Causal Mediation Analysis
Jie Zhou
2023-11-29
Last updated: 2024-06-09
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madi-brussels-pertussis-thailand/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 8c46744 | Jie Zhou | 2024-06-03 | remove antigen elisa |
| html | 8c46744 | Jie Zhou | 2024-06-03 | remove antigen elisa |
| Rmd | 532d320 | Jie Zhou | 2024-02-21 | madi meeting |
| html | 532d320 | Jie Zhou | 2024-02-21 | madi meeting |
| Rmd | 528d126 | Jie Zhou | 2024-01-23 | added pls and pca based mediation analysis |
| html | 528d126 | Jie Zhou | 2024-01-23 | added pls and pca based mediation analysis |
| Rmd | 30792a7 | Jie Zhou | 2024-01-13 | added pls mediation analysis |
| html | 30792a7 | Jie Zhou | 2024-01-13 | added pls mediation analysis |
Attaching package: 'glue'The following object is masked from 'package:gdata':
trimhere() starts at C:/Users/Jie Zhou/Desktop/madi-brussels-pertussis-thailand0.1 Model description
0.1.1 Definition
Let \(a\) be the treatment whit \(a=0\) for no maternal vaccination and \(a=1\) for maternal vaccination. \(M\) represents mediator,i.e, maternal antibodies, and \(Y\) the outcome, i.e., infant antibodies.
Causal direct effects of maternal vaccination on infant antibodies are defined as \[\tau_i=Y_i(1,M_i(a))-Y_i(0,M_i(a));\] while causal mediation effects of maternal antibodies on infant antibodies are defined as \[\alpha_i=Y_i(a,M_i(1))-Y_i(a,M_i(0))\]
0.1.2 model
For mediator, we have \[M_i=\gamma_0+\gamma_1a_i+e_{mi}\] For outcome, we have \[Y_i=\beta_0+\beta_1M_i+\beta_2a_i+e_{yi}\]
0.2 Analysis pipeline
The treatment is infant vaccination plus maternal vaccination, mediator is maternal cord blood features, and outcome is infant features. Even though there are eight cord blood features in total, only the ELISA-related three features are measured in both maternal +/- groups. So these three features will be used as mediators and fifty three infant features as outcomes.
[1] "All the outcome (infant antibodies) considered: " [1] "DT_FcgR2a" "DT_FcgR3b" "DT_IgG" "DT_IgG1" "DT_IgG2"
[6] "DT_IgG3" "DT_IgG4" "FHA_FcgR2a" "FHA_FcgR3b" "FHA_IgG"
[11] "FHA_IgG1" "FHA_IgG2" "FHA_IgG3" "FHA_IgG4" "PRN_FcgR2a"
[16] "PRN_FcgR3b" "PRN_IgG" "PRN_IgG1" "PRN_IgG2" "PRN_IgG3"
[21] "PRN_IgG4" "PT_FcgR2a" "PT_FcgR3b" "PT_IgG" "PT_IgG1"
[26] "PT_IgG2" "PT_IgG3" "PT_IgG4" "TT_FcgR2a" "TT_FcgR3b"
[31] "TT_IgG" "TT_IgG1" "TT_IgG2" "TT_IgG3" "TT_IgG4"
[36] "DT_ADCD" "FHA_ADCD" "PRN_ADCD" "PT_ADCD" "TT_ADCD"
[41] "DT_ADCP" "FHA_ADCP" "PRN_ADCP" "PT_ADCP" "TT_ADCP"
