Limit of Detection (LoD) Estimation Using Maximum Likelihood from (Hit) Rate Data: The LoD_MLE SAS Macro

Jesse Canchola, Jeffrey E. Vaks, Shaowu Tang
Roche Molecular Systems, Inc.


Abstract

The Limit of Detection (LoD) is defined as the lowest concentration or amount of material, target or analyte that is consistently detectable (for PCR quantitative studies, in at least 95% of the samples tested)1. In practice, the estimation of the LoD uses a parametric curve fit to a set of panel member (PM1, PM2, PM3, etc.) data where the responses are binary. Typically, the parametric curve fit to the percent detection levels takes on the form of a probit or logistic distribution. The LoD_Est SAS Macro (Canchola & Hemyari, SAS Global Forum 2016), using the SAS PROBIT procedure as the main engine, is used to fit such a parametric curves. The rarely used but preferred method uses the method of maximum likelihood (ML) to estimate the LoD assuming one detectable copy of template. We introduce the LOD_MLE SAS macro that maximizes the log likelihood function and returns the ML estimate (MLE) of the LoD along with its 95% confidence interval (CI). In addition, the macro returns the percent detection table with associated 95% exact (Clopper-Pearson) confidence intervals for the hit rates at each level.