High-dimensional mediation analysis for continuous outcome with confounders using overlap weighting method in observational epigenetic study.
Composite null hypothesis
High-dimensional mediation model
Joint significant test
Overlap weighting
Propensity score
Journal
BMC medical research methodology
ISSN: 1471-2288
Titre abrégé: BMC Med Res Methodol
Pays: England
ID NLM: 100968545
Informations de publication
Date de publication:
03 Jun 2024
03 Jun 2024
Historique:
received:
15
03
2024
accepted:
22
05
2024
medline:
4
6
2024
pubmed:
4
6
2024
entrez:
3
6
2024
Statut:
epublish
Résumé
Mediation analysis is a powerful tool to identify factors mediating the causal pathway of exposure to health outcomes. Mediation analysis has been extended to study a large number of potential mediators in high-dimensional data settings. The presence of confounding in observational studies is inevitable. Hence, it's an essential part of high-dimensional mediation analysis (HDMA) to adjust for the potential confounders. Although the propensity score (PS) related method such as propensity score regression adjustment (PSR) and inverse probability weighting (IPW) has been proposed to tackle this problem, the characteristics with extreme propensity score distribution of the PS-based method would result in the biased estimation. In this article, we integrated the overlapping weighting (OW) technique into HDMA workflow and proposed a concise and powerful high-dimensional mediation analysis procedure consisting of OW confounding adjustment, sure independence screening (SIS), de-biased Lasso penalization, and joint-significance testing underlying the mixture null distribution. We compared the proposed method with the existing method consisting of PS-based confounding adjustment, SIS, minimax concave penalty (MCP) variable selection, and classical joint-significance testing. Simulation studies demonstrate the proposed procedure has the best performance in mediator selection and estimation. The proposed procedure yielded the highest true positive rate, acceptable false discovery proportion level, and lower mean square error. In the empirical study based on the GSE117859 dataset in the Gene Expression Omnibus database using the proposed method, we found that smoking history may lead to the estimated natural killer (NK) cell level reduction through the mediation effect of some methylation markers, mainly including methylation sites cg13917614 in CNP gene and cg16893868 in LILRA2 gene. The proposed method has higher power, sufficient false discovery rate control, and precise mediation effect estimation. Meanwhile, it is feasible to be implemented with the presence of confounders. Hence, our method is worth considering in HDMA studies.
Sections du résumé
BACKGROUND
BACKGROUND
Mediation analysis is a powerful tool to identify factors mediating the causal pathway of exposure to health outcomes. Mediation analysis has been extended to study a large number of potential mediators in high-dimensional data settings. The presence of confounding in observational studies is inevitable. Hence, it's an essential part of high-dimensional mediation analysis (HDMA) to adjust for the potential confounders. Although the propensity score (PS) related method such as propensity score regression adjustment (PSR) and inverse probability weighting (IPW) has been proposed to tackle this problem, the characteristics with extreme propensity score distribution of the PS-based method would result in the biased estimation.
METHODS
METHODS
In this article, we integrated the overlapping weighting (OW) technique into HDMA workflow and proposed a concise and powerful high-dimensional mediation analysis procedure consisting of OW confounding adjustment, sure independence screening (SIS), de-biased Lasso penalization, and joint-significance testing underlying the mixture null distribution. We compared the proposed method with the existing method consisting of PS-based confounding adjustment, SIS, minimax concave penalty (MCP) variable selection, and classical joint-significance testing.
RESULTS
RESULTS
Simulation studies demonstrate the proposed procedure has the best performance in mediator selection and estimation. The proposed procedure yielded the highest true positive rate, acceptable false discovery proportion level, and lower mean square error. In the empirical study based on the GSE117859 dataset in the Gene Expression Omnibus database using the proposed method, we found that smoking history may lead to the estimated natural killer (NK) cell level reduction through the mediation effect of some methylation markers, mainly including methylation sites cg13917614 in CNP gene and cg16893868 in LILRA2 gene.
