Estimation of Low Quantity Genes: A Hierarchical Model for Analyzing Censored Quantitative Real-Time PCR Data

Analysis of gene quantities measured by quantitative real-time PCR (qPCR) can be complicated by observations that are below the limit of quantification (LOQ) of the assay. A hierarchical model estimated using MCMC methods was developed to analyze qPCR data of genes with observations that fall below the LOQ (censored observations). Simulated datasets with moderate to very high levels of censoring were used to assess the performance of the model; model results were compared to approaches that replace censored observations with a value on the log scale approximating zero or with values ranging from one to the LOQ of ten gene copies. The model was also compared to a Tobit regression model. Finally, all approaches for handling censored observations were evaluated with DNA extracted from samples that were spiked with known quantities of the antibiotic resistance gene tetL. For the simulated datasets, the model outperformed substitution of all values from 1–10 under all censoring scenarios in terms of bias, mean square error, and coverage of 95% confidence intervals for regression parameters. The model performed as well or better than substitution of a value approximating zero under two censoring scenarios (approximately 57% and 79% censored values). The model also performed as well or better than Tobit regression in two of three censoring scenarios (approximately 79% and 93% censored values). Under the levels of censoring present in the three scenarios of this study, substitution of any values greater than 0 produced the least accurate results. When applied to data produced from spiked samples, the model produced the lowest mean square error of the three approaches. This model provides a good alternative for analyzing large amounts of left-censored qPCR data when the goal is estimation of population parameters. The flexibility of this approach can accommodate complex study designs such as longitudinal studies.