Apply SER module
Yunqi Yang
2/5/2023
Last updated: 2023-02-23
Checks: 7 0
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
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 with X independent
\(\log T_i =\beta_0+\epsilon_i\) 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)0.737 sec elapsedpar(mfrow = c(1,2))
hist(fit1$alpha, breaks = 20)
hist(fit1$mu* fit1$alpha, breaks = 20)
Run IBSS on data from null model, L = 5.
# IBSS of susie
t1 <- proc.time()
fit2 <- ibss_from_ser(X, y, L = 5, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)6.08 sec elapsedt2 <- proc.time()
t(apply(fit2$alpha, 1, function(x) sort(x, decreasing = TRUE))) [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.08984177 0.08650426 0.03921342 0.03302722 0.03219966 0.03071463
[2,] 0.08916461 0.08682954 0.03926150 0.03300684 0.03218343 0.03073894
[3,] 0.08879543 0.08718917 0.03928974 0.03299034 0.03216084 0.03074854
[4,] 0.08897614 0.08725231 0.03927855 0.03299155 0.03215396 0.03073903
[5,] 0.08947213 0.08693215 0.03924252 0.03300889 0.03217200 0.03072290
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 0.02755177 0.02707912 0.02629695 0.02480311 0.02294156 0.02128756
[2,] 0.02760066 0.02714516 0.02628316 0.02479515 0.02295210 0.02128774
[3,] 0.02763087 0.02718022 0.02626070 0.02477921 0.02295596 0.02127687
[4,] 0.02762062 0.02716148 0.02625211 0.02477181 0.02295165 0.02126778
[5,] 0.02758327 0.02711356 0.02626885 0.02478283 0.02294480 0.02127252
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] 0.01951480 0.01950644 0.01857692 0.01847012 0.01830947 0.01783370
[2,] 0.01952505 0.01951917 0.01857494 0.01846863 0.01831853 0.01784421
[3,] 0.01953180 0.01952313 0.01856891 0.01846265 0.01831656 0.01785087
[4,] 0.01952400 0.01952339 0.01856543 0.01845883 0.01830842 0.01784888
[5,] 0.01951952 0.01951190 0.01856910 0.01846224 0.01830487 0.01784079
[,19] [,20] [,21] [,22] [,23] [,24]
[1,] 0.01694499 0.01653597 0.01630564 0.01575089 0.01570535 0.01549161
[2,] 0.01695230 0.01655639 0.01630510 0.01574863 0.01570784 0.01549731
[3,] 0.01695116 0.01656883 0.01629974 0.01574182 0.01570296 0.01549640
[4,] 0.01694498 0.01656442 0.01629576 0.01573786 0.01569715 0.01549159
[5,] 0.01694193 0.01654888 0.01629842 0.01574201 0.01569811 0.01548922
[,25] [,26] [,27] [,28] [,29] [,30]
[1,] 0.01482062 0.01429626 0.01425941 0.01394507 0.01382752 0.01348085
[2,] 0.01483535 0.01431081 0.01426769 0.01395116 0.01382384 0.01348288
[3,] 0.01484127 0.01431859 0.01426878 0.01395067 0.01381742 0.01347879
[4,] 0.01483557 0.01431457 0.01426372 0.01394591 0.01381482 0.01347397
[5,] 0.01482573 0.01430399 0.01425919 0.01394316 0.01381949 0.01347481
[,31] [,32] [,33] [,34] [,35] [,36]
[1,] 0.01347401 0.01340920 0.01332747 0.01323908 0.01313411 0.01308708
[2,] 0.01347775 0.01341196 0.01333131 0.01324522 0.01314162 0.01309164
[3,] 0.01347655 0.01341100 0.01332959 0.01324521 0.01314351 0.01309067
[4,] 0.01347291 0.01340828 0.01332543 0.01324080 0.01313970 0.01308661
[5,] 0.01347163 0.01340737 0.01332433 0.01323781 0.01313519 0.01308483
[,37] [,38] [,39] [,40] [,41] [,42]
[1,] 0.01303144 0.01282827 0.01273372 0.01255941 0.01234632 0.01214886
[2,] 0.01303691 0.01283066 0.01275039 0.01256421 0.01235193 0.01215881
[3,] 0.01303613 0.01282827 0.01275731 0.01256280 0.01235156 0.01216061
[4,] 0.01303158 0.01282461 0.01275100 0.01255821 0.01234724 0.01215494
[5,] 0.01302926 0.01282452 0.01273976 0.01255650 0.01234467 0.01214928
[,43] [,44] [,45] [,46] [,47] [,48]
[1,] 0.01194127 0.01165035 0.01140048 0.01118717 0.01103446 0.01093593
[2,] 0.01194860 0.01165052 0.01140503 0.01119176 0.01103753 0.01094008
[3,] 0.01194882 0.01164765 0.01140511 0.01119154 0.01103637 0.01093942
[4,] 0.01194374 0.01164518 0.01140194 0.01118808 0.01103321 0.01093591
[5,] 0.01194006 0.01164639 0.01139969 0.01118594 0.01103223 0.01093418
[,49] [,50]
[1,] 0.01079593 0.01069878
[2,] 0.01079772 0.01069769
[3,] 0.01079568 0.01069393
[4,] 0.01079272 0.01069165
[5,] 0.01079276 0.01069387beta <- colSums(fit2$alpha * fit2$mu)
hist(beta, breaks = 20)
Data 2: simulated from null model with highly correlated X.
