Comparison of two distributions in the presence of length bias

Issue title: Statistical Models and Applications in Biomedicine

Guest editors: Boris Zaslavsky

Article type: Research Article

Authors: Song, Kyunghee K.^{a; *} | Weissfeld, Lisa A.^b

Affiliations: [a] CDRH/FDA, 10903 New Hampshire Ave, Silver Spring, MD, USA | [b] Department of Biostatistics, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA, USA | Division of Biostatistics, Food and Drug Administration, Rockville, MD, USA

Correspondence: [*] Corresponding author. E-mail: Kyunghee.Song@fda.hhs.gov.

Abstract: The linear rank test statistic has been an important test statistic in the area of nonparametrics. In this study, new test statistics based on the linear rank test are derived and applied to compare two length biased distributions. Through a series of size and power simulations, it is found that the new tests adjust for length biasing so efficiently that they behave similarly to the corresponding linear rank tests without length biasing. In practice, these new test procedures can be utilized as a proper tool to adjust length bias, which enables us to analyze a length biased sample.

Keywords: length biased distribution, linear rank test, Vardi's estimator, bias adjustment, martingale

DOI: 10.3233/MAS-2010-0165

Journal: Model Assisted Statistics and Applications, vol. 5, no. 3, pp. 179-186, 2010