Non-Parametric Inference for the Effect of a Treatment on Survival Times with Application in the Health and Social Sciences

29 Pages Posted: 2 Feb 2009

See all articles by Xavier de Luna

Xavier de Luna

University of Umea - Department of Economics

Per Johansson

IFAU - Institute for Labour Market Policy Evaluation; Uppsala University - Department of Economics; IZA Institute of Labor Economics

Abstract

In this paper 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. Two such studies are discussed: a heart transplant program and a study of Swedish unemployed eligible for employment subsidy. 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 waiting time. 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.

Keywords: potential outcome, observational study, matching estimator, heart transplant, employment subsidy, survival function

JEL Classification: C12, C13, C14

Suggested Citation

de Luna, Xavier and Johansson, Per, Non-Parametric Inference for the Effect of a Treatment on Survival Times with Application in the Health and Social Sciences. IZA Discussion Paper No. 3966, Available at SSRN: https://ssrn.com/abstract=1336083

Xavier De Luna (Contact Author)

University of Umea - Department of Economics ( email )

UmeƄ University
Umea, SE - 90187
Sweden

Per Johansson

IFAU - Institute for Labour Market Policy Evaluation ( email )

Box 513
751 20 Uppsala
Sweden
+ 46 18 471 70 86 (Phone)
+ 46 18 471 70 71 (Fax)

Uppsala University - Department of Economics ( email )

Uppsala, 751 20
Sweden

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

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