CONCLUSIONS
CONCLUSIONS
The proposed method has higher power, sufficient false discovery rate control, and precise mediation effect estimation. Meanwhile, it is feasible to be implemented with the presence of confounders. Hence, our method is worth considering in HDMA studies.
Identifiants
pubmed: 38831262
doi: 10.1186/s12874-024-02254-x
pii: 10.1186/s12874-024-02254-x
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
125Subventions
Organisme : National Social Science Fund of China
ID : 21CTJ009
Organisme : National Natural Science Foundation of China
ID : 81703325
Informations de copyright
© 2024. The Author(s).
Références
Baron RM, Kenny DA. The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. J Personal Soc Psychol. 1986;51(6):1173–82. https://doi.org/10.1037//0022-3514.51.6.1173.
doi: 10.1037//0022-3514.51.6.1173
Huan T, Joehanes R, Schurmann C, Schramm K, Pilling LC, Peters MJ, et al. A whole-blood transcriptome meta-analysis identifies gene expression signatures of cigarette smoking. Hum Mol Genet. 2016;25(21):4611–23. https://doi.org/10.1093/hmg/ddw288 .
doi: 10.1093/hmg/ddw288
pubmed: 28158590
pmcid: 5975607
MacKinnon DP, Lockwood CM, Hoffman JM, West SG, Sheets V. A comparison of methods to test mediation and other intervening variable effects. Psychol Methods. 2002;7(1):83–104. https://doi.org/10.1037/1082-989x.7.1.83 .
doi: 10.1037/1082-989x.7.1.83
pubmed: 11928892
pmcid: 2819363
Biesanz JC, Falk CF, Savalei V. Assessing Mediational models: testing and interval estimation for Indirect effects. Multivar Behav Res. 2010;45(4):661–701. https://doi.org/10.1080/00273171.2010.498292 .
doi: 10.1080/00273171.2010.498292
Gao Y, Yang H, Fang R, Zhang Y, Goode EL, Cui Y. Testing mediation effects in high-dimensional epigenetic studies. Front Genet. 2019;10:1195. https://doi.org/10.3389/fgene.2019.01195 .
doi: 10.3389/fgene.2019.01195
pubmed: 31824577
pmcid: 6883258
Taylor AB, MacKinnon DP. Four applications of permutation methods to testing a single-mediator model. Behav Res Methods. 2012;44(3):806–44. https://doi.org/10.3758/s13428-011-0181-x .
doi: 10.3758/s13428-011-0181-x
pubmed: 22311738
pmcid: 3428517
VanderWeele TJ. Marginal structural models for the estimation of direct and indirect effects. Epidemiol (Cambridge Mass). 2009;20(1):18–26. https://doi.org/10.1097/EDE.0b013e31818f69ce .
doi: 10.1097/EDE.0b013e31818f69ce
VanderWeele TJ, Vansteelandt S. Mediation analysis with multiple mediators. Epidemiol Methods. 2014;2(1):95–115. https://doi.org/10.1515/em-2012-0010 .
doi: 10.1515/em-2012-0010
pubmed: 25580377
pmcid: 4287269
Zhang H, Zheng Y, Zhang Z, Gao T, Joyce B, Yoon G, et al. Estimating and testing high-dimensional mediation effects in epigenetic studies. Bioinf (Oxford England). 2016;32(20):3150–4. https://doi.org/10.1093/bioinformatics/btw351 .
doi: 10.1093/bioinformatics/btw351
Bibikova M, Barnes B, Tsan C, Ho V, Klotzle B, Le JM, et al. High density DNA methylation array with single CpG site resolution. Genomics. 2011;98(4):288–95. https://doi.org/10.1016/j.ygeno.2011.07.007 .
doi: 10.1016/j.ygeno.2011.07.007
pubmed: 21839163
Harlid S, Xu Z, Panduri V, Sandler DP, Taylor JA. CpG sites associated with cigarette smoking: analysis of epigenome-wide data from the Sister Study. Environ Health Perspect. 2014;122(7):673–8. https://doi.org/10.1289/ehp.1307480 .
