Robust Inference for Causal Mediation Analysis of Recurrent Event Data
Recurrent events, including cardiovascular events, are commonly observed in biomedical studies. Researchers must understand the effects of various treatments on recurrent events and investigate the underlying mediation mechanisms by which treatments …
Authors: Yan-Lin Chen, Yan-Hong Chen, Pei-Fang Su
1 Robust Infer ence for Causal Mediation Analysis of Recurr ent Event Dat a 1 2 3 4 3 1 Institute of Statistics, National Yang Ming Chiao Tung Unive rsity, Hsin -Chu, Taiwan 2 Institute of Statistical Science , Academia Sinica, Taipei, Taiwan 3 Department of Statistics, National Cheng Kung University, Tainan, Ta iw an. *Corre spon ding author S UMMAR Y : 2 1. Introduction Mediation pr oblem with r ecurr ent event data 3 Related work s 4 Contribution s of the pr esent study 5 2. M ediation an aly sis with outcome s of a counting process outcome Notations and definitions 6 Figure 1. 7 Dir ect and indir ect effect s Assump tions and identifica tion 8 (A1) (A2) (A3) (A4) (A5) (A6) 9 3. Estimation usi ng a proportional mean model 10 Regr ession-based estimati on p p ( CA. 1 ) 11 12 T riply r obust estim ation 13 14 (CA.2) (CA.3) 15 T able 1. Estimator Censoring Assumption ◯ ◯ ◯ ◯ ◯ ◯ ◯ ◯ ◯ ◯ ◯ Abbr eviations: RB, regr ession -base d; TR, triply r obust. 16 T HEOREM 1 : Consistency and asymptotic pr operties Suppose that identification assumptions (A1)–(A6) and independent c ensoring assumptions (CA.1)–(CA.3) hold. (a) is consistent in . (b) is asymptotically normal with mean zer o and varian ce in , wher e 17 4. Numerical studies Experiment 1: Robustness of the TR estimator under differ ent scenarios 18 T able 2. Abbr eviations: ESE, empirical standar d e rror; RB, regr ession -base d ; TR, trip ly r obust ; NDE, natural direc t effect; NIE, natural indir ect effect. 19 Experiment 2: Performance of the TR estimator with a low occurr ence rate T able 3. 20 Abbr eviations: ESE, empirical standar d err or; NDE, natural dire ct effect; NIE, natural indire ct effect. Experiment 3: Behavior of the TR estimator under early censoring 21 T able 4. Abbr eviations: ES E, empirical st andar d err or; PC , mean pr opo rtion of c ensored time; NDE, na tural dir ect effec t; NIE, na tural indire ct effect. Experiment 4: Effect of the violation of independent censoring assumptions 22 23 Figure 2. 24 5. Real data analysis 25 — — 26 • • • 27 Figure 3. 28 Figure 4. T able 5. Abbr eviations: TE, total effect; NDE, natural dir ect effect; NIE, natural indir ect effect. 6. Discussion 29 30 31 Figure 5. Acknowledgemen t Re fer enc e Statistical models based on counting pr ocesses Diabetes Car e 41 , et al. Cir culation 129 The statist ic al analysis of re curr ent events 32 , et al. Diabetes Car e 41 BMJ open 11 Expert Opin Investig Drugs 12 , et al. Diabetes Car e 46 , et al. Lancet 380 Communications in Statistics - Theory and Methods 45 33 N Engl J Med 351 V it al statistics rates in the United States, 1940-1960 J Am Soc Nephr o l 28 Causal Infer ence: What If Natl V ital Stat Rep 70 , et al. Diabetes 63 J Pharmacol Exp Ther 345 Epidemiology 22 , et al. Kidney Int 72 34 Journal of the Royal Statistical Society: Series B (Statistical Methodology) 62 , et al. J Pharmacol Exp Ther 340 , et al. Lancet 375 Diabetes Car e 44 N Engl J Med 377 Statistical Science 5 Horm Metab Res 47 Proce edings of the Seventeenth confer ence on 35 Uncertainty in artificial intelligence Clin Res Car diol 107 Epidemiology 3 Journal of educational Psychology 66 , et al. Cir culation 108 , et al. Int J Car diol 220 , et al. J Hypertens 32 36 Hypertension 37 Car dio vasc Diabetol 17 Statistics in medicine 39 Biostatistics 23 The international journal of biostatistics 7 The Annals of Statistics 40 Annu Rev Med 66 Epidemiology 22 Statistics and its Interface 2 , et al. Curr 37 V asc Pharmacol 12 , et al. N Engl J Med 375 J Am Coll C ar diol 72 Stat Med 40 38 Appendix Appendix 1: Procedure of identification Assumptions (A1) (A2) (A3) (A4) (A5) (A6) 39 Appendix 2: Resu lts for th e binary mediator Appendix 3: Consistency and asymptotic normality Appendix 3.1 Con sistency 40 (CA.1) (CA.2) (CA.3) 41 Case 1: In 42 Case 2: In 43 44 Case 3: In 45 46 47 48 Appendix 3. 2 Asymptotic distr ibution 49 50 51 52 53 54 55 56 57 Appendix 4: Procedure for misspecif ied mo dels 58 59 Appendix 5 : Estimated regr essio n parameters 60 61 Re fer enc e The Ame rican Statistician 67 Journal of the Royal Statistical Society: Series B (Statistical Methodology) 62 Statistics in medicine 39
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