Semiparametric and Nonparametric Methods for Comparing Biomarker Levels between Groups

Comparing the distribution of biomarker measurements between two groups under either an unpaired or paired design is a common goal in many biomarker studies. However, analyzing biomarker data is sometimes challenging because the data may not be normally distributed and contain a large fraction of zero values or missing values. Although several statistical methods have been proposed, they either require data normality assumption, or are inefficient. We proposed a novel two-part semiparametric method for data under an unpaired setting and a nonparametric method for data under a paired setting. The semiparametric method considers a two-part model, a logistic regression for the zero proportion and a semi-parametric log-linear model for the non-zero values. It is free of distributional assumption and also allows for adjustment of covariates. We propose a kernel-smoothed likelihood method to estimate regression coefficients in the two-part model and construct a likelihood ratio test for the analysis. The nonparametric method considers weighted mean difference statistics for paired data with missing values. It uses all the available data, and it is also free of distributional assumptions. We construct a Wald test for the analysis in this part. Simulations and real data analyses demonstrate that our methods outperform existing methods