\(\log T_i =\beta_0+\epsilon_i\) and \(\beta_0 = 1\).
## Create survival object. status == 2 is death
dat[[2]]$y <- with(dat[[2]], Surv(surT, status == 2))
# Fit cox ph. Cox ph model with select multiple significant predictors..
cox1 <- coxph(y ~ .-status - surT, data = dat[[2]])Run IBSS on data from null model with L=1.
p = 50
X = as.matrix(dat[[2]][, c(2:(p+1))])
y = dat[[2]]$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)0.456 sec elapsedpar(mfrow = c(1,2))
hist(fit1$alpha, breaks = 20)
hist(fit1$mu* fit1$alpha, breaks = 20)
Run IBSS on data from null model, L = 5.
# IBSS of susie
t1 <- proc.time()
fit2 <- ibss_from_ser(X, y, L = 5, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)5.654 sec elapsedt2 <- proc.time()
t(apply(fit2$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 0.017869278beta <- colSums(fit2$alpha * fit2$mu)
hist(beta, breaks = 20)
| Version | Author | Date |
|---|---|---|
| 7fc8ac9 | yunqiyang0215 | 2023-02-23 |
Data 3: simulated from \(\log T_i=\beta_0 + \beta_1x_{i1}\). Predictors are independent.
\(\beta_0 = 1, \beta_1 = 3\)
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)4.971 sec elapsedt2 <- proc.time()
t2 - t1 user system elapsed
4.885 0.059 4.974 fit3$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(fit3$alpha * fit3$mu)
hist(beta, breaks = 20)
| Version | Author | Date |
|---|---|---|
| 7fc8ac9 | yunqiyang0215 | 2023-02-23 |
Data 4: simulated from \(\log T_i=\beta_0 + \beta_1x_{i1}\). Predictors have high correlation.
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)12.243 sec elapsedt2 <- proc.time()
t2 - t1 user system elapsed
11.380 0.184 12.247 t(apply(fit4$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-02beta <- colSums(fit4$alpha * fit4$mu)
hist(beta, breaks = 20)
| Version | Author | Date |
|---|---|---|
| 7fc8ac9 | yunqiyang0215 | 2023-02-23 |
Data 5: 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[[5]]$y <- with(dat[[5]], Surv(surT, status == 2))
X = as.matrix(dat[[5]][, c(2:(p+1))])
y = dat[[5]]$y
# IBSS of susie
t1 <- proc.time()
fit5 <- 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)10.007 sec elapsedt2 <- proc.time()
t2 - t1 user system elapsed
8.011 0.163 10.010 fit5$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(fit5$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-02beta <- colSums(fit5$alpha * fit5$mu)
hist(beta, breaks = 20)
| Version | Author | Date |
|---|---|---|
| 7fc8ac9 | yunqiyang0215 | 2023-02-23 |
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 evaluate_0.14 memoise_2.0.1
[29] knitr_1.36 callr_3.7.0 fastmap_1.1.0 httpuv_1.6.3
[33] ps_1.6.0 fansi_0.5.0 highr_0.9 Rcpp_1.0.8.3
[37] promises_1.2.0.1 cachem_1.0.6 desc_1.4.0 pkgload_1.2.3
[41] jsonlite_1.7.2 fs_1.5.0 digest_0.6.28 stringi_1.7.5
[45] dplyr_1.0.7 processx_3.5.2 rprojroot_2.0.2 grid_4.1.1
[49] cli_3.1.0 tools_4.1.1 magrittr_2.0.1 sass_0.4.4
[53] tibble_3.1.5 crayon_1.4.1 whisker_0.4 pkgconfig_2.0.3
[57] ellipsis_0.3.2 Matrix_1.5-3 prettyunits_1.1.1 rmarkdown_2.11
[61] rstudioapi_0.13 R6_2.5.1 git2r_0.28.0 compiler_4.1.1