BootstRatio: A web-based statistical analysis of fold-change in qPCR and RT-qPCR data using resampling methods

https://doi.org/10.1016/j.compbiomed.2011.12.012Get rights and content

Abstract

Real-time quantitative polymerase chain reaction (qPCR) is widely used in biomedical sciences quantifying its results through the relative expression (RE) of a target gene versus a reference one. Obtaining significance levels for RE assuming an underlying probability distribution of the data may be difficult to assess. We have developed the web-based application BootstRatio, which tackles the statistical significance of the RE and the probability that RE>1 through resampling methods without any assumption on the underlying probability distribution for the data analyzed. BootstRatio perform these statistical analyses of gene expression ratios in two settings: (1) when data have been already normalized against a control sample and (2) when the data control samples are provided. Since the estimation of the probability that RE>1 is an important feature for this type of analysis, as it is used to assign statistical significance and it can be also computed under the Bayesian framework, a simulation study has been carried out comparing the performance of BootstRatio versus a Bayesian approach in the estimation of that probability. In addition, two analyses, one for each setting, carried out with data from real experiments are presented showing the performance of BootstRatio. Our simulation study suggests that Bootstratio approach performs better than the Bayesian one excepting in certain situations of very small sample size (N≤12). The web application BootstRatio is accessible through http://regstattools.net/br and developed for the purpose of these intensive computation statistical analyses.

Introduction

Real-time quantitative polymerase chain reaction (qPCR) is widely used in research and diagnostics as a method to reliably quantify nucleic acid amount due to its robustness, easy procedures, reproducibility and the lower sample amount needed in comparison with other methods. When used in combination with retrotranscription (RT-qPCR) it allows determining gene expression. Quantification results are based on either the relative expression (RE) of a target gene versus a reference one or an absolute quantification based on internal or external calibration curves [1]. RE is widely used by researchers as it avoids the complications of generating calibrating material and it is measured as the ratio between the mean target gene expression and that of the reference one. MIQE guidelines for publication of RT-qPCR data suggest that data analysis procedures and statistical methods to assign significance to the data should be indicated when publishing [2]. In the literature, few statistical methods have been developed for the statistical data analysis of RT-qPCR [3], [4], [5], [6], [7], [8]. Obtaining significance levels for the RE through statistical modeling entail assuming an underlying probability distribution of the data that may be difficult to assess, specially when data is based on small sample size (n<20) on both target and reference samples. In these situations, resampling methods may be used to assess percentiles, and therefore, statistically significance of a statistical estimator such as the mean, median or standard error of the data [9]. Successful biological applications of these techniques such as computing confidence intervals [10], clustering [11], robust estimation of statistics [12] and non-linear regression [13] have been previously described. These methods can be also useful to efficiently calculate very low P-values from a large number of resampled measurements [14].

In this paper we apply bootstrap and permutation tests to assess the statistical significance of the gene expression ratios of RT-qPCR without any assumption on the underlying probability distribution of our data. The web application BootstRatio has been developed to perform statistical analyses of gene expression ratios either when data has been already normalized against a control sample or when control samples are provided. A simulation study has been carried out comparing the performance of the method presented here versus a Bayesian one, this last requiring certain prior distribution for the data to be assumed. In addition, we also show the results of the analysis of real-data, one for each of the possible data sets indicated above, showing the performance of the method.

Section snippets

Statistical methods

The Bootstrap method: Analysis of gene expression ratios with no control sample (samples already normalized against a control sample).

Let G be the gene of interest for which we have a sample of m observed expression ratio values SG={RG1,...,RGm} assuming RGi≥0 ∀i=1,...,m. We can estimate the mean ratio as μRGX¯RG=(1/m)i=1mRGi. Our interest is to assess whether μRG>1 and therefore, to assess its statistical significance estimating P(μRG>1) through Bootstrap [9]. The bootstrap is a general

Simulation study: BootstRatio versus Bayesian approach

Table 1 shows results of the simulation study comparing the Bootstratio approach with the Bayesian one in the estimation of P(RGT>1) highlighting which one of the methods perform better in each situation. The upper part of the table shows the REP as well as P(RBt>1) and P(RBY>1) assuming a Gamma probability distribution and a Uniform probability distribution for the numerator (XT) of the simulated ratio. The Bayesian approach performed slightly better than the Bootstratio one when the simulated

Conclusions

Real-time PCR is an easy to perform methodology, provides the necessary accuracy and produces reliable as well as rapid quantification results which require a reproducible methodology and adequate mathematical models for data analysis. Other statistical methods have been described for this type of analysis [3], [4], [5], [6], [7], [8] which may entail assuming an underlying probability distribution of the data. As the gene expression ratio is a positive function which may depend on the ratio of

Authors' contributions

RC developed the statistical model, programmed its R code and analyzed the data. RC and JR designed the web application and drafted the article. MLH carried out real-time PCR experiments, analyzed the data, provided assistance with the design of the web application and finalized the draft. JG programmed the web application and provided assistance to adapt the R code to the web server. ME and VN carried out real-time PCR experiments, provided oversight of the work and co-designed experiments,

Acknowledgments

This work was partially supported by CIBER de Enfermedades Raras, an initiative of the ISCIII Institute of Health Research of the Spanish Governement. This work was also supported in part by SAF2009-12606-C02-02 and 09SGR1490 to V. Nunes by MICINN and Generalitat de Catalunya, respectively. Study sponsors had no involvement in the study design, in the collection, analysis and interpretation of data; in the writing of the manuscript; and in the decision to submit the manuscript for publication.

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