Statistical Method for Determining and Comparing Limits of Detection of Bioassays

Abstract

The current bioassay development literature lacks the use of statistically robust methods for calculating the limit of detection of a given assay. Instead, researchers often employ simple methods that provide a rough estimate of the limit of detection, often without a measure of the confidence in the estimate. This scarcity of robust methods is likely due to a realistic preference for simple and accessible methods and to a lack of such methods that have reduced the concepts of limit of detection theory to practice for the specific application of bioassays. Here, we have developed a method for determining limits of detection for bioassays that is statistically robust and reduced to practice in a clear and accessible manner geared at researchers, not statisticians. This method utilizes a four-parameter logistic curve fit to translate signal intensity to analyte concentration, which is a curve that is commonly employed in quantitative bioassays. This method generates a 95% confidence interval of the limit of detection estimate to provide a measure of uncertainty and a means by which to compare the analytical sensitivities of different assays statistically. We have demonstrated this method using real data from the development of a paper-based influenza assay in our laboratory to illustrate the steps and features of the method. Using this method, assay developers can calculate statistically valid limits of detection and compare these values for different assays to determine when a change to the assay design results in a statistically significant improvement in analytical sensitivity.

Principles for Sensitive and Robust Biomolecular Interaction Analysis: The Limits of Detection and Resolution of Diffraction-Limited Focal Molography

“…After having described the possible sources of background light and formulated the figure of merits we will use this knowledge to analyze the limits of detection and resolution of focal molography. The proper limit of detection for a specific assay is elaborate [51,52]. Yet, it is not practically feasible to compare different sensing platforms at the assay level since this would require a standard assays to be performed with each of them.…”

Nonlinear Regression Improves Accuracy of Characterization of Multiplexed Mass Spectrometric Assays

“…To account for the non-linearity of the apparent calibration curve, alternative approaches fitting a logistic response curve [21,22,23] have been proposed. However, as illustrated in Figure 2, they do not fully capture the intensities at low concentrations.…”

“…To place the proposed approach in the context of existing work, in this section we describe the definitions, notation, and current approaches for assay characterization based on linear [9] and logistic [21] curve fit with unequal variance. We assume that the characterization is performed at the peptide level (i.e., after summarizing all the transitions or fragments of the peptide), and describe the model for a single representative peptide.…”

Estimation in generalized linear models under censored covariates with an application to MIREC data

“…where is the correlation between v i1 and v i2 , and = ( x 1 , x 1 , x 1 , x 2 , x 1 x 2 ) ′ is the vector of nuisance parameters of the distribution of (x i1 , x i2 ), which are estimated simultaneously along with the regression coefficients = ( 0 , 1 , 2 ) ′ for the binary regression model (10). From (8), the likelihood score equations for take the form…”

“…Helsel 3 reviewed a number of existing methods for dealing with censored observations commonly encountered in clinical and environmental studies, which include the nonparametric Kaplan-Meier method for determining descriptive statistics and regression on order statistics for imputing the nondetects. Analysis of data subject to detection limits has been extensively studied in the literature in recent years (eg, other works [4][5][6][7][8][9][10][11][12][13] ). Helsel 4 reviewed existing statistical methods for dealing with nondetects in environmental data.…”