Songthip T. Ounpraseuth
Department of Biostatistics, University of Arkansas for Medical Sciences
Weighted Log-Rank Tests for 'Flipped-Data' Survival Analysis of Data with Non-Detects
Eric R. Siegel
University of Arkansas for Medical Sciences
Songthip T. Ounpraseuth
Department of Biostatistics, University of Arkansas for Medical Sciences
Ralph L. Kodell
University of Arkansas for Medical Sciences
Non-detects are data whose values are left-censored at a limit of detection (LOD). Data with non-detects arise in fields as diverse as metabolomics, environmental monitoring, and AIDS research. To analyze data with non-detects, methods such as maximum-likelihood estimation and multiple imputation have been deployed, but these methods require fitting a model whose error term follows the Normal or other parametric distribution. A simple, non-parametric alternative was proposed by Helsel (2005), in which data with non-detects are 'flipped' or converted into right-censored forms by subtracting them from a suitably large number, then analyzed via Kaplan-Meier curves and the log-rank test. In a simulation study, we investigated the performance of Helsel's method on normally distributed data subjected to left-censoring at an LOD. We found that Gehan's generalized Wilcoxon test, a weighted version of the log-rank test, had significantly more power to detect group differences than the standard log-rank test. Here, we explore whether Gehan's test continues to be superior to the log-rank test when the left-censored data are generated using alternatives to the normal distribution.