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

Abstract

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.

Replication Study: Fusobacterium nucleatum infection is prevalent in human colorectal carcinoma

“…In these samples, the Ct was set to 40, even though no amplicon was observed (also known as ‘non-detects’). While others have suggested methods to reduce the bias introduced when non-detects are set to Ct values of 40, such as setting the value to 35 ( McCall et al, 2014 ), or using imputation methods and hierarchical models to deal with non-detects ( McCall et al, 2014 ; Boyer et al, 2013 ), the approach should be based on evidence ( Caraguel et al, 2011 ) and introduced prior to data collection, such as in a pre-registered analysis plan, to minimize confirmation bias ( Wagenmakers et al, 2012 ). Furthermore, in the samples in which F. nucleatum was detectable, it was often at the edge of detectability, requiring more than 30 cycles of PCR to be detected ( Figure 1—figure supplement 1B ).…”

Impact of treatment strategies on cephalosporin and tetracycline resistance gene quantities in the bovine fecal metagenome

“…We based our imputation model on unique animal identifier (which comprised pen as well as CCFA and CTC treatment status), sampling day, and the number of observations missing among the triplicate of each sample (i.e., 1, 2, or all 3 triplicates were missing). The number of missing observations among the triplicates was considered as an important predictor, similar to the previous dairy study that imputed missing quantitative real-time PCR data44. The histograms as well as the supplementary Table 1 resulting from the imputed datasets, demonstrating log 10 distributions of gene copies per wet gram feces, and based on the number of missing observations per triplicate, reveal that the distribution of missing observations shifts towards the left (including additional imputed observations at lower gene copies) as the number of missing values among triplicates increases.…”

Effects of chlortetracycline and copper supplementation on the prevalence, distribution, and quantity of antimicrobial resistance genes in the fecal metagenome of weaned pigs

“…In each case, only one of the duplicate readings had no CT value, thus, it did not yield a negative result at the sample level. To deal with missing observations, these observations were initially assigned a value of zero, while for later analyses we added half the value of the lowest nonzero value observed in the samples to all observations (following Boyer et al, 2013). The estimated gene copy numbers in each reaction were back-calculated to gene copies per gram of wet feces for each sample, which was then transformed to log 10 to achieve normality.…”