Power vs. fdr: version 4

Last updated: 2023-05-11

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Description:

Version 4 simulation results, comparing power vs. FDR across 3 methods. I vary the threshold for claiming effect variables based on marginal PIP value.

Difference between v3 and v4 simulation:

Only susie has been changed, not the other two methods.
Used corrected ABF instead of original Wakefeld ABF.
Computed susie credible sets.

Conclusion:

After using corrected ABF, susie performance is improved. Now it’s better than bvsnlp almost all the time.
Power of the credible sets and coverage of credible sets also look fine.


calculate_tpr_vs_fdr <- function(pip, is_effect, ts){
  res <- matrix(NA, nrow = length(ts), ncol = 2)
  colnames(res) = c("tpr", "fdr")
  for (i in 1:length(ts)){
    pred_pos = pip >= ts[i]
    tp = pip >= ts[i] & is_effect == 1
    fp = pip >= ts[i] & is_effect == 0
    tpr = sum(tp)/sum(is_effect)
    fdr = sum(fp)/sum(pred_pos)
    res[i, ] = c(tpr, fdr)
  }
  return(res)
}

# coverage: the proportion of CSs that contain an effect variable
# @param dat_indx: the indx for the data from dsc
calculate_cs_coverage = function(dat_indx){
  contain_status = c()
  for (indx in dat_indx){
     cs = susie$susie.cs[[indx]]$cs
     true_effect = which(susie$simulate.is_effect[[indx]] == 1)
     if (!is.null(cs)){
       for (j in 1:length(cs)){
         res = ifelse(sum(true_effect %in% unlist(cs[j])) ==  1, 1, 0)
         contain_status = c(contain_status, res)
        }
     }
  }
  coverage = sum(contain_status)/length(contain_status)
  return(coverage)
}


# @param dat_indx: the indx for the data from dsc
# @p: number of variables in each simulation replicate. 
get_cs_effect = function(dat_indx, p){
  cs_effect = c()
  for (indx in dat_indx){
    effect = rep(0, p)
    cs_effect_indx = c(unlist(susie$susie.cs[[indx]]$cs))
    effect[cs_effect_indx] = 1
    cs_effect = c(cs_effect, effect)
  }
  return(cs_effect)
}

susie = readRDS("./data/dsc3/susie.cs.rds")
survsvb = readRDS("./data/dsc3/survsvb.rds")
bvsnlp = readRDS("./data/dsc3/bvsnlp.rds")

1. Results using real correlation structure from data

par(mfrow = c(2,3), cex.axis = 1.5)
censor_lvl = c(0, 0.2, 0.4, 0.6, 0.8)
for (i in 1:5){
  indx = which(susie$simulate.cor_type == "real" & susie$simulate.censor_lvl == censor_lvl[i])
  pip.susie = unlist(lapply(indx, function(x) susie$susie.pip[[x]]))
  pip.survsvb = unlist(lapply(indx, function(x) survsvb$survivalsvb.pip[[x]]))
  pip.bvsnlp = unlist(lapply(indx, function(x) bvsnlp$bvsnlp.pip[[x]]))
  is_effect = unlist(lapply(indx, function(x) susie$simulate.is_effect[[x]]))
  
  ts = seq(from = 0, to = 1, by = 0.01)
  res.susie = calculate_tpr_vs_fdr(pip.susie, is_effect, ts)
  res.svb = calculate_tpr_vs_fdr(pip.survsvb, is_effect, ts)
  res.bvsnlp = calculate_tpr_vs_fdr(pip.bvsnlp, is_effect, ts)
  
  plot(res.susie[,2], res.susie[,1], type = "l", xlim = c(0,1), ylim = c(0, 1), xlab = "FDR", ylab = "Power",
       main = paste0("Real correlation, effect 0-3", ",censor=", censor_lvl[i]))
  lines(res.svb[,2], res.svb[,1], type = "l", col = 2)
  lines(res.bvsnlp[,2], res.bvsnlp[,1], type = "l", col = 3)
  
  points(res.susie[96,2], res.susie[96, 1])
  points(res.svb[96,2], res.svb[96, 1])
  points(res.bvsnlp[96,2], res.bvsnlp[96, 1])
  
  legend("topleft", legend = c("susie", "survival.svb", "bvsnlp"), col = c(1,2,3), lty = 1)
}

