Apply SER module

Last updated: 2023-02-15

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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 logisticsusie

surv_uni_fun <- function(x, y, o, prior_variance, estimate_intercept = 0, ...){
  fit <- coxph(y~ x + 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
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)

0.974 sec elapsed

hist(fit1$alpha, breaks = 20)

Version	Author	Date
fa55cee	yunqiyang0215	2023-02-15

# 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)

166.351 sec elapsed

t2 <- proc.time()
t(apply(fit2$alpha, 1, function(x) sort(x, decreasing = TRUE)))

          [,1]       [,2]        [,3]         [,4]         [,5]         [,6]
[1,] 0.3201872 0.14395828 0.091173528 0.0675306806 0.0435699788 0.0324928040
[2,] 0.9380270 0.01056279 0.004659749 0.0043633568 0.0036519319 0.0028952734
[3,] 0.3201863 0.14405996 0.091192886 0.0675319224 0.0435749373 0.0324858331
[4,] 0.3202654 0.14458939 0.091268761 0.0675129544 0.0435869549 0.0324358403
[5,] 0.9830219 0.00216134 0.001380015 0.0006959555 0.0005651195 0.0005338577
             [,7]         [,8]         [,9]        [,10]        [,11]
[1,] 0.0319658542 0.0246220217 0.0238471602 0.0190600669 0.0187922033
[2,] 0.0028720533 0.0024827248 0.0021856415 0.0016265846 0.0015223691
[3,] 0.0319490685 0.0246178707 0.0238423810 0.0190505298 0.0187902696
[4,] 0.0318665215 0.0245912999 0.0238165657 0.0189969570 0.0187743884
[5,] 0.0005072184 0.0004958501 0.0004294527 0.0004172577 0.0003918185
            [,12]        [,13]        [,14]        [,15]        [,16]
[1,] 0.0172246101 0.0156892034 0.0143229969 0.0138053123 0.0126416916
[2,] 0.0014432943 0.0013535617 0.0013237170 0.0013004189 0.0012908938
[3,] 0.0172178251 0.0156858639 0.0143188873 0.0137983353 0.0126353832
[4,] 0.0171818579 0.0156637551 0.0142991020 0.0137628284 0.0126057862
[5,] 0.0003432337 0.0003213817 0.0003171534 0.0003163787 0.0003118893
            [,17]        [,18]        [,19]        [,20]        [,21]
[1,] 0.0114846767 0.0109778251 0.0109522809 0.0097539199 0.0073438848
[2,] 0.0011465746 0.0011414727 0.0010323238 0.0010296987 0.0009315128
[3,] 0.0114816403 0.0109721609 0.0109465895 0.0097493014 0.0073406756
[4,] 0.0114632905 0.0109420668 0.0109176415 0.0097266693 0.0073238146
[5,] 0.0003093339 0.0002965729 0.0002917439 0.0002879094 0.0002810426
            [,22]        [,23]        [,24]        [,25]        [,26]
[1,] 0.0058563061 0.0052791933 0.0047683259 0.0043382674 0.0043178089
[2,] 0.0007797500 0.0007415940 0.0007093584 0.0007085260 0.0006757508
[3,] 0.0058542931 0.0052759047 0.0047649574 0.0043355430 0.0043155599
[4,] 0.0058436863 0.0052599068 0.0047478990 0.0043226093 0.0043043382
[5,] 0.0002799291 0.0002760559 0.0002750040 0.0002678636 0.0002673743
            [,27]        [,28]        [,29]        [,30]        [,31]
[1,] 0.0036748727 0.0031771698 0.0025679166 0.0025219711 0.0024374083
[2,] 0.0006587700 0.0006406515 0.0005878769 0.0005306127 0.0004942152
[3,] 0.0036735496 0.0031755214 0.0025664852 0.0025205186 0.0024359192
[4,] 0.0036662093 0.0031668459 0.0025592941 0.0025131743 0.0024284466
[5,] 0.0002612222 0.0002506222 0.0002469951 0.0002370878 0.0002309457
            [,32]        [,33]        [,34]        [,35]        [,36]
[1,] 0.0020286433 0.0017719539 0.0016182168 0.0015405215 0.0014274127
[2,] 0.0004681445 0.0004528113 0.0003946111 0.0003943673 0.0003885699
[3,] 0.0020272193 0.0017705205 0.0016175532 0.0015397479 0.0014266920
[4,] 0.0020200113 0.0017637859 0.0016140274 0.0015357470 0.0014231315
[5,] 0.0002210837 0.0002197350 0.0002175597 0.0002155991 0.0002146579
            [,37]        [,38]        [,39]        [,40]        [,41]
[1,] 0.0014249748 0.0012089200 0.0011213411 0.0011068510 0.0009855017
[2,] 0.0003767287 0.0003752659 0.0003553673 0.0003551564 0.0003487148
[3,] 0.0014241278 0.0012083770 0.0011206546 0.0011061160 0.0009849461
[4,] 0.0014200506 0.0012056240 0.0011172374 0.0011025270 0.0009821769
[5,] 0.0002143267 0.0002086843 0.0002015862 0.0001944479 0.0001941168
            [,42]        [,43]        [,44]        [,45]        [,46]
[1,] 0.0009489153 0.0009058451 0.0007383022 0.0007284525 0.0006115750
[2,] 0.0003450335 0.0003366448 0.0003188689 0.0003099663 0.0002959457
[3,] 0.0009486874 0.0009052874 0.0007379278 0.0007279496 0.0006112308
[4,] 0.0009474186 0.0009025142 0.0007360426 0.0007253712 0.0006095155
[5,] 0.0001918138 0.0001913990 0.0001882584 0.0001851010 0.0001788870
            [,47]        [,48]        [,49]        [,50]
[1,] 0.0005222298 0.0003615688 0.0003295289 0.0002838575
[2,] 0.0002897974 0.0002866436 0.0002819833 0.0002553427
[3,] 0.0005217448 0.0003613356 0.0003293312 0.0002836486
[4,] 0.0005193692 0.0003601734 0.0003283488 0.0002826538
[5,] 0.0001764384 0.0001757427 0.0001756328 0.0001654527

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 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 = 10, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)