doi: 10.1289/ehp.1307480
pubmed: 24704585
pmcid: 4080519
Toyooka S, Maruyama R, Toyooka KO, McLerran D, Feng Z, Fukuyama Y, et al. Smoke exposure, histologic type and geography-related differences in the methylation profiles of non-small cell lung cancer. Int J Cancer. 2003;103(2):153–60. https://doi.org/10.1002/ijc.10787 .
doi: 10.1002/ijc.10787
pubmed: 12455028
Liu Z, Shen J, Barfield R, Schwartz J, Baccarelli AA, Lin X. Large-scale hypothesis testing for Causal Mediation effects with Applications in Genome-wide epigenetic studies. J Am Stat Assoc. 2022;117(537):67–81. https://doi.org/10.1080/01621459.2021.1914634 .
doi: 10.1080/01621459.2021.1914634
pubmed: 35989709
Luo L, Yan Y, Cui Y, Yuan X, Yu Z. Linear high-dimensional mediation models adjusting for confounders using propensity score method. Front Genet. 2022;13:961148. https://doi.org/10.3389/fgene.2022.961148 .
doi: 10.3389/fgene.2022.961148
pubmed: 36299590
pmcid: 9589256
Luo C, Fa B, Yan Y, Wang Y, Zhou Y, Zhang Y, et al. High-dimensional mediation analysis in survival models. PLoS Comput Biol. 2020;16(4):e1007768. https://doi.org/10.1371/journal.pcbi.1007768 .
doi: 10.1371/journal.pcbi.1007768
pubmed: 32302299
pmcid: 7190184
Yu Z, Cui Y, Wei T, Ma Y, Luo C. High-dimensional mediation analysis with confounders in Survival models. Front Genet. 2021;12:688871. https://doi.org/10.3389/fgene.2021.688871 .
doi: 10.3389/fgene.2021.688871
pubmed: 34262599
pmcid: 8273300
Perera C, Zhang H, Zheng Y, Hou L, Qu A, Zheng C, et al. HIMA2: high-dimensional mediation analysis and its application in epigenome-wide DNA methylation data. BMC Bioinformatics. 2022;23(1):296. https://doi.org/10.1186/s12859-022-04748-1 .
doi: 10.1186/s12859-022-04748-1
pubmed: 35879655
pmcid: 9310002
Dai JY, Stanford JL, LeBlanc M. A multiple-testing procedure for high-dimensional mediation hypotheses. J Am Stat Assoc. 2022;117(537):198–213. https://doi.org/10.1080/01621459.2020.1765785 .
doi: 10.1080/01621459.2020.1765785
pubmed: 35400115
Zhang H, Zheng Y, Hou L, Zheng C, Liu L. Mediation analysis for survival data with high-dimensional mediators. Bioinf (Oxford England). 2021;37(21):3815–21. https://doi.org/10.1093/bioinformatics/btab564 .
doi: 10.1093/bioinformatics/btab564
Heinze G, Jüni P. An overview of the objectives of and the approaches to propensity score analyses. Eur Heart J. 2011;32(14):1704–8. https://doi.org/10.1093/eurheartj/ehr031 .
doi: 10.1093/eurheartj/ehr031
pubmed: 21362706
Stuart EA. Matching methods for causal inference: a review and a look forward. Stat Science: Rev J Inst Math Stat. 2010;25(1):1–21. https://doi.org/10.1214/09-STS313 .
doi: 10.1214/09-STS313
pubmed: 20871802
pmcid: 2943670
Lee BK, Lessler J, Stuart EA. Weight trimming and propensity score weighting. PLoS One. 2011;6(3):e18174. https://doi.org/10.1371/journal.pone.0018174 .