[46] "DT_ADNP" "FHA_ADNP" "PRN_ADNP" "PT_ADNP" "TT_ADNP" [1] "All the mediators (maternal cord blood total IgG): "[1] "ELISA_FHA_IgG" "ELISA_PRN_IgG" "ELISA_PT_IgG" 
0.3 Results 1: matimm+/-
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0.3.1 Direct causal effects
outcome mediator deffect dlower dupper dpvalue dfdr
1 PT_IgG ELISA_PT_IgG -0.471 -0.742 -0.204 0.000 0.000
2 FHA_ADCP ELISA_FHA_IgG -0.122 -0.215 -0.032 0.008 0.120
3 FHA_IgG ELISA_FHA_IgG -0.241 -0.430 -0.039 0.020 0.168
4 FHA_IgG2 ELISA_FHA_IgG -0.273 -0.518 -0.033 0.028 0.168
5 PT_IgG1 ELISA_PT_IgG -0.463 -0.865 -0.058 0.028 0.168
6 FHA_IgG4 ELISA_FHA_IgG -0.353 -0.699 -0.004 0.050 0.249
7 PRN_FcgR2a ELISA_PRN_IgG 0.299 -0.011 0.615 0.058 0.249
8 PT_IgG3 ELISA_PT_IgG 0.224 -0.024 0.465 0.080 0.300
9 FHA_ADNP ELISA_FHA_IgG 0.079 -0.021 0.190 0.130 0.425
10 PRN_FcgR3b ELISA_PRN_IgG 0.417 -0.135 0.994 0.142 0.425
11 FHA_FcgR2a ELISA_FHA_IgG 0.163 -0.055 0.394 0.156 0.425
12 PT_IgG2 ELISA_PT_IgG -0.083 -0.201 0.040 0.182 0.441
13 PRN_ADCD ELISA_PRN_IgG 0.156 -0.080 0.390 0.202 0.441
14 PT_ADNP ELISA_PT_IgG 0.112 -0.053 0.290 0.206 0.441
15 PRN_IgG2 ELISA_PRN_IgG 0.158 -0.101 0.411 0.222 0.444
16 FHA_FcgR3b ELISA_FHA_IgG 0.226 -0.176 0.624 0.252 0.473
17 PT_IgG4 ELISA_PT_IgG -0.055 -0.156 0.048 0.272 0.480
18 PRN_IgG ELISA_PRN_IgG -0.132 -0.407 0.136 0.324 0.540
19 PRN_IgG1 ELISA_PRN_IgG 0.219 -0.233 0.697 0.348 0.543
20 PRN_ADNP ELISA_PRN_IgG 0.032 -0.033 0.099 0.362 0.543
21 PT_ADCD ELISA_PT_IgG 0.149 -0.251 0.539 0.446 0.637
22 PRN_IgG3 ELISA_PRN_IgG 0.100 -0.229 0.413 0.500 0.682
23 FHA_ADCD ELISA_FHA_IgG 0.070 -0.190 0.327 0.582 0.697
24 PRN_ADCP ELISA_PRN_IgG -0.028 -0.131 0.082 0.592 0.697
25 PRN_IgG4 ELISA_PRN_IgG 0.060 -0.182 0.297 0.600 0.697
26 FHA_IgG3 ELISA_FHA_IgG 0.085 -0.234 0.383 0.604 0.697
27 PT_FcgR3b ELISA_PT_IgG -0.054 -0.346 0.245 0.724 0.804
28 PT_ADCP ELISA_PT_IgG -0.021 -0.150 0.101 0.754 0.808
29 PT_FcgR2a ELISA_PT_IgG -0.040 -0.372 0.281 0.824 0.852
30 FHA_IgG1 ELISA_FHA_IgG 0.015 -0.295 0.324 0.896 0.8960.3.2 Mediation causal effects
outcome mediator meffect mlower mupper mpvalue mfdr
1 PT_IgG3 ELISA_PT_IgG -0.034 -0.127 0.018 0.278 0.966
2 PT_ADCD ELISA_PT_IgG 0.041 -0.034 0.166 0.366 0.966
3 FHA_IgG1 ELISA_FHA_IgG -0.030 -0.143 0.038 0.464 0.966
4 PT_IgG ELISA_PT_IgG 0.022 -0.028 0.101 0.480 0.966
5 FHA_IgG2 ELISA_FHA_IgG -0.032 -0.139 0.053 0.482 0.966
6 PT_IgG1 ELISA_PT_IgG 0.026 -0.054 0.141 0.538 0.966
7 PT_FcgR2a ELISA_PT_IgG 0.021 -0.039 0.119 0.542 0.966
8 FHA_IgG ELISA_FHA_IgG -0.012 -0.064 0.024 0.546 0.966
9 PRN_ADNP ELISA_PRN_IgG -0.004 -0.022 0.008 0.594 0.966
10 FHA_ADNP ELISA_FHA_IgG -0.005 -0.035 0.013 0.624 0.966
11 FHA_ADCP ELISA_FHA_IgG -0.005 -0.028 0.012 0.626 0.966
12 PRN_IgG ELISA_PRN_IgG 0.008 -0.040 0.064 0.702 0.966
13 FHA_ADCD ELISA_FHA_IgG -0.010 -0.072 0.033 0.702 0.966
14 FHA_IgG3 ELISA_FHA_IgG -0.010 -0.086 0.042 0.704 0.966
15 PRN_FcgR3b ELISA_PRN_IgG 0.019 -0.079 0.147 0.708 0.966
16 PRN_ADCP ELISA_PRN_IgG 0.003 -0.014 0.027 0.708 0.966
17 FHA_IgG4 ELISA_FHA_IgG -0.013 -0.093 0.050 0.720 0.966
18 FHA_FcgR3b ELISA_FHA_IgG 0.010 -0.058 0.092 0.722 0.966
19 PT_FcgR3b ELISA_PT_IgG 0.011 -0.044 0.091 0.726 0.966
20 PRN_IgG1 ELISA_PRN_IgG 0.014 -0.056 0.123 0.732 0.966
21 PRN_ADCD ELISA_PRN_IgG -0.007 -0.056 0.034 0.736 0.966
22 PT_IgG2 ELISA_PT_IgG -0.005 -0.037 0.020 0.780 0.966
23 PRN_IgG4 ELISA_PRN_IgG 0.005 -0.029 0.051 0.782 0.966
24 FHA_FcgR2a ELISA_FHA_IgG 0.003 -0.037 0.045 0.878 0.966
25 PRN_IgG3 ELISA_PRN_IgG -0.005 -0.083 0.050 0.892 0.966
26 PT_ADNP ELISA_PT_IgG -0.003 -0.049 0.035 0.912 0.966
27 PT_ADCP ELISA_PT_IgG 0.001 -0.025 0.031 0.942 0.966
28 PT_IgG4 ELISA_PT_IgG 0.001 -0.020 0.022 0.948 0.966
29 PRN_IgG2 ELISA_PRN_IgG 0.000 -0.045 0.047 0.954 0.966
30 PRN_FcgR2a ELISA_PRN_IgG 0.000 -0.058 0.050 0.966 0.9660.3.3 Total effects
outcome mediator teffect tlower tupper tpvalue tfdr
1 PT_IgG ELISA_PT_IgG -0.449 -0.717 -0.182 0.000 0.000
2 FHA_ADCP ELISA_FHA_IgG -0.127 -0.220 -0.034 0.002 0.030
3 FHA_IgG2 ELISA_FHA_IgG -0.305 -0.559 -0.046 0.018 0.150
4 FHA_IgG ELISA_FHA_IgG -0.254 -0.450 -0.040 0.020 0.150
5 PT_IgG1 ELISA_PT_IgG -0.437 -0.840 -0.031 0.034 0.204
6 FHA_IgG4 ELISA_FHA_IgG -0.367 -0.724 -0.010 0.046 0.230
7 PRN_FcgR2a ELISA_PRN_IgG 0.299 -0.012 0.618 0.060 0.257
8 PT_IgG3 ELISA_PT_IgG 0.190 -0.056 0.433 0.130 0.420
9 PRN_FcgR3b ELISA_PRN_IgG 0.436 -0.116 1.030 0.136 0.420
10 FHA_FcgR2a ELISA_FHA_IgG 0.166 -0.061 0.397 0.154 0.420
11 PT_IgG2 ELISA_PT_IgG -0.087 -0.211 0.036 0.158 0.420
12 FHA_ADNP ELISA_FHA_IgG 0.074 -0.025 0.179 0.168 0.420
13 PT_ADNP ELISA_PT_IgG 0.109 -0.063 0.294 0.208 0.431
14 PRN_ADCD ELISA_PRN_IgG 0.149 -0.095 0.385 0.226 0.431
15 FHA_FcgR3b ELISA_FHA_IgG 0.236 -0.183 0.644 0.230 0.431
16 PRN_IgG2 ELISA_PRN_IgG 0.158 -0.095 0.406 0.230 0.431
17 PT_IgG4 ELISA_PT_IgG -0.054 -0.154 0.047 0.274 0.484
18 PRN_IgG1 ELISA_PRN_IgG 0.233 -0.219 0.709 0.308 0.513
19 PT_ADCD ELISA_PT_IgG 0.190 -0.203 0.600 0.332 0.524
20 PRN_IgG ELISA_PRN_IgG -0.124 -0.399 0.146 0.358 0.537
21 PRN_ADNP ELISA_PRN_IgG 0.028 -0.036 0.098 0.420 0.600
22 PRN_IgG3 ELISA_PRN_IgG 0.094 -0.233 0.407 0.520 0.709
23 PRN_IgG4 ELISA_PRN_IgG 0.065 -0.177 0.309 0.594 0.775
24 PRN_ADCP ELISA_PRN_IgG -0.025 -0.129 0.081 0.640 0.775
25 FHA_ADCD ELISA_FHA_IgG 0.060 -0.201 0.332 0.666 0.775
26 FHA_IgG3 ELISA_FHA_IgG 0.075 -0.238 0.380 0.672 0.775
27 PT_ADCP ELISA_PT_IgG -0.020 -0.151 0.102 0.746 0.829
28 PT_FcgR3b ELISA_PT_IgG -0.042 -0.330 0.251 0.780 0.836
29 FHA_IgG1 ELISA_FHA_IgG -0.015 -0.334 0.301 0.924 0.934
30 PT_FcgR2a ELISA_PT_IgG -0.018 -0.344 0.291 0.934 0.934
sessionInfo()R version 4.4.0 (2024-04-24 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows 10 x64 (build 19045)
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.utf8
[2] LC_CTYPE=English_United States.utf8
[3] LC_MONETARY=English_United States.utf8
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.utf8
time zone: America/New_York
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] RColorBrewer_1.1-3 here_1.0.1 glue_1.7.0 RPostgres_1.4.6
[5] DT_0.33 DBI_1.2.2 pls_2.8-3 mediation_4.5.0
[9] sandwich_3.1-0 mvtnorm_1.2-4 Matrix_1.7-0 MASS_7.3-60.2
[13] ggpubr_0.6.0 ggExtra_0.10.1 e1071_1.7-14 ggfortify_0.4.17
[17] rmarkdown_2.26 knitr_1.46 ggplot2_3.5.1 gdata_3.0.0
[21] tidyr_1.3.1 tidyquery_0.2.4 dplyr_1.1.4
loaded via a namespace (and not attached):
[1] tidyselect_1.2.1 blob_1.2.4 fastmap_1.1.1 promises_1.3.0
[5] digest_0.6.35 rpart_4.1.23 timechange_0.3.0 mime_0.12
[9] lifecycle_1.0.4 cluster_2.1.6 magrittr_2.0.3 compiler_4.4.0
[13] rlang_1.1.3 Hmisc_5.1-2 sass_0.4.9 tools_4.4.0
[17] utf8_1.2.4 yaml_2.3.8 data.table_1.15.4 ggsignif_0.6.4
[21] htmlwidgets_1.6.4 bit_4.0.5 abind_1.4-5 miniUI_0.1.1.1
[25] workflowr_1.7.1 withr_3.0.0 foreign_0.8-86 purrr_1.0.2
[29] nnet_7.3-19 grid_4.4.0 fansi_1.0.6 git2r_0.33.0
[33] xtable_1.8-4 colorspace_2.1-0 scales_1.3.0 gtools_3.9.5
[37] cli_3.6.2 generics_0.1.3 rstudioapi_0.16.0 minqa_1.2.6
[41] cachem_1.0.8 proxy_0.4-27 stringr_1.5.1 splines_4.4.0
[45] base64enc_0.1-3 vctrs_0.6.5 boot_1.3-30 jsonlite_1.8.8
[49] carData_3.0-5 queryparser_0.3.2 car_3.1-2 hms_1.1.3
[53] bit64_4.0.5 rstatix_0.7.2 Formula_1.2-5 htmlTable_2.4.2
[57] jquerylib_0.1.4 nloptr_2.0.3 lubridate_1.9.3 stringi_1.8.3
[61] gtable_0.3.5 later_1.3.2 lme4_1.1-35.3 munsell_0.5.1
[65] tibble_3.2.1 pillar_1.9.0 htmltools_0.5.8.1 R6_2.5.1
[69] rprojroot_2.0.4 lpSolve_5.6.20 evaluate_0.23 shiny_1.8.1.1
[73] lattice_0.22-6 backports_1.4.1 broom_1.0.5 httpuv_1.6.15
[77] bslib_0.7.0 class_7.3-22 Rcpp_1.0.12 nlme_3.1-164
[81] gridExtra_2.3 checkmate_2.3.1 whisker_0.4.1 xfun_0.43
[85] fs_1.6.4 zoo_1.8-12 pkgconfig_2.0.3