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Description:

I simulated data in 5 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.

Here I use corrected ABF instead of original Wakefeld ABF.

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 log of approximate BF based on Wakefield approximation
# @param z: zscore of the regression coefficient
# @param s: standard deviation of the estimated coefficient
compute_lbf <- function(z, s, prior_variance){
  abf <- sqrt(s^2/(s^2+prior_variance))
  lbf <- log(sqrt(s^2/(s^2+prior_variance))) + z^2/2*(prior_variance/(s^2+prior_variance))
  return(lbf)
}

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 logisticsusie
surv_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
  lbf <- compute_lbf(zscore, sd, prior_variance)
  lbf.corr <- lbf - bhat^2/sd^2/2+ summary(fit)$logtest[1]/2
  var <- compute_approx_post_var(zscore, sd, prior_variance)
  mu <- compute_approx_post_mean(var, sd, bhat)
  return(list(mu = mu, var=var, lbf=lbf.corr, 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]]$y
# IBSS of susie
set.seed(1)
fit1 <- ibss_from_ser(X, y, L = 1, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)
1.791 sec elapsed
par(mfrow = c(1,2))
hist(fit1$alpha, breaks = 20)
hist(fit1$mu* fit1$alpha, breaks = 20)

Version Author Date
ea24571 yunqiyang0215 2023-04-14
7fc8ac9 yunqiyang0215 2023-02-23
7a533c6 yunqiyang0215 2023-02-21
fa55cee yunqiyang0215 2023-02-15

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)
8.951 sec elapsed
t2 <- proc.time()
t(apply(fit2$alpha, 1, function(x) sort(x, decreasing = TRUE)))
           [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
[1,] 0.06368851 0.04802958 0.02913436 0.02796950 0.02618090 0.02466443
[2,] 0.06047537 0.04590021 0.02871672 0.02765142 0.02579570 0.02452988
[3,] 0.06006763 0.04558375 0.02865655 0.02759997 0.02573326 0.02450743
[4,] 0.05989448 0.04542096 0.02862764 0.02757228 0.02569902 0.02449542
[5,] 0.05974755 0.04527704 0.02860237 0.02754755 0.02566839 0.02448468
           [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,] 0.02397859 0.02345858 0.02285416 0.02224116 0.02194645 0.02151051
[2,] 0.02380903 0.02341834 0.02272439 0.02218136 0.02190995 0.02148081
[3,] 0.02378181 0.02340480 0.02270128 0.02217108 0.02190746 0.02146982
[4,] 0.02376735 0.02339450 0.02268770 0.02216548 0.02190815 0.02146104
[5,] 0.02375446 0.02338477 0.02267542 0.02216046 0.02190907 0.02145273
          [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
[1,] 0.02064813 0.02025334 0.01992059 0.01888059 0.01866199 0.01865506
[2,] 0.02071544 0.02031118 0.01998635 0.01899466 0.01877445 0.01875909
[3,] 0.02071885 0.02031735 0.01999636 0.01900992 0.01878766 0.01877487
[4,] 0.02071748 0.02031955 0.02000180 0.01901697 0.01879263 0.01878317
[5,] 0.02071572 0.02032131 0.02000665 0.01902306 0.01879672 0.01879055
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,] 0.01826220 0.01818305 0.01808749 0.01798445 0.01768478 0.01755945
[2,] 0.01840019 0.01830835 0.01822728 0.01814709 0.01784869 0.01774461
[3,] 0.01841640 0.01832324 0.01824642 0.01816889 0.01786961 0.01777124
[4,] 0.01842249 0.01832891 0.01825538 0.01817885 0.01787849 0.01778436
[5,] 0.01842750 0.01833359 0.01826314 0.01818744 0.01788603 0.01779586
          [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
[1,] 0.01743423 0.01719726 0.01719235 0.01680875 0.01675892 0.01659271
[2,] 0.01760102 0.01737357 0.01736935 0.01700166 0.01695079 0.01679251
[3,] 0.01762538 0.01739995 0.01739286 0.01702923 0.01697788 0.01682137
[4,] 0.01763758 0.01741310 0.01740373 0.01704266 0.01699089 0.01683556
[5,] 0.01764833 0.01742466 0.01741313 0.01705441 0.01700223 0.01684801
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,] 0.01656479 0.01647769 0.01640428 0.01639075 0.01629782 0.01628327
[2,] 0.01676407 0.01668004 0.01661294 0.01659867 0.01650864 0.01649537
[3,] 0.01679290 0.01670988 0.01664331 0.01662846 0.01653915 0.01652573
[4,] 0.01680710 0.01672488 0.01665838 0.01664297 0.01655416 0.01654049
[5,] 0.01681956 0.01673810 0.01667162 0.01665567 0.01656734 0.01655341
          [,37]      [,38]      [,39]      [,40]      [,41]      [,42]
[1,] 0.01620079 0.01614771 0.01603969 0.01599384 0.01590029 0.01585428
[2,] 0.01641860 0.01636489 0.01626341 0.01621718 0.01612495 0.01608277
[3,] 0.01644901 0.01639628 0.01629648 0.01624999 0.01615909 0.01611585
[4,] 0.01646337 0.01641170 0.01631313 0.01626639 0.01617675 0.01613211
[5,] 0.01647587 0.01642522 0.01632782 0.01628083 0.01619239 0.01614637
          [,43]      [,44]      [,45]      [,46]      [,47]      [,48]
[1,] 0.01574695 0.01558757 0.01550994 0.01533760 0.01528081 0.01527380
[2,] 0.01598098 0.01582239 0.01575005 0.01558145 0.01552650 0.01552149
[3,] 0.01601532 0.01585809 0.01578707 0.01561812 0.01556353 0.01555776
[4,] 0.01603245 0.01587653 0.01580646 0.01563683 0.01558247 0.01557576
[5,] 0.01604751 0.01589288 0.01582369 0.01565338 0.01559922 0.01559158
          [,49]      [,50]
[1,] 0.01517476 0.01511132
[2,] 0.01542345 0.01536270
[3,] 0.01546114 0.01540057
[4,] 0.01548052 0.01541992
[5,] 0.01549769 0.01543703
beta <- colSums(fit2$alpha * fit2$mu)
pip <- logisticsusie:::get_pip(fit2$alpha)
pip
 [1] 0.09748285 0.07799943 0.09599781 0.07518383 0.07911623 0.07469998
 [7] 0.13089440 0.10859316 0.11680743 0.09031150 0.20996861 0.10286113
[13] 0.07979130 0.09931725 0.08556686 0.08604348 0.07441235 0.07544199
[19] 0.12258281 0.08028092 0.07864310 0.08186057 0.08059893 0.07731492
[25] 0.08819061 0.08861001 0.07842552 0.07657791 0.10610624 0.08782141
[31] 0.08021170 0.13570771 0.07623986 0.08490666 0.08384156 0.09035850
[37] 0.11170651 0.07515363 0.08098953 0.08381612 0.09138866 0.07972689
[43] 0.26911978 0.08112200 0.08743763 0.11355168 0.07936132 0.08209964
[49] 0.10488200 0.07779130
hist(beta, breaks = 20)

Version Author Date
ea24571 yunqiyang0215 2023-04-14
7fc8ac9 yunqiyang0215 2023-02-23
babbca4 yunqiyang0215 2023-02-21

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]]$y
# IBSS of susie
set.seed(1)
fit1 <- ibss_from_ser(X, y, L = 1, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)
0.921 sec elapsed
par(mfrow = c(1,2))
hist(fit1$alpha, breaks = 20)
hist(fit1$mu* fit1$alpha, breaks = 20)

Version Author Date
ea24571 yunqiyang0215 2023-04-14
7fc8ac9 yunqiyang0215 2023-02-23
2edb747 yunqiyang0215 2023-02-21

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)
6.088 sec elapsed
t2 <- proc.time()
t(apply(fit2$alpha, 1, function(x) sort(x, decreasing = TRUE)))
           [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
[1,] 0.02881676 0.02485934 0.02384393 0.02334564 0.02306719 0.02293221
[2,] 0.02462537 0.02260902 0.02201792 0.02177196 0.02154821 0.02153039
[3,] 0.02449712 0.02253777 0.02196273 0.02172522 0.02150021 0.02148359
[4,] 0.02441036 0.02248939 0.02192571 0.02169407 0.02146751 0.02145137
[5,] 0.02433602 0.02244796 0.02189397 0.02166738 0.02143942 0.02142371
           [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,] 0.02262641 0.02259612 0.02255042 0.02213961 0.02128135 0.02127131
[2,] 0.02135479 0.02134657 0.02134169 0.02109122 0.02064704 0.02064476
[3,] 0.02131475 0.02130899 0.02130106 0.02105802 0.02062942 0.02062551
[4,] 0.02128745 0.02128359 0.02127345 0.02103549 0.02061780 0.02061285
[5,] 0.02126401 0.02126183 0.02124973 0.02101611 0.02060782 0.02060197
          [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
[1,] 0.02125440 0.02124881 0.02085620 0.02079462 0.02063354 0.02061058
[2,] 0.02064444 0.02064149 0.02042332 0.02042102 0.02034106 0.02031477
[3,] 0.02062366 0.02062180 0.02041314 0.02040960 0.02033073 0.02030756
[4,] 0.02060916 0.02060840 0.02040687 0.02040200 0.02032363 0.02030310
[5,] 0.02059688 0.02059668 0.02040151 0.02039548 0.02031751 0.02029931
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,] 0.02038459 0.01991267 0.01980673 0.01971735 0.01968219 0.01966548
[2,] 0.02017470 0.01994861 0.01992506 0.01984147 0.01979871 0.01979133
[3,] 0.02016826 0.01994977 0.01992614 0.01984597 0.01980357 0.01979833
[4,] 0.02016391 0.01995062 0.01992654 0.01984915 0.01980705 0.01980361
[5,] 0.02016016 0.01995134 0.01992685 0.01985189 0.01981003 0.01980817
          [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
[1,] 0.01949482 0.01947690 0.01923563 0.01905372 0.01902366 0.01881856
[2,] 0.01973149 0.01967257 0.01957180 0.01950152 0.01946188 0.01936032
[3,] 0.01973923 0.01968204 0.01958415 0.01951478 0.01947653 0.01937898
[4,] 0.01974456 0.01968896 0.01959280 0.01952363 0.01948657 0.01939188
[5,] 0.01974914 0.01969493 0.01960024 0.01953120 0.01949519 0.01940298
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,] 0.01872413 0.01872002 0.01863835 0.01853535 0.01849969 0.01840709
[2,] 0.01935580 0.01929735 0.01927773 0.01921812 0.01920740 0.01917460
[3,] 0.01937359 0.01931772 0.01929865 0.01924092 0.01923014 0.01919797
[4,] 0.01938536 0.01933185 0.01931296 0.01925659 0.01924564 0.01921370
[5,] 0.01939543 0.01934401 0.01932525 0.01927005 0.01925894 0.01922719
          [,37]      [,38]      [,39]      [,40]      [,41]      [,42]
[1,] 0.01834207 0.01826280 0.01824219 0.01822804 0.01822594 0.01822192
[2,] 0.01913922 0.01912962 0.01910646 0.01909883 0.01907547 0.01901828
[3,] 0.01916326 0.01915454 0.01913184 0.01912446 0.01910196 0.01904707
[4,] 0.01917905 0.01917145 0.01914877 0.01914155 0.01911988 0.01906715
[5,] 0.01919253 0.01918597 0.01916328 0.01915619 0.01913525 0.01908445
          [,43]      [,44]      [,45]      [,46]      [,47]      [,48]
[1,] 0.01793771 0.01791748 0.01789232 0.01769225 0.01745322 0.01739444
[2,] 0.01900970 0.01890939 0.01884429 0.01877641 0.01870756 0.01870234
[3,] 0.01903763 0.01894086 0.01887819 0.01881171 0.01874460 0.01873949
[4,] 0.01905564 0.01896231 0.01890172 0.01883576 0.01876931 0.01876403
[5,] 0.01907099 0.01898073 0.01892200 0.01885643 0.01879047 0.01878504
          [,49]      [,50]
[1,] 0.01704101 0.01662323
[2,] 0.01861543 0.01824153
[3,] 0.01865508 0.01829168
[4,] 0.01868045 0.01832537
[5,] 0.01870207 0.01835430
beta <- colSums(fit2$alpha * fit2$mu)
pip <- logisticsusie:::get_pip(fit2$alpha)
pip
 [1] 0.08910855 0.09503361 0.10326712 0.09271018 0.09384918 0.09186725
 [7] 0.10545318 0.10320685 0.10978083 0.09139977 0.08839303 0.10418722
[13] 0.09239397 0.10191275 0.09953890 0.08957917 0.09581446 0.09325685
[19] 0.10437165 0.09144306 0.09831169 0.09525417 0.09443196 0.09166243
[25] 0.09704879 0.09126609 0.09787318 0.09506558 0.10324446 0.09122015
[31] 0.09194057 0.10676993 0.09028244 0.09950294 0.09777081 0.09953811
[37] 0.08666645 0.09562837 0.09342421 0.09465719 0.09838381 0.09224778
[43] 0.12043357 0.09260067 0.09953853 0.09061666 0.09001125 0.09114191
[49] 0.08903452 0.09094407
hist(beta, breaks = 20)

Version Author Date
ea24571 yunqiyang0215 2023-04-14
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)
12.232 sec elapsed
t2 <- proc.time()
t2 - t1
   user  system elapsed 
 11.973   0.162  12.235 
fit3$alpha
           [,1]         [,2]         [,3]         [,4]         [,5]
[1,] 1.00000000 3.073730e-47 1.298948e-46 1.595314e-47 1.525453e-47
[2,] 0.01951114 1.658570e-02 2.395650e-02 1.673006e-02 1.803249e-02
[3,] 0.01950431 1.656358e-02 2.397881e-02 1.670870e-02 1.801632e-02
[4,] 0.01949572 1.653197e-02 2.401069e-02 1.667816e-02 1.799372e-02
[5,] 0.01948719 1.650150e-02 2.404134e-02 1.664872e-02 1.797177e-02
             [,6]         [,7]         [,8]         [,9]        [,10]
[1,] 1.439780e-47 1.517504e-47 1.637731e-47 2.331776e-47 1.425913e-47
[2,] 1.713214e-02 2.301498e-02 1.915718e-02 2.070524e-02 1.967524e-02
[3,] 1.711372e-02 2.302971e-02 1.914827e-02 2.070528e-02 1.967269e-02
[4,] 1.708706e-02 2.305054e-02 1.913615e-02 2.070536e-02 1.966878e-02
[5,] 1.706141e-02 2.307047e-02 1.912429e-02 2.070532e-02 1.966503e-02
            [,11]        [,12]        [,13]        [,14]        [,15]
[1,] 1.725218e-47 1.487990e-47 1.523747e-47 1.289493e-47 1.332745e-47
[2,] 3.422323e-02 1.818470e-02 1.733025e-02 3.101637e-02 1.584878e-02
[3,] 3.433157e-02 1.816977e-02 1.731171e-02 3.108579e-02 1.582422e-02
[4,] 3.449046e-02 1.814886e-02 1.728531e-02 3.118648e-02 1.578891e-02
[5,] 3.464350e-02 1.812856e-02 1.725982e-02 3.128294e-02 1.575496e-02
            [,16]        [,17]        [,18]        [,19]        [,20]
[1,] 1.438722e-47 2.876329e-47 4.993311e-47 1.976118e-47 1.591846e-47
[2,] 1.805333e-02 1.633550e-02 1.676786e-02 1.842894e-02 1.695975e-02
[3,] 1.803682e-02 1.631263e-02 1.674674e-02 1.841812e-02 1.693934e-02
[4,] 1.801376e-02 1.627984e-02 1.671651e-02 1.840245e-02 1.691022e-02
[5,] 1.799135e-02 1.624827e-02 1.668738e-02 1.838735e-02 1.688212e-02
            [,21]        [,22]        [,23]        [,24]        [,25]
[1,] 1.840754e-47 1.978865e-47 1.729242e-47 1.314026e-47 2.959457e-47
[2,] 1.849329e-02 1.744090e-02 1.853372e-02 1.683794e-02 1.786690e-02
[3,] 1.848252e-02 1.742258e-02 1.852281e-02 1.681637e-02 1.785056e-02
[4,] 1.846649e-02 1.739661e-02 1.850721e-02 1.678565e-02 1.782760e-02
[5,] 1.845109e-02 1.737151e-02 1.849212e-02 1.675600e-02 1.780536e-02
            [,26]        [,27]        [,28]        [,29]        [,30]
[1,] 1.754919e-47 1.299432e-47 1.966159e-47 1.433306e-47 1.722858e-47
[2,] 1.842826e-02 1.644831e-02 1.940127e-02 2.054548e-02 1.733933e-02
[3,] 1.841425e-02 1.642575e-02 1.939566e-02 2.054727e-02 1.732056e-02
[4,] 1.839481e-02 1.639346e-02 1.938715e-02 2.054954e-02 1.729389e-02
[5,] 1.837589e-02 1.636236e-02 1.937895e-02 2.055170e-02 1.726813e-02
            [,31]        [,32]        [,33]        [,34]        [,35]
[1,] 1.408407e-47 4.600677e-47 3.646996e-47 1.842043e-47 1.513775e-47
[2,] 1.698187e-02 2.441334e-02 1.871990e-02 1.794232e-02 2.166908e-02
[3,] 1.696154e-02 2.444330e-02 1.870904e-02 1.792683e-02 2.167734e-02
[4,] 1.693254e-02 2.448542e-02 1.869311e-02 1.790484e-02 2.168869e-02
[5,] 1.690457e-02 2.452609e-02 1.867769e-02 1.788356e-02 2.169958e-02
            [,36]        [,37]        [,38]        [,39]        [,40]
[1,] 9.133164e-47 1.126210e-47 1.441175e-47 2.221720e-47 1.697772e-47
[2,] 1.980086e-02 1.653337e-02 1.884905e-02 1.744059e-02 1.806443e-02
[3,] 1.979326e-02 1.651083e-02 1.883538e-02 1.742231e-02 1.804915e-02
[4,] 1.978340e-02 1.647864e-02 1.881669e-02 1.739639e-02 1.802776e-02
[5,] 1.977361e-02 1.644762e-02 1.879839e-02 1.737134e-02 1.800701e-02
            [,41]        [,42]        [,43]        [,44]        [,45]
[1,] 1.354994e-47 1.841670e-47 2.239157e-47 1.727746e-47 1.502923e-47
[2,] 1.956936e-02 1.697079e-02 4.390237e-02 1.682193e-02 2.611133e-02
[3,] 1.956454e-02 1.694983e-02 4.411027e-02 1.680081e-02 2.614739e-02
[4,] 1.955710e-02 1.692010e-02 4.439978e-02 1.677068e-02 2.619950e-02
[5,] 1.954992e-02 1.689138e-02 4.468211e-02 1.674162e-02 2.624941e-02
            [,46]        [,47]        [,48]        [,49]        [,50]
[1,] 1.882920e-47 1.400435e-47 1.510961e-47 1.563912e-46 2.873710e-47
[2,] 2.981733e-02 1.697265e-02 2.111409e-02 2.183384e-02 1.748672e-02
[3,] 2.989799e-02 1.695177e-02 2.112033e-02 2.184331e-02 1.746831e-02
[4,] 3.001267e-02 1.692213e-02 2.112880e-02 2.185608e-02 1.744232e-02
[5,] 3.012363e-02 1.689351e-02 2.113695e-02 2.186842e-02 1.741717e-02
beta <- colSums(fit3$alpha * fit3$mu)
pip <- logisticsusie:::get_pip(fit3$alpha)
pip
 [1] 1.00000000 0.06455824 0.09258720 0.06511255 0.07009277 0.06666008
 [7] 0.08902890 0.07439542 0.08028426 0.07639048 0.13074123 0.07067746
[13] 0.06741263 0.11887220 0.06173396 0.07016943 0.06360049 0.06525786
[19] 0.07162831 0.06599244 0.07187091 0.06783440 0.07202451 0.06552160
[25] 0.06946394 0.07160594 0.06403224 0.07533604 0.07969507 0.06744567
[31] 0.06607708 0.09433457 0.07272766 0.06975490 0.08395416 0.07683264
[37] 0.06435630 0.07319983 0.06783349 0.07021971 0.07597510 0.06603108
[43] 0.16567705 0.06546371 0.10066754 0.11457178 0.06603864 0.08186008
[49] 0.08457850 0.06800792
hist(beta, breaks = 20)

Version Author Date
ea24571 yunqiyang0215 2023-04-14
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)
Warning in coxph.fit(X, Y, istrat, offset, init, control, weights = weights, :
Loglik converged before variable 1 ; coefficient may be infinite.
