Statistics and Its Interface

Volume 7 (2014)

Number 1

We dedicate this special issue to Dr. Gang Zheng, a great colleague and dear friend to many of us.

Semiparametric mixture survival model with application to MRFIT study

Pages: 19 – 26

DOI: http://dx.doi.org/10.4310/SII.2014.v7.n1.a3

Authors

Zonghui Hu (Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland, U.S.A.)

Jing Qin (Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland, U.S.A.)

Dean A. Follmann (Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland, U.S.A.)

Abstract

We study the mixture survival model where subject $i$ has a probability $p_i$ following one survival distribution and $1 - p_i$ following the other. The two survival distributions are unspecified except for an exponential tilting between the failure densities. Semiparametric likelihood estimation is proposed to handle censoring through conditional likelihood and inverse-censoring-probability weighted likelihood. Though full likelihood estimation is introduced, it is not always preferred over the other estimations due to its computational complexity and that its improvement in efficiency depends on the pattern of censoring. In the motivating example—the MRFIT study—we apply mixture survival modeling to uncover the underlying survival patterns in the control arm: one for the would-be compliers and one for the would-be non-compliers, where compliance of each subject is not observable but associated with a probability.

Keywords

censoring, empirical likelihood, exponential tilting, inverse-censoring-probability weighting, mixture distribution, survival function

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