Erratum
Following publication of our article [1], it has come to our attention that two of the formulae in Table 1 were incorrect. The formulae for the measures of precision and burden have been corrected (Table 1). We are publishing this erratum to update these formulae to the following:
Table 1
Definitions of performance measures reported in the studies
Measure | # | Definition | Formula |
|---|---|---|---|
Recall (sensitivity)
| 22 | Proportion of correctly identified positives amongst all real positives |
\( \frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{F}\mathrm{N}} \)
|
Precision
| 18 | Proportion of correctly identified positives amongst all positives. |
\( \frac{TP}{TP+FP} \)
|
F measure
| 10 | Combines precision and recall. Values of β < 1.0 indicate precision is more important than recall, whilst values of β > 1.0 indicate recall is more important than precision | \( {F}_{\beta, k}\kern0.5em =\kern0.5em \frac{\left({\beta}^2+1\right){\mathrm{TP}}_k}{\left({\beta}^2+1\right){\mathrm{TP}}_k+{\mathrm{FP}}_k+{\beta}^2{\mathrm{FN}}_k} \) Where β is a value that specifies the relative importance of recall and precision. |
ROC (AUC)
| 10 | Area under the curve traced out by graphing the true positive rate against the false positive rate. 1.0 is a perfect score and 0.50 is equivalent to a random ordering | |
Accuracy
| 8 | Proportion of agreements to total number of documents. |
\( \frac{\mathrm{TP}+\mathrm{T}\mathrm{N}}{\mathrm{TP}+\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N}+\mathrm{T}\mathrm{N}} \)
|
Work saved over sampling
| 8 | The percentage of papers that the reviewers do not have to read because they have been screened out by the classifier |
\( \mathrm{W}\mathrm{S}\mathrm{S}\ \mathrm{at}\ 95\%\ \mathrm{recall} = \kern0.5em \frac{\mathrm{TN}+\mathrm{F}\mathrm{N}}{N-0.05} \)
|
Time
| 7 | Time taken to screen (usually in minutes) | |
Burden
| 4 | The fraction of the total number of items that a human must screen (active learning) |
\( Burden=\frac{t{p}^T+t{n}^T+f{p}^T+t{p}^U+f{p}^U}{N} \)
|
Yield
| 3 | The fraction of items that are identified by a given screening approach (active learning) |
\( \mathrm{Yield}\kern0.5em =\kern0.5em \frac{{\mathrm{tp}}^T+{\mathrm{tp}}^U}{{\mathrm{tp}}^T+{\mathrm{tp}}^U+{\mathrm{fn}}^U} \)
|
Utility
| 5 | Relative measure of burden and yield that takes into account reviewer preferences for weighting these two concepts (active learning) | \( \frac{\beta \cdot \mathrm{yield}+\left(1\kern0.5em -\kern0.5em \mathrm{burden}\right)}{\beta +1} \) Where β is the user-defined weight |
Baseline inclusion rate
| 2 | The proportion of includes in a random sample of items before prioritisation or classification takes place. The number to be screened is determined using a power calculation | \( \frac{n_i}{n_t} \) Where n
i
= number of items included in the random sample; n
t
= total number of items in the random sample |
Performance (efficiency)
a
| 2 | Number of relevant items selected divided by the time spent screening, where relevant items were those marked as included by two or more people |
\( \frac{\mathrm{Selected},\kern0.5em \mathrm{relevant}\kern0.5em \mathrm{items}}{\mathrm{Time}} \)
|
Specificity
| 2 | The proportion of correctly identified negatives (excludes) out of the total number of negatives |
\( \frac{\mathrm{TN}}{\mathrm{TN}+\mathrm{F}\mathrm{P}} \)
|
True positives
| 2 | The number of correctly identified positives (includes) | TP |
False negatives
| 1 | The number of incorrectly identified negatives (excludes) | FN |
Coverage
| 1 | The ratio of positives in the data pool that are annotated during active learning | \( \frac{{\mathrm{TP}}^L}{{\mathrm{TP}}^L+{\mathrm{FN}}^L+{\mathrm{TP}}^U+{\mathrm{FN}}^U} \) Where L refers to labelled items and U refers to unlabelled items |
Unit cost
| 1 | Expected time to label an item multiplied by the unit cost of the labeler (salary per unit of time), as calculated from their (known or estimated) salary | timeexpected × costunit |
Classification error
| 1 | Proportion of disagreements to total number of documents | 100 % − accuracy % |
Error
| 1 | Total number of falsely classified items divided by the total number of items |
\( \frac{\sum \left(\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N}\right)}{\sum \left(\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N}+\mathrm{T}\mathrm{N}\right)} \)
|
Absolute screening reduction
| 1 | Number of items excluded by the classifier that do not need to be manually screened | TN + FN |
Prioritised inclusion rate
| 1 | The proportion of includes out of the total number screened, after prioritisation or classification takes place | \( \frac{n_{\mathrm{ip}}}{n_{\mathrm{tp}}} \) Where nip = number of items included in prioritised sample; ntp = total number of items in the prioritised sample |
Precision = \( \frac{TP}{TP+FP} \)
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Burden = \( \frac{t{p}^T+t{n}^T+f{p}^T+t{p}^U+f{p}^U}{N} \)
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