4.297 sec elapsed

t2 <- proc.time()
t2 - t1

   user  system elapsed 
  4.233   0.048   4.299

fit2$alpha

      [,1]         [,2]         [,3]         [,4]         [,5]         [,6]
 [1,]    1 1.703997e-25 5.945257e-25 1.755176e-25 2.288233e-25 1.925916e-25
 [2,]    1 1.703997e-25 5.945257e-25 1.755176e-25 2.288233e-25 1.925916e-25
 [3,]    1 1.703997e-25 5.945257e-25 1.755176e-25 2.288233e-25 1.925916e-25
 [4,]    1 1.703997e-25 5.945257e-25 1.755176e-25 2.288233e-25 1.925916e-25
 [5,]    1 1.703997e-25 5.945257e-25 1.755176e-25 2.288233e-25 1.925916e-25
 [6,]    1 1.703997e-25 5.945257e-25 1.755176e-25 2.288233e-25 1.925916e-25
 [7,]    1 1.703997e-25 5.945257e-25 1.755176e-25 2.288233e-25 1.925916e-25
 [8,]    1 1.703997e-25 5.945257e-25 1.755176e-25 2.288233e-25 1.925916e-25
 [9,]    1 1.703997e-25 5.945257e-25 1.755176e-25 2.288233e-25 1.925916e-25
[10,]    1 1.703997e-25 5.945257e-25 1.755176e-25 2.288233e-25 1.925916e-25
             [,7]        [,8]         [,9]        [,10]        [,11]
 [1,] 5.36994e-25 3.17988e-25 3.553885e-25 3.521652e-25 3.119528e-24
 [2,] 5.36994e-25 3.17988e-25 3.553885e-25 3.521652e-25 3.119528e-24
 [3,] 5.36994e-25 3.17988e-25 3.553885e-25 3.521652e-25 3.119528e-24
 [4,] 5.36994e-25 3.17988e-25 3.553885e-25 3.521652e-25 3.119528e-24
 [5,] 5.36994e-25 3.17988e-25 3.553885e-25 3.521652e-25 3.119528e-24
 [6,] 5.36994e-25 3.17988e-25 3.553885e-25 3.521652e-25 3.119528e-24
 [7,] 5.36994e-25 3.17988e-25 3.553885e-25 3.521652e-25 3.119528e-24
 [8,] 5.36994e-25 3.17988e-25 3.553885e-25 3.521652e-25 3.119528e-24
 [9,] 5.36994e-25 3.17988e-25 3.553885e-25 3.521652e-25 3.119528e-24
[10,] 5.36994e-25 3.17988e-25 3.553885e-25 3.521652e-25 3.119528e-24
             [,12]        [,13]       [,14]        [,15]        [,16]
 [1,] 2.389125e-25 2.004097e-25 1.27905e-24 1.499504e-25 2.233957e-25
 [2,] 2.389125e-25 2.004097e-25 1.27905e-24 1.499504e-25 2.233957e-25
 [3,] 2.389125e-25 2.004097e-25 1.27905e-24 1.499504e-25 2.233957e-25
 [4,] 2.389125e-25 2.004097e-25 1.27905e-24 1.499504e-25 2.233957e-25
 [5,] 2.389125e-25 2.004097e-25 1.27905e-24 1.499504e-25 2.233957e-25
 [6,] 2.389125e-25 2.004097e-25 1.27905e-24 1.499504e-25 2.233957e-25
 [7,] 2.389125e-25 2.004097e-25 1.27905e-24 1.499504e-25 2.233957e-25
 [8,] 2.389125e-25 2.004097e-25 1.27905e-24 1.499504e-25 2.233957e-25
 [9,] 2.389125e-25 2.004097e-25 1.27905e-24 1.499504e-25 2.233957e-25
[10,] 2.389125e-25 2.004097e-25 1.27905e-24 1.499504e-25 2.233957e-25
             [,17]        [,18]        [,19]        [,20]        [,21]
 [1,] 1.639732e-25 1.773557e-25 2.724362e-25 1.837206e-25 2.497231e-25
 [2,] 1.639732e-25 1.773557e-25 2.724362e-25 1.837206e-25 2.497231e-25
 [3,] 1.639732e-25 1.773557e-25 2.724362e-25 1.837206e-25 2.497231e-25
 [4,] 1.639732e-25 1.773557e-25 2.724362e-25 1.837206e-25 2.497231e-25
 [5,] 1.639732e-25 1.773557e-25 2.724362e-25 1.837206e-25 2.497231e-25
 [6,] 1.639732e-25 1.773557e-25 2.724362e-25 1.837206e-25 2.497231e-25
 [7,] 1.639732e-25 1.773557e-25 2.724362e-25 1.837206e-25 2.497231e-25
 [8,] 1.639732e-25 1.773557e-25 2.724362e-25 1.837206e-25 2.497231e-25
 [9,] 1.639732e-25 1.773557e-25 2.724362e-25 1.837206e-25 2.497231e-25
[10,] 1.639732e-25 1.773557e-25 2.724362e-25 1.837206e-25 2.497231e-25
             [,22]        [,23]        [,24]        [,25]        [,26]
 [1,] 2.040575e-25 2.688967e-25 1.760976e-25 2.269901e-25 2.485756e-25
 [2,] 2.040575e-25 2.688967e-25 1.760976e-25 2.269901e-25 2.485756e-25
 [3,] 2.040575e-25 2.688967e-25 1.760976e-25 2.269901e-25 2.485756e-25
 [4,] 2.040575e-25 2.688967e-25 1.760976e-25 2.269901e-25 2.485756e-25
 [5,] 2.040575e-25 2.688967e-25 1.760976e-25 2.269901e-25 2.485756e-25
 [6,] 2.040575e-25 2.688967e-25 1.760976e-25 2.269901e-25 2.485756e-25
 [7,] 2.040575e-25 2.688967e-25 1.760976e-25 2.269901e-25 2.485756e-25
 [8,] 2.040575e-25 2.688967e-25 1.760976e-25 2.269901e-25 2.485756e-25
 [9,] 2.040575e-25 2.688967e-25 1.760976e-25 2.269901e-25 2.485756e-25
[10,] 2.040575e-25 2.688967e-25 1.760976e-25 2.269901e-25 2.485756e-25
             [,27]        [,28]        [,29]        [,30]        [,31]
 [1,] 1.659991e-25 2.987126e-25 3.808359e-25 1.991809e-25 1.852187e-25
 [2,] 1.659991e-25 2.987126e-25 3.808359e-25 1.991809e-25 1.852187e-25
 [3,] 1.659991e-25 2.987126e-25 3.808359e-25 1.991809e-25 1.852187e-25
 [4,] 1.659991e-25 2.987126e-25 3.808359e-25 1.991809e-25 1.852187e-25
 [5,] 1.659991e-25 2.987126e-25 3.808359e-25 1.991809e-25 1.852187e-25
 [6,] 1.659991e-25 2.987126e-25 3.808359e-25 1.991809e-25 1.852187e-25
 [7,] 1.659991e-25 2.987126e-25 3.808359e-25 1.991809e-25 1.852187e-25
 [8,] 1.659991e-25 2.987126e-25 3.808359e-25 1.991809e-25 1.852187e-25
 [9,] 1.659991e-25 2.987126e-25 3.808359e-25 1.991809e-25 1.852187e-25
[10,] 1.659991e-25 2.987126e-25 3.808359e-25 1.991809e-25 1.852187e-25
            [,32]        [,33]        [,34]        [,35]        [,36]
 [1,] 7.54603e-25 2.572113e-25 2.262302e-25 4.615932e-25 3.172465e-25
 [2,] 7.54603e-25 2.572113e-25 2.262302e-25 4.615932e-25 3.172465e-25
 [3,] 7.54603e-25 2.572113e-25 2.262302e-25 4.615932e-25 3.172465e-25
 [4,] 7.54603e-25 2.572113e-25 2.262302e-25 4.615932e-25 3.172465e-25
 [5,] 7.54603e-25 2.572113e-25 2.262302e-25 4.615932e-25 3.172465e-25
 [6,] 7.54603e-25 2.572113e-25 2.262302e-25 4.615932e-25 3.172465e-25
 [7,] 7.54603e-25 2.572113e-25 2.262302e-25 4.615932e-25 3.172465e-25
 [8,] 7.54603e-25 2.572113e-25 2.262302e-25 4.615932e-25 3.172465e-25
 [9,] 7.54603e-25 2.572113e-25 2.262302e-25 4.615932e-25 3.172465e-25
[10,] 7.54603e-25 2.572113e-25 2.262302e-25 4.615932e-25 3.172465e-25
             [,37]       [,38]        [,39]        [,40]        [,41]
 [1,] 1.674966e-25 2.50397e-25 2.041832e-25 2.388949e-25 3.086044e-25
 [2,] 1.674966e-25 2.50397e-25 2.041832e-25 2.388949e-25 3.086044e-25
 [3,] 1.674966e-25 2.50397e-25 2.041832e-25 2.388949e-25 3.086044e-25
 [4,] 1.674966e-25 2.50397e-25 2.041832e-25 2.388949e-25 3.086044e-25
 [5,] 1.674966e-25 2.50397e-25 2.041832e-25 2.388949e-25 3.086044e-25
 [6,] 1.674966e-25 2.50397e-25 2.041832e-25 2.388949e-25 3.086044e-25
 [7,] 1.674966e-25 2.50397e-25 2.041832e-25 2.388949e-25 3.086044e-25
 [8,] 1.674966e-25 2.50397e-25 2.041832e-25 2.388949e-25 3.086044e-25
 [9,] 1.674966e-25 2.50397e-25 2.041832e-25 2.388949e-25 3.086044e-25
[10,] 1.674966e-25 2.50397e-25 2.041832e-25 2.388949e-25 3.086044e-25
             [,42]       [,43]        [,44]        [,45]        [,46]
 [1,] 1.825289e-25 3.22661e-24 1.782184e-25 7.896422e-25 1.758257e-24
 [2,] 1.825289e-25 3.22661e-24 1.782184e-25 7.896422e-25 1.758257e-24
 [3,] 1.825289e-25 3.22661e-24 1.782184e-25 7.896422e-25 1.758257e-24
 [4,] 1.825289e-25 3.22661e-24 1.782184e-25 7.896422e-25 1.758257e-24
 [5,] 1.825289e-25 3.22661e-24 1.782184e-25 7.896422e-25 1.758257e-24
 [6,] 1.825289e-25 3.22661e-24 1.782184e-25 7.896422e-25 1.758257e-24
 [7,] 1.825289e-25 3.22661e-24 1.782184e-25 7.896422e-25 1.758257e-24
 [8,] 1.825289e-25 3.22661e-24 1.782184e-25 7.896422e-25 1.758257e-24
 [9,] 1.825289e-25 3.22661e-24 1.782184e-25 7.896422e-25 1.758257e-24
[10,] 1.825289e-25 3.22661e-24 1.782184e-25 7.896422e-25 1.758257e-24
             [,47]        [,48]        [,49]        [,50]
 [1,] 1.830873e-25 4.541854e-25 4.223712e-25 2.048776e-25
 [2,] 1.830873e-25 4.541854e-25 4.223712e-25 2.048776e-25
 [3,] 1.830873e-25 4.541854e-25 4.223712e-25 2.048776e-25
 [4,] 1.830873e-25 4.541854e-25 4.223712e-25 2.048776e-25
 [5,] 1.830873e-25 4.541854e-25 4.223712e-25 2.048776e-25
 [6,] 1.830873e-25 4.541854e-25 4.223712e-25 2.048776e-25
 [7,] 1.830873e-25 4.541854e-25 4.223712e-25 2.048776e-25
 [8,] 1.830873e-25 4.541854e-25 4.223712e-25 2.048776e-25
 [9,] 1.830873e-25 4.541854e-25 4.223712e-25 2.048776e-25
[10,] 1.830873e-25 4.541854e-25 4.223712e-25 2.048776e-25

