E2P Simulator LogoE2P Simulator

From Effect Size to 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, predictive modelling, 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

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

From Single to Multiple Predictors

While the interactive graph above explores a single predictor, here you can estimate the combined effect of multiple predictors and determine how many are needed to achieve a desired level of real-world predictive utility. The combined effect is estimated by first computing Mahalanobis D, a multivariate generalization of Cohen's d, and then computing PR-AUC, which is sensitive to the base rate. For simplicity, the estimation assumes predictors to have the same effect sizes, uniform collinearity, and no interaction effects.

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

\[D = d \sqrt{\dfrac{p}{1 + (p-1)r_{ij}}}\]
Target Mahalanobis D
Target PR-AUC
Base rate (%)
Effect size of each predictor (d)
Collinearity among predictors (rij)
Number of predictors (p)