GLP-1 Dosage Calculator - assumptions and limitations

Assumptions

• Per-injection mg = weekly mg / doses per week

  The injection-mass split is dimensional: what you put in the syringe is what reaches the SC tissue. Steady-state body load is computed separately from mean_load = (mg_per_injection × F) / (k × tau), where F is the published subcutaneous bioavailability per drug (semaglutide 0.89, tirzepatide 0.80, dulaglutide 0.60, liraglutide 0.55) - see formulas list.

• Schedule math assumes consistent intervals

  doses_per_week = 7 / interval_days assumes the chosen cadence is followed exactly across the week (a planning default). Real adherence has missed/late doses; the steady-state PK output makes the cost of a missed dose explicit via `trough × e^(-k × tau)`.

• U-100 syringe units (definitional)

  U-100 insulin syringes are defined by USP <1601> and ISO 8537:2016 as 100 units = 1 mL (so 1 unit = 0.01 mL). The conversion units = volume_mL * 100 is dimensional, not modelled. Confirm the markings on your specific device before drawing.

• Vial usage rounds down (conservative policy)

  Doses per vial floors to whole doses; days of supply counts full doses only. Floor is the tightest bound that does not overstate supply - the partial-dose remainder is surfaced separately as 'Leftover' so nothing is hidden. This is a documented rounding policy, not a model.

• Blood-level chart is relative (population-mean t1/2)

  The 'Estimated drug levels' chart uses a one-compartment terminal-half-life model with population-mean t1/2 and a published 90% CI per drug: semaglutide 165 h (124-218), tirzepatide 120 h (96-150), retatrutide 150 h (130-175), dulaglutide 120 h (96-156), liraglutide 13 h (10-18). All values from each drug's USPI clinical pharmacology section. Y-axis is mg-equivalent body load - NOT absolute plasma concentration. Subcutaneous absorption (t_max ~24-72 h for the long-acting GLP-1s) is collapsed into the decay term, so the early rise after the first dose is faster than the real plasma curve; at steady state for weekly drugs the simplification is small. A two-compartment Bateman simulator with per-drug ka / V_d / F is wired and tested in `glp1/pk.ts` for a future µg/L axis swap.

• Steady state ≈ 4.32 × half-life (closed form)

  The 95%-of-steady-state marker uses t_95 = 4.32 × t_half (≈ -ln(0.05) / ln(2)). The accumulation ratio per interval is 1 / (1 - e^(-k × tau)). Both are exact closed-form identities for one-compartment dosing at constant interval (Rowland & Tozer, Clinical Pharmacokinetics and Pharmacodynamics, 4th ed., §6.3; Gibaldi & Perrier, Pharmacokinetics, 2nd ed., §3.5). Dosing interval changes the *number of doses* needed but not the time. A `numericalT95FromCurve` helper (lib/calculators/glp1/pk.ts) is wired in for the future two-compartment Bateman swap, where the closed form becomes an approximation.

• Missed-dose recommendation restates the labelled rule

  The 'Did you miss a dose?' panel applies a per-drug cutoff sourced from each brand's prescribing info (Ozempic/Wegovy, Mounjaro/Zepbound, Trulicity, Victoza/Saxenda) and the conservative default for retatrutide. The decision is a closed-form take-now-vs-skip rule based on hours-late vs the labelled cutoff: it does not consult plasma levels, individual half-life, or interaction risks. This restates labelled guidance verbatim - it is not personalised clinical advice.

• Drug-switching maps trial-mean weight-loss effect (NOT equipotency)

  The 'Considering a switch?' card maps source vs target by approximate trial-mean weight-loss % at each dose tier - NOT receptor equipotency, NOT a clinical conversion factor. Tier weights come from STEP-1/2/3 (semaglutide), SURMOUNT-1 (tirzepatide), AWARD (dulaglutide), SCALE (liraglutide), and TRIUMPH-1 phase 2 (retatrutide). The starter dose recommendation always uses the target's labelled titration tier, regardless of source dose. Inter-individual variability is large (interquartile range often ±5pp around the trial mean). This card is an illustrative comparison only - real equivalent doses depend on indication, comorbidities, response history, and prescriber judgement.

• Refill timeline is arithmetic only (no shipping / approval logic)

  The Refill timeline projects per-vial coverage dates and an order-by date by anchoring `vialFills.{first,last}DoseNumber` on `schedule.startDate` + N × intervalDays. The 'Order by' line subtracts a default 7-day lead time from the inