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Installation of Logica

library(devtools)
# Install Logica
install_github("borangao/Logica",dependencies = FALSE)
── R CMD build ─────────────────────────────────────────────────────────────────
* checking for file ‘/tmp/RtmpHa3036/remotesafabd40a97eda/borangao-Logica-ee9bdd6/DESCRIPTION’ ... OK
* preparing ‘Logica’:
* checking DESCRIPTION meta-information ... OK
* cleaning src
* checking for LF line-endings in source and make files and shell scripts
* checking for empty or unneeded directories
* building ‘Logica_0.1.0.tar.gz’
Warning: invalid uid value replaced by that for user 'nobody'
# Load Logica
library(Logica)

Logica Example

1. Data Formatting for Logica:

Use the example from Data preparation.

library(data.table)
library(Logica)
block_index = 1
trait = "LDL"
ancestry_1 = "EUR"
ancestry_2 = "EAS"
z1<-fread(file.path("/net/fantasia/home/borang/MALGC/pipeline_example/LDL/LDL_Block",paste0(trait , "_",ancestry_1,"_block_",block_index ,".txt")))
z2<-fread(file.path("/net/fantasia/home/borang/MALGC/pipeline_example/LDL/LDL_Block",paste0(trait , "_",ancestry_2,"_block_",block_index ,".txt")))
load(file.path("/net/fantasia/home/borang/MALGC/pipeline_example/LDL/LD_ref",paste0("LD_",block_index ,".RData")))
load(file.path("/net/fantasia/home/borang/MALGC/pipeline_example/LDL/LDL_Block",paste0(trait,"_intercept.RData")))

preprocess_data_file<-preprocess_data(z1,z2,ancestry_1_cov,ancestry_2_cov)
SNP pair up successful

2. Run Logica:

logica_res<-run_Logica(preprocess_data_file$pop1$z,preprocess_data_file$pop2$z, preprocess_data_file$pop1$R, preprocess_data_file$pop2$R, median(preprocess_data_file$pop1$z$N), 
                        median(preprocess_data_file$pop2$z$N), 
                        z1_intercept = ancestry_1_lder_intercept, z2_intercept = ancestry_2_lder_intercept, fix_intercept = TRUE)

Logica Result Interpretation:

print(logica_res)
  chr     start     end     Est_h2_1     Est_h2_2      Est_cov      Est_rho
1   1 838.67 KB 1.86 MB 8.981867e-06 4.328855e-15 6.776611e-18 3.436709e-08
     P_h2_1    P_h2_2 P_rho_score P_rho_LLK
1 0.2711317 0.5964003   0.1269275 0.9999878

Logica Result Interpretation:

  • chr: Chromosome identifier for the genomic region analyzed.
  • start and end: Genomic coordinates marking the start and end positions of the analyzed region.
  • Est_h2_1: Estimated heritability for ancestry 1, indicating the proportion of phenotypic variance explained by genetic factors within this region.
  • Est_h2_2: Estimated heritability for ancestry 2, interpreted similarly to Est_h2_1.
  • Est_cov: Estimated genetic covariance between ancestry 1 and ancestry 2, measuring the degree of shared genetic influence.
  • Est_rho: Estimated genetic correlation derived from covariance (Est_cov), standardized by heritabilities, quantifying genetic similarity across ancestries.
  • P_h2_1: P-value testing if heritability for ancestry 1 differs significantly from zero.
  • P_h2_2: P-value testing if heritability for ancestry 2 differs significantly from zero.
  • P_rho_score: Score-based test P-value assessing the significance of genetic correlation.
  • P_rho_LLK: Likelihood-based test P-value assessing the significance of genetic correlation.

Note: We also provided code for submitting slurm array jobs to enable parallele computing Step4_Logica.R and Step4_Logica.sh

3. Testing Composite Null Hypothesis

The composite null hypothesis is constructed by combining the individual null hypotheses from each genomic region.

setwd("/net/fantasia/home/borang/MALGC/pipeline_example/LDL_Block")
list.files(pattern = "Logica_res_LDL_block") -> file_list
library(data.table)
all_file<-c()
for(file in file_list){
  logica_res<-fread(file)
  all_file<-rbind(all_file,logica_res)
}

