PMC:4979053 / 14831-19304
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{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/4979053","sourcedb":"PMC","sourceid":"4979053","source_url":"https://www.ncbi.nlm.nih.gov/pmc/4979053","text":"2.4.2. Between-Platform Agreement\nIn the microarray literature, concordance between platforms has been often studied using the correlation coefficient. Not only is this the wrong approach, but additionally, correlation coefficients are computed assuming that intensity/expression values do not suffer from any measurement error, thus leading to possible underestimates of the real level of correlation between platforms [34]. Here, agreement between platforms was evaluated using a modified version of the Bland–Altman approach. Such a modification, suggested by Liao et al. [35], allows one not only to assess whether two methods of measurement are concordant, but also to provide information on the eventual sources of disagreement. In a nutshell (greater details can be read in the original paper), the method involved the estimation, for each platform pair and separately for each sample, of a measurement error model, i.e., a model where also the independent variable(s) X were assumed to be affected by uncertainty, of the form:(6) Yi=a0+b0Xi0+ϵi (7) Xi=Xi0+δi where (Xi0,Yi0),i=1,...,n were the unobserved true values of the two measurement methods to be compared, i.e., miRNAs intensities on the two platforms, and ϵi and δi, were the i.i.d. error components of the model, which followed a normal distribution with the mean equal to 0 and variances equal to σϵ2 and σδ2, respectively. To estimate this model, the ratio λ of the error variances of Y and X had to be known, possibly by means of replication or, when replication is not feasible, by setting it equal to 1, thus assuming equal error variances for both methods. In this study, both strategies were evaluated, using the technical replicates to estimate λ by fitting a linear model with the factor “replicate” as the covariate. The estimated residual variance was then used as the sample error variance for the platform. Once the parameters of the model were estimated, assuming that Y−X∼N(a0+(b0−1)X0,1+λσδ2), modified versions of the agreement interval for Y−X proposed by Bland and Altman [36,37] were estimated according to the bias (fixed or proportional) needed to correct for when comparing two platforms, as follows: (a) No bias: (a0 = 0, b0 = 1) (8) Δ=−t1−α/2,n−11+λσ^δ,+t1−α/2,n−11+λσ^δ(b) Fixed bias: (a0≠ 0, b0 = 1) (9) Δ=a0−t1−α/2,n−11+λσ^δ,a0+t1−α/2,n−11+λσ^δ(c) Proportional bias: (a0 = 0, b0≠ 1) (10) Δ=b0−1Xi−t1−α/2,n−11+λσ^δ,b0−1Xi+t1−α/2,n−11+λσ^δ(d) Fixed and Proportional bias: ( a0≠ 0, b0≠ 1) (11) Δ=a0+b0−1Xi−t1−α/2,n−11+λσ^δ,a0+b0−1Xi+t1−α/2,n−11+λσ^δ where Xi were the actual measured values of the method. Including only the parameter a0 in the agreement interval meant that the two methods differ only by a “fixed” shift that did not depend on the value of Xi (thus, fixed bias). Including only (or also) b0, on the other hand, meant that the differences between the two methods increased proportionally with the increase of the value of measurement Xi according to the value of the parameter b0 itself (thus, proportional bias). Finally, let n be the number of subjects and 0\u003ck\u003cn; the methods were considered to be in agreement, after eventual bias correction, if no more than k subjects showed Y−X differences outside these intervals. The choice of k depends on the acceptable tolerance: the lower the tolerance for disagreeing subjects, the lower the value of k. The method thus involved estimation of the full model (both intercept and slope) and then evaluation of the most proper bias correction, according to inference on the parameter.\nWith respect to the common use, this method was used in a slightly different way. In a nutshell, commonly, there are n subjects on which specific biological quantities are measured using k measurement methods (k≥2), and the goal is to evaluate whether measurements from the k methods agree using information on n samples. Had this procedure been followed, each miRNA should have been evaluated separately (since the miRNA is the biological quantity of interest), and the intensities in the n samples (in our case, the two cell lines) should have been compared between the k platforms (in this case, 3), jointly, for both cell lines. Actually, the miRNAs were considered to be “subjects” and the entire profile of intensity on a platform to be the vector of measurements to be compared between different platforms (that is, k=3), separately, for each cell line.\nAll of the analyses were performed using R [21] and Bioconductor [23].","divisions":[{"label":"Title","span":{"begin":0,"end":33}}],"tracks":[{"project":"2_test","denotations":[{"id":"27600350-8664775-69476972","span":{"begin":421,"end":423},"obj":"8664775"},{"id":"27600350-2868172-69476973","span":{"begin":2063,"end":2065},"obj":"2868172"},{"id":"27600350-15461798-69476974","span":{"begin":4469,"end":4471},"obj":"15461798"}],"attributes":[{"subj":"27600350-8664775-69476972","pred":"source","obj":"2_test"},{"subj":"27600350-2868172-69476973","pred":"source","obj":"2_test"},{"subj":"27600350-15461798-69476974","pred":"source","obj":"2_test"}]}],"config":{"attribute types":[{"pred":"source","value type":"selection","values":[{"id":"2_test","color":"#93a0ec","default":true}]}]}}