doi: 10.1371/journal.pone.0018174
pubmed: 21483818
pmcid: 3069059
Li F, Thomas LE, Li F. Addressing Extreme Propensity scores via the Overlap weights. Am J Epidemiol. 2019;188(1):250–7. https://doi.org/10.1093/aje/kwy201 .
doi: 10.1093/aje/kwy201
pubmed: 30189042
Thomas LE, Li F, Pencina MJ. Overlap weighting: a propensity score method that mimics attributes of a Randomized Clinical Trial. JAMA. 2020;323(23):2417. https://doi.org/10.1001/jama.2020.7819 .
doi: 10.1001/jama.2020.7819
pubmed: 32369102
Mlcoch T, Hrnciarova T, Tuzil J, Zadak J, Marian M, Dolezal T. Propensity Score Weighting Using Overlap Weights: A New Method Applied to Regorafenib Clinical Data and a Cost-Effectiveness Analysis. Value in Health. 2019;22(12):1370-7. doi: 10.1016/j.jval.2019.06.010.
doi: 10.1016/j.jval.2019.06.010
pubmed: 31806193
Vanderweele TJ, Vansteelandt S, Robins JM. Effect decomposition in the presence of an exposure-induced mediator-outcome confounder. Epidemiol (Cambridge Mass). 2014;25(2):300–6. https://doi.org/10.1097/EDE.0000000000000034 .
doi: 10.1097/EDE.0000000000000034
Perera C, Zhang H, Zheng Y, Hou L, Qu A, Zheng C, et al. HIMA2: high-dimensional mediation analysis and its application in epigenome-wide DNA methylation data. BMC Bioinformatics. 2022;23(1). https://doi.org/10.1186/s12859-022-04748-1 .
doi: 10.1186/s12859-022-04748-1
pubmed: 35879655
pmcid: 9310002
Basu D. Randomization analysis of Experimental Data: the Fisher randomization test. J Am Stat Assoc. 1980;75(371):575–82. https://doi.org/10.1080/01621459.1980.10477512 .
doi: 10.1080/01621459.1980.10477512
Rubin DB. Comment. J American Statis Assoc. 1986;81(396):961–2. https://doi.org/10.1080/01621459.1986.10478355 .
doi: 10.1080/01621459.1986.10478355
Imbens GW, Rubin DB. Causal inference for statistics, Social, and Biomedical sciences: an introduction. Cambridge: Cambridge University Press; 2015.
doi: 10.1017/CBO9781139025751
Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika. 1983;70(1):41–55. https://doi.org/10.1093/biomet/70.1.41 .
doi: 10.1093/biomet/70.1.41
Haukoos JS, Lewis RJ. The Propensity score. JAMA. 2015;314(15):1637–8. https://doi.org/10.1001/jama.2015.13480 .
doi: 10.1001/jama.2015.13480
pubmed: 26501539
pmcid: 4866501
Lee BK, Lessler J, Stuart EA. Improving propensity score weighting using machine learning. Stat Med. 2010;29(3):337–46. https://doi.org/10.1002/sim.3782 .
doi: 10.1002/sim.3782
pubmed: 19960510
pmcid: 2807890
Abdia Y, Kulasekera KB, Datta S, Boakye M, Kong M. Propensity scores based methods for estimating average treatment effect and average treatment effect among treated: a comparative study. Biometrical J Biometrische Z. 2017;59(5):967–85. https://doi.org/10.1002/bimj.201600094 .
doi: 10.1002/bimj.201600094
pubmed: 28436047
Rosenbaum PR, Rubin DB. Constructing a Control Group Using Multivariate Matched Sampling Methods That Incorporate the Propensity Score. Am Stat. 1985;39(1):33–8. https://doi.org/10.1080/00031305.1985.10479383 .
doi: 10.1080/00031305.1985.10479383
Rosenbaum PR, Rubin DB. Reducing Bias in Observational studies using subclassification on the Propensity score. J Am Stat Assoc. 1984;79(387):516–24. https://doi.org/10.1080/01621459.1984.10478078 .
