Anastasios A. Tsiatis

TL;DR: The authors summarizes current knowledge regarding the theory of estimation for semiparametric models with missing data, in an organized and comprehensive manner, and applies these methods to problems with missing, censored and coarsened data with the goal of deriving estimators that are as robust and efficient as possible.

TL;DR: This work argues that the Cox proportional hazards regression model method is superior to naive methods where one maximizes the partial likelihood of the Cox model using the observed covariate values and improves on two-stage methods where empirical Bayes estimates of the covariate process are computed and then used as time-dependent covariates.

TL;DR: This discussion aims to complement the presentation of the authors by elaborating on the view from the vantage point of semi-parametric theory, focusing on the assumptions embedded in the statistical models leading to different “types” of estimators rather than on the forms of the estimators themselves.

TL;DR: The relationship between the net and the crude probabilities of survival was established by Therorems 1 and 2 as mentioned in this paper, which showed that, without the not directly verifiable assumption that in their joint distribution the variables Y1, Y2,..., Yk are mutually independent, a given set of crude survival probabilities Qi(t) does not identify the corresponding net probabilities.