E2P Simulator LogoE2P Simulator

Understanding Real-World Predictive Utility

E2P Simulator estimates the real-world predictive utility of research findings by accounting for measurement reliability and outcome base rates. It is designed to help researchers interpret findings and plan studies across biomedical and behavioral sciences, particularly in individual differences research, biomarker development, and precision medicine/psychiatry.

See Get Started guide for more details.

Developed by Povilas Karvelis

Outcomes
Effects
True Obs.
Cohen's d
Cohen's U3
Odds Ratio
Log Odds Ratio
Point-biserial r
η²
Group 1 reliability, ICC1
Group 2 reliability, ICC2
Grouping reliability, κ
Base rate (%)

AUC: 0.00

Accuracy: 0.00

Sensitivity: 0.00

Specificity: 0.00

BA: 0.00

NPV: 0.00

PPV: 0.00

F1-score: 0.00

MCC: 0.00

Cohen's d attenuation by reliability

\[d_{obs} = d_{true} \sqrt{\frac{2ICC_1ICC_2}{ICC_1+ICC_2}\sin\left(\frac{\pi}{2}\kappa\right)}\]

d to Log Odds Ratio

\[\log(OR) = \frac{d\pi}{\sqrt{3}}\]

d to AUC

\[AUC = \Phi\left(\frac{d}{\sqrt{2}}\right)\]

d to Point-biserial r

\[r_{pb} = \frac{d}{\sqrt{d^2 + \frac{1}{p(1-p)}}}\]

d to Eta squared

\[\eta^2 = \frac{d^2}{d^2 + \frac{1}{p(1-p)}}\]

Mahalanobis D Calculator

Instead of using a single large effect, it is often necessary to combine multiple smaller effects to achieve the desired level of predictive performance. This calculator shows how many predictors
are needed, given their individual effect sizes and collinearity, to achieve a desired level of group separation. The separation is quantified using Mahalanobis D, which generalizes Cohen's d to multivariate settings.

A simplified Mahalanobis D formula when all predictors have the same effect size and collinearity:

\[D = d \sqrt{\dfrac{p}{1 + (p-1)r_{ij}}}\]
Needed Mahalanobis D
Effect size of each predictor (d)
Collinearity among predictors (r_ij)
Number of predictors (p)