doi: 10.1080/01621459.1984.10478078
Robins JM, Rotnitzky A, Zhao LP. Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. J Am Stat Assoc. 1995;90(429):106–21. https://doi.org/10.1080/01621459.1995.10476493 .
doi: 10.1080/01621459.1995.10476493
Austin PC. An introduction to propensity score methods for reducing the effects of confounding in observational studies. Multivar Behav Res. 2011;46(3):399–424. https://doi.org/10.1080/00273171.2011.568786 .
doi: 10.1080/00273171.2011.568786
Li F, Morgan KL, Zaslavsky AM. Balancing covariates via Propensity score weighting. J Am Stat Assoc. 2018;113(521):390–400. https://doi.org/10.1080/01621459.2016.1260466 .
doi: 10.1080/01621459.2016.1260466
Fan J, Lv J. Sure Independence Screening for Ultrahigh Dimensional Feature Space. J Royal Stat Soc Ser B: Stat Methodol. 2008;70(5):849–911. https://doi.org/10.1111/j.1467-9868.2008.00674.x .
doi: 10.1111/j.1467-9868.2008.00674.x
Zhang C-H. Nearly unbiased variable selection under minimax concave penalty. Annals Stat. 2010;38(2):894–942. https://doi.org/10.1214/09-AOS729 .
doi: 10.1214/09-AOS729
Maity AK, Basu S. Highest posterior model computation and variable selection via simulated annealing. The New England J Statis Data Sci. 2023;1(2):200–7. https://doi.org/10.51387/23-NEJSDS40 .
doi: 10.51387/23-NEJSDS40
Breheny P, Huang J. Coordinate Descent algorithms for Nonconvex Penalized Regression, with applications to Biological feature selection. Annals Appl Stat. 2011;5(1):232–53. https://doi.org/10.1214/10-AOAS388 .
doi: 10.1214/10-AOAS388
Huang Y-T, Pan W-C. Hypothesis test of mediation effect in causal mediation model with high-dimensional continuous mediators. Biometrics. 2016;72(2):402–13. https://doi.org/10.1111/biom.12421 .
doi: 10.1111/biom.12421
pubmed: 26414245
Benjamini Y, Hochberg Y. Controlling the false Discovery rate: a practical and powerful Approach to multiple testing. J Roy Stat Soc: Ser B (Methodol). 1995;57(1):289–300. https://doi.org/10.1111/j.2517-6161.1995.tb02031.x .
doi: 10.1111/j.2517-6161.1995.tb02031.x
Hochberg Y. A sharper Bonferroni procedure for multiple tests of significance. Biometrika. 1988;75(4):800–2. https://doi.org/10.1093/biomet/75.4.800 .
doi: 10.1093/biomet/75.4.800
Huang Y-T. Joint significance tests for mediation effects of socioeconomic adversity on adiposity via epigenetics. Annals Appl Stat. 2018;12(3):1535–57. https://doi.org/10.1214/17-AOAS1120 .
doi: 10.1214/17-AOAS1120
Fang EX, Ning Y, Liu H. Testing and confidence intervals for high Dimensional Proportional hazards Model. J Royal Stat Soc Ser B Stat Methodol. 2017;79(5):1415–37. https://doi.org/10.1111/rssb.12224 .
doi: 10.1111/rssb.12224
Chen F, Hu W, Cai J, Chen S, Si A, Zhang Y, et al. Instrumental variable-based high-dimensional mediation analysis with unmeasured confounders for survival data in the observational epigenetic study. Front Genet. 2023;14:1092489. https://doi.org/10.3389/fgene.2023.1092489 .
doi: 10.3389/fgene.2023.1092489
pubmed: 36816039
pmcid: 9932046
Qiu F, Liang C-L, Liu H, Zeng Y-Q, Hou S, Huang S, et al. Impacts of cigarette smoking on immune responsiveness: up and down or upside down? Oncotarget. 2017;8(1):268–84. https://doi.org/10.18632/oncotarget.13613 .