49.314 sec elapsed
t2 <- proc.time()
t2 - t1
   user  system elapsed 
 32.055   0.974  49.322 
t(apply(fit4$alpha, 1, function(x) sort(x, decreasing = TRUE)))
           [,1]         [,2]         [,3]         [,4]         [,5]
[1,] 1.00000000 5.740795e-18 2.637565e-18 1.665748e-19 8.117544e-20
[2,] 0.02535279 2.211503e-02 2.189982e-02 2.176016e-02 2.149363e-02
[3,] 0.02483087 2.193155e-02 2.174861e-02 2.160029e-02 2.136322e-02
[4,] 0.02468071 2.187895e-02 2.170576e-02 2.155438e-02 2.132584e-02
[5,] 0.02460813 2.185378e-02 2.168562e-02 2.153238e-02 2.130792e-02
             [,6]         [,7]         [,8]         [,9]        [,10]
[1,] 6.771053e-20 5.948093e-20 5.485413e-20 5.449799e-20 4.733259e-20
[2,] 2.126097e-02 2.117924e-02 2.113293e-02 2.111570e-02 2.065213e-02
[3,] 2.110690e-02 2.104593e-02 2.102919e-02 2.100177e-02 2.060169e-02
[4,] 2.106198e-02 2.100737e-02 2.100482e-02 2.096349e-02 2.058754e-02
[5,] 2.103996e-02 2.099347e-02 2.098866e-02 2.094467e-02 2.058102e-02
            [,11]        [,12]        [,13]        [,14]        [,15]
[1,] 2.579566e-20 2.481952e-20 1.744179e-20 9.605000e-21 8.725733e-21
[2,] 2.048402e-02 2.038262e-02 2.018086e-02 2.017778e-02 2.006881e-02
[3,] 2.042979e-02 2.035300e-02 2.016685e-02 2.016474e-02 2.005839e-02
[4,] 2.041391e-02 2.034484e-02 2.016387e-02 2.016018e-02 2.005563e-02
[5,] 2.040611e-02 2.034119e-02 2.016254e-02 2.015805e-02 2.005445e-02
            [,16]        [,17]        [,18]        [,19]        [,20]
[1,] 4.020765e-21 3.267914e-21 3.121848e-21 2.614214e-21 2.204486e-21
[2,] 2.004710e-02 2.001459e-02 1.998622e-02 1.998599e-02 1.997099e-02
[3,] 2.004256e-02 2.001327e-02 1.999064e-02 1.998714e-02 1.997543e-02
[4,] 2.004133e-02 2.001291e-02 1.999226e-02 1.998780e-02 1.997712e-02
[5,] 2.004079e-02 2.001276e-02 1.999327e-02 1.998833e-02 1.997820e-02
            [,21]        [,22]        [,23]        [,24]        [,25]
[1,] 1.844560e-21 1.531344e-21 6.819790e-22 6.309838e-22 4.292884e-22
[2,] 1.992869e-02 1.989747e-02 1.988841e-02 1.987104e-02 1.986043e-02
[3,] 1.993344e-02 1.989800e-02 1.989332e-02 1.988232e-02 1.987247e-02
[4,] 1.993499e-02 1.990087e-02 1.989183e-02 1.988581e-02 1.987604e-02
[5,] 1.993584e-02 1.990234e-02 1.989093e-02 1.988764e-02 1.987783e-02
            [,26]        [,27]        [,28]        [,29]        [,30]
[1,] 4.170235e-22 3.510403e-22 3.282266e-22 3.219393e-22 3.065963e-22
[2,] 1.974412e-02 1.960537e-02 1.958490e-02 1.955139e-02 1.953466e-02
[3,] 1.976807e-02 1.965402e-02 1.962160e-02 1.959427e-02 1.957773e-02
[4,] 1.977514e-02 1.966690e-02 1.963217e-02 1.960675e-02 1.959066e-02
[5,] 1.977865e-02 1.967249e-02 1.963725e-02 1.961284e-02 1.959719e-02
            [,31]        [,32]        [,33]        [,34]        [,35]
[1,] 2.833471e-22 1.678212e-22 1.543826e-22 1.508822e-22 1.306414e-22
[2,] 1.951694e-02 1.943234e-02 1.932442e-02 1.932158e-02 1.928509e-02
[3,] 1.956404e-02 1.948586e-02 1.938978e-02 1.938483e-02 1.935184e-02
[4,] 1.957760e-02 1.950135e-02 1.940855e-02 1.940333e-02 1.937121e-02
[5,] 1.958414e-02 1.950886e-02 1.941756e-02 1.941241e-02 1.938063e-02
            [,36]        [,37]        [,38]        [,39]        [,40]
[1,] 7.023907e-23 4.810587e-23 4.360302e-23 4.354370e-23 2.219068e-23
[2,] 1.928319e-02 1.925504e-02 1.925114e-02 1.922552e-02 1.916248e-02
[3,] 1.934892e-02 1.933605e-02 1.932707e-02 1.929779e-02 1.923972e-02
[4,] 1.936782e-02 1.935897e-02 1.934764e-02 1.931859e-02 1.926203e-02
[5,] 1.937691e-02 1.936917e-02 1.935744e-02 1.932860e-02 1.927280e-02
            [,41]        [,42]        [,43]        [,44]        [,45]
[1,] 1.015248e-23 9.985132e-24 7.179473e-24 1.437682e-24 1.383195e-24