Version	Author	Date
f07fc2e	yunqiyang0215	2023-05-08

The dots indicate PIP threshold = 0.95

2. Results using independent X, without data from null model.

par(mfrow = c(2,3),cex.axis = 1.5)
censor_lvl = c(0, 0.2, 0.4, 0.6, 0.8)

for (i in 1:5){
  indx = which(susie$simulate.cor_type == "independent" & susie$simulate.censor_lvl == censor_lvl[i] & susie$simulate.num_effect != 0)
  pip.susie = unlist(lapply(indx, function(x) susie$susie.pip[[x]]))
  pip.survsvb = unlist(lapply(indx, function(x) survsvb$survivalsvb.pip[[x]]))
  pip.bvsnlp = unlist(lapply(indx, function(x) bvsnlp$bvsnlp.pip[[x]]))
  is_effect = unlist(lapply(indx, function(x) susie$simulate.is_effect[[x]]))
  
  
  ts = seq(from = 0, to = 1, by = 0.01)
  res.susie = calculate_tpr_vs_fdr(pip.susie, is_effect, ts)
  res.svb = calculate_tpr_vs_fdr(pip.survsvb, is_effect, ts)
  res.bvsnlp = calculate_tpr_vs_fdr(pip.bvsnlp, is_effect, ts)
  
  
  plot(res.susie[,2], res.susie[,1], type = "l", xlim = c(0, 0.1), ylim = c(0, 1), xlab = "FDR", ylab = "Power",
       main = paste0("X independent, effect 1-3", ",censor=", censor_lvl[i]))
  lines(res.svb[,2], res.svb[,1], type = "l", col = 2)
  lines(res.bvsnlp[,2], res.bvsnlp[,1], type = "l", col = 3)
  points(res.susie[96,2], res.susie[96, 1])
  points(res.svb[96,2], res.svb[96, 1])
  points(res.bvsnlp[96,2], res.bvsnlp[96, 1])
  legend("bottomright", legend = c("susie", "survival.svb", "bvsnlp"), col = c(1,2,3), lty = 1)
}

Version	Author	Date
f07fc2e	yunqiyang0215	2023-05-08

The dots indicate PIP threshold = 0.95.

3. Results using independent X, with data from null model.

par(mfrow = c(2,3),cex.axis = 1.5)
censor_lvl = c(0, 0.2, 0.4, 0.6, 0.8)


for (i in 1:5){
  indx = which(susie$simulate.cor_type == "independent" & susie$simulate.censor_lvl == censor_lvl[i])
  pip.susie = unlist(lapply(indx, function(x) susie$susie.pip[[x]]))
  pip.survsvb = unlist(lapply(indx, function(x) survsvb$survivalsvb.pip[[x]]))
  pip.bvsnlp = unlist(lapply(indx, function(x) bvsnlp$bvsnlp.pip[[x]]))
  is_effect = unlist(lapply(indx, function(x) susie$simulate.is_effect[[x]]))
  
  
  ts = seq(from = 0, to = 1, by = 0.01)
  res.susie = calculate_tpr_vs_fdr(pip.susie, is_effect, ts)
  res.svb = calculate_tpr_vs_fdr(pip.survsvb, is_effect, ts)
  res.bvsnlp = calculate_tpr_vs_fdr(pip.bvsnlp, is_effect, ts)
  
  
  plot(res.susie[,2], res.susie[,1], type = "l", xlim = c(0, 1), ylim = c(0, 1), xlab = "FDR", ylab = "Power",
       main = paste0("X independent, effect 0-3", ",censor=", censor_lvl[i]))
  lines(res.svb[,2], res.svb[,1], type = "l", col = 2)
  lines(res.bvsnlp[,2], res.bvsnlp[,1], type = "l", col = 3)
  points(res.susie[96,2], res.susie[96, 1])
  points(res.svb[96,2], res.svb[96, 1])
  points(res.bvsnlp[96,2], res.bvsnlp[96, 1])
  legend("bottomright", legend = c("susie", "survival.svb", "bvsnlp"), col = c(1,2,3), lty = 1)
}

Version	Author	Date
f07fc2e	yunqiyang0215	2023-05-08

The dots indicate PIP threshold = 0.95.

