# Reply to the comment made by Šicho, Vorśilák and Svozil on ‘The Power metric: a new statistically robust enrichment-type metric for virtual screening applications with early recovery capability’

- Hans De Winter
^{1}Email authorView ORCID ID profile and - Julio Cesar Dias Lopes
^{1}

**Received: **13 January 2018

**Accepted: **15 February 2018

**Published: **15 March 2018

The original article was published in Journal of Cheminformatics 2018 10:13

The authors of the comment [1] raised an interesting remark about the relation between the power metric (*PM*) [2] and the precision metric (*PR*), also known as the positive predictive value (*PPV*).

*EF*) and

*ROC*enrichment (

*ROCE*), as can be noted by these equations:

*R*

_{ i }and

*R*

_{ a }being the proportion of active and inactive instances in the whole dataset with

*N*instances:

*n*

_{ a }and

*n*

_{ i }the number of active and inactive instances in the dataset.

- (a)in
*EF*, χ is the fraction of compounds selected (χ =*N*_{ s }/*N*), related to the number of true and false positives (*TP*and*FP*):$$\chi = \frac{TP + FP}{N}$$(7) - (b)in
*ROCE*, χ can be related to the fraction of inactive instances wrongly classified as positives:$$\chi = FPR = \frac{FP}{{n_{i} }}$$(8) - (c)in
*PM*, χ can be related to the sum of the true and false positive rates:$$\chi = TPR + FPR = \frac{TP}{{n_{a} }} + \frac{FP}{{n_{i} }}$$(9)

Due to these characteristics all these metrics are interconvertible.

*PM*as a function of χ and

*FPR*:

In addition, using the number of actives and inactives, all values of *TP*, *FP*, *TN* (true negatives) and *FN* (false negatives) can be calculated, and from these values any metric can be derived.

The fact that all these metrics are functionally related to the precision metric do not invalidated them as being useful metrics (‘not suitable for performance assessment’, as stated by the authors of the comment). All these metrics have their scopes, strengths and weaknesses. Each one has its meaning and can be used by the user depending on the desired aims. For example, the precision or *EF* metrics might be more appropriate if the user is more concerned about false positives, while in applications with more emphasis on true positive rates the *PM* or *ROCE* metrics would be recommended instead.

*PM*on threshold χ. In case of a ‘perfect’ screening method in which

*FPR*approaches zero, the

*PM*tends to approach one (Eq. 10) and

*TPR*tends to become equal to χ (Eq. 9). Thus, in this case the maximum value of the

*TPR*is limited by the user-defined threshold value χ:

This leads us to the interpretation of the *PM* as the fraction of active compounds that are correctly predicted in relation to the maximum fraction of active compounds that could be recovered at the chosen threshold χ, or, in other words, *PM* express the probability of an active compound to be correctly classified.

## Notes

## Declarations

### Authors’ contributions

HDW and JCDL wrote, reviewed and edited the manuscript. Both authors read and approved the final manuscript.

### Competing interests

The authors declare that they have no competing interests.

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## Authors’ Affiliations

## References

- Svozil D, Šícho M, Voršilák M (2018) Comment on “The power metric: a new statistically robust enrichment-type metric for virtual screening applications with early recovery capability”. J Cheminf. https://doi.org/10.1186/s13321-018-0267-x Google Scholar
- Lopes JCD, Dos Santos FM, Martins-José A, Augustyns K, De Winter H (2017) The power metric: a new statistically robust enrichment-type metric for virtual screening applications with early recovery capability. J Cheminform 9:7View ArticleGoogle Scholar