Non-parametric tests for distributional treatment effect for randomly censored responses

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Abstract

For a binary treatment ν=0, 1 and the corresponding 'potential response'Y0 for the control group (ν=0) and Y1 for the treatment group (ν=1), one definition of no treatment effect is that Y 0 and Y1 follow the same distribution given a covariate vector X. Koul and Schick have provided a non-parametric test for no distributional effect when the realized response (1-ν)Y0+ν Y1 is fully observed and the distribution of X is the same across the two groups. This test is thus not applicable to censored responses, nor to non-experimental (i.e. observational) studies that entail different distributions of X across the two groups. We propose 'X-matched' non-parametric tests generalizing the test of Koul and Schick following an idea of Gehan. Our tests are applicable to non-experimental data with randomly censored responses. In addition to these motivations, the tests have several advantages. First, they have the intuitive appeal of comparing all available pairs across the treatment and control groups, instead of selecting a number of matched controls (or treated) in the usual pair or multiple matching. Second, whereas most matching estimators or tests have a non-overlapping support (of X) problem across the two groups, our tests have a built-in protection against the problem. Third, Gehan's idea allows the tests to make good use of censored observations. A simulation study is conducted, and an empirical illustration for a job training effect on the duration of unemployment is provided.

Original languageEnglish
Pages (from-to)243-264
Number of pages22
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume71
Issue number1
DOIs
Publication statusPublished - 2009 Jan 1

Fingerprint

Non-parametric test
Treatment Effects
Censored Observations
Observational Study
Unemployment
Appeal
Nonparametric test
Treatment effects
Covariates
Intuitive
Simulation Study
Binary
Estimator

Keywords

  • Censoring
  • Duration
  • Mann-Whitney statistic
  • Non-parametric tests
  • Treatment effect

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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abstract = "For a binary treatment ν=0, 1 and the corresponding 'potential response'Y0 for the control group (ν=0) and Y1 for the treatment group (ν=1), one definition of no treatment effect is that Y 0 and Y1 follow the same distribution given a covariate vector X. Koul and Schick have provided a non-parametric test for no distributional effect when the realized response (1-ν)Y0+ν Y1 is fully observed and the distribution of X is the same across the two groups. This test is thus not applicable to censored responses, nor to non-experimental (i.e. observational) studies that entail different distributions of X across the two groups. We propose 'X-matched' non-parametric tests generalizing the test of Koul and Schick following an idea of Gehan. Our tests are applicable to non-experimental data with randomly censored responses. In addition to these motivations, the tests have several advantages. First, they have the intuitive appeal of comparing all available pairs across the treatment and control groups, instead of selecting a number of matched controls (or treated) in the usual pair or multiple matching. Second, whereas most matching estimators or tests have a non-overlapping support (of X) problem across the two groups, our tests have a built-in protection against the problem. Third, Gehan's idea allows the tests to make good use of censored observations. A simulation study is conducted, and an empirical illustration for a job training effect on the duration of unemployment is provided.",
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AB - For a binary treatment ν=0, 1 and the corresponding 'potential response'Y0 for the control group (ν=0) and Y1 for the treatment group (ν=1), one definition of no treatment effect is that Y 0 and Y1 follow the same distribution given a covariate vector X. Koul and Schick have provided a non-parametric test for no distributional effect when the realized response (1-ν)Y0+ν Y1 is fully observed and the distribution of X is the same across the two groups. This test is thus not applicable to censored responses, nor to non-experimental (i.e. observational) studies that entail different distributions of X across the two groups. We propose 'X-matched' non-parametric tests generalizing the test of Koul and Schick following an idea of Gehan. Our tests are applicable to non-experimental data with randomly censored responses. In addition to these motivations, the tests have several advantages. First, they have the intuitive appeal of comparing all available pairs across the treatment and control groups, instead of selecting a number of matched controls (or treated) in the usual pair or multiple matching. Second, whereas most matching estimators or tests have a non-overlapping support (of X) problem across the two groups, our tests have a built-in protection against the problem. Third, Gehan's idea allows the tests to make good use of censored observations. A simulation study is conducted, and an empirical illustration for a job training effect on the duration of unemployment is provided.

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