Modeling qRT-PCR dynamics with application to cancer biomarker quantification

Quantitative reverse transcription polymerase chain reaction (qRT-PCR) is widely used for molecular diagnostics and evaluating prognosis in cancer. The utility of mRNA expression biomarkers relies heavily on the accuracy and precision of quantification, which is still challenging for low abundance transcripts. The critical step for quantification is accurate estimation of efficiency needed for computing a relative qRT-PCR expression. We propose a new approach to estimating qRT-PCR efficiency based on modeling dynamics of polymerase chain reaction amplification. In contrast, only models for fluorescence intensity as a function of polymerase chain reaction cycle have been used so far for quantification. The dynamics of qRT-PCR efficiency is modeled using an ordinary differential equation model, and the fitted ordinary differential equation model is used to obtain effective polymerase chain reaction efficiency estimates needed for efficiency-adjusted quantification. The proposed new qRT-PCR efficiency estimates were used to quantify GUCY2C (Guanylate Cyclase 2C) mRNA expression in the blood of colorectal cancer patients. Time to recurrence and GUCY2C expression ratios were analyzed in a joint model for survival and longitudinal outcomes. The joint model with GUCY2C quantified using the proposed polymerase chain reaction efficiency estimates provided clinically meaningful results for association between time to recurrence and longitudinal trends in GUCY2C expression.