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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.Contact: mccallm@gmail.com [ABSTRACT FROM PUBLISHER]