Comparison of models for analyzing two-group, cross-sectional data with a Gaussian outcome subject to a detection limit

Abstract

A potential difficulty in the analysis of biomarker data occurs when data are subject to a detection limit. This detection limit is often defined as the point at which the true values cannot be measured reliably. Multiple, regression-type models designed to analyze such data exist. Studies have compared the bias among such models, but few have compared their statistical power. This simulation study provides a comparison of approaches for analyzing two-group, cross-sectional data with a Gaussian-distributed outcome by exploring statistical power and effect size confidence interval coverage of four models able to be implemented in standard software. We found using a Tobit model fit by maximum likelihood provides the best power and coverage. An example using human immunodeficiency virus type 1 ribonucleic acid data is used to illustrate the inferential differences in these models.

Keywords: limit of detection; regression; statistical power.