In disease screening, a biomarker combination developed by combining multiple markers tends to have a higher sensitivity than an individual marker. Parametric methods for marker combination rely on the inverse of covariance matrices, which is often a non-trivial problem for high-dimensional data generated by modern high-throughput technologies. Additionally, another common problem in disease diagnosis is the existence of limit of detection (LOD) for an instrument – that is, when a biomarker's value falls below the limit, it cannot be observed and is assigned an NA value. To handle these two challenges in combining high-dimensional biomarkers with the presence of LOD, we propose a resample-replace lasso procedure. We first impute the values below LOD and then use the graphical lasso method to estimate the means and precision matrices for the high-dimensional biomarkers. The simulation results show that our method outperforms alternative methods such as either substitute NA values with LOD values or remove observations that have NA values. A real case analysis on a protein profiling study of glioblastoma patients on their survival status indicates that the biomarker combination obtained through the proposed method is more accurate in distinguishing between two groups.