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

Author

Listed:
  • de Luna, Xavier

    (Umeå University)

  • Johansson, Per

    (Uppsala University)

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.

Suggested Citation

  • de Luna, Xavier & Johansson, Per, 2009. "Non-Parametric Inference for the Effect of a Treatment on Survival Times with Application in the Health and Social Sciences," IZA Discussion Papers 3966, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp3966
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    References listed on IDEAS

    as
    1. Fredriksson, Peter & Johansson, Per, 2008. "Dynamic Treatment Assignment," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 435-445.
    2. 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.
    3. 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, August.
    4. Michael Lechner, 1999. "Nonparametric bounds on employment and income effects of continuous vocational training in East Germany," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 1-28.
    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.
    6. 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, September.
    7. Forslund, Anders & Johansson, Per & Lindqvist, Linus, 2004. "Employment subsidies - A fast lane from unemployment to work?," Working Paper Series 2004:18, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    8. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Aderonke Osikominu, 2013. "Quick Job Entry or Long-Term Human Capital Development? The Dynamic Effects of Alternative Training Schemes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(1), pages 313-342.
    2. Martin Biewen & Bernd Fitzenberger & Aderonke Osikominu & Marie Paul, 2014. "The Effectiveness of Public-Sponsored Training Revisited: The Importance of Data and Methodological Choices," Journal of Labor Economics, University of Chicago Press, vol. 32(4), pages 837-897.
    3. Anders Stenberg & Xavier Luna & Olle Westerlund, 2012. "Can adult education delay retirement from the labour market?," Journal of Population Economics, Springer;European Society for Population Economics, vol. 25(2), pages 677-696, January.
    4. de Luna, Xavier & Johansson, Per, 2012. "Testing for Nonparametric Identification of Causal Effects in the Presence of a Quasi-Instrument," IZA Discussion Papers 6692, Institute of Labor Economics (IZA).
    5. Vikman, Johan, 2014. "IPW estimation and related estimators for evaluation of active labor market policies in a dynamic setting," Working Paper Series, Center for Labor Studies 2014:8, Uppsala University, Department of Economics.
    6. Lee, Myoung-jae & Johansson, Per, 2013. "A Simple Approach to Treatment Effects on Durations When the Treatment Timing is Chosen," IZA Discussion Papers 7249, Institute of Labor Economics (IZA).
    7. Marco Mariani & Alessandra Mattei & Lorenzo Storchi & Daniele Vignoli, 2017. "The ambiguous effects of public assistance to youth and female start-ups between job creation and entrepreneurship enhancement," Econometrics Working Papers Archive 2017_04, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".

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    More about this item

    Keywords

    employment subsidy; heart transplant; matching estimator; observational study; potential outcome; survival function;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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