MOTIVATION: Current methods used to analyze real-time quantitative polymerase chain reaction (qPCR) data exhibit systematic deviations from the assumed model over the progression of the reaction. Slight variations in the amount of the initial target molecule or in early amplifications are likely responsible for these deviations. Commonly used 4- and 5-parameter sigmoidal models appear to be particularly susceptible to this issue, often displaying patterns of autocorrelation in the residuals. The presence of this phenomenon, even for technical replicates, suggests that these parametric models may be misspecified. Specifically, they do not account for the sequential dependent nature of the amplification process that underlies qPCR fluorescence measurements. RESULTS: We demonstrate that a Smooth Transition Autoregressive (STAR) model addresses this limitation by explicitly modeling the dependence between cycles and the gradual transition between amplification regimes. In summary, application of a STAR model to qPCR amplification data improves model fit and reduces autocorrelation in the residuals. AVAILABILITY AND IMPLEMENTATION: R scripts to reproduce all the analyses and results described in this manuscript can be found at: https://github.com/bhsu4/GAPDH.SO. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Quantitative real-time PCR (qPCR) is one of the most widely used methods to measure gene expression. An important aspect of qPCR data that has been largely ignored is the presence of non-detects: reactions failing to exceed the quantification threshold and therefore lacking a measurement of expression. While most current software replaces these non-detects with a value representing the limit of detection, this introduces substantial bias in the estimation of both absolute and differential expression. Single imputation procedures, while an improvement on previously used methods, underestimate residual variance, which can lead to anti-conservative inference. RESULTS: We propose to treat non-detects as non-random missing data, model the missing data mechanism, and use this model to impute missing values or obtain direct estimates of model parameters. To account for the uncertainty inherent in the imputation, we propose a multiple imputation procedure, which provides a set of plausible values for each non-detect. We assess the proposed methods via simulation studies and demonstrate the applicability of these methods to three experimental data sets. We compare our methods to mean imputation, single imputation, and a penalized EM algorithm incorporating non-random missingness (PEMM). The developed methods are implemented in the R/Bioconductor package nondetects. CONCLUSIONS: The statistical methods introduced here reduce discrepancies in gene expression values derived from qPCR experiments in the presence of non-detects, providing increased confidence in downstream analyses.