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

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2009 · Volume 71 · Issue 1

DOI: 10.1111/j.1467-9868.2008.00683.x

Abstract

Summary.For a binary treatmentν=0, 1 and the corresponding ‘potential response’Y0for the control group (ν=0) andY1for the treatment group (ν=1), one definition of no treatment effect is thatY0andY1follow the same distribution given a covariate vectorX. Koul and Schick have provided a non-parametric test for no distributional effect when the realized response (1−ν)Y0+νY1is fully observed and the distribution ofXis 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 ofXacross 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 (ofX) 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.

Keywords

Censoring, Duration, Mann–Whitney statistic, Non-parametric tests, Treatment effect

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