2.4. Background Correction
Let x={x1,x2,…,xn} and y={y1,y2,…,yn} be the true expressions of the entire miRNA population being tested in two cell populations—a control sample, which is an untreated specimen or a specimen treated with saline, and a test sample, which is a specimen treated with a drug. Sometimes, the control sample can also be a specimen from a subject without disease, and the test sample is a specimen from a subject with a certain disease. In practice, both x and y are not observable. Instead, x and y are usually measured using microarrays or other analytical platforms, and the corresponding measurements. X and Y. are usually coupled with errors. It is common in practice that x and y are approximated by simply subtracting the local estimates of the background noises from the intensity measures from the corresponding spots. Or, if replicates exist, the median or mean values will be used for different miRNAs, respectively. For miRNA microarrays, background correction via local background subtraction may cause difficulties in data analysis. First, the majority of miRNAs are weakly or not expressed, and as a result, background-subtraction using local estimates may result in negative values in x and y, which is not acceptable. Second, ignoring the probes that are flagged as weakly expressed may result in too many missing values or over-estimate the true expression levels of some miRNAs—either way will introduce significant bias to the detection of differentially expressed miRNAs.
It is commonly observed that the standard deviation of the measurements in microarray rises proportionally to the expression level. However, for totally unexpressed genes, this proportionality won’t continue down to zero, due to the fact that measurement errors always exist [16]. Motivated by these observations, two measurement error models are introduced [17,18,19]. Both models describe the measurement error for a given transcript for gene expression arrays using two error components—the multiplicative and additive errors. A generalized logarithm transformation (GLOG) is proposed for gene-expression microarray data analyses [20]. The GLOG can stabilize the variance of the measurements and take care of the measures of the weakly expressed miRNAs quite well and, hence, are suitable for miRNA microarray data analysis (more details in the Materials and Methods section).