IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i1p246-d1023559.html
   My bibliography  Save this article

Non-Parametric Non-Inferiority Assessment in a Three-Arm Trial with Non-Ignorable Missing Data

Author

Listed:
  • Wei Li

    (Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, China)

  • Yunqi Zhang

    (Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, China)

  • Niansheng Tang

    (Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, China)

Abstract

A three-arm non-inferiority trial including a placebo is usually utilized to assess the non-inferiority of an experimental treatment to a reference treatment. Existing methods for assessing non-inferiority mainly focus on the fully observed endpoints. However, in some clinical trials, treatment endpoints may be subject to missingness for various reasons, such as the refusal of subjects or their migration. To address this issue, this paper aims to develop a non-parametric approach to assess the non-inferiority of an experimental treatment to a reference treatment in a three-arm trial with non-ignorable missing endpoints. A logistic regression is adopted to specify a non-ignorable missingness data mechanism. A semi-parametric imputation method is proposed to estimate parameters in the considered logistic regression. Inverse probability weighting, augmented inverse probability weighting and non-parametric methods are developed to estimate treatment efficacy for known and unknown parameters in the considered logistic regression. Under some regularity conditions, we show asymptotic normality of the constructed estimators for treatment efficacy. A bootstrap resampling method is presented to estimate asymptotic variances of the estimated treatment efficacy. Three Wald-type statistics are constructed to test the non-inferiority based on the asymptotic properties of the estimated treatment efficacy. Empirical studies show that the proposed Wald-type test procedure is robust to the misspecified missingness data mechanism, and behaves better than the complete-case method in the sense that the type I error rates for the former are closer to the pre-given significance level than those for the latter.

Suggested Citation

  • Wei Li & Yunqi Zhang & Niansheng Tang, 2023. "Non-Parametric Non-Inferiority Assessment in a Three-Arm Trial with Non-Ignorable Missing Data," Mathematics, MDPI, vol. 11(1), pages 1-26, January.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:1:p:246-:d:1023559
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/1/246/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/1/246/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Li, Huiqiong & Tian, Guoliang & Tang, Niansheng & Cao, Hongyuan, 2018. "Assessing non-inferiority for incomplete paired-data under non-ignorable missing mechanism," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 69-81.
    2. S. C. Choi & D. M. Stablein, 1982. "Practical Tests for Comparing Two Proportions with Incomplete Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 256-262, November.
    3. Sik-Yum Lee, 2006. "Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 541-564, September.
    4. Ghosh, Santu & Guo, Wenge & Ghosh, Samiran, 2022. "A hierarchical testing procedure for three arm non-inferiority trials," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    5. Man-Lai Tang & Nian-Sheng Tang & Ivan Siu-Fung Chan & Ben Ping-Shing Chan, 2002. "Sample Size Determination for Establishing Equivalence/Noninferiority via Ratio of Two Proportions in Matched–Pair Design," Biometrics, The International Biometric Society, vol. 58(4), pages 957-963, December.
    6. Kim, Jae Kwang & Yu, Cindy Long, 2011. "A Semiparametric Estimation of Mean Functionals With Nonignorable Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 157-165.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cui, Li-E & Zhao, Puying & Tang, Niansheng, 2022. "Generalized empirical likelihood for nonsmooth estimating equations with missing data," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    2. Zhao, Hui & Zhao, Pu-Ying & Tang, Nian-Sheng, 2013. "Empirical likelihood inference for mean functionals with nonignorably missing response data," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 101-116.
    3. Zhang, Yan-Qing & Tang, Nian-Sheng, 2017. "Bayesian local influence analysis of general estimating equations with nonignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 184-200.
    4. Nian-Sheng Tang & Pu-Ying Zhao, 2013. "Empirical likelihood semiparametric nonlinear regression analysis for longitudinal data with responses missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 639-665, August.
    5. Song, Xin-Yuan & Chen, Fei & Lu, Zhao-Hua, 2013. "A Bayesian semiparametric dynamic two-level structural equation model for analyzing non-normal longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 87-108.
    6. Jiwei Zhao, 2017. "Reducing bias for maximum approximate conditional likelihood estimator with general missing data mechanism," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 577-593, July.
    7. Tang, Niansheng & Wang, Wenjun, 2019. "Robust estimation of generalized estimating equations with finite mixture correlation matrices and missing covariates at random for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 640-655.
    8. Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    9. Zhang, Jing & Wang, Qihua & Kang, Jian, 2020. "Feature screening under missing indicator imputation with non-ignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    10. Aiai Yu & Yujie Zhong & Xingdong Feng & Ying Wei, 2023. "Quantile regression for nonignorable missing data with its application of analyzing electronic medical records," Biometrics, The International Biometric Society, vol. 79(3), pages 2036-2049, September.
    11. Jingxuan Guo & Fuguo Liu & Wolfgang Karl Härdle & Xueliang Zhang & Kai Wang & Ting Zeng & Liping Yang & Maozai Tian, 2023. "Sampling Importance Resampling Algorithm with Nonignorable Missing Response Variable Based on Smoothed Quantile Regression," Mathematics, MDPI, vol. 11(24), pages 1-30, December.
    12. Jiang, Depeng & Zhao, Puying & Tang, Niansheng, 2016. "A propensity score adjustment method for regression models with nonignorable missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 98-119.
    13. Chen, Xue-Dong & Tang, Nian-Sheng, 2010. "Bayesian analysis of semiparametric reproductive dispersion mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2145-2158, September.
    14. Leiva, Victor & Barros, Michelli & Paula, Gilberto A. & Galea, Manuel, 2007. "Influence diagnostics in log-Birnbaum-Saunders regression models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5694-5707, August.
    15. Yujing Shao & Lei Wang, 2022. "Generalized partial linear models with nonignorable dropouts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 223-252, February.
    16. Yilin Li & Wang Miao & Ilya Shpitser & Eric J. Tchetgen Tchetgen, 2023. "A self‐censoring model for multivariate nonignorable nonmonotone missing data," Biometrics, The International Biometric Society, vol. 79(4), pages 3203-3214, December.
    17. Carlos A. Dos Santos & Daniele C. T. Granzotto & Vera L. D. Tomazella & Francisco Louzada, 2018. "Hierarchical Transmuted Log-Logistic Model: A Subjective Bayesian Analysis," JRFM, MDPI, vol. 11(1), pages 1-12, March.
    18. Kano, Yutaka & Takai, Keiji, 2011. "Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1241-1255, October.
    19. Xinyuan Song & Yemao Xia & Hongtu Zhu, 2017. "Hidden Markov latent variable models with multivariate longitudinal data," Biometrics, The International Biometric Society, vol. 73(1), pages 313-323, March.
    20. Fayyaz Bahari & Safar Parsi & Mojtaba Ganjali, 2021. "Empirical likelihood inference in general linear model with missing values in response and covariates by MNAR mechanism," Statistical Papers, Springer, vol. 62(2), pages 591-622, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:1:p:246-:d:1023559. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.