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 = 1, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)

0.442 sec elapsed

t2 <- proc.time()
t2 - t1

   user  system elapsed 
  0.435   0.005   0.444

fit3$alpha

          [,1]         [,2]        [,3]        [,4]         [,5]         [,6]
[1,] 0.9999907 1.567435e-08 1.93253e-10 8.04475e-08 6.905913e-08 1.069103e-08
             [,7]         [,8]         [,9]        [,10]        [,11]
[1,] 3.592092e-07 5.765639e-08 7.577177e-11 7.977227e-09 8.847508e-08
            [,12]        [,13]        [,14]        [,15]        [,16]
[1,] 2.502203e-09 6.281601e-08 1.392935e-09 8.914891e-10 2.544198e-08
            [,17]        [,18]        [,19]        [,20]        [,21]
[1,] 7.700038e-11 7.748153e-09 7.448784e-09 6.410945e-09 8.701265e-10
            [,22]        [,23]        [,24]        [,25]       [,26]
[1,] 2.211322e-08 7.167358e-08 3.865536e-09 5.272047e-09 1.46579e-09
            [,27]        [,28]       [,29]        [,30]        [,31]
[1,] 7.133814e-09 5.589628e-09 9.94712e-10 4.583663e-08 2.242277e-06
            [,32]        [,33]        [,34]        [,35]        [,36]
[1,] 1.572915e-09 1.420206e-10 6.514977e-09 7.028173e-08 7.609461e-10
           [,37]        [,38]        [,39]        [,40]        [,41]
[1,] 3.79113e-07 2.581716e-10 1.017795e-09 3.465629e-07 1.451801e-06
            [,42]        [,43]        [,44]        [,45]       [,46]
[1,] 9.232644e-07 4.859094e-10 1.976958e-09 9.466556e-10 2.90021e-08
            [,47]        [,48]        [,49]        [,50]
[1,] 2.517204e-06 4.200088e-08 2.622045e-07 1.775289e-08

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 = 10, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)

104.966 sec elapsed

t2 <- proc.time()
t2 - t1

   user  system elapsed 
102.707   1.373 104.972

t(apply(fit3$alpha, 1, function(x) sort(x, decreasing = TRUE)))

