title: A Bayesian approach for estimating calibration curves and unknown concentrations in immunoassays.
abstract: BACKGROUND
  Immunoassays are primary diagnostic and research tools throughout the medical and life sciences. The common approach to the processing of immunoassay data involves estimation of the calibration curve followed by inversion of the calibration function to read off the concentration estimates. This approach, however, does not lend itself easily to acceptable estimation of confidence limits on the estimated concentrations. Such estimates must account for uncertainty in the calibration curve as well as uncertainty in the target measurement. Even point estimates can be problematic: because of the non-linearity of calibration curves and error heteroscedasticity, the neglect of components of measurement error can produce significant bias.
  
  
  METHODS
  We have developed a Bayesian approach for the estimation of concentrations from immunoassay data that treats the propagation of measurement error appropriately. The method uses Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution of the target concentrations and numerically compute the relevant summary statistics. Software implementing the method is freely available for public use.
  
  
  RESULTS
  The new method was tested on both simulated and experimental datasets with different measurement error models. The method outperformed the common inverse method on samples with large measurement errors. Even in cases with extreme measurements where the common inverse method failed, our approach always generated reasonable estimates for the target concentrations.
  
  
  BACKGROUND
  Project name: Baecs; Project home page: www.computationalimmunology.org/utilities/; Operating systems: Linux, MacOS X and Windows; Programming language: C++; License: Free for Academic Use.
authors.affiliation: Center for Computational Immunology, Department of Biostatistics and Bioinformatics, Duke University Medical Center, Durham, NC 27705, USA. feng.feng@duke.edu
authors.forename: Feng
authors.initials: F
authors.lastname: Feng
authors.forename: Ana Paula
authors.initials: AP
authors.lastname: Sales
authors.forename: Thomas B
authors.initials: TB
authors.lastname: Kepler
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D002138:Calibration; D019295:Computational Biology / Q000379:methods; D003198:Computer Simulation; D005069:Evaluation Studies as Topic; D007118:Immunoassay / Q000379:methods*; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D012984:Software; D035501:Uncertainty