A popular way to estimate an unknown parameter is with substitution, or evaluating the parameter at a likelihood based fit of the data generating density. In many cases, such estimators have substantial bias and can fail to converge at the parametric rate. van der Laan and Rubin (2006) introduced targeted maximum likelihood learning, removing these shackles from substitution estimators, which were made in full agreement with the locally efficient estimating equation procedures as presented in Robins and Rotnitzsky (1992) and van der Laan and Robins (2003). This note illustrates how targeted maximum likelihood can be applied in right censored data structures. In particular, we show that when an initial substitution estimator is based on a Cox proportional hazards model, the targeted likelihood algorithm can be implemented by iteratively adding an appropriate time-dependent covariate.
Statistical Methodology | Statistical Theory | Survival Analysis
van der Laan, Mark J. and Rubin, Daniel, "A Note on Targeted Maximum Likelihood and Right Censored Data" (October 2007). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 226.