Open Access
June 2014 Maximum likelihood and pseudo score approaches for parametric time-to-event analysis with informative entry times
Brian D. M. Tom, Vernon T. Farewell, Sheila M. Bird
Ann. Appl. Stat. 8(2): 726-746 (June 2014). DOI: 10.1214/14-AOAS725


We develop a maximum likelihood estimating approach for time-to-event Weibull regression models with outcome-dependent sampling, where sampling of subjects is dependent on the residual fraction of the time left to developing the event of interest. Additionally, we propose a two-stage approach which proceeds by iteratively estimating, through a pseudo score, the Weibull parameters of interest (i.e., the regression parameters) conditional on the inverse probability of sampling weights; and then re-estimating these weights (given the updated Weibull parameter estimates) through the profiled full likelihood. With these two new methods, both the estimated sampling mechanism parameters and the Weibull parameters are consistently estimated under correct specification of the conditional referral distribution. Standard errors for the regression parameters are obtained directly from inverting the observed information matrix in the full likelihood specification and by either calculating bootstrap or robust standard errors for the hybrid pseudo score/profiled likelihood approach. Loss of efficiency with the latter approach is considered. Robustness of the proposed methods to misspecification of the referral mechanism and the time-to-event distribution is also briefly examined. Further, we show how to extend our methods to the family of parametric time-to-event distributions characterized by the generalized gamma distribution. The motivation for these two approaches came from data on time to cirrhosis from hepatitis C viral infection in patients referred to the Edinburgh liver clinic. We analyze these data here.


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Brian D. M. Tom. Vernon T. Farewell. Sheila M. Bird. "Maximum likelihood and pseudo score approaches for parametric time-to-event analysis with informative entry times." Ann. Appl. Stat. 8 (2) 726 - 746, June 2014.


Published: June 2014
First available in Project Euclid: 1 July 2014

zbMATH: 06333774
MathSciNet: MR3262532
Digital Object Identifier: 10.1214/14-AOAS725

Keywords: Biased data , generalized gamma distribution , outcome-dependent sampling , pseudo score , robust standard error , Survival analysis , Weibull distribution

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.8 • No. 2 • June 2014
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