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Matching estimators for the effect of a treatment on survival times

Author: Xavier de Luna, And Per Johansson, And

Published in: Journal of Statistical Planning and Inference 2010, vol. 140, no. 7, pp. 2122-2137

Summary of Working paper 2007:1

We perform inference on the effect of a treatment on survival
times in studies where the treatment assignment is not randomized
and the assignment time is not known in advance. We estimate survival
functions on a treated and a control group which are made
comparable through matching on observed covariates. The inference
is performed by conditioning on waiting time to treatment, that is
time between the entrance in the study and treatment. This can be
done only when sufficient data is available. In other cases, averaging
over waiting times is a possibility, although the classical interpretation
of the estimated survival functions is lost unless hazards are
not functions of the waiting times. To show unbiasedness and to
obtain an estimator of the variance, we build on the potential outcome
framework, which was introduced by J. Neyman in the context
of randomized experiments, and adapted to observational studies by
D. B. Rubin. Our approach does not make parametric or distributional
assumptions. In particular, we do not assume proportionality
of the hazards compared. Small sample performance of the estimator
and a derived test of no treatment effect are studied in a Monte
Carlo study.

We perform inference on the effect of a treatment on survival times in studies where the treatment assignment is not randomized and the assignment time is not known in advance. We estimate survival functions on a treated and a control group which are made comparable through matching on observed covariates. The inferenceis performed by conditioning on waiting time to treatment, that is time between the entrance in the study and treatment. This can be done only when sufficient data is available. In other cases, averaging over waiting times is a possibility, although the classical interpretation of the estimated survival functions is lost unless hazards are not functions of the waiting times. To show unbiasedness and to obtain an estimator of the variance, we build on the potential outcome framework, which was introduced by J. Neyman in the context of randomized experiments, and adapted to observational studies by D. B. Rubin. Our approach does not make parametric or distributional assumptions. In particular, we do not assume proportionality of the hazards compared. Small sample performance of the estimator and a derived test of no treatment effect are studied in a Monte Carlo study.

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