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Kaili Ren Dissertation.pdf (530.92 KB)

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Empirical likelihood methods in missing response problems and causal inference

Ren, Kaili
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1470184291

Abstract Details

2016, Doctor of Philosophy, University of Toledo, Mathematics.
This manuscript contains three topics in missing data problems and causal inference. First, we propose an empirical likelihood estimator as an alternative to Qin and Zhang (2007) in missing response problems under MAR assumption. A likelihood-based method is used to obtain the mean propensity score instead of a moment-based method. Our proposed estimator shares the double-robustness property and achieves the semiparametric efficiency lower bound when the regression model and the propensity score model are both correctly specified. Our proposed estimator has better performance when the propensity score is correctly specified. In addition, we extend our proposed method to the estimation of ATE in observational causal inferences. By utilizing the proposed method on a dataset from the CORAL clinical trial, we study the causal effect of cigarette smoking on renal function in patients with ARAS. The higher cystatin C and lower CKD-EPI GFR for smokers demonstrate the negative effect of smoking on renal function in patients with ARAS. Second, we explore a more efficient approach in missing response problems under MAR assumption. Instead of using one propensity score model and one working regression model, we postulate multiple working regression and propensity score models. Moreover, rather than maximizing the conditional likelihood, we maximize the full likelihood under constraints with respect to the postulated parametric functions. Our proposed estimator is consistent if one of the propensity scores is correctly specified and it achieves the semiparametric efficiency lower bound when one of the working regression models is correctly specified as well. This estimator is more efficient than other current estimators when one of the propensity scores is correctly specified. Finally, I propose empirical likelihood confidence intervals in missing data problems, which make very weak distribution assumptions. We show that the -2 empirical log-likelihood ratio function follows a scaled chi-squared distribution if either the working propensity score or the working regression model is correctly specified. If the two models are both correctly specified, the -2 empirical log-likelihood ratio function follows a chi-squared distribution. Empirical likelihood confidence intervals perform better than Wald confidence intervals of the AIPW estimator, when sample size is small and distribution of the response is highly skewed. In addition, empirical likelihood confidence intervals for ATE can also be built in causal inference.
Biao Zhang (Advisor)
Donald White (Committee Member)
Rong Liu (Committee Member)
Tian Chen (Committee Member)
Pamela Brewster (Committee Member)
Jiang Tian (Committee Member)
Steven Haller (Committee Member)
114 p.
Statistics

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Citations

  • Ren, K. (2016). Empirical likelihood methods in missing response problems and causal inference [Doctoral dissertation, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1470184291

    APA Style (7th edition)

  • Ren, Kaili. Empirical likelihood methods in missing response problems and causal inference. 2016. University of Toledo, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo1470184291.

    MLA Style (8th edition)

  • Ren, Kaili. "Empirical likelihood methods in missing response problems and causal inference." Doctoral dissertation, University of Toledo, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1470184291

    Chicago Manual of Style (17th edition)

toledo1470184291
476
© 2016, all rights reserved.
This open access ETD is published by University of Toledo and OhioLINK.