4. Real/independent X, censoring = 0.8.

For independent X, susie has ~1-1.5% less power than bvsnlp when fdr is around 0.1.

par(mfrow = c(1,2))
censor_lvl = 0.8
indx = which(susie$simulate.cor_type == "real" & susie$simulate.censor_lvl == censor_lvl)
pip.susie = unlist(lapply(indx, function(x) susie$susie.pip[[x]]))
pip.bvsnlp = unlist(lapply(indx, function(x) bvsnlp$bvsnlp.pip[[x]]))
is_effect = unlist(lapply(indx, function(x) susie$simulate.is_effect[[x]]))
  
ts = seq(from = 0, to = 1, by = 0.01)
res.susie = calculate_tpr_vs_fdr(pip.susie, is_effect, ts)
res.bvsnlp = calculate_tpr_vs_fdr(pip.bvsnlp, is_effect, ts)
  
  
plot(res.susie[,2], res.susie[,1], type = "l", xlim = c(0, 0.4), ylim = c(0,0.2), xlab = "FDR", ylab = "Power", main = paste0("Real X, effect 0-3", ",censor=", censor_lvl))
lines(res.bvsnlp[,2], res.bvsnlp[,1], type = "l", col = 3)
points(res.susie[96,2], res.susie[96, 1])
points(res.bvsnlp[96,2], res.bvsnlp[96, 1])
legend("topleft", legend = c("susie", "bvsnlp"), col = c(1,3), lty = 1)

#####
indx = which(susie$simulate.cor_type == "independent" & susie$simulate.censor_lvl == censor_lvl)
pip.susie = unlist(lapply(indx, function(x) susie$susie.pip[[x]]))
pip.bvsnlp = unlist(lapply(indx, function(x) bvsnlp$bvsnlp.pip[[x]]))
is_effect = unlist(lapply(indx, function(x) susie$simulate.is_effect[[x]]))
  
ts = seq(from = 0, to = 1, by = 0.01)
res.susie = calculate_tpr_vs_fdr(pip.susie, is_effect, ts)
res.bvsnlp = calculate_tpr_vs_fdr(pip.bvsnlp, is_effect, ts)
  
  
plot(res.susie[,2], res.susie[,1], type = "l", xlim = c(0, 0.15), xlab = "FDR", ylab = "Power", main = paste0("X independent, effect 0-3", ",censor=", censor_lvl))
lines(res.bvsnlp[,2], res.bvsnlp[,1], type = "l", col = 3)
points(res.susie[96,2], res.susie[96, 1])
points(res.bvsnlp[96,2], res.bvsnlp[96, 1])
legend("bottomright", legend = c("susie", "bvsnlp"), col = c(1,3), lty = 1)

Version	Author	Date
f07fc2e	yunqiyang0215	2023-05-08

5. Assess Susie CS

Among the 1000 null data, susie only wrongly output 1 credible set as below:

indx = which(susie$simulate.num_effect == 0)
res = lapply(indx, function(x) is.null(susie$susie.cs[[x]]$cs))
which(res == FALSE)
susie$susie.cs[[indx[756]]]$cs
# [1] 756
# $L1
#  [1] 178 190 203 215 230 234 269 279 281 285 287 290 296 315 321 323 326 332 343
# [20] 347 407 413 414 419 428 433 436 439 440 446 450 452 453 454 457 459 461 462
# [39] 464 470 478 482 500 517 522 527 531 563 564 567 568 573

coverage = matrix(NA, ncol = 3, nrow = 5)
censoring = c(0, 0.2, 0.4, 0.6, 0.8)
colnames(coverage) = c("effect:1", "effect:2", "effect:3")
rownames(coverage) = c("censor:0", "censor:0.2", "censor:0.4", "censor:0.6", "censor:0.8")
for (i in 1:3){
  for (j in 1:5){
    dat_indx = which(susie$simulate.num_effect == i & susie$simulate.censor_lvl == censoring[j])
    coverage[j, i] = calculate_cs_coverage(dat_indx)
  }
}

coverage
#             effect:1  effect:2  effect:3
# censor:0   0.9934211 0.9717314 0.9630542
# censor:0.2 1.0000000 0.9696970 0.9473684
# censor:0.4 0.9767442 0.9664179 0.9697802
# censor:0.6 0.9823009 0.9832636 0.9417989
# censor:0.8 0.9670330 0.9906542 0.9607143

