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Estimating the effect of treatment in a proportional hazards model in the presence of non‐compliance and contamination
Author(s) -
Cuzick Jack,
Sasieni Peter,
Myles Jonathan,
Tyrer Jonathan
Publication year - 2007
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00600.x
Subject(s) - covariate , estimator , statistics , generalization , proportional hazards model , econometrics , mathematics , mathematical analysis
Summary. Methods for adjusting for non‐compliance and contamination, which respect the randomization, are extended from binary outcomes to time‐to‐event analyses by using a proportional hazards model. A simple non‐iterative method is developed when there are no covariates, which is a generalization of the Mantel–Haenszel estimator. More generally, a ‘partial likelihood’ is developed which accommodates covariates under the assumption that they are independent of compliance. A key feature is that the proportion of contaminators and non‐compliers in the risk set is updated at each failure time. When covariates are not independent of compliance, a full likelihood is developed and explored, but this leads to a complex estimator. Estimating equations and information matrices are derived for these estimators and they are evaluated by simulation studies.