doi: 10.18632/oncotarget.13613
pubmed: 27902485
Elisia I, Lam V, Cho B, Hay M, Li MY, Yeung M, et al. The effect of smoking on chronic inflammation, immune function and blood cell composition. Sci Rep. 2020;10:19480. https://doi.org/10.1038/s41598-020-76556-7 .
doi: 10.1038/s41598-020-76556-7
pubmed: 33173057
pmcid: 7655856
Breitling LP, Yang R, Korn B, Burwinkel B, Brenner H. Tobacco-smoking-related differential DNA methylation: 27K discovery and replication. Am J Hum Genet. 2011;88(4):450–7. https://doi.org/10.1016/j.ajhg.2011.03.003 .
doi: 10.1016/j.ajhg.2011.03.003
pubmed: 21457905
pmcid: 3071918
Wiencke JK, Butler R, Hsuang G, Eliot M, Kim S, Sepulveda MA, et al. The DNA methylation profile of activated human natural killer cells. Epigenetics. 2016;11(5):363–80. https://doi.org/10.1080/15592294.2016.1163454 .
doi: 10.1080/15592294.2016.1163454
pubmed: 26967308
pmcid: 4889279
Gao X, Jia M, Zhang Y, Breitling LP, Brenner H. DNA methylation changes of whole blood cells in response to active smoking exposure in adults: a systematic review of DNA methylation studies. Clin Epigenetics. 2015;7:113. https://doi.org/10.1186/s13148-015-0148-3 .
doi: 10.1186/s13148-015-0148-3
pubmed: 26478754
pmcid: 4609112
Zhang X, Hu Y, Aouizerat BE, Peng G, Marconi VC, Corley MJ, et al. Machine learning selected smoking-associated DNA methylation signatures that predict HIV prognosis and mortality. Clin Epigenetics. 2018;10(1):155. https://doi.org/10.1186/s13148-018-0591-z .
doi: 10.1186/s13148-018-0591-z
pubmed: 30545403
pmcid: 6293604
Houseman EA, Accomando WP, Koestler DC, Christensen BC, Marsit CJ, Nelson HH, et al. DNA methylation arrays as surrogate measures of cell mixture distribution. BMC Bioinformatics. 2012;13(1):86. https://doi.org/10.1186/1471-2105-13-86 .
doi: 10.1186/1471-2105-13-86
pubmed: 22568884
pmcid: 3532182
Wan ES, Qiu W, Baccarelli A, Carey VJ, Bacherman H, Rennard SI, et al. Cigarette smoking behaviors and time since quitting are associated with differential DNA methylation across the human genome. Hum Mol Genet. 2012;21(13):3073–82. https://doi.org/10.1093/hmg/dds135 .
doi: 10.1093/hmg/dds135
pubmed: 22492999
pmcid: 3373248
Bao Q, Zhang B, Zhou L, Yang Q, Mu X, Liu X, et al. CNP Ameliorates Macrophage Inflammatory Response and Atherosclerosis. Circ Res. 0(0). https://doi.org/10.1161/CIRCRESAHA.123.324086 .
Bae C-R, Hino J, Hosoda H, Arai Y, Son C, Makino H, et al. Overexpression of C-type natriuretic peptide in endothelial cells protects against Insulin Resistance and inflammation during Diet-induced obesity. Sci Rep. 2017;7(1):9807. https://doi.org/10.1038/s41598-017-10240-1 .
doi: 10.1038/s41598-017-10240-1
pubmed: 28852070
pmcid: 5574992
Lu HK, Mitchell A, Endoh Y, Hampartzoumian T, Huynh O, Borges L, et al. LILRA2 selectively modulates LPS-mediated cytokine production and inhibits phagocytosis by monocytes. PLoS ONE. 2012;7(3):e33478. https://doi.org/10.1371/journal.pone.0033478 .
