### Abstract

Missing data is a very common problem in medical and social studies, especially when data are collected longitudinally. It is a challenging problem to utilize observed data effectively. Many papers on missing data problems can be found in statistical literature. It is well known that the inverse weighted estimation is neither efficient nor robust. On the other hand, the doubly robust (DR) method can improve the efficiency and robustness. As is known, the DR estimation requires a missing data model (i.e., a model for the probability that data are observed) and a working regression model (i.e., a model for the outcome variable given covariates and surrogate variables). Because the DR estimating function has mean zero for any parameters in the working regression model when the missing data model is correctly specified, in this paper, we derive a formula for the estimator of the parameters of the working regression model that yields the optimally efficient estimator of the marginal mean model (the parameters of interest) when the missing data model is correctly specified. Furthermore, the proposed method also inherits the DR property. Simulation studies demonstrate the greater efficiency of the proposed method compared with the standard DR method. A longitudinal dementia data set is used for illustration.

Original language | English (US) |
---|---|

Pages (from-to) | 4763-4780 |

Number of pages | 18 |

Journal | Statistics in Medicine |

Volume | 32 |

Issue number | 27 |

DOIs | |

State | Published - Jan 1 2013 |

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### Keywords

- Longitudinal data
- Missing data
- Optimal
- Surrogate outcome

### ASJC Scopus subject areas

- Epidemiology
- Statistics and Probability

### Cite this

*Statistics in Medicine*,

*32*(27), 4763-4780. https://doi.org/10.1002/sim.5875

**A new estimation with minimum trace of asymptotic covariance matrix for incomplete longitudinal data with a surrogate process.** / Chen, Baojiang; Qin, Jing.

Research output: Contribution to journal › Article

*Statistics in Medicine*, vol. 32, no. 27, pp. 4763-4780. https://doi.org/10.1002/sim.5875

}

TY - JOUR

T1 - A new estimation with minimum trace of asymptotic covariance matrix for incomplete longitudinal data with a surrogate process

AU - Chen, Baojiang

AU - Qin, Jing

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Missing data is a very common problem in medical and social studies, especially when data are collected longitudinally. It is a challenging problem to utilize observed data effectively. Many papers on missing data problems can be found in statistical literature. It is well known that the inverse weighted estimation is neither efficient nor robust. On the other hand, the doubly robust (DR) method can improve the efficiency and robustness. As is known, the DR estimation requires a missing data model (i.e., a model for the probability that data are observed) and a working regression model (i.e., a model for the outcome variable given covariates and surrogate variables). Because the DR estimating function has mean zero for any parameters in the working regression model when the missing data model is correctly specified, in this paper, we derive a formula for the estimator of the parameters of the working regression model that yields the optimally efficient estimator of the marginal mean model (the parameters of interest) when the missing data model is correctly specified. Furthermore, the proposed method also inherits the DR property. Simulation studies demonstrate the greater efficiency of the proposed method compared with the standard DR method. A longitudinal dementia data set is used for illustration.

AB - Missing data is a very common problem in medical and social studies, especially when data are collected longitudinally. It is a challenging problem to utilize observed data effectively. Many papers on missing data problems can be found in statistical literature. It is well known that the inverse weighted estimation is neither efficient nor robust. On the other hand, the doubly robust (DR) method can improve the efficiency and robustness. As is known, the DR estimation requires a missing data model (i.e., a model for the probability that data are observed) and a working regression model (i.e., a model for the outcome variable given covariates and surrogate variables). Because the DR estimating function has mean zero for any parameters in the working regression model when the missing data model is correctly specified, in this paper, we derive a formula for the estimator of the parameters of the working regression model that yields the optimally efficient estimator of the marginal mean model (the parameters of interest) when the missing data model is correctly specified. Furthermore, the proposed method also inherits the DR property. Simulation studies demonstrate the greater efficiency of the proposed method compared with the standard DR method. A longitudinal dementia data set is used for illustration.

KW - Longitudinal data

KW - Missing data

KW - Optimal

KW - Surrogate outcome

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U2 - 10.1002/sim.5875

DO - 10.1002/sim.5875

M3 - Article

VL - 32

SP - 4763

EP - 4780

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 27

ER -