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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
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    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)

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