all_file$p_h2_HDMT<-p_HDMT(all_file$P_h2_1,all_file$P_h2_2)
head(all_file,10)
       V1   chr     start       end     Est_h2_1     Est_h2_2       Est_cov
    <int> <int>    <char>    <char>        <num>        <num>         <num>
 1:     1     1 838.67 KB   1.86 MB 3.433780e-10 5.794911e-11  4.018560e-18
 2:     1     1  12.19 MB   14.2 MB 9.346353e-11 6.075627e-09  2.581690e-18
 3:     1     1 226.15 MB 227.67 MB 3.273844e-09 1.138188e-09 -9.915197e-17
 4:     1    12 101.44 MB 102.73 MB 1.793660e-07 2.549977e-11  3.025052e-16
 5:     1    12 102.74 MB 104.21 MB 6.536525e-06 5.809106e-09  2.106393e-12
 6:     1    12 104.21 MB  106.2 MB 6.124684e-05 2.735646e-04  1.168637e-04
 7:     1    12  106.2 MB 108.71 MB 2.610318e-04 2.620476e-03 -4.042489e-04
 8:     1    12 108.71 MB 110.47 MB 5.898692e-06 1.891828e-09  1.916613e-13
 9:     1    12 110.47 MB 111.71 MB 2.594760e-09 7.504605e-09  3.615900e-16
10:     1    12 111.71 MB 114.12 MB 3.411864e-11 4.058087e-11 -1.007814e-20
          Est_rho       P_h2_1       P_h2_2  P_rho_score  P_rho_LLK
            <num>        <num>        <num>        <num>      <num>
 1:  2.848792e-08 2.658201e-01 5.881214e-01 0.1031767466 1.00000000
 2:  3.426000e-09 4.093623e-01 9.140943e-02 0.7841214151 0.99996779
 3: -5.136478e-08 7.025177e-02 1.748074e-01 0.5216719826 0.99411936
 4:  1.414473e-07 9.053309e-02 6.919098e-01 0.1929000374 1.00000000
 5:  1.080964e-05 4.214835e-02 1.396832e-01 0.0008370038 1.00000000
 6:  9.028337e-01 2.927519e-05 8.369749e-11 0.0672410940 0.08787425
 7: -4.887785e-01 0.000000e+00 0.000000e+00 0.3244676996 0.21361400
 8:  1.814328e-06 1.100304e-02 1.432371e-01 0.0134956030 0.99995871
 9:  8.194149e-08 8.796662e-02 6.260364e-02 0.1786418356 0.99998509
10: -2.708470e-10 7.899428e-01 8.589039e-01 0.6360415264 1.00000000
       p_h2_HDMT
           <num>
 1: 4.803381e-01
 2: 3.017791e-01
 3: 1.106228e-01
 4: 5.970586e-01
 5: 8.621228e-02
 6: 1.624945e-05
 7: 0.000000e+00
 8: 8.863226e-02
 9: 5.226862e-02
10: 8.049808e-01

sessionInfo()
R version 4.5.0 (2025-04-11)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 20.04.6 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/liblapack.so.3;  LAPACK version 3.9.0

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

time zone: America/New_York
tzcode source: system (glibc)

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] data.table_1.16.0 Logica_0.1.0      devtools_2.4.5    usethis_3.0.0    
[5] workflowr_1.7.1  

loaded via a namespace (and not attached):
 [1] gtable_0.3.5           xfun_0.47              bslib_0.8.0           
 [4] ggplot2_3.5.1          htmlwidgets_1.6.4      remotes_2.5.0         
 [7] processx_3.8.4         lattice_0.22-5         CompQuadForm_1.4.3    
[10] callr_3.7.6            vctrs_0.6.5            tools_4.5.0           
[13] ps_1.7.7               generics_0.1.4         curl_5.2.2            
[16] tibble_3.2.1           fansi_1.0.6            pkgconfig_2.0.3       
[19] Matrix_1.6-2           desc_1.4.3             lifecycle_1.0.4       
[22] compiler_4.5.0         stringr_1.5.1          git2r_0.33.0          
[25] munsell_0.5.1          getPass_0.2-4          httpuv_1.6.15         
[28] htmltools_0.5.8.1      sass_0.4.9             fdrtool_1.2.18        
[31] yaml_2.3.10            crayon_1.5.3           later_1.4.2           
[34] pillar_1.9.0           jquerylib_0.1.4        urlchecker_1.0.1      
[37] whisker_0.4.1          ellipsis_0.3.2         cachem_1.1.0          
[40] sessioninfo_1.2.3      mime_0.13              tidyselect_1.2.1      
[43] digest_0.6.37          stringi_1.8.4          reshape2_1.4.4        
[46] dplyr_1.1.4            purrr_1.0.2            RcppArmadillo_14.4.2-1
[49] splines_4.5.0          rprojroot_2.0.4        fastmap_1.2.0         
[52] grid_4.5.0             colorspace_2.1-1       cli_3.6.3             
[55] magrittr_2.0.3         pkgbuild_1.4.7         utf8_1.2.4            
[58] scales_1.3.0           promises_1.3.0         rmarkdown_2.28        
[61] httr_1.4.7             matrixStats_1.4.1      qvalue_2.36.0         
[64] HDMT_1.0.5             memoise_2.0.1          shiny_1.9.1           
[67] evaluate_0.24.0        knitr_1.48             irlba_2.3.5.1         
[70] miniUI_0.1.2           profvis_0.4.0          rlang_1.1.4           
[73] mixsqp_0.3-54          Rcpp_1.0.14            xtable_1.8-4          
[76] glue_1.8.0             susieR_0.12.35         pkgload_1.4.0         
[79] reshape_0.8.9          rstudioapi_0.16.0      jsonlite_1.8.7        
[82] plyr_1.8.9             R6_2.6.1               fs_1.6.6