doi: 10.1371/journal.pone.0033478
pubmed: 22479404
pmcid: 3316576
Lewis Marffy AL, McCarthy AJ. Leukocyte Immunoglobulin-Like receptors (LILRs) on human neutrophils: modulators of infection and immunity. Front Immunol. 2020;11:857. https://doi.org/10.3389/fimmu.2020.00857 .
doi: 10.3389/fimmu.2020.00857
pubmed: 32477348
pmcid: 7237751
Sikdar S, Joehanes R, Joubert BR, Xu C-J, Vives-Usano M, Rezwan FI, et al. Comparison of smoking-related DNA methylation between newborns from prenatal exposure and adults from personal smoking. Epigenomics. 2019;11(13):1487–500. https://doi.org/10.2217/epi-2019-0066 .
doi: 10.2217/epi-2019-0066
pubmed: 31536415
pmcid: 6836223
Joehanes R, Just AC, Marioni RE, Pilling LC, Reynolds LM, Mandaviya PR, et al. Epigenetic signatures of cigarette smoking. Circulation Cardiovasc Genet. 2016;9(5):436–47. https://doi.org/10.1161/CIRCGENETICS.116.001506 .
doi: 10.1161/CIRCGENETICS.116.001506
pubmed: 27651444
pmcid: 5267325
Sun YV, Smith AK, Conneely KN, Chang Q, Li W, Lazarus A, et al. Epigenomic association analysis identifies smoking-related DNA methylation sites in African americans. Hum Genet. 2013;132(9):1027–37. https://doi.org/10.1007/s00439-013-1311-6 .
doi: 10.1007/s00439-013-1311-6
pubmed: 23657504
pmcid: 3744600
Luo C, Wang G, Hu F. Two-Step Gene Feature Selection Algorithm Based on Permutation Test. In: Yao J, Yang Y, Słowiński R, Greco S, Li H, Mitra S, et al., editors. Springer; 2012. p. 249−58. https://doi.org/10.1111/ppe.12382 .
Liu D, Yeung EH, McLain AC, Xie Y, Buck Louis GM, Sundaram R. A two-step Approach for Analysis of Nonignorable Missing outcomes in Longitudinal Regression: an application to Upstate KIDS Study. Paediatr Perinat Epidemiol. 2017;31(5):468–78. https://doi.org/10.1111/ppe.12382 .
doi: 10.1111/ppe.12382
pubmed: 28767145
pmcid: 5610633
Newcombe PJ, Connolly S, Seaman S, Richardson S, Sharp SJ. A two-step method for variable selection in the analysis of a case-cohort study. Int J Epidemiol. 2018;47(2):597–604. https://doi.org/10.1093/ije/dyx224 .
doi: 10.1093/ije/dyx224
pubmed: 29136145
Song J, Shin SJ. A two-step approach for variable selection in linear regression with measurement error. Commun Stat Appl Methods. 2019;26(1):47–55. https://doi.org/10.29220/CSAM.2019.26.1.047 .
doi: 10.29220/CSAM.2019.26.1.047
Liu Y, Qin SJ. A Novel two-step sparse Learning Approach for Variable Selection and Optimal Predictive modeling. IFAC-PapersOnLine. 2022;55(7):57–64. https://doi.org/10.1016/j.ifacol.2022.07.422 .
doi: 10.1016/j.ifacol.2022.07.422
Chamlal H, Benzmane A, Ouaderhman T. A Two-Step Feature Selection Procedure to Handle High-Dimensional Data in Regression Problems. 2023 International Conference on Decision Aid Sciences and Applications (DASA). 2023. p. 592–6.
Wickramarachchi DS, Lim LHM, Sun B. Mediation analysis with multiple mediators under unmeasured mediator-outcome confounding. Stat Med. 2023;42(4):422–32. https://doi.org/10.1002/sim.9624 .
doi: 10.1002/sim.9624
pubmed: 36502820