.950099e-02 1.949585e-02 1.919763e-02
[4,] 1.959289e-02 1.937419e-02 1.936887e-02 1.930050e-02 1.925443e-02
[5,] 2.016384e-02 1.948479e-02 1.933915e-02 1.909220e-02 1.907918e-02
[,21] [,22] [,23] [,24] [,25]
[1,] 1.360481e-07 1.296982e-07 9.392248e-08 7.139341e-08 5.703098e-08
[2,] 1.867244e-02 1.864432e-02 1.855068e-02 1.847495e-02 1.838000e-02
[3,] 1.881009e-02 1.853858e-02 1.842802e-02 1.838719e-02 1.835316e-02
[4,] 1.923710e-02 1.894578e-02 1.886790e-02 1.872295e-02 1.850146e-02
[5,] 1.892436e-02 1.883572e-02 1.883290e-02 1.874236e-02 1.864524e-02
[,26] [,27] [,28] [,29] [,30]
[1,] 4.009682e-08 3.930486e-08 2.651245e-08 2.497218e-08 2.304859e-08
[2,] 1.834848e-02 1.833844e-02 1.830613e-02 1.826313e-02 1.826281e-02
[3,] 1.826319e-02 1.823735e-02 1.821347e-02 1.818663e-02 1.810132e-02
[4,] 1.835433e-02 1.834315e-02 1.831643e-02 1.825185e-02 1.824077e-02
[5,] 1.854049e-02 1.834298e-02 1.822391e-02 1.821059e-02 1.820733e-02
[,31] [,32] [,33] [,34] [,35]
[1,] 2.272884e-08 1.677608e-08 1.352317e-08 1.338892e-08 1.239902e-08
[2,] 1.819833e-02 1.814234e-02 1.812143e-02 1.799278e-02 1.797794e-02
[3,] 1.806854e-02 1.805402e-02 1.804641e-02 1.799291e-02 1.795163e-02
[4,] 1.822718e-02 1.812593e-02 1.809853e-02 1.801765e-02 1.790576e-02
[5,] 1.811122e-02 1.806737e-02 1.806621e-02 1.806195e-02 1.806018e-02
[,36] [,37] [,38] [,39] [,40]
[1,] 9.515233e-09 8.495920e-09 6.910143e-09 5.402280e-09 4.465426e-09
[2,] 1.792216e-02 1.776625e-02 1.758140e-02 1.751661e-02 1.735864e-02
[3,] 1.782753e-02 1.769811e-02 1.757320e-02 1.747955e-02 1.720872e-02
[4,] 1.780908e-02 1.779736e-02 1.775942e-02 1.774160e-02 1.773031e-02
[5,] 1.804226e-02 1.802174e-02 1.793167e-02 1.791618e-02 1.783958e-02
[,41] [,42] [,43] [,44] [,45]
[1,] 4.425620e-09 3.932818e-09 2.873236e-09 2.857335e-09 2.641937e-09
[2,] 1.735184e-02 1.719088e-02 1.706006e-02 1.695498e-02 1.691129e-02
[3,] 1.718913e-02 1.693648e-02 1.686200e-02 1.682594e-02 1.672039e-02
[4,] 1.766149e-02 1.750260e-02 1.737158e-02 1.735684e-02 1.733606e-02
[5,] 1.780413e-02 1.778540e-02 1.767143e-02 1.759025e-02 1.753913e-02
[,46] [,47] [,48] [,49] [,50]
[1,] 1.222350e-09 1.075611e-09 6.611139e-10 4.946253e-10 3.088339e-10
[2,] 1.688266e-02 1.685215e-02 1.676987e-02 1.627919e-02 1.509408e-02
[3,] 1.668792e-02 1.667264e-02 1.664982e-02 1.624125e-02 1.494147e-02
[4,] 1.723302e-02 1.720847e-02 1.703353e-02 1.635244e-02 1.542918e-02
[5,] 1.744093e-02 1.738553e-02 1.712836e-02 1.642592e-02 1.587569e-02
Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.
