Improvement score

high-resolution terminology - matching measurements at high-resolution

Improvement score

Description

The relative improvement score, RIS, provides a measure of improvement of a trait from a value measured at baseline, B, to a value measured after treatment, T, expressing the total improvement, T-B, in relation to the theoretical scope of improvement and the level of the trait observed at baseline. 'RIS incorporates the concept of diminishing returns and consideres maintaining a high value of a trait as an improvement relative to the potential loss.

Abbreviation: RIS

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What is positive and negative improvement?

A relative improvement score, RIS, requires measurements at baseline, B, and after treatment, T, of a trait that increases as a positive measure of improvement (B>0 and T>0).

The absolute improvement is the difference T-B and distinguishes three conditions:

1. T-B > 0. There is positive improvement, and RIS > 0.
2. T-B < 0. There is negative improvement, and RIS < 0.
3. T-B = 0. There is no absolute change. The value of RIS is zero if the lowest baseline score, B=1, has not improved. In contrast, the relative improvement should be considered as a positive result, if a high value of B is maintained. Improvement is then considered relative to a potential decline of T compared to B.

When does improvement become more difficult to achieve?

The same absolute improvement, T-B, is more easily achieved when the trait has a low value at baseline (B is low). As B approaches the theoretical maximum, B_max = T_max, the scope for absolute improvement diminishes, and the same small absolute improvement becomes more difficult to achieve. Even maintaining rather than loosing B_max is a significant achievement, which is considered as a positive RIS.

How does the relative improvement score behave?

1. If T>B, T-B is positive; there is a positive RIS.
2. If T<B, T-B is negative; there is a negative RIS.
3. A positive T-B value is more difficult to achieve, the higher the initial value of B. Therefore, the same value of T-B should have a higher RIS at higher values of B and T.
4. The relationship between T-B and RIS should have the same proportionality for positive and negative T-B values, i.e., if the highest RIS=9, then the worst is -9.
5. Positive and zero values of T-B are treated by an equation that is different from the equation for negative values of T-B.
6. If B=T_min=1, T-B=0, then RIS=0.
7. If B=T>1, T-B=0, then RIS has a positive value that increases with increasing B.
8. If B=T_max, T-B=0, then RIS has a relatively high positive value.

These criteria are met by application of two equations:

Positive improvement, T>B, and maintenance of the baseline value, T=B

Eq.(1)

RIS = (T*T-B)/(T+B)

Negative improvement, T<B

Eq.(2)

RIS = (T-B*B)/(T+B)

Alternative models

No improvement at T=B?

T=B indicates no absolute improvement. It may be considered to assign a zero value to the relative improvement score. This is problematic, if the baseline score is at a maximum value, leaving no scope for absolute improvement, and the absolute improvement score equals zero. The same zero value would be given for maintaining a minimum score B_min, when the scope for improvement is actually very high. This problem is solved by applying Eq.(1) to T=B.

A quick comparison

The resulting Bioblast Relative Improvement Score, RIS, represents a significant improvement in comparison to previous concepts.

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» https://www.nngroup.com/articles/improvement-score/