Gold standard
Positive
Negative
New biomarker
Positive
TP
FP
PPV = TP/(TP + FP)
Negative
FN
TN
NPV = TN/(TN + FN)
Sensitivity = TP/(TP + FN)
Specificity = TN/(TN + FP)
The Receiver Operating Characteristic (ROC) curve provides a summary method for examining the performance of a biomarker in terms of its sensitivity and specificity over a range of potential cutoffs that could be used to dichotomise the population into biomarker positives and negatives. These can then be summarised by an area under the ROC curve (AUC), which ends up being a scaled version of the Mann–Whitney statistic comparing the biomarker between the two groups. Recently the theoretical basis of the AUC has been criticised with Hand (2009) proposing the H-measure as an alternative with improved properties.
14.3.8 Evaluating Concordance
A typical concordance study will assess a number of samples a number of times, depending upon the source of variability being studied. A simple overall agreement can be calculated by counting the proportion of times the ratings from the same sample agrees. However, this is highly dependent upon the overall prevalence, for example if predicting a rare disease the majority of samples will be negative so a new diagnostics could attain a high overall agreement by scoring every single sample as negative, which is not very informative. The Kappa statistic provides a chance corrected measure of agreement. The original Cohen’s kappa was calculated for two raters and allowed for the two raters to have different marginal distributions. Fleiss’s Kappa assumes a common marginal distribution for all raters, allowing extension to any number of assessors. Krippendorf’s Alpha provides a method for calculating Fleiss’s Kappa for incomplete data with missing values.
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