Data 4: simulated from \(\log T_i=\beta_0 + \beta_1x_{i1} + \beta_1x_{i2}\). Predictors have high correlation
\(\beta_0 = 1, \beta_1 = 3, \beta_2 = 1.5\) and \(cor=0.9\).
dat[[4]]$y <- with(dat[[4]], Surv(surT, status == 2))
X = as.matrix(dat[[4]][, c(2:(p+1))])
y = dat[[4]]$y
# IBSS of susie
t1 <- proc.time()
fit4 <- ibss_from_ser(X, y, L = 5, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)8.496 sec elapsedt2 <- proc.time()
t2 - t1 user system elapsed
7.849 0.145 8.499
Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.
fit4$alpha [,1] [,2] [,3] [,4] [,5]
[1,] 1.000000e+00 2.933205e-12 4.087642e-12 2.366477e-10 6.257578e-11
[2,] 1.850792e-05 9.943400e-01 1.385772e-05 3.700979e-05 1.013017e-05
[3,] 4.536854e-02 1.871102e-02 1.791956e-02 1.678350e-02 1.959784e-02
[4,] 4.555811e-02 1.873738e-02 1.783248e-02 1.678433e-02 1.950136e-02
[5,] 4.508341e-02 1.866958e-02 1.805353e-02 1.678148e-02 1.974599e-02
[,6] [,7] [,8] [,9] [,10]
[1,] 1.694674e-10 7.732188e-11 3.660192e-11 3.030459e-12 6.169283e-11
[2,] 3.731885e-05 9.823877e-06 1.015834e-05 2.212862e-05 6.528051e-04
[3,] 1.826711e-02 1.993589e-02 2.347674e-02 1.649439e-02 2.241567e-02
[4,] 1.830700e-02 1.981386e-02 2.330862e-02 1.643295e-02 2.248801e-02
[5,] 1.820522e-02 2.012350e-02 2.373685e-02 1.658883e-02 2.230418e-02
[,11] [,12] [,13] [,14] [,15]
[1,] 6.666085e-09 5.848923e-12 1.934489e-10 3.039833e-11 6.544899e-12
[2,] 4.385076e-04 9.447618e-06 4.810615e-04 3.495016e-06 3.581897e-05
[3,] 4.840652e-02 2.666774e-02 1.977692e-02 2.046824e-02 1.579463e-02
[4,] 4.887295e-02 2.644747e-02 1.980515e-02 2.034759e-02 1.575066e-02
[5,] 4.769422e-02 2.700837e-02 1.973304e-02 2.065309e-02 1.586157e-02
[,16] [,17] [,18] [,19] [,20]
[1,] 2.769809e-10 2.606908e-12 1.398502e-09 6.197536e-11 1.710988e-10
[2,] 2.398309e-04 1.466066e-04 2.843799e-05 6.826647e-05 1.077129e-04
[3,] 2.486840e-02 1.577565e-02 1.724187e-02 1.743459e-02 2.052182e-02
[4,] 2.500067e-02 1.574703e-02 1.725621e-02 1.738277e-02 2.057818e-02
[5,] 2.466546e-02 1.581902e-02 1.721918e-02 1.751410e-02 2.043483e-02
[,21] [,22] [,23] [,24] [,25]
[1,] 1.718176e-11 6.041372e-11 7.271671e-10 2.631022e-11 2.394387e-11
[2,] 4.311060e-05 2.349391e-05 8.942508e-05 7.110254e-05 1.260295e-04
[3,] 1.588409e-02 1.762074e-02 1.646286e-02 1.655209e-02 1.753709e-02
[4,] 1.587840e-02 1.756408e-02 1.646071e-02 1.656291e-02 1.750750e-02
