Velocity
Speed wins the patient. Inertia sets the speed limit.
Flow velocity (hub and pharmacy)
How fast each patient gets from prescription to first fill or first dose.
Approval, pickup and r are the Baseline inputs from the Model. Default h = −ln 0.7 / 5 ≈ 0.071 (Claritas): each day of delay cuts fill odds by about 6.9%.
Time-to-therapy equation
Pfill(T) = Pmax · e−h(T − Tmin)
PM = Rx × P(approval) × Pfill(T) × 1/(1 − r)
h = −ln 0.7 / 5 ≈ 0.071 per day, from the Claritas benchmark.
Patient-months today
188
per 100 Rx
Lost per day of delay
13.4
∂PM/∂T = −h · PM
Pickup, 3 days faster
58.2%
from 47.0%
Patient-months, 3 days faster
233
+24% vs today
Patient-months per 100 Rx: 188 today, rising to 233 if starts come 3 days faster.
Share velocity (payer contracting)
How fast biosimilar share moves when payer contracts change who stays put.
IQVIA found Humira patients switched abruptly only after PBM formulary restrictions, not discounts. Delay during the switch leaves patients on the original brand by default; Claritas Rx found pharmacy-type transfers can take up to 320% longer.
Share-gain equation
vt = (1 − λ) × (S* − St−1)
share gained = (1 − λ) × remaining gap
t½ = ln 0.5 / ln λ is the months it takes to close half the gap to S*. Share only moves through the (1 − λ) part.
Half-life, patients stay put
13.5 mo
ln 0.5 / ln λ
Half-life, payer drives switch
1.9 mo
ln 0.5 / ln λ′
Month-1 gain, stay put
2.5%
(1 − λ) × gap
Month-1 gain, payer
15.0%
(1 − λ′) × gap