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.

MOTIVATION: Quantitative real-time PCR (qPCR) is one of the most widely used methods to measure gene expression. Despite extensive research in qPCR laboratory protocols, normalization and statistical analysis, little attention has been given to qPCR non-detects-those reactions failing to produce a minimum amount of signal. RESULTS: We show that the common methods of handling qPCR non-detects lead to biased inference. Furthermore, we show that non-detects do not represent data missing completely at random and likely represent missing data occurring not at random. We propose a model of the missing data mechanism and develop a method to directly model non-detects as missing data. Finally, we show that our approach results in a sizeable reduction in bias when estimating both absolute and differential gene expression. AVAILABILITY AND IMPLEMENTATION: The proposed algorithm is implemented in the R package, nondetects. This package also contains the raw data for the three example datasets used in this manuscript. The package is freely available at http://mnmccall.com/software and as part of the Bioconductor project.