            [,1]         [,2]         [,3]         [,4]         [,5]
 [1,] 0.99999698 1.052155e-06 4.521763e-07 3.791215e-07 3.688574e-07
 [2,] 0.04443501 4.139252e-02 3.742983e-02 3.220094e-02 2.857274e-02
 [3,] 0.04436356 4.154946e-02 3.756040e-02 3.225919e-02 2.864139e-02
 [4,] 0.04432799 4.162538e-02 3.762326e-02 3.228693e-02 2.867464e-02
 [5,] 0.04435819 4.155399e-02 3.756318e-02 3.225975e-02 2.864391e-02
 [6,] 0.04446539 4.130870e-02 3.735780e-02 3.216708e-02 2.853727e-02
 [7,] 0.04463249 4.092365e-02 3.703517e-02 3.201986e-02 2.836848e-02
 [8,] 0.92633850 1.367061e-02 1.322881e-02 7.705824e-03 5.771116e-03
 [9,] 0.83350885 3.348414e-02 2.173540e-02 2.169557e-02 1.381444e-02
[10,] 0.04459936 4.107726e-02 3.716962e-02 3.208576e-02 2.842870e-02
              [,6]         [,7]         [,8]         [,9]        [,10]
 [1,] 1.063574e-07 9.170682e-08 8.482000e-08 7.789812e-08 7.787209e-08
 [2,] 2.809040e-02 2.703073e-02 2.629240e-02 2.623714e-02 2.548382e-02
 [3,] 2.817898e-02 2.707243e-02 2.636357e-02 2.630041e-02 2.553564e-02
 [4,] 2.822183e-02 2.709351e-02 2.639781e-02 2.633078e-02 2.556036e-02
 [5,] 2.818167e-02 2.707741e-02 2.636494e-02 2.630149e-02 2.553598e-02
 [6,] 2.804340e-02 2.701702e-02 2.625283e-02 2.620160e-02 2.545350e-02
 [7,] 2.782602e-02 2.691994e-02 2.607692e-02 2.604442e-02 2.532393e-02
 [8,] 4.622791e-03 4.122711e-03 3.444368e-03 3.368677e-03 2.588945e-03
 [9,] 9.078574e-03 6.196018e-03 4.853759e-03 4.756574e-03 4.133717e-03
[10,] 2.790948e-02 2.692429e-02 2.614984e-02 2.610961e-02 2.538195e-02
             [,11]        [,12]        [,13]        [,14]        [,15]
 [1,] 4.892535e-08 3.776524e-08 3.320419e-08 2.748700e-08 2.508287e-08
 [2,] 2.453986e-02 2.169659e-02 2.118537e-02 2.028791e-02 1.991780e-02
 [3,] 2.456731e-02 2.170575e-02 2.119356e-02 2.028942e-02 1.993350e-02
 [4,] 2.458057e-02 2.171013e-02 2.119738e-02 2.029025e-02 1.994108e-02
 [5,] 2.456838e-02 2.170591e-02 2.119343e-02 2.028995e-02 1.993401e-02
 [6,] 2.452569e-02 2.169142e-02 2.118008e-02 2.028818e-02 1.990953e-02
 [7,] 2.445715e-02 2.166829e-02 2.115860e-02 2.028478e-02 1.987079e-02
 [8,] 1.789485e-03 1.485237e-03 1.193223e-03 1.162873e-03 1.125601e-03
 [9,] 4.011405e-03 3.939442e-03 3.716092e-03 3.661610e-03 2.937007e-03
[10,] 2.448385e-02 2.167802e-02 2.116969e-02 2.028289e-02 1.988524e-02
             [,16]        [,17]        [,18]        [,19]        [,20]
 [1,] 2.280982e-08 1.956384e-08 1.939523e-08 1.707932e-08 9.872685e-09
 [2,] 1.962502e-02 1.917252e-02 1.855645e-02 1.835742e-02 1.808267e-02
 [3,] 1.962055e-02 1.916672e-02 1.848118e-02 1.836582e-02 1.806021e-02
 [4,] 1.961837e-02 1.916388e-02 1.844508e-02 1.836971e-02 1.804940e-02
 [5,] 1.962045e-02 1.916653e-02 1.847947e-02 1.836565e-02 1.805986e-02
 [6,] 1.962743e-02 1.917554e-02 1.859793e-02 1.835192e-02 1.809534e-02
 [7,] 1.963794e-02 1.918936e-02 1.878641e-02 1.832964e-02 1.815066e-02
 [8,] 1.078771e-03 7.863945e-04 7.811649e-04 7.793910e-04 6.400288e-04
 [9,] 2.722111e-03 1.769252e-03 1.712252e-03 1.412523e-03 1.297458e-03
[10,] 1.963354e-02 1.918458e-02 1.870874e-02 1.834122e-02 1.812647e-02
             [,21]        [,22]        [,23]        [,24]        [,25]
 [1,] 8.975284e-09 8.220208e-09 7.095732e-09 6.725587e-09 4.910950e-09
 [2,] 1.771616e-02 1.764584e-02 1.763599e-02 1.726930e-02 1.719357e-02
 [3,] 1.768678e-02 1.765772e-02 1.763319e-02 1.726446e-02 1.719536e-02
 [4,] 1.767268e-02 1.766332e-02 1.763174e-02 1.726209e-02 1.719614e-02
 [5,] 1.768623e-02 1.765760e-02 1.763281e-02 1.726426e-02 1.719514e-02
 [6,] 1.773256e-02 1.763841e-02 1.763676e-02 1.727173e-02 1.719198e-02
 [7,] 1.780552e-02 1.764275e-02 1.760811e-02 1.728327e-02 1.718696e-02
 [8,] 5.789253e-04 4.731607e-04 4.591056e-04 4.527058e-04 3.487912e-04
 [9,] 1.229887e-03 1.186325e-03 1.124523e-03 1.121907e-03 1.105537e-03
[10,] 1.777453e-02 1.764286e-02 1.762293e-02 1.727925e-02 1.719021e-02
             [,26]        [,27]        [,28]        [,29]        [,30]
 [1,] 4.359662e-09 4.114918e-09 2.878084e-09 2.286150e-09 2.286049e-09
 [2,] 1.709352e-02 1.706796e-02 1.690906e-02 1.670320e-02 1.637994e-02
 [3,] 1.709357e-02 1.704394e-02 1.688009e-02 1.669816e-02 1.636479e-02
 [4,] 1.709362e-02 1.703243e-02 1.686617e-02 1.669573e-02 1.635751e-02
 [5,] 1.709371e-02 1.704358e-02 1.687951e-02 1.669803e-02 1.636449e-02
 [6,] 1.709382e-02 1.708155e-02 1.692518e-02 1.670592e-02 1.638837e-02
 [7,] 1.714128e-02 1.709386e-02 1.699722e-02 1.671830e-02 1.642615e-02
 [8,] 3.296368e-04 2.142778e-04 2.129617e-04 1.882316e-04 1.432112e-04
 [9,] 1.050810e-03 1.012467e-03 9.010285e-04 8.981399e-04 8.382903e-04
[10,] 1.711564e-02 1.709300e-02 1.696669e-02 1.671269e-02 1.641044e-02
             [,31]        [,32]        [,33]        [,34]        [,35]
 [1,] 2.009247e-09 1.990324e-09 1.890739e-09 1.743024e-09 1.472155e-09
 [2,] 1.636796e-02 1.628005e-02 1.624300e-02 1.608356e-02 1.606931e-02
 [3,] 1.635187e-02 1.624958e-02 1.621377e-02 1.605409e-02 1.602636e-02
 [4,] 1.634414e-02 1.623492e-02 1.619969e-02 1.603994e-02 1.600577e-02
 [5,] 1.635159e-02 1.624886e-02 1.621307e-02 1.605346e-02 1.602549e-02
 [6,] 1.637696e-02 1.629671e-02 1.625898e-02 1.609985e-02 1.609320e-02
 [7,] 1.641665e-02 1.637226e-02 1.633134e-02 1.620067e-02 1.617334e-02
 [8,] 1.427012e-04 1.284169e-04 7.811385e-05 7.608845e-05 6.859669e-05
 [9,] 7.149877e-04 6.938952e-04 6.679215e-04 6.672474e-04 6.257890e-04
[10,] 1.639992e-02 1.634147e-02 1.630181e-02 1.615561e-02 1.614285e-02
             [,36]        [,37]        [,38]        [,39]        [,40]
 [1,] 1.427190e-09 9.416325e-10 8.647769e-10 5.951679e-10 5.181345e-10
 [2,] 1.596913e-02 1.595689e-02 1.588084e-02 1.572801e-02 1.568565e-02
 [3,] 1.594671e-02 1.594426e-02 1.585002e-02 1.567643e-02 1.566843e-02
 [4,] 1.594177e-02 1.593228e-02 1.583523e-02 1.566008e-02 1.565168e-02
 [5,] 1.594634e-02 1.594364e-02 1.584943e-02 1.567528e-02 1.566781e-02
 [6,] 1.598264e-02 1.596214e-02 1.589801e-02 1.575643e-02 1.569459e-02
 [7,] 1.604408e-02 1.598696e-02 1.597473e-02 1.588518e-02 1.573681e-02
 [8,] 6.855061e-05 5.918835e-05 5.752368e-05 4.495573e-05 3.465002e-05
 [9,] 6.168079e-04 5.691247e-04 5.449257e-04 4.826782e-04 4.743063e-04
[10,] 1.601931e-02 1.597766e-02 1.594243e-02 1.583224e-02 1.572137e-02
             [,41]        [,42]        [,43]        [,44]        [,45]
 [1,] 5.038005e-10 4.434817e-10 4.051437e-10 3.886707e-10 1.647665e-10
 [2,] 1.554825e-02 1.547688e-02 1.537992e-02 1.528228e-02 1.520010e-02
 [3,] 1.554534e-02 1.542838e-02 1.534190e-02 1.525063e-02 1.517178e-02
 [4,] 1.554396e-02 1.540511e-02 1.532363e-02 1.523543e-02 1.516394e-02
 [5,] 1.554538e-02 1.542727e-02 1.534108e-02 1.524994e-02 1.517140e-02
 [6,] 1.555006e-02 1.550356e-02 1.540093e-02 1.529976e-02 1.522659e-02
 [7,] 1.562479e-02 1.555723e-02 1.549555e-02 1.537876e-02 1.534568e-02
 [8,] 3.436165e-05 3.347509e-05 2.811367e-05 2.204717e-05 9.321038e-06
 [9,] 4.530960e-04 4.074441e-04 3.690268e-04 3.149585e-04 2.945255e-04
[10,] 1.557500e-02 1.555378e-02 1.545637e-02 1.534607e-02 1.529565e-02
             [,46]        [,47]        [,48]        [,49]        [,50]
 [1,] 9.665311e-11 7.985264e-11 6.460685e-11 5.430768e-11 1.432724e-11
 [2,] 1.518805e-02 1.480966e-02 1.467105e-02 1.459447e-02 1.338326e-02
 [3,] 1.515251e-02 1.481452e-02 1.466007e-02 1.455842e-02 1.336782e-02
 [4,] 1.512970e-02 1.481667e-02 1.465474e-02 1.454112e-02 1.336044e-02
 [5,] 1.515156e-02 1.481392e-02 1.465965e-02 1.455766e-02 1.336767e-02
 [6,] 1.519694e-02 1.480540e-02 1.467669e-02 1.461446e-02 1.339217e-02
 [7,] 1.523710e-02 1.479221e-02 1.470451e-02 1.470356e-02 1.343067e-02
 [8,] 9.187843e-06 7.408400e-06 5.722453e-06 5.528439e-06 5.116560e-07
 [9,] 2.675404e-04 2.647668e-04 2.561531e-04 2.319128e-04 1.777891e-04
[10,] 1.522077e-02 1.480469e-02 1.469406e-02 1.466702e-02 1.341360e-02