[5,] 1.589220e-02 1.770794e-02 1.646586e-02 1.653464e-02 1.758226e-02
[,26] [,27] [,28] [,29] [,30]
[1,] 5.468033e-11 7.795080e-11 1.001601e-09 4.589769e-11 1.391003e-10
[2,] 1.465558e-04 1.997978e-05 1.088381e-05 2.775068e-05 8.511050e-05
[3,] 1.995778e-02 1.620291e-02 1.701408e-02 1.804331e-02 2.010464e-02
[4,] 2.001545e-02 1.619618e-02 1.699197e-02 1.796793e-02 2.015262e-02
[5,] 1.986870e-02 1.621258e-02 1.704734e-02 1.815877e-02 2.003019e-02
[,31] [,32] [,33] [,34] [,35]
[1,] 4.392514e-10 2.126822e-12 1.379937e-12 9.496262e-11 1.283533e-10
[2,] 4.066977e-05 1.418038e-05 9.662177e-05 9.304704e-06 2.596032e-05
[3,] 1.755409e-02 1.979152e-02 1.503885e-02 1.583168e-02 1.711033e-02
[4,] 1.756053e-02 1.965909e-02 1.504818e-02 1.580055e-02 1.707435e-02
[5,] 1.754364e-02 1.999599e-02 1.502366e-02 1.587928e-02 1.716489e-02
[,36] [,37] [,38] [,39] [,40]
[1,] 1.244254e-11 1.095376e-09 1.222179e-11 1.528442e-11 1.005406e-10
[2,] 8.854091e-05 2.771415e-04 2.388364e-04 2.445607e-04 5.453538e-05
[3,] 1.688026e-02 2.775137e-02 1.721127e-02 1.860950e-02 1.837969e-02
[4,] 1.685411e-02 2.792212e-02 1.721253e-02 1.861818e-02 1.834406e-02
[5,] 1.692003e-02 2.749011e-02 1.720836e-02 1.859542e-02 1.843408e-02
[,41] [,42] [,43] [,44] [,45]
[1,] 3.773320e-10 5.691097e-10 7.162237e-12 2.447135e-11 6.571003e-12
[2,] 7.040821e-06 3.794516e-04 6.362457e-06 6.049160e-05 4.984366e-05
[3,] 1.590548e-02 2.109172e-02 2.175785e-02 1.771424e-02 1.681899e-02
[4,] 1.586574e-02 2.115994e-02 2.158632e-02 1.771971e-02 1.678517e-02
[5,] 1.596622e-02 2.098678e-02 2.202348e-02 1.770502e-02 1.686990e-02
[,46] [,47] [,48] [,49] [,50]
[1,] 5.396012e-11 1.172468e-09 1.870435e-11 1.093238e-08 2.967319e-11
[2,] 7.567777e-05 6.167971e-04 2.244213e-04 2.579889e-05 1.094100e-04
[3,] 1.994731e-02 2.531449e-02 1.744199e-02 2.156550e-02 1.697764e-02
[4,] 2.000116e-02 2.544556e-02 1.746130e-02 2.164236e-02 1.698849e-02
[5,] 1.986392e-02 2.511383e-02 1.741165e-02 2.144735e-02 1.696047e-02t(apply(fit4$alpha, 1, function(x) sort(x, decreasing = TRUE))) [,1] [,2] [,3] [,4] [,5]
[1,] 0.99999997 1.093238e-08 6.666085e-09 1.398502e-09 1.172468e-09
[2,] 0.99433998 6.528051e-04 6.167971e-04 4.810615e-04 4.385076e-04
[3,] 0.04840652 4.536854e-02 2.775137e-02 2.666774e-02 2.531449e-02
[4,] 0.04887295 4.555811e-02 2.792212e-02 2.644747e-02 2.544556e-02
[5,] 0.04769422 4.508341e-02 2.749011e-02 2.700837e-02 2.511383e-02
[,6] [,7] [,8] [,9] [,10]