[2,] 1.916070e-02 1.915298e-02 1.912162e-02 1.910818e-02 1.906794e-02
[3,] 1.923876e-02 1.923482e-02 1.920361e-02 1.919048e-02 1.916144e-02
[4,] 1.926134e-02 1.925809e-02 1.922733e-02 1.921430e-02 1.918755e-02
[5,] 1.927226e-02 1.926913e-02 1.923881e-02 1.922583e-02 1.919968e-02
            [,46]        [,47]        [,48]        [,49]        [,50]
[1,] 1.236411e-24 7.838517e-25 7.581654e-25 3.785880e-25 1.837366e-25
[2,] 1.903668e-02 1.899575e-02 1.889126e-02 1.885281e-02 1.882647e-02
[3,] 1.913109e-02 1.908956e-02 1.898955e-02 1.896068e-02 1.893708e-02
[4,] 1.915768e-02 1.911649e-02 1.901836e-02 1.899140e-02 1.896853e-02
[5,] 1.917015e-02 1.912940e-02 1.903250e-02 1.900600e-02 1.898343e-02
beta <- colSums(fit4$alpha * fit4$mu)
pip <- logisticsusie:::get_pip(fit4$alpha)
pip
 [1] 1.00000000 0.07753935 0.08152519 0.07517171 0.07768222 0.07417394
 [7] 0.08493192 0.08278872 0.08368496 0.07472485 0.07510245 0.08143107
[13] 0.07619655 0.07926263 0.07990966 0.07368276 0.07759643 0.07516047
[19] 0.08159840 0.07496586 0.07896915 0.07718639 0.07785514 0.07474562
[25] 0.07675243 0.07568054 0.07714869 0.07723041 0.08183161 0.07531462
[31] 0.07609226 0.08423983 0.07379680 0.07758409 0.07825647 0.07738047
[37] 0.07359270 0.07779350 0.07597679 0.07826325 0.07603100 0.07474187
[43] 0.09582325 0.07507592 0.07724554 0.07444330 0.07455860 0.07460819
[49] 0.07432910 0.07529750
hist(beta, breaks = 20)

Version Author Date
ea24571 yunqiyang0215 2023-04-14
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)
16.937 sec elapsed
t2 <- proc.time()
t2 - t1
   user  system elapsed 
 14.270   0.235  16.940 
fit5$alpha
             [,1]         [,2]         [,3]         [,4]         [,5]
[1,] 1.000000e+00 3.372584e-22 4.338680e-22 6.442686e-20 1.198643e-20
[2,] 2.314709e-06 9.980772e-01 3.999939e-06 1.015279e-05 2.543360e-06
[3,] 2.023041e-02 1.975990e-02 2.027852e-02 1.965712e-02 2.051472e-02
[4,] 2.022883e-02 1.976018e-02 2.027864e-02 1.965854e-02 2.051377e-02
[5,] 2.022805e-02 1.975930e-02 2.028011e-02 1.965847e-02 2.051516e-02
             [,6]         [,7]         [,8]         [,9]        [,10]
[1,] 3.335693e-20 1.088764e-20 6.034760e-21 2.682378e-22 2.421118e-20
[2,] 9.346136e-06 2.368570e-06 2.804041e-06 7.369128e-06 2.742442e-04
[3,] 1.961277e-02 2.089848e-02 2.089016e-02 1.987816e-02 1.992214e-02
[4,] 1.961377e-02 2.089625e-02 2.088743e-02 1.987974e-02 1.992149e-02
[5,] 1.961305e-02 2.089827e-02 2.088904e-02 1.988087e-02 1.992028e-02
            [,11]        [,12]        [,13]        [,14]        [,15]
[1,] 5.109136e-17 7.803619e-22 3.553549e-19 6.273264e-21 5.988086e-22
[2,] 1.928072e-04 2.725114e-06 1.869467e-04 1.020812e-06 1.067675e-05
[3,] 2.142928e-02 2.102102e-02 1.984485e-02 2.100076e-02 1.979331e-02
[4,] 2.142109e-02 2.101582e-02 1.984513e-02 2.099791e-02 1.979495e-02
[5,] 2.141676e-02 2.101691e-02 1.984464e-02 2.099976e-02 1.979576e-02
            [,16]        [,17]        [,18]        [,19]        [,20]
[1,] 3.620424e-19 1.934700e-22 1.876669e-18 2.203600e-20 1.839880e-19
[2,] 9.391147e-05 5.256012e-05 7.775184e-06 2.008392e-05 3.078186e-05
[3,] 2.010027e-02 1.961979e-02 1.964878e-02 1.999119e-02 1.978466e-02
[4,] 2.009824e-02 1.962176e-02 1.965015e-02 1.999177e-02 1.978478e-02
[5,] 2.009607e-02 1.962215e-02 1.965000e-02 1.999246e-02 1.978384e-02
            [,21]        [,22]        [,23]        [,24]        [,25]
[1,] 3.235812e-21 2.631211e-20 1.097206e-18 9.233284e-21 1.021010e-20
[2,] 1.264410e-05 6.916387e-06 2.273538e-05 2.046398e-05 3.864478e-05
[3,] 1.955006e-02 1.999158e-02 1.965175e-02 1.954678e-02 1.985006e-02
[4,] 1.955199e-02 1.999224e-02 1.965342e-02 1.954842e-02 1.985096e-02