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 = 10, prior_variance = 1., prior_weights = rep(1/p, p), tol = 1e-3, maxit = 500, estimate_intercept = TRUE, ser_function = fit_coxph)

48.476 sec elapsed

t2 <- proc.time()
t2 - t1

   user  system elapsed 
 34.633   0.851  48.480

fit4$alpha

              [,1]         [,2]         [,3]         [,4]         [,5]
 [1,] 1.000000e+00 5.462073e-15 5.878062e-15 7.908404e-13 3.127903e-13
 [2,] 1.218094e-08 9.999294e-01 5.309247e-08 8.740058e-08 2.705689e-08
 [3,] 3.570948e-02 2.492915e-02 1.878042e-02 1.531881e-02 2.510584e-02
 [4,] 3.586999e-02 2.487214e-02 1.867543e-02 1.535015e-02 2.493102e-02
 [5,] 3.601484e-02 2.481580e-02 1.857759e-02 1.537833e-02 2.476811e-02
 [6,] 3.607353e-02 2.479168e-02 1.853702e-02 1.538973e-02 2.470057e-02
 [7,] 3.602649e-02 2.481151e-02 1.856952e-02 1.538060e-02 2.475469e-02
 [8,] 3.590179e-02 2.486105e-02 1.865406e-02 1.535633e-02 2.489548e-02
 [9,] 3.575831e-02 2.491369e-02 1.874858e-02 1.532830e-02 2.505292e-02
[10,] 3.566541e-02 2.494570e-02 1.880832e-02 1.531010e-02 2.515243e-02
              [,6]         [,7]         [,8]         [,9]        [,10]
 [1,] 4.813312e-13 2.964555e-13 1.268710e-13 3.736764e-15 3.248483e-14
 [2,] 1.125053e-07 2.812564e-08 4.376611e-08 1.942261e-07 6.965236e-06
 [3,] 1.551654e-02 3.150950e-02 3.160673e-02 1.636298e-02 1.748556e-02
 [4,] 1.561327e-02 3.118398e-02 3.122083e-02 1.629688e-02 1.758284e-02
 [5,] 1.570246e-02 3.088257e-02 3.086631e-02 1.623514e-02 1.767215e-02
 [6,] 1.573916e-02 3.075812e-02 3.072073e-02 1.620951e-02 1.770879e-02
 [7,] 1.570974e-02 3.085780e-02 3.083735e-02 1.623009e-02 1.767940e-02
 [8,] 1.563274e-02 3.111811e-02 3.114319e-02 1.628349e-02 1.760231e-02
 [9,] 1.554582e-02 3.141089e-02 3.148955e-02 1.634306e-02 1.751497e-02
[10,] 1.549043e-02 3.159682e-02 3.171085e-02 1.638067e-02 1.745912e-02
             [,11]        [,12]        [,13]        [,14]        [,15]
 [1,] 5.386879e-11 1.589717e-14 5.108270e-13 1.322122e-13 4.482215e-15
 [2,] 2.528000e-06 4.434115e-08 5.476186e-06 3.117614e-09 1.473406e-07
 [3,] 4.067655e-02 3.983076e-02 1.962509e-02 2.862063e-02 1.928395e-02
 [4,] 4.148250e-02 3.925963e-02 1.963784e-02 2.843965e-02 1.920721e-02
 [5,] 4.224721e-02 3.873593e-02 1.964788e-02 2.826890e-02 1.913414e-02
 [6,] 4.256798e-02 3.852110e-02 1.965154e-02 2.819753e-02 1.910345e-02
 [7,] 4.231046e-02 3.869322e-02 1.964865e-02 2.825469e-02 1.912816e-02
 [8,] 4.164821e-02 3.914513e-02 1.964017e-02 2.840231e-02 1.919152e-02
 [9,] 4.091941e-02 3.965781e-02 1.962909e-02 2.856558e-02 1.926102e-02
[10,] 4.046486e-02 3.998595e-02 1.962125e-02 2.866774e-02 1.930427e-02
             [,16]        [,17]        [,18]        [,19]        [,20]
 [1,] 8.461749e-13 2.437675e-15 3.151304e-11 2.500937e-13 2.406229e-13
 [2,] 1.529384e-06 3.858431e-06 7.734469e-08 9.606877e-07 3.948449e-07
 [3,] 2.046743e-02 1.566720e-02 1.570248e-02 2.196391e-02 1.659927e-02
 [4,] 2.072471e-02 1.564193e-02 1.575828e-02 2.183533e-02 1.669588e-02
 [5,] 2.096617e-02 1.561763e-02 1.580897e-02 2.171570e-02 1.678485e-02
 [6,] 2.106674e-02 1.560734e-02 1.582962e-02 2.166619e-02 1.682143e-02
 [7,] 2.098604e-02 1.561563e-02 1.581307e-02 2.170594e-02 1.679209e-02
 [8,] 2.077709e-02 1.563676e-02 1.576938e-02 2.180932e-02 1.671528e-02
 [9,] 2.054490e-02 1.565974e-02 1.571939e-02 2.192509e-02 1.662849e-02
[10,] 2.039888e-02 1.567394e-02 1.568719e-02 2.199839e-02 1.657312e-02
             [,21]        [,22]        [,23]        [,24]        [,25]
 [1,] 1.361300e-14 3.295044e-13 5.074858e-12 2.486214e-14 2.842661e-14
 [2,] 2.955632e-07 1.584879e-07 7.812304e-07 3.423552e-07 2.307278e-06
 [3,] 1.454931e-02 1.783813e-02 1.614177e-02 1.431941e-02 1.764240e-02
 [4,] 1.456969e-02 1.777431e-02 1.614754e-02 1.436978e-02 1.760731e-02
 [5,] 1.458773e-02 1.771513e-02 1.615237e-02 1.441550e-02 1.757425e-02
 [6,] 1.459495e-02 1.769068e-02 1.615422e-02 1.443410e-02 1.756046e-02
 [7,] 1.458918e-02 1.771027e-02 1.615274e-02 1.441919e-02 1.757154e-02
 [8,] 1.457366e-02 1.776136e-02 1.614861e-02 1.437980e-02 1.760016e-02
