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. 2016 Jan 1:143:327-344.
doi: 10.1016/j.jmva.2015.10.001.

The Fine-Gray Model Under Interval Censored Competing Risks Data

Chenxi Li  1
Affiliations

The Fine-Gray Model Under Interval Censored Competing Risks Data

Chenxi Li. J Multivar Anal. .

Abstract

We consider semiparametric analysis of competing risks data subject to mixed case interval censoring. The Fine-Gray model (Fine & Gray, 1999) is used to model the cumulative incidence function and is coupled with sieve semiparametric maximum likelihood estimation based on univariate or multivariate likelihood. The univariate likelihood of cause-specific data enables separate estimation of cumulative incidence function for each competing risk, in contrast with the multivariate likelihood of full data which estimates cumulative incidence functions for multiple competing risks jointly. Under both likelihoods and certain regularity conditions, we show that the regression parameter estimator is asymptotically normal and semiparametrically efficient, although the spline-based sieve estimator of the baseline cumulative subdistribution hazard converges at a rate slower than root-n. The proposed method is evaluated by simulation studies regarding its finite sample performance and is illustrated by a competing risk analysis of data from an dementia cohort study.

Keywords: Competing risk; Cumulative incidence function; Interval censored data; Semiparametric efficiency; Sieve estimation; Subdistribution hazard.

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Figures

Figure 1
Figure 1
Averaged estimates of the baseline cumulative subdistribution hazard functions for Cause 1 over the 1000 Monte Carlo samples.
Figure 2
Figure 2
Averaged estimates of the baseline cumulative subdistribution hazard functions for Cause 2 over the 1000 Monte Carlo samples.
Figure 3
Figure 3
Cumulative incidence functions of dementia estimated from the univariate analysis for women with baseline age 80.28 years, the mean baseline age of the sample. Plots (a) and (b) show the cumulative incidence functions for no MCI at baseline and having MCI at baseline respectively. Solid lines are for no college education and no ApoE4 allele; Dashed lines are for no college education and having ApoE4 allele; Dotted lines are for having college education and no ApoE4 allele; Dotdash lines are for having college education and ApoE4 allele.
Figure 4
Figure 4
Cumulative incidence functions of dementia estimated from the multivariate analysis for women with baseline age 80.28 years, the mean baseline age of the sample. Plots (a) and (b) show the cumulative incidence functions for no MCI at baseline and having MCI at baseline respectively. Solid lines are for no college education and no ApoE4 allele; Dashed lines are for no college education and having ApoE4 allele; Dotted lines are for having college education and no ApoE4 allele; Dotdash lines are for having college education and ApoE4 allele.
Figure 5
Figure 5
Cumulative incidence functions of death estimated from the multivariate analysis for people with college education and baseline age 80.28 years, the mean baseline age of the sample. Plots (a) and (b) show the cumulative incidence functions for female and male respectively. Solid lines are for no MCI at baseline and no ApoE4 allele; Dashed lines are for no MCI at baseline and having ApoE4 allele; Dotted lines are for having MCI at baseline and no ApoE4 allele; Dotdash lines are for having MCI at baseline and ApoE4 allele.
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