[5,] 1.955202e-02 1.999299e-02 1.965362e-02 1.954812e-02 1.985122e-02
            [,26]        [,27]        [,28]        [,29]        [,30]
[1,] 9.419822e-21 2.282061e-20 1.688438e-18 1.335006e-20 1.420325e-20
[2,] 4.111929e-05 5.476202e-06 2.782407e-06 8.372804e-06 2.622364e-05
[3,] 1.975333e-02 1.962608e-02 1.985813e-02 2.017075e-02 1.981442e-02
[4,] 1.975348e-02 1.962780e-02 1.985903e-02 2.017063e-02 1.981447e-02
[5,] 1.975243e-02 1.962793e-02 1.985940e-02 2.017158e-02 1.981359e-02
            [,31]        [,32]        [,33]        [,34]        [,35]
[1,] 2.346064e-19 1.001472e-22 8.630311e-23 2.938954e-20 3.674709e-20
[2,] 1.042339e-05 3.986226e-06 4.066566e-05 2.640814e-06 6.467632e-06
[3,] 1.973743e-02 2.083151e-02 1.936865e-02 1.970238e-02 1.991180e-02
[4,] 1.973851e-02 2.083062e-02 1.937067e-02 1.970434e-02 1.991268e-02
[5,] 1.973842e-02 2.083329e-02 1.937005e-02 1.970510e-02 1.991320e-02
            [,36]        [,37]        [,38]        [,39]        [,40]
[1,] 3.565711e-21 1.989030e-18 1.350980e-21 3.386334e-21 3.881062e-20
[2,] 3.202825e-05 8.320109e-05 7.600211e-05 8.445745e-05 1.390734e-05
[3,] 1.977077e-02 2.020180e-02 1.967563e-02 1.981435e-02 1.997168e-02
[4,] 1.977199e-02 2.019925e-02 1.967685e-02 1.981484e-02 1.997214e-02
[5,] 1.977225e-02 2.019691e-02 1.967663e-02 1.981444e-02 1.997244e-02
            [,41]        [,42]        [,43]        [,44]        [,45]
[1,] 1.917214e-19 1.967009e-19 8.823268e-22 2.097414e-21 9.747863e-22
[2,] 1.895949e-06 1.113324e-04 1.824605e-06 1.588246e-05 1.232920e-05
[3,] 1.989231e-02 1.980626e-02 2.117094e-02 1.972711e-02 1.986800e-02
[4,] 1.989372e-02 1.980618e-02 2.116741e-02 1.972810e-02 1.986888e-02
[5,] 1.989476e-02 1.980511e-02 2.116990e-02 1.972786e-02 1.986925e-02
            [,46]        [,47]        [,48]        [,49]        [,50]
[1,] 1.256020e-20 7.219380e-19 2.464274e-21 4.259661e-17 4.480929e-21
[2,] 2.413593e-05 1.911675e-04 7.367668e-05 6.071931e-06 3.092555e-05
[3,] 1.978526e-02 2.004756e-02 1.963934e-02 1.973912e-02 1.964885e-02
[4,] 1.978522e-02 2.004599e-02 1.964045e-02 1.973935e-02 1.965012e-02
[5,] 1.978409e-02 2.004429e-02 1.963995e-02 1.973833e-02 1.964985e-02
t(apply(fit5$alpha, 1, function(x) sort(x, decreasing = TRUE)))
           [,1]         [,2]         [,3]         [,4]         [,5]
[1,] 1.00000000 5.109136e-17 4.259661e-17 1.989030e-18 1.876669e-18
[2,] 0.99807717 2.742442e-04 1.928072e-04 1.911675e-04 1.869467e-04
[3,] 0.02142928 2.117094e-02 2.102102e-02 2.100076e-02 2.089848e-02
[4,] 0.02142109 2.116741e-02 2.101582e-02 2.099791e-02 2.089625e-02
[5,] 0.02141676 2.116990e-02 2.101691e-02 2.099976e-02 2.089827e-02
             [,6]         [,7]         [,8]         [,9]        [,10]
[1,] 1.688438e-18 1.097206e-18 7.219380e-19 3.620424e-19 3.553549e-19
[2,] 1.113324e-04 9.391147e-05 8.445745e-05 8.320109e-05 7.600211e-05
[3,] 2.089016e-02 2.083151e-02 2.051472e-02 2.027852e-02 2.023041e-02
[4,] 2.088743e-02 2.083062e-02 2.051377e-02 2.027864e-02 2.022883e-02
[5,] 2.088904e-02 2.083329e-02 2.051516e-02 2.028011e-02 2.022805e-02
            [,11]        [,12]        [,13]        [,14]        [,15]
[1,] 2.346064e-19 1.967009e-19 1.917214e-19 1.839880e-19 6.442686e-20
[2,] 7.367668e-05 5.256012e-05 4.111929e-05 4.066566e-05 3.864478e-05
[3,] 2.020180e-02 2.017075e-02 2.010027e-02 2.004756e-02 1.999158e-02
[4,] 2.019925e-02 2.017063e-02 2.009824e-02 2.004599e-02 1.999224e-02
[5,] 2.019691e-02 2.017158e-02 2.009607e-02 2.004429e-02 1.999299e-02
            [,16]        [,17]        [,18]        [,19]        [,20]
[1,] 3.881062e-20 3.674709e-20 3.335693e-20 2.938954e-20 2.631211e-20
[2,] 3.202825e-05 3.092555e-05 3.078186e-05 2.622364e-05 2.413593e-05