 [9,] 1.455548e-02 1.781872e-02 1.614351e-02 1.433470e-02 1.763184e-02
[10,] 1.454355e-02 1.785511e-02 1.614003e-02 1.430562e-02 1.765172e-02
             [,26]        [,27]        [,28]        [,29]        [,30]
 [1,] 5.100067e-14 2.228931e-13 2.222310e-11 1.464532e-13 2.765254e-13
 [2,] 1.941303e-06 6.785370e-08 1.867813e-08 1.620806e-07 3.857104e-07
 [3,] 1.683264e-02 1.473248e-02 1.646160e-02 2.477907e-02 1.665124e-02
 [4,] 1.697244e-02 1.476730e-02 1.646880e-02 2.461047e-02 1.675940e-02
 [5,] 1.710258e-02 1.479877e-02 1.647418e-02 2.445268e-02 1.685955e-02
 [6,] 1.715649e-02 1.481155e-02 1.647603e-02 2.438713e-02 1.690089e-02
 [7,] 1.711325e-02 1.480131e-02 1.647453e-02 2.443980e-02 1.686774e-02
 [8,] 1.700072e-02 1.477419e-02 1.646999e-02 2.457630e-02 1.678122e-02
 [9,] 1.687478e-02 1.474303e-02 1.646378e-02 2.472837e-02 1.668393e-02
[10,] 1.679509e-02 1.472288e-02 1.645922e-02 2.482424e-02 1.662212e-02
             [,31]        [,32]        [,33]        [,34]        [,35]
 [1,] 2.772113e-12 2.315126e-15 4.059533e-16 1.010916e-12 4.558022e-13
 [2,] 2.012678e-07 1.293445e-07 9.878602e-07 1.942955e-08 8.637753e-08
 [3,] 1.618867e-02 2.285974e-02 1.271087e-02 1.417202e-02 1.745145e-02
 [4,] 1.623872e-02 2.263979e-02 1.275616e-02 1.419213e-02 1.742784e-02
 [5,] 1.628441e-02 2.243688e-02 1.279768e-02 1.421056e-02 1.740448e-02
 [6,] 1.630309e-02 2.235331e-02 1.281471e-02 1.421812e-02 1.739442e-02
 [7,] 1.628811e-02 2.242030e-02 1.280106e-02 1.421206e-02 1.740249e-02
 [8,] 1.624870e-02 2.259552e-02 1.276522e-02 1.419612e-02 1.742280e-02
 [9,] 1.620381e-02 2.279324e-02 1.272456e-02 1.417805e-02 1.744434e-02
[10,] 1.617499e-02 2.291921e-02 1.269854e-02 1.416647e-02 1.745733e-02
             [,36]        [,37]        [,38]        [,39]        [,40]
 [1,] 1.550987e-14 1.415505e-12 1.098762e-14 1.352398e-14 3.933191e-13
 [2,] 9.674681e-07 1.818342e-06 4.235214e-06 2.439048e-06 3.510392e-07
 [3,] 1.659455e-02 2.159109e-02 1.547214e-02 1.788202e-02 1.914194e-02
 [4,] 1.657493e-02 2.186007e-02 1.550905e-02 1.790105e-02 1.910316e-02
 [5,] 1.655611e-02 2.211231e-02 1.554218e-02 1.791761e-02 1.906643e-02
 [6,] 1.654817e-02 2.221730e-02 1.555556e-02 1.792415e-02 1.905106e-02
 [7,] 1.655455e-02 2.213307e-02 1.554485e-02 1.791894e-02 1.906340e-02
 [8,] 1.657086e-02 2.191488e-02 1.551637e-02 1.790477e-02 1.909518e-02
 [9,] 1.658864e-02 2.167225e-02 1.548343e-02 1.788790e-02 1.913021e-02
[10,] 1.659963e-02 2.151959e-02 1.546203e-02 1.787670e-02 1.915209e-02
             [,41]        [,42]        [,43]        [,44]        [,45]
 [1,] 4.460373e-12 8.177907e-13 1.436130e-14 2.099208e-14 1.549666e-15
 [2,] 1.109067e-08 4.437556e-06 1.230095e-08 4.234839e-07 1.535883e-07
 [3,] 1.548843e-02 1.716043e-02 3.043474e-02 1.607125e-02 2.082654e-02
 [4,] 1.547435e-02 1.726136e-02 3.001777e-02 1.611487e-02 2.077749e-02
 [5,] 1.546063e-02 1.735435e-02 2.963504e-02 1.615438e-02 2.072913e-02
 [6,] 1.545477e-02 1.739260e-02 2.947799e-02 1.617044e-02 2.070839e-02
 [7,] 1.545945e-02 1.736192e-02 2.960383e-02 1.615757e-02 2.072514e-02
 [8,] 1.547132e-02 1.728163e-02 2.993394e-02 1.612353e-02 2.076726e-02
 [9,] 1.548407e-02 1.719094e-02 3.030806e-02 1.608449e-02 2.081206e-02
[10,] 1.549183e-02 1.713309e-02 3.054727e-02 1.605927e-02 2.083920e-02
             [,46]        [,47]        [,48]        [,49]        [,50]
 [1,] 2.020794e-13 2.586569e-12 1.047822e-14 4.149980e-10 5.331764e-14
 [2,] 3.316499e-07 2.059592e-05 3.218721e-06 2.978091e-08 1.145830e-06
 [3,] 1.697099e-02 1.995204e-02 1.532269e-02 1.761134e-02 1.538672e-02
 [4,] 1.711780e-02 2.015371e-02 1.537503e-02 1.773518e-02 1.544302e-02
 [5,] 1.725458e-02 2.034239e-02 1.542296e-02 1.784950e-02 1.549499e-02
 [6,] 1.731127e-02 2.042079e-02 1.544259e-02 1.789659e-02 1.551639e-02
 [7,] 1.726579e-02 2.035787e-02 1.542685e-02 1.785886e-02 1.549922e-02
 [8,] 1.714752e-02 2.019467e-02 1.538548e-02 1.776019e-02 1.545432e-02
 [9,] 1.701523e-02 2.001282e-02 1.533851e-02 1.764893e-02 1.540369e-02
[10,] 1.693159e-02 1.989817e-02 1.530842e-02 1.757809e-02 1.537145e-02

