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1. Identification and estimation of causal effects with outcomes truncated by death

Author

Thomas S. Richardson, Linbo Wang, and Xiao-Hua Zhou

Subjects
Statistics and Probability, FOS: Computer and information sciences, Survivor average causal effect, General Mathematics, media_common.quotation_subject, Principal stratification, 01 natural sciences, Methodology (stat.ME), 010104 statistics & probability, 03 medical and health sciences, 0302 clinical medicine, Statistics, Model parameterization, 030212 general & internal medicine, 0101 mathematics, Statistics - Methodology, media_common, Mathematics, Selection bias, Applied Mathematics, Substitution (logic), Instrumental variable, Articles, Agricultural and Biological Sciences (miscellaneous), Identification (information), Variable (computer science), Causal inference, Observational study, Statistics, Probability and Uncertainty, General Agricultural and Biological Sciences
Abstract

It is common in medical studies that the outcome of interest is truncated by death, meaning that a subject has died before the outcome could be measured. In this case, restricted analysis among survivors may be subject to selection bias. Hence, it is of interest to estimate the survivor average causal effect, defined as the average causal effect among the subgroup consisting of subjects who would survive under either exposure. In this paper, we consider the identification and estimation problems of the survivor average causal effect. We propose to use a substitution variable in place of the latent membership in the always-survivor group. The identification conditions required for a substitution variable are conceptually similar to conditions for a conditional instrumental variable, and may apply to both randomized and observational studies. We show that the survivor average causal effect is identifiable with use of such a substitution variable, and propose novel model parameterizations for estimation of the survivor average causal effect under our identification assumptions. Our approaches are illustrated via simulation studies and a data analysis., Comment: Correct a typo in equation (8)

Published
2017

2. Non-strange Weird Resampling for Complex Survival Data

Author

Markus Pauly, Jan Beyersmann, Dennis Dobler, and Mathematics

Subjects
Statistics and Probability, Statistics::Theory, Correctness, SDG 16 - Peace, General Mathematics, Inference, Mathematics - Statistics Theory, Statistics Theory (math.ST), 01 natural sciences, 010104 statistics & probability, 03 medical and health sciences, 0302 clinical medicine, Resampling, FOS: Mathematics, Statistics::Methodology, 030212 general & internal medicine, 0101 mathematics, Mathematics, Counting process, Applied Mathematics, SDG 16 - Peace, Justice and Strong Institutions, Nonparametric statistics, Agricultural and Biological Sciences (miscellaneous), Justice and Strong Institutions, 62N03, 62N01, Multiplier (economics), Statistics, Probability and Uncertainty, Standard normal table, General Agricultural and Biological Sciences, Algorithm, Confidence and prediction bands
Abstract

This paper introduces the new data-dependent multiplier bootstrap for non-parametric analysis of survival data, possibly subject to competing risks. The new resampling procedure includes both the general wild bootstrap and the weird bootstrap as special cases. The data may be subject to independent right-censoring and left-truncation. We rigorously prove asymptotic correctness which has in particular been pending for the weird bootstrap. As a consequence, pointwise as well as time-simultaneous inference procedures for, amongst others, the classical survival setting are deduced. We report simulation results and a real data analysis of the cumulative cardiovascular event probability. The simulation results suggest that both the weird bootstrap and use of non-standard multipliers in the wild bootstrap may perform preferably., 16 pages, 2 figures

Published
2017