[3,] 1.999119e-02 1.997168e-02 1.992214e-02 1.991180e-02 1.989231e-02
[4,] 1.999177e-02 1.997214e-02 1.992149e-02 1.991268e-02 1.989372e-02
[5,] 1.999246e-02 1.997244e-02 1.992028e-02 1.991320e-02 1.989476e-02
            [,21]        [,22]        [,23]        [,24]        [,25]
[1,] 2.421118e-20 2.282061e-20 2.203600e-20 1.420325e-20 1.335006e-20
[2,] 2.273538e-05 2.046398e-05 2.008392e-05 1.588246e-05 1.390734e-05
[3,] 1.987816e-02 1.986800e-02 1.985813e-02 1.985006e-02 1.984485e-02
[4,] 1.987974e-02 1.986888e-02 1.985903e-02 1.985096e-02 1.984513e-02
[5,] 1.988087e-02 1.986925e-02 1.985940e-02 1.985122e-02 1.984464e-02
            [,26]        [,27]        [,28]        [,29]        [,30]
[1,] 1.256020e-20 1.198643e-20 1.088764e-20 1.021010e-20 9.419822e-21
[2,] 1.264410e-05 1.232920e-05 1.067675e-05 1.042339e-05 1.015279e-05
[3,] 1.981442e-02 1.981435e-02 1.980626e-02 1.979331e-02 1.978526e-02
[4,] 1.981484e-02 1.981447e-02 1.980618e-02 1.979495e-02 1.978522e-02
[5,] 1.981444e-02 1.981359e-02 1.980511e-02 1.979576e-02 1.978409e-02
            [,31]        [,32]        [,33]        [,34]        [,35]
[1,] 9.233284e-21 6.273264e-21 6.034760e-21 4.480929e-21 3.565711e-21
[2,] 9.346136e-06 8.372804e-06 7.775184e-06 7.369128e-06 6.916387e-06
[3,] 1.978466e-02 1.977077e-02 1.975990e-02 1.975333e-02 1.973912e-02
[4,] 1.978478e-02 1.977199e-02 1.976018e-02 1.975348e-02 1.973935e-02
[5,] 1.978384e-02 1.977225e-02 1.975930e-02 1.975243e-02 1.973842e-02
            [,36]        [,37]        [,38]        [,39]        [,40]
[1,] 3.386334e-21 3.235812e-21 2.464274e-21 2.097414e-21 1.350980e-21
[2,] 6.467632e-06 6.071931e-06 5.476202e-06 3.999939e-06 3.986226e-06
[3,] 1.973743e-02 1.972711e-02 1.970238e-02 1.967563e-02 1.965712e-02
[4,] 1.973851e-02 1.972810e-02 1.970434e-02 1.967685e-02 1.965854e-02
[5,] 1.973833e-02 1.972786e-02 1.970510e-02 1.967663e-02 1.965847e-02
            [,41]        [,42]        [,43]        [,44]        [,45]
[1,] 9.747863e-22 8.823268e-22 7.803619e-22 5.988086e-22 4.338680e-22
[2,] 2.804041e-06 2.782407e-06 2.725114e-06 2.640814e-06 2.543360e-06
[3,] 1.965175e-02 1.964885e-02 1.964878e-02 1.963934e-02 1.962608e-02
[4,] 1.965342e-02 1.965015e-02 1.965012e-02 1.964045e-02 1.962780e-02
[5,] 1.965362e-02 1.965000e-02 1.964985e-02 1.963995e-02 1.962793e-02
            [,46]        [,47]        [,48]        [,49]        [,50]
[1,] 3.372584e-22 2.682378e-22 1.934700e-22 1.001472e-22 8.630311e-23
[2,] 2.368570e-06 2.314709e-06 1.895949e-06 1.824605e-06 1.020812e-06
[3,] 1.961979e-02 1.961277e-02 1.955006e-02 1.954678e-02 1.936865e-02
[4,] 1.962176e-02 1.961377e-02 1.955199e-02 1.954842e-02 1.937067e-02
[5,] 1.962215e-02 1.961305e-02 1.955202e-02 1.954812e-02 1.937005e-02
beta <- colSums(fit5$alpha * fit5$mu)
pip <- logisticsusie:::get_pip(fit5$alpha)
pip
 [1] 1.00000000 0.99818891 0.05961565 0.05783198 0.06029214 0.05770192
 [7] 0.06139421 0.06136934 0.05846797 0.05883942 0.06308089 0.06174033
[13] 0.05853702 0.06168572 0.05822635 0.05917924 0.05776580 0.05780551
[19] 0.05880330 0.05821575 0.05752669 0.05879224 0.05782909 0.05752374
[25] 0.05841430 0.05813512 0.05773884 0.05840389 0.05930844 0.05829715
[31] 0.05806309 0.06120631 0.05702942 0.05795723 0.05856214 0.05818015
[37] 0.05946042 0.05794685 0.05835310 0.05874066 0.05850317 0.05835336
[43] 0.06217502 0.05803817 0.05844128 0.05821073 0.05912028 0.05783956
[49] 0.05806133 0.05782722
hist(beta, breaks = 20)

Version Author Date
ea24571 yunqiyang0215 2023-04-14
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_3.7.3        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_3.8.1     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