[1,] 1.095376e-09 1.001601e-09 7.271671e-10 5.691097e-10 4.392514e-10
[2,] 3.794516e-04 2.771415e-04 2.445607e-04 2.398309e-04 2.388364e-04
[3,] 2.486840e-02 2.347674e-02 2.241567e-02 2.175785e-02 2.156550e-02
[4,] 2.500067e-02 2.330862e-02 2.248801e-02 2.164236e-02 2.158632e-02
[5,] 2.466546e-02 2.373685e-02 2.230418e-02 2.202348e-02 2.144735e-02
[,11] [,12] [,13] [,14] [,15]
[1,] 3.773320e-10 2.769809e-10 2.366477e-10 1.934489e-10 1.710988e-10
[2,] 2.244213e-04 1.466066e-04 1.465558e-04 1.260295e-04 1.094100e-04
[3,] 2.109172e-02 2.052182e-02 2.046824e-02 2.010464e-02 1.995778e-02
[4,] 2.115994e-02 2.057818e-02 2.034759e-02 2.015262e-02 2.001545e-02
[5,] 2.098678e-02 2.065309e-02 2.043483e-02 2.012350e-02 2.003019e-02
[,16] [,17] [,18] [,19] [,20]
[1,] 1.694674e-10 1.391003e-10 1.283533e-10 1.005406e-10 9.496262e-11
[2,] 1.077129e-04 9.662177e-05 8.942508e-05 8.854091e-05 8.511050e-05
[3,] 1.994731e-02 1.993589e-02 1.979152e-02 1.977692e-02 1.959784e-02
[4,] 2.000116e-02 1.981386e-02 1.980515e-02 1.965909e-02 1.950136e-02
[5,] 1.999599e-02 1.986870e-02 1.986392e-02 1.974599e-02 1.973304e-02
[,21] [,22] [,23] [,24] [,25]
[1,] 7.795080e-11 7.732188e-11 6.257578e-11 6.197536e-11 6.169283e-11
[2,] 7.567777e-05 7.110254e-05 6.826647e-05 6.049160e-05 5.453538e-05
[3,] 1.871102e-02 1.860950e-02 1.837969e-02 1.826711e-02 1.804331e-02
[4,] 1.873738e-02 1.861818e-02 1.834406e-02 1.830700e-02 1.796793e-02
[5,] 1.866958e-02 1.859542e-02 1.843408e-02 1.820522e-02 1.815877e-02
[,26] [,27] [,28] [,29] [,30]
[1,] 6.041372e-11 5.468033e-11 5.396012e-11 4.589769e-11 3.660192e-11
[2,] 4.984366e-05 4.311060e-05 4.066977e-05 3.731885e-05 3.700979e-05
[3,] 1.791956e-02 1.771424e-02 1.762074e-02 1.755409e-02 1.753709e-02
[4,] 1.783248e-02 1.771971e-02 1.756408e-02 1.756053e-02 1.750750e-02
[5,] 1.805353e-02 1.770794e-02 1.770502e-02 1.758226e-02 1.754364e-02
[,31] [,32] [,33] [,34] [,35]
[1,] 3.039833e-11 2.967319e-11 2.631022e-11 2.447135e-11 2.394387e-11
[2,] 3.581897e-05 2.843799e-05 2.775068e-05 2.596032e-05 2.579889e-05
[3,] 1.744199e-02 1.743459e-02 1.724187e-02 1.721127e-02 1.711033e-02
[4,] 1.746130e-02 1.738277e-02 1.725621e-02 1.721253e-02 1.707435e-02
[5,] 1.751410e-02 1.741165e-02 1.721918e-02 1.720836e-02 1.716489e-02
[,36] [,37] [,38] [,39] [,40]
[1,] 1.870435e-11 1.718176e-11 1.528442e-11 1.244254e-11 1.222179e-11
[2,] 2.349391e-05 2.212862e-05 1.997978e-05 1.850792e-05 1.418038e-05
