Performance of robust regression methods in real-time polymerase chain reaction calibration

Introduction Controlled calibration enables determining the unknown concentration of a particular substance in a given solution. The assay method of concern here is the real-time polymerase chain reaction (PCR). Ordinary Least Squares (OLS) method is routinely used to estimate the standard curve and the concentration of an unknown sample. It was found that many laboratories participating to a project of External Quality Control concerning quantitative real-time PCR presented outliers, most frequently in the lowest concentrations. Objectives This work aims at investigating and comparing the performance of OLS, Least Absolute Deviation (LAD) method [1] and biweight MM-estimator [2,3] in real-time PCR calibration via a Monte Carlo simulation. Methods The statistical model corresponding to the standard curve is a simple linear regression. Calibration enables predicting the unknown x0 (nucleic acid content of the unknown sample), for a given y0 (value of the fractional cycle where a threshold amount of amplified nucleic acid is produced in the sample), through inverse regression: x . The Monte Carlo simulation mimicked the design adopted in the Italian project of External Quality Control. Outliers were introduced by contamination. The 90% confidence intervals for x0 were obtained by resorting to the approximate variance of x computed by the Delta method and their coverage probability was investigated. Results When contamination is absent, the coverage of OLS estimator interval is at the nominal level and its width is the smallest, MM-estimator performance is similar to OLS, whereas LAD interval has an acceptable coverage at the expense of width. On the contrary the contamination of all concentration levels makes the OLS performance worse: even though the width tends to increase when contamination increases, the coverage tends to decrease and to appear unacceptable; as regards the robust methods we can observe a tradeoff between width and coverage: MM estimator seems resistant to contamination, as the intervals widths remain short, but this is associated with reduction in coverages, whereas LAD intervals widths are constantly larger so that their coverages are acceptable at the nominal level. With reference to contamination of the lowest concentrations only, when x0=2.5 or x0=3.5 all the methods tend to underestimate the nominal coverage, however the performance of LAD method compares favourably to that of the other two. On the contrary when x0=5.5 or x0=6.5 we observe an improper increase of the confidence intervals width for all methods studied and consequently highly overestimating coverages, particularly for MM estimator and LAD. Conclusions In performing real-time PCR calibration, it seems reasonable to postulate a heterogeneous distribution of measurements errors; hence robust regression methods should be implemented to estimate x0 and to compute its confidence interval. However to select the most appropriate robust procedure a thorough investigation of the features of the process generating measurements in each laboratory is needed.