PMC:4979053 / 10981-19305 JSONTXT

{"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. Statistical Analysis\n\n2.4.1. Intra-Platform Reliability\nTo assess the reliability of the three miRNA microarray platforms, pair-wise concordance correlation coefficients [17] were computed for all possible pairs of technical replicates for all platforms, within each sample. The CCC ρc between two series of n measurements x and y is defined as: (1) ρc=2σxyσx2+σy2+μx−μy2=2ρσxσyσx2+σy2+μx−μy2 where ρ=σxyσxσy=∑i=1n(xi−x¯)(yi−y¯)∑i=1n(xi−x¯)2∑i=1n(yi−y¯)2 is the Pearson correlation coefficient between x and y, μx=∑i=1nxin and μy=∑i=1nyin are the sample means of x and y and σx2=∑i=1n(xi−x¯)2n−1 and σy2=∑i=1n(yi−y¯)2n−1 are the sample variances of x and y. Unlike the correlation coefficients, which only can give information about the existence of a linear relationship between two measurement methods, the CCC provides information on both precision (best-fit line) and accuracy (how far the best-fit line deviates from the concordance line) and is thus a better measure to assess platform reliability [30]. Additionally, the pairwise CCCs were combined within each sample and platform into an overall measure of reliability, the overall concordance correlation coefficient (OCCC) [31], a weighted mean of pairwise CCCs, which is defined as follows: (2) ρc0=∑j=1J−1∑k=j+1Jξjkρcjk∑j=1J−1∑k=j+1Jξjk where ρcjk is the standard Lin’s CCC between j-th and k-th replicate measurement series (in this study, these are the replicate arrays), and ξjk are the weights, specific for each paired comparison:(3) ξjk=σj2+σk2+μj−μk2\nConfidence intervals for the OCCC were computed using the bootstrap [32]. Specifically, 1000 bootstrap samples were extracted, and for each of these samples, sample means, variances, covariances, CCC and OCCC were computed. Then, using the empirical distribution of the bootstrap, estimates of the OCCC percentile confidence intervals at 95% were estimated.\nTo evaluate whether pairs of technical replicates are actually in agreement, the non-inferiority approach proposed by Liao and colleagues [33] for gene expression microarrays was followed. This approach consists of defining a threshold, or lower-bound, ρc(CL) reflecting the minimal value that the CCC should assume to conclude that two methods agree and then testing the following hypothesis: (4) H0:ρc≤ρc(CL)vs.H1:ρc\u003eρc(CL)\nThis can be done using the confidence intervals for both CCC and OCCC, interpreting the results as follows: if the lower confidence bound falls below ρc(CL), then the null hypothesis cannot be rejected and the two replicates cannot be said to be in agreement; otherwise, the two replicates are in agreement. To determine the value of ρCL, the authors define the minimum thresholds of precision and accuracy, and then, since the CCC can be seen as a product of a precision and accuracy term, ρc(CL) is computed as the product of these two thresholds. In their example, they propose a threshold of 0.90, yet in this paper, we have chosen to use the value of 0.96, according to the following formula: (5) ρc(CL)=2ρCLvCL+vCL−1+uCL2=2*0.980.9+0.9−1+0.152=0.9638≈0.96 where v=σ1/σ2 represents the scale shift between the two measurements series and u=(μ1−μ2)/σ1σ2 is the location shift relative to the scale. The reason for the choice of these values is subjective, but in this case, there has been the attempt to be conservative: a higher value for ρCL means a relationship between technical replicates as linear as possible, though leaving space for small departures due to ineffective probes or small experimental effects. On the other hand, increasing vCL to 0.9 is due to the fact that miRNA measurements are assumed to be less variable than gene expression, so that technical replicates may show very similar patterns of variability. Only uCL is unchanged, because the value proposed in [33] appeared reasonable also for miRNA microarrays.\n\n2.4.2. 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].\n","divisions":[{"label":"Title","span":{"begin":0,"end":25}},{"label":"Section","span":{"begin":27,"end":3848}},{"label":"Title","span":{"begin":27,"end":60}},{"label":"Section","span":{"begin":3850,"end":8323}},{"label":"Title","span":{"begin":3850,"end":3883}}],"tracks":[{"project":"2_test","denotations":[{"id":"27600350-2720055-69476967","span":{"begin":176,"end":178},"obj":"2720055"},{"id":"27600350-16822306-69476968","span":{"begin":1010,"end":1012},"obj":"16822306"},{"id":"27600350-12495158-69476969","span":{"begin":1189,"end":1191},"obj":"12495158"},{"id":"27600350-17365226-69476970","span":{"begin":2022,"end":2024},"obj":"17365226"},{"id":"27600350-17365226-69476971","span":{"begin":3797,"end":3799},"obj":"17365226"},{"id":"27600350-8664775-69476972","span":{"begin":4271,"end":4273},"obj":"8664775"},{"id":"27600350-2868172-69476973","span":{"begin":5913,"end":5915},"obj":"2868172"},{"id":"27600350-15461798-69476974","span":{"begin":8319,"end":8321},"obj":"15461798"}],"attributes":[{"subj":"27600350-2720055-69476967","pred":"source","obj":"2_test"},{"subj":"27600350-16822306-69476968","pred":"source","obj":"2_test"},{"subj":"27600350-12495158-69476969","pred":"source","obj":"2_test"},{"subj":"27600350-17365226-69476970","pred":"source","obj":"2_test"},{"subj":"27600350-17365226-69476971","pred":"source","obj":"2_test"},{"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":"#de93ec","default":true}]}]}}