Research calculator

ARPI Treatment Effect Estimator

A model for estimating ARPI treatment effects from baseline characteristics in metastatic hormone-sensitive prostate cancer.

Development data: This calculator was developed using individual participant data from 4,706 patients across four phase 3 randomized clinical trials: LATITUDE, TITAN, ARASENS, and ARCHES.

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Step 1

Patient characteristics

9 predictors

Enter baseline characteristics used to estimate treatment effects.

Step 2

Estimated ARPI treatment effect

Model-based treatment effect estimate

ARPI compared with control, with 95% confidence intervals.

Effect pattern

How the effect changes with baseline risk

About the model

How this calculator estimates treatment effects

The calculator first summarizes baseline prognosis with a Cox-model risk score based on nine patient characteristics. It then estimates the relative and absolute effects of adding an ARPI at that position on the baseline-risk spectrum.

Prediction target: Risk of all-cause death by 4 years under the control treatment strategy.
Development population: 4,706 patients from LATITUDE, TITAN, ARASENS, and ARCHES.
Predictors: Nine baseline characteristics; five continuous predictors were modeled flexibly with restricted cubic splines.
Validation: Internal validation with 1,000 bootstrap samples and leave-one-trial-out internal-external cross-validation.

Technical calculation details

Treatment is set to the control arm (ARM = 0) so the score represents baseline prognosis independent of assigned treatment. For continuous predictor v in {PSA, hemoglobin, albumin, alkaline phosphatase, lactate dehydrogenase}, B₁(v) is the observed value and B₂(v) and B₃(v) are restricted cubic spline terms.

B1(x) = x

Bj+1(x) = [(x−kj)+³ − (x−k3)+³(k4−kj)/(k4−k3) + (x−k4)+³(k3−kj)/(k4−k3)]/(k4−k1)², j = 1, 2

(z)+ = max(z, 0)

LPraw = Σv Σj βv,j Bj(v) + 0.25046359 I(bone 4–6) + 0.28942287 I(bone 7–9) + 0.34768018 I(bone 10–19) + 0.53991769 I(bone ≥20) + 0.21277111 I(ECOG ≥1) + 0.32095198 I(Gleason ≥9) + 0.36649089 I(visceral metastasis)

LP = 0.95619432 × (LPraw − (−2.39245883))

LPused = min(max(LP, −0.86989729), 1.81907311)

The binary indicators equal 1 for ECOG performance status of 1 or higher, Gleason score of 9 or higher, and presence of visceral metastasis. The reference bone-metastasis group is 3 or fewer. The app interpolates the hazard ratio, added survival time, and 4-year survival difference from their modeled curves at LPused.

Model coefficients

Coefficients used in the implemented linear predictor
Predictor or category	β1	β2	β3
PSA, ng/mL	0.01444192	−19.31153630	22.31835208
Hemoglobin, g/L	−0.01562826	0.00665150	−0.01094183
Albumin, g/L	−0.03777922	0.02344675	−0.10302783
Alkaline phosphatase, U/L	0.00798842	−0.83039660	1.07052058
Lactate dehydrogenase, U/L	−0.00139190	0.05079425	−0.11841729
4–6 bone metastases	0.25046359	—	—
7–9 bone metastases	0.28942287	—	—
10–19 bone metastases	0.34768018	—	—
20 or more bone metastases	0.53991769	—	—
ECOG performance status ≥1	0.21277111	—	—
Gleason score ≥9	0.32095198	—	—
Visceral metastasis present	0.36649089	—	—

Restricted cubic spline knots

Four knots used for each continuous predictor
Predictor	Knot 1	Knot 2	Knot 3	Knot 4
PSA	0.15	4.4775	32.3275	725.875
Hemoglobin	104	128	141	157
Albumin	36	41	44	48
Alkaline phosphatase	55	96	237	1616
Lactate dehydrogenase	134	170	202	375.75

Because five predictors use nonlinear spline terms, their individual coefficients should not be interpreted separately. These details support reproducibility and independent implementation; they are not intended as a simplified bedside score.

Methodological framework: Harrell FE Jr. Regression Modeling Strategies, 2nd ed. Springer; 2015.