[3,] 1.701408e-02 1.697764e-02 1.688026e-02 1.681899e-02 1.678350e-02
[4,] 1.699197e-02 1.698849e-02 1.685411e-02 1.678517e-02 1.678433e-02
[5,] 1.704734e-02 1.696047e-02 1.692003e-02 1.686990e-02 1.678148e-02
[,41] [,42] [,43] [,44] [,45]
[1,] 7.162237e-12 6.571003e-12 6.544899e-12 5.848923e-12 4.087642e-12
[2,] 1.385772e-05 1.088381e-05 1.015834e-05 1.013017e-05 9.823877e-06
[3,] 1.655209e-02 1.649439e-02 1.646286e-02 1.620291e-02 1.590548e-02
[4,] 1.656291e-02 1.646071e-02 1.643295e-02 1.619618e-02 1.587840e-02
[5,] 1.658883e-02 1.653464e-02 1.646586e-02 1.621258e-02 1.596622e-02
[,46] [,47] [,48] [,49] [,50]
[1,] 3.030459e-12 2.933205e-12 2.606908e-12 2.126822e-12 1.379937e-12
[2,] 9.447618e-06 9.304704e-06 7.040821e-06 6.362457e-06 3.495016e-06
[3,] 1.588409e-02 1.583168e-02 1.579463e-02 1.577565e-02 1.503885e-02
[4,] 1.586574e-02 1.580055e-02 1.575066e-02 1.574703e-02 1.504818e-02
[5,] 1.589220e-02 1.587928e-02 1.586157e-02 1.581902e-02 1.502366e-02
sessionInfo()R version 4.1.1 (2021-08-10)
Platform: x86_64-apple-darwin20.6.0 (64-bit)
Running under: macOS Monterey 12.0.1
Matrix products: default
BLAS: /usr/local/Cellar/openblas/0.3.18/lib/libopenblasp-r0.3.18.dylib
LAPACK: /usr/local/Cellar/r/4.1.1_1/lib/R/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] logisticsusie_0.0.0.9004 testthat_3.1.0 survival_3.2-11
[4] workflowr_1.6.2
loaded via a namespace (and not attached):
[1] tidyselect_1.1.1 xfun_0.27 bslib_0.4.1 remotes_2.4.1
[5] purrr_0.3.4 splines_4.1.1 lattice_0.20-44 generics_0.1.2
[9] vctrs_0.3.8 usethis_2.1.3 htmltools_0.5.2 yaml_2.2.1
[13] utf8_1.2.2 rlang_1.0.6 pkgbuild_1.2.0 jquerylib_0.1.4
[17] later_1.3.0 pillar_1.6.4 glue_1.4.2 withr_2.5.0
[21] sessioninfo_1.1.1 matrixStats_0.63.0 lifecycle_1.0.1 stringr_1.4.0
[25] tictoc_1.1 devtools_2.4.2 codetools_0.2-18 evaluate_0.14
[29] memoise_2.0.1 knitr_1.36 callr_3.7.0 fastmap_1.1.0
[33] httpuv_1.6.3 ps_1.6.0 fansi_0.5.0 highr_0.9
[37] Rcpp_1.0.8.3 promises_1.2.0.1 cachem_1.0.6 desc_1.4.0
[41] pkgload_1.2.3 jsonlite_1.7.2 fs_1.5.0 digest_0.6.28
[45] stringi_1.7.5 dplyr_1.0.7 processx_3.5.2 rprojroot_2.0.2
[49] grid_4.1.1 cli_3.1.0 tools_4.1.1 magrittr_2.0.1
[53] sass_0.4.4 tibble_3.1.5 crayon_1.4.1 whisker_0.4
[57] pkgconfig_2.0.3 ellipsis_0.3.2 Matrix_1.5-3 prettyunits_1.1.1
[61] rmarkdown_2.11 rstudioapi_0.13 R6_2.5.1 git2r_0.28.0
[65] compiler_4.1.1