Predicting protein concentrations with ELISA microarray assays, monotonic splines and Monte Carlo simulation
Background: A microarray of enzyme-linked immunosorbent assays, or ELISA microarray, predicts simultaneously the concentrations of numerous proteins in a small sample. These predictions, however, are uncertain due to processing error and biological variability. Making sound biological inferences as well as improving the ELISA microarray process require require both concentration predictions and creditable estimates of their errors. Methods: We present a statistical method based on monotonic spline statistical models, penalized constrained least squares fitting (PCLS) and Monte Carlo simulation (MC) to predict concentrations and estimate prediction errors in ELISA microarray. PCLS restrains the flexible spline to a fit of assay intensity that is a monotone function of protein concentration. With MC, both modeling and measurement errors are combined to estimate prediction error. The spline/PCLS/MC method is compared to a common method using simulated and real ELISA microarray data sets. Results: In contrast to the rigid logistic model, the flexible spline model gave credible fits in almost all test cases including troublesome cases with left and/or right censoring, or other asymmetries. For the real data sets, 61% of the spline predictions were more accurate than their comparable logistic predictions; especially the spline predictions at the extremes of the prediction curve. The relative errors of 50% of comparable spline and logistic predictions differed by less than 20%. Monte Carlo simulation rendered acceptable asymmetric prediction intervals for both spline and logistic models while propagation of error produced symmetric intervals that diverged unrealistically as the standard curves approached horizontal asymptotes. Conclusions: The spline/PCLS/MC method is a flexible, robust alternative to a logistic/NLS/propagation-of-error method to reliably predict protein concentrations and estimate their errors. The spline method simplifies model selection and fitting, and reliably estimates believable prediction errors. For the 50% of the real data sets fit well by both methods, spline and logistic predictions are practically indistinguishable, varying in accuracy by less than 15%. The spline method may be useful when automated prediction across simultaneous assays of numerous proteins must be applied routinely with minimal user intervention.
- Research Organization:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC05-76RL01830
- OSTI ID:
- 935899
- Report Number(s):
- PNNL-SA-53347; 400412000; TRN: US200816%%1031
- Journal Information:
- Statistical Applications in Genetics and Molecular Biology, 7(1):Article 21, Vol. 7, Issue 1
- Country of Publication:
- United States
- Language:
- English
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