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

  • de Luna, Xavier

    ()

    (Umeå University)

  • Johansson, Per

    ()

    (Uppsala University)

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.

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Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 3966.

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Length: 29 pages
Date of creation: Jan 2009
Date of revision:
Publication status: published in: Journal of Statistical Planning and Inference, 2010, 140 (7), 2122-2137
Handle: RePEc:iza:izadps:dp3966
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  1. Guido W. Imbens, 2003. "Nonparametric Estimation of Average Treatment Effects under Exogeneity: A Review," NBER Technical Working Papers 0294, National Bureau of Economic Research, Inc.
  2. Glenn Heller & E. S. Venkatraman, 2004. "A nonparametric test to compare survival distributions with covariate adjustment," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 719-733.
  3. Jaap H. Abbring & Gerard J. van den Berg, 2003. "The Nonparametric Identification of Treatment Effects in Duration Models," Econometrica, Econometric Society, vol. 71(5), pages 1491-1517, 09.
  4. Barbara Sianesi, 2004. "An Evaluation of the Swedish System of Active Labor Market Programs in the 1990s," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 133-155, February.
  5. Lechner, Michael, 1999. "Earnings and Employment Effects of Continuous Off-the-Job Training in East Germany after Unification," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 74-90, January.
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