Last updated: 2023-04-20

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Description:

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

Difference between old and new simulation:

  1. New simulation removed SNPs with MAF < 5%.

  2. Added the null data, no effect variable.

  3. Added censoring to data simulation.

  4. Force the effect variable not to be the first varaible.

  5. Added the procedure for estimating prior variance.

Other simulation settings, see here: https://yunqiyang0215.github.io/survival-susie/compare_pip.html

Conclusion:

  1. When X are highly correlated, susie performs best.

  2. When X are independent, and without null model data, all methods are similar.

  3. survival.svb and bvsnlp doesn’t perform well after adding data from null model.

  4. When censoring level = 0.4, susie performance starts to get worse.

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)
}
susie = readRDS("./data/dsc2/susie.rds")
survsvb = readRDS("./data/dsc2/survsvb.rds")
bvsnlp = readRDS("./data/dsc2/bvsnlp.rds")
names(susie)
[1] "DSC"                   "simulate.cor_type"     "simulate.num_effect"  
[4] "simulate.censor_lvl"   "simulate.effect_indx"  "simulate.b"           
[7] "simulate.is_effect"    "susie.effect_estimate" "susie.pip"

1. Results using real correlation structure from data

par(mfrow = c(1,3))
censor_lvl = c(0, 0.2, 0.4)
for (i in 1:3){
  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("Effect 0-3 & max cor(X)=0.9-0.99", ",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[which(ts == 0.9),2], res.susie[which(ts == 0.9), 1])
  points(res.svb[which(ts == 0.9),2], res.svb[which(ts == 0.9), 1])
  points(res.bvsnlp[which(ts == 0.9),2], res.bvsnlp[which(ts == 0.9), 1])
  
  legend("topleft", legend = c("susie", "survival.svb", "bvsnlp"), col = c(1,2,3), lty = 1)
}

Version Author Date
ba4a07c yunqiyang0215 2023-04-17

The dots indicate PIP threshold = 0.9

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

par(mfrow = c(1,3))
censor_lvl = c(0, 0.2, 0.4)

for (i in 1:3){
  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("Effect 1-3 & X independent", ",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[which(ts == 0.9),2], res.susie[which(ts == 0.9), 1])
  points(res.svb[which(ts == 0.9),2], res.svb[which(ts == 0.9), 1])
  points(res.bvsnlp[which(ts == 0.9),2], res.bvsnlp[which(ts == 0.9), 1])
  legend("bottomright", legend = c("susie", "survival.svb", "bvsnlp"), col = c(1,2,3), lty = 1)
}

Version Author Date
ba4a07c yunqiyang0215 2023-04-17

The dots indicate PIP threshold = 0.9.

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

par(mfrow = c(1,3))
censor_lvl = c(0, 0.2, 0.4)

for (i in 1:3){
  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("Effect 0-3 & X independent", ",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[which(ts == 0.9),2], res.susie[which(ts == 0.9), 1])
  points(res.svb[which(ts == 0.9),2], res.svb[which(ts == 0.9), 1])
  points(res.bvsnlp[which(ts == 0.9),2], res.bvsnlp[which(ts == 0.9), 1])
  legend("bottomright", legend = c("susie", "survival.svb", "bvsnlp"), col = c(1,2,3), lty = 1)
}

Version Author Date
904f196 yunqiyang0215 2023-04-17
ba4a07c yunqiyang0215 2023-04-17

The dots indicate PIP threshold = 0.9.

par(mfrow = c(1,3))
censor_lvl = c(0, 0.2, 0.4)

for (i in 1:3){
  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, 0.1), ylim = c(0, 1), xlab = "FDR", ylab = "Power",
       main = paste0("Effect 0-3 & X independent", ",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[which(ts == 0.9),2], res.susie[which(ts == 0.9), 1])
  points(res.svb[which(ts == 0.9),2], res.svb[which(ts == 0.9), 1])
  points(res.bvsnlp[which(ts == 0.9),2], res.bvsnlp[which(ts == 0.9), 1])
  legend("bottomright", legend = c("susie", "survival.svb", "bvsnlp"), col = c(1,2,3), lty = 1)
}

Version Author Date
904f196 yunqiyang0215 2023-04-17
ba4a07c yunqiyang0215 2023-04-17

4. Check results for survival svb

4.1 Under real correlation The null data contains 300 replicates, the non-null data has 900 replicates. On average, the non-null data contains 2 effects per data.

indx1 = which(survsvb$simulate.cor_type == "real" & survsvb$simulate.num_effect == 0)
pip1 = unlist(lapply(indx1, function(x) survsvb$survivalsvb.pip[[x]]))
sum(pip1 > 0.9)
[1] 2164
length(indx1)
[1] 300
indx2 = which(survsvb$simulate.cor_type == "real" & survsvb$simulate.num_effect != 0)
pip2 = unlist(lapply(indx2, function(x) survsvb$survivalsvb.pip[[x]]))
sum(pip2 > 0.9)
[1] 4337
length(indx2)
[1] 900
par(mfrow = c(1,2))
hist(pip1, xlab = "pip", main = "Null data: X high correlation")
hist(pip2, xlab = "pip", main = "Non-null data:  X high correlation")

4.2 Under real correlation The null data contains 300 replicates, the non-null data has 900 replicates. On average, the non-null data contains 2 effects per data.

indx1 = which(survsvb$simulate.cor_type == "independent" & survsvb$simulate.num_effect == 0)
pip1 = unlist(lapply(indx1, function(x) survsvb$survivalsvb.pip[[x]]))
sum(pip1 > 0.9)
[1] 1868
length(indx1)
[1] 300
indx2 = which(survsvb$simulate.cor_type == "independent" & survsvb$simulate.num_effect != 0)
pip2 = unlist(lapply(indx2, function(x) survsvb$survivalsvb.pip[[x]]))
sum(pip2 > 0.9)
[1] 1208
length(indx2)
[1] 900
par(mfrow = c(1,2))
hist(pip1, xlab = "pip", main = "Null data: X independent")
hist(pip2, xlab = "pip", main = "Non-null data: X independent")


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