An internal calibration method for protein-array studies.

Nuisance factors in a protein-array study add obfuscating variation to spot intensity measurements, diminishing the accuracy and precision of protein concentration predictions. The effects of nuisance factors may be reduced by design of experiments, and by estimating and then subtracting nuisance effects. Estimated nuisance effects also inform about the quality of the study and suggest refinements for future studies.We demonstrate a method to reduce nuisance effects by incorporating a non-interfering internal calibration in the study design and its complemental analysis of variance. We illustrate this method by applying a chip-level internal calibration in a biomarker discovery study. The variability of sample intensity estimates was reduced 16% to 92% with a median of 58%; confidence interval widths were reduced 8% to 70% with a median of 35%. Calibration diagnostics revealed processing nuisance trends potentially related to spot print order and chip location on a slide. The accuracy and precision of a protein-array study may be increased by incorporating a non-interfering internal calibration. Internal calibration modeling diagnostics improve confidence in study results and suggest process steps that may need refinement. Though developed for our protein-array studies, this internal calibration method is applicable to other targeted array-based studies.

Predicting protein concentrations with ELISA microarray assays, monotonic splines and Monte Carlo simulation.

Making sound proteomic inferences using ELISA microarray assay requires both an accurate prediction of protein concentration and a credible estimate of its error. We present a method using monotonic spline statistical models (MS), penalized constrained least squares fitting (PCLS) and Monte Carlo simulation (MC) to predict ELISA microarray protein concentrations and estimate their prediction errors. We contrast the MSMC (monotone spline Monte Carlo) method with a LNLS (logistic nonlinear least squares) method using simulated and real ELISA microarray data sets.MSMC rendered good fits in almost all tests, including those with left and/or right clipped standard curves. MS predictions were nominally more accurate; especially at the extremes of the prediction curve. MC provided credible asymmetric prediction intervals for both MS and LN fits that were superior to LNLS propagation-of-error intervals in achieving the target statistical confidence. MSMC was more reliable when automated prediction across simultaneous assays was applied routinely with minimal user guidance.

Evaluating concentration estimation errors in ELISA microarray experiments.

BACKGROUND: Enzyme-linked immunosorbent assay (ELISA) is a standard immunoassay to estimate a protein's concentration in a sample. Deploying ELISA in a microarray format permits simultaneous estimation of the concentrations of numerous proteins in a small sample. These estimates, however, are uncertain due to processing error and biological variability. Evaluating estimation error is critical to interpreting biological significance and improving the ELISA microarray process. Estimation error evaluation must be automated to realize a reliable high-throughput ELISA microarray system. In this paper, we present a statistical method based on propagation of error to evaluate concentration estimation errors in the ELISA microarray process. Although propagation of error is central to this method and the focus of this paper, it is most effective only when comparable data are available. Therefore, we briefly discuss the roles of experimental design, data screening, normalization, and statistical diagnostics when evaluating ELISA microarray concentration estimation errors. RESULTS: We use an ELISA microarray investigation of breast cancer biomarkers to illustrate the evaluation of concentration estimation errors. The illustration begins with a description of the design and resulting data, followed by a brief discussion of data screening and normalization. In our illustration, we fit a standard curve to the screened and normalized data, review the modeling diagnostics, and apply propagation of error. We summarize the results with a simple, three-panel diagnostic visualization featuring a scatterplot of the standard data with logistic standard curve and 95% confidence intervals, an annotated histogram of sample measurements, and a plot of the 95% concentration coefficient of variation, or relative error, as a function of concentration. CONCLUSIONS: This statistical method should be of value in the rapid evaluation and quality control of high-throughput ELISA microarray analyses. Applying propagation of error to a variety of ELISA microarray concentration estimation models is straightforward. Displaying the results in the three-panel layout succinctly summarizes both the standard and sample data while providing an informative critique of applicability of the fitted model, the uncertainty in concentration estimates, and the quality of both the experiment and the ELISA microarray process.