power_cs = matrix(NA, ncol = 3, nrow = 5)
censoring = c(0, 0.2, 0.4, 0.6, 0.8)
colnames(power_cs) = c("effect:1", "effect:2", "effect:3")
rownames(power_cs) = c("censor:0", "censor:0.2", "censor:0.4", "censor:0.6", "censor:0.8")
for (i in 1:3){
  for (j in 1:5){
    dat_indx = which(susie$simulate.num_effect == i & susie$simulate.censor_lvl == censoring[j])
    cs_effect = get_cs_effect(dat_indx, p = 1000)
    is_effect = unlist(lapply(dat_indx, function(x) susie$simulate.is_effect[[x]]))
    power = sum(cs_effect ==1 & is_effect == 1)/sum(is_effect)
    power_cs[j, i] = power
  }
}

power_cs
#            effect:1  effect:2  effect:3
# censor:0      0.755 0.6992481 0.6600000
# censor:0.2    0.765 0.6450000 0.6510851
# censor:0.4    0.630 0.6641604 0.5950000
# censor:0.6    0.555 0.5925000 0.5976628
# censor:0.8    0.440 0.5300000 0.4533333

coverage = matrix(NA, ncol = 2, nrow = 5)
censoring = c(0, 0.2, 0.4, 0.6, 0.8)
cor_type = c("real", "independent")
colnames(coverage) = c("real correlation", "independent")
rownames(coverage) = c("censor:0", "censor:0.2", "censor:0.4", "censor:0.6", "censor:0.8")
for (i in 1:2){
  for (j in 1:5){
    dat_indx = which(susie$simulate.num_effect != 0 & susie$simulate.cor_type == cor_type[i] & susie$simulate.censor_lvl == censoring[j])
    coverage[j, i] = calculate_cs_coverage(dat_indx)
  }
}

coverage
#            real correlation independent
# censor:0          0.9418886   1.0000000
# censor:0.2        0.9282051   0.9976526
# censor:0.4        0.9393140   1.0000000
# censor:0.6        0.9256198   0.9972752
# censor:0.8        0.9436620   1.0000000

power_cs = matrix(NA, ncol = 2, nrow = 5)
censoring = c(0, 0.2, 0.4, 0.6, 0.8)
colnames(power_cs) = c("real correlation", "independent")
rownames(power_cs) = c("censor:0", "censor:0.2", "censor:0.4", "censor:0.6", "censor:0.8")
for (i in 1:2){
  for (j in 1:5){
    dat_indx = which(susie$simulate.num_effect != 0 & susie$simulate.cor_type == cor_type[i] & susie$simulate.censor_lvl == censoring[j])
    cs_effect = get_cs_effect(dat_indx, p = 1000)
    is_effect = unlist(lapply(dat_indx, function(x) susie$simulate.is_effect[[x]]))
    power = sum(cs_effect ==1 & is_effect == 1)/sum(is_effect)
    power_cs[j, i] = power
  }
}

power_cs
#            real correlation independent
# censor:0          0.6644407   0.7133333
# censor:0.2        0.6277129   0.7083333
# censor:0.4        0.6110184   0.6366667
# censor:0.6        0.5676127   0.6100000
# censor:0.8        0.4516667   0.5016667

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] workflowr_1.6.2
# 
# loaded via a namespace (and not attached):
#  [1] Rcpp_1.0.8.3     highr_0.9        pillar_1.6.4     compiler_4.1.1  
#  [5] bslib_0.4.1      later_1.3.0      jquerylib_0.1.4  git2r_0.28.0    
#  [9] tools_4.1.1      digest_0.6.28    jsonlite_1.7.2   evaluate_0.14   
# [13] lifecycle_1.0.1  tibble_3.1.5     pkgconfig_2.0.3  rlang_1.0.6     
# [17] cli_3.1.0        rstudioapi_0.13  yaml_2.2.1       xfun_0.27       
# [21] fastmap_1.1.0    stringr_1.4.0    knitr_1.36       fs_1.5.0        
# [25] vctrs_0.3.8      sass_0.4.4       rprojroot_2.0.2  glue_1.4.2      
# [29] R6_2.5.1         fansi_0.5.0      rmarkdown_2.11   magrittr_2.0.1  
# [33] whisker_0.4      promises_1.2.0.1 ellipsis_0.3.2   htmltools_0.5.2 
# [37] httpuv_1.6.3     utf8_1.2.2       stringi_1.7.5    cachem_1.0.6    
# [41] crayon_1.4.1