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Empirical likelihood method for non-ignorable missing data problems.

Zhong Guan1, Jing Qin2

  • 1Department of Mathematical Sciences, Indiana University South Bend, South Bend, IN, 46634, USA. zguan@iusb.edu.

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|September 21, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a semiparametric model for non-ignorable missing data, crucial in medical and social science research. It demonstrates that missing CD4 counts in AIDS trials are non-ignorable, leading to biased results from observed data alone.

Keywords:
Constrained estimationEmpirical likelihoodNon-ignorable missing dataSurvey sampling

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Area of Science:

  • Statistics
  • Epidemiology
  • Biostatistics

Background:

  • Missing data is a pervasive challenge in various scientific fields, particularly when missingness depends on the unobserved values (non-ignorable missingness).
  • Existing statistical methods for non-ignorable missing data are often limited to full parametric models, leaving a gap in semiparametric approaches.
  • Addressing non-ignorable missing data is critical for unbiased analysis in medical and social science studies.

Purpose of the Study:

  • To develop and evaluate a semiparametric model for analyzing non-ignorable missing data.
  • To introduce an empirical likelihood method for estimating parameters in the presence of non-ignorable missingness.
  • To provide a statistical test for distinguishing between non-ignorable and completely random missing data.

Main Methods:

  • A semiparametric model is proposed where missing probabilities are parameterized but underlying distributions remain unspecified.
  • Owen (1988)'s empirical likelihood method is employed to derive constrained maximum empirical likelihood estimators.
  • A likelihood ratio statistic is developed for hypothesis testing regarding the missing data mechanism.

Main Results:

  • The proposed estimators for missing probability and mean response parameters are shown to be asymptotically normal.
  • The likelihood ratio test effectively distinguishes between non-ignorable and completely random missing data.
  • Analysis of AIDS trial data revealed non-ignorable missing CD4 counts, indicating bias in analyses using only observed data.

Conclusions:

  • The semiparametric empirical likelihood approach provides a robust method for handling non-ignorable missing data.
  • This method allows for valid statistical inference even when underlying distributions are unknown.
  • The findings highlight the importance of accounting for non-ignorable missingness in epidemiological studies, as demonstrated by the AIDS trial example.