t(apply(fit4$alpha, 1, function(x) sort(x, decreasing = TRUE)))

            [,1]         [,2]         [,3]         [,4]         [,5]
 [1,] 1.00000000 4.149980e-10 5.386879e-11 3.151304e-11 2.222310e-11
 [2,] 0.99992940 2.059592e-05 6.965236e-06 5.476186e-06 4.437556e-06
 [3,] 0.04067655 3.983076e-02 3.570948e-02 3.160673e-02 3.150950e-02
 [4,] 0.04148250 3.925963e-02 3.586999e-02 3.122083e-02 3.118398e-02
 [5,] 0.04224721 3.873593e-02 3.601484e-02 3.088257e-02 3.086631e-02
 [6,] 0.04256798 3.852110e-02 3.607353e-02 3.075812e-02 3.072073e-02
 [7,] 0.04231046 3.869322e-02 3.602649e-02 3.085780e-02 3.083735e-02
 [8,] 0.04164821 3.914513e-02 3.590179e-02 3.114319e-02 3.111811e-02
 [9,] 0.04091941 3.965781e-02 3.575831e-02 3.148955e-02 3.141089e-02
[10,] 0.04046486 3.998595e-02 3.566541e-02 3.171085e-02 3.159682e-02
              [,6]         [,7]         [,8]         [,9]        [,10]
 [1,] 5.074858e-12 4.460373e-12 2.772113e-12 2.586569e-12 1.415505e-12
 [2,] 4.235214e-06 3.858431e-06 3.218721e-06 2.528000e-06 2.439048e-06
 [3,] 3.043474e-02 2.862063e-02 2.510584e-02 2.492915e-02 2.477907e-02
 [4,] 3.001777e-02 2.843965e-02 2.493102e-02 2.487214e-02 2.461047e-02
 [5,] 2.963504e-02 2.826890e-02 2.481580e-02 2.476811e-02 2.445268e-02
 [6,] 2.947799e-02 2.819753e-02 2.479168e-02 2.470057e-02 2.438713e-02
 [7,] 2.960383e-02 2.825469e-02 2.481151e-02 2.475469e-02 2.443980e-02
 [8,] 2.993394e-02 2.840231e-02 2.489548e-02 2.486105e-02 2.457630e-02
 [9,] 3.030806e-02 2.856558e-02 2.505292e-02 2.491369e-02 2.472837e-02
[10,] 3.054727e-02 2.866774e-02 2.515243e-02 2.494570e-02 2.482424e-02
             [,11]        [,12]        [,13]        [,14]        [,15]
 [1,] 1.010916e-12 8.461749e-13 8.177907e-13 7.908404e-13 5.108270e-13
 [2,] 2.307278e-06 1.941303e-06 1.818342e-06 1.529384e-06 1.145830e-06
 [3,] 2.285974e-02 2.196391e-02 2.159109e-02 2.082654e-02 2.046743e-02
 [4,] 2.263979e-02 2.186007e-02 2.183533e-02 2.077749e-02 2.072471e-02
 [5,] 2.243688e-02 2.211231e-02 2.171570e-02 2.096617e-02 2.072913e-02
 [6,] 2.235331e-02 2.221730e-02 2.166619e-02 2.106674e-02 2.070839e-02
 [7,] 2.242030e-02 2.213307e-02 2.170594e-02 2.098604e-02 2.072514e-02
 [8,] 2.259552e-02 2.191488e-02 2.180932e-02 2.077709e-02 2.076726e-02
 [9,] 2.279324e-02 2.192509e-02 2.167225e-02 2.081206e-02 2.054490e-02
[10,] 2.291921e-02 2.199839e-02 2.151959e-02 2.083920e-02 2.039888e-02
             [,16]        [,17]        [,18]        [,19]        [,20]
 [1,] 4.813312e-13 4.558022e-13 3.933191e-13 3.295044e-13 3.127903e-13
 [2,] 9.878602e-07 9.674681e-07 9.606877e-07 7.812304e-07 4.234839e-07
 [3,] 1.995204e-02 1.962509e-02 1.928395e-02 1.914194e-02 1.878042e-02
 [4,] 2.015371e-02 1.963784e-02 1.920721e-02 1.910316e-02 1.867543e-02
 [5,] 2.034239e-02 1.964788e-02 1.913414e-02 1.906643e-02 1.857759e-02
 [6,] 2.042079e-02 1.965154e-02 1.910345e-02 1.905106e-02 1.853702e-02
 [7,] 2.035787e-02 1.964865e-02 1.912816e-02 1.906340e-02 1.856952e-02
 [8,] 2.019467e-02 1.964017e-02 1.919152e-02 1.909518e-02 1.865406e-02
 [9,] 2.001282e-02 1.962909e-02 1.926102e-02 1.913021e-02 1.874858e-02
[10,] 1.989817e-02 1.962125e-02 1.930427e-02 1.915209e-02 1.880832e-02
             [,21]        [,22]        [,23]        [,24]        [,25]
 [1,] 2.964555e-13 2.765254e-13 2.500937e-13 2.406229e-13 2.228931e-13
 [2,] 3.948449e-07 3.857104e-07 3.510392e-07 3.423552e-07 3.316499e-07
 [3,] 1.788202e-02 1.783813e-02 1.764240e-02 1.761134e-02 1.748556e-02
 [4,] 1.790105e-02 1.777431e-02 1.773518e-02 1.760731e-02 1.758284e-02
 [5,] 1.791761e-02 1.784950e-02 1.771513e-02 1.767215e-02 1.757425e-02
 [6,] 1.792415e-02 1.789659e-02 1.770879e-02 1.769068e-02 1.756046e-02
 [7,] 1.791894e-02 1.785886e-02 1.771027e-02 1.767940e-02 1.757154e-02
 [8,] 1.790477e-02 1.776136e-02 1.776019e-02 1.760231e-02 1.760016e-02
 [9,] 1.788790e-02 1.781872e-02 1.764893e-02 1.763184e-02 1.751497e-02
[10,] 1.787670e-02 1.785511e-02 1.765172e-02 1.757809e-02 1.745912e-02
             [,26]        [,27]        [,28]        [,29]        [,30]
 [1,] 2.020794e-13 1.464532e-13 1.322122e-13 1.268710e-13 5.331764e-14
 [2,] 2.955632e-07 2.012678e-07 1.942261e-07 1.620806e-07 1.584879e-07
 [3,] 1.745145e-02 1.716043e-02 1.697099e-02 1.683264e-02 1.665124e-02
 [4,] 1.742784e-02 1.726136e-02 1.711780e-02 1.697244e-02 1.675940e-02
 [5,] 1.740448e-02 1.735435e-02 1.725458e-02 1.710258e-02 1.685955e-02
 [6,] 1.739442e-02 1.739260e-02 1.731127e-02 1.715649e-02 1.690089e-02
 [7,] 1.740249e-02 1.736192e-02 1.726579e-02 1.711325e-02 1.686774e-02
 [8,] 1.742280e-02 1.728163e-02 1.714752e-02 1.700072e-02 1.678122e-02
 [9,] 1.744434e-02 1.719094e-02 1.701523e-02 1.687478e-02 1.668393e-02
[10,] 1.745733e-02 1.713309e-02 1.693159e-02 1.679509e-02 1.662212e-02
             [,31]        [,32]        [,33]        [,34]        [,35]
 [1,] 5.100067e-14 3.248483e-14 2.842661e-14 2.486214e-14 2.099208e-14
 [2,] 1.535883e-07 1.473406e-07 1.293445e-07 1.125053e-07 8.740058e-08
 [3,] 1.659927e-02 1.659455e-02 1.646160e-02 1.636298e-02 1.618867e-02
 [4,] 1.669588e-02 1.657493e-02 1.646880e-02 1.629688e-02 1.623872e-02
 [5,] 1.678485e-02 1.655611e-02 1.647418e-02 1.628441e-02 1.623514e-02
 [6,] 1.682143e-02 1.654817e-02 1.647603e-02 1.630309e-02 1.620951e-02
 [7,] 1.679209e-02 1.655455e-02 1.647453e-02 1.628811e-02 1.623009e-02
 [8,] 1.671528e-02 1.657086e-02 1.646999e-02 1.628349e-02 1.624870e-02
 [9,] 1.662849e-02 1.658864e-02 1.646378e-02 1.634306e-02 1.620381e-02
[10,] 1.659963e-02 1.657312e-02 1.645922e-02 1.638067e-02 1.617499e-02
             [,36]        [,37]        [,38]        [,39]        [,40]
 [1,] 1.589717e-14 1.550987e-14 1.436130e-14 1.361300e-14 1.352398e-14
 [2,] 8.637753e-08 7.734469e-08 6.785370e-08 5.309247e-08 4.434115e-08
 [3,] 1.614177e-02 1.607125e-02 1.570248e-02 1.566720e-02 1.551654e-02
 [4,] 1.614754e-02 1.611487e-02 1.575828e-02 1.564193e-02 1.561327e-02
 [5,] 1.615438e-02 1.615237e-02 1.580897e-02 1.570246e-02 1.561763e-02
 [6,] 1.617044e-02 1.615422e-02 1.582962e-02 1.573916e-02 1.560734e-02
 [7,] 1.615757e-02 1.615274e-02 1.581307e-02 1.570974e-02 1.561563e-02
 [8,] 1.614861e-02 1.612353e-02 1.576938e-02 1.563676e-02 1.563274e-02
 [9,] 1.614351e-02 1.608449e-02 1.571939e-02 1.565974e-02 1.554582e-02
[10,] 1.614003e-02 1.605927e-02 1.568719e-02 1.567394e-02 1.549183e-02
             [,41]        [,42]        [,43]        [,44]        [,45]
 [1,] 1.098762e-14 1.047822e-14 5.878062e-15 5.462073e-15 4.482215e-15
 [2,] 4.376611e-08 2.978091e-08 2.812564e-08 2.705689e-08 1.942955e-08
 [3,] 1.548843e-02 1.547214e-02 1.538672e-02 1.532269e-02 1.531881e-02
 [4,] 1.550905e-02 1.547435e-02 1.544302e-02 1.537503e-02 1.535015e-02
 [5,] 1.554218e-02 1.549499e-02 1.546063e-02 1.542296e-02 1.537833e-02
 [6,] 1.555556e-02 1.551639e-02 1.545477e-02 1.544259e-02 1.538973e-02
 [7,] 1.554485e-02 1.549922e-02 1.545945e-02 1.542685e-02 1.538060e-02
 [8,] 1.551637e-02 1.547132e-02 1.545432e-02 1.538548e-02 1.535633e-02
 [9,] 1.548407e-02 1.548343e-02 1.540369e-02 1.533851e-02 1.532830e-02
[10,] 1.549043e-02 1.546203e-02 1.537145e-02 1.531010e-02 1.530842e-02
             [,46]        [,47]        [,48]        [,49]        [,50]
 [1,] 3.736764e-15 2.437675e-15 2.315126e-15 1.549666e-15 4.059533e-16
 [2,] 1.867813e-08 1.230095e-08 1.218094e-08 1.109067e-08 3.117614e-09
 [3,] 1.473248e-02 1.454931e-02 1.431941e-02 1.417202e-02 1.271087e-02
 [4,] 1.476730e-02 1.456969e-02 1.436978e-02 1.419213e-02 1.275616e-02
 [5,] 1.479877e-02 1.458773e-02 1.441550e-02 1.421056e-02 1.279768e-02
 [6,] 1.481155e-02 1.459495e-02 1.443410e-02 1.421812e-02 1.281471e-02
 [7,] 1.480131e-02 1.458918e-02 1.441919e-02 1.421206e-02 1.280106e-02
 [8,] 1.477419e-02 1.457366e-02 1.437980e-02 1.419612e-02 1.276522e-02
 [9,] 1.474303e-02 1.455548e-02 1.433470e-02 1.417805e-02 1.272456e-02
[10,] 1.472288e-02 1.454355e-02 1.430562e-02 1.416647e-02 1.269854e-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

Apply SER module

Yunqi Yang

2/5/2023

Description:

The Wakefield approximation:

Data 1: simulated from null model:

Run IBSS on data from null model with L=1.

Data 2: simulated from \(\log T_i=\beta_0 + \beta_1x_{i1}\). Predictors are independent.

Data 3: simulated from \(\log T_i=\beta_0 + \beta_1x_{i1}\). Predictors have high correlation.

Data 4: simulated from \(\log T_i=\beta_0 + \beta_1x_{i1} + \beta_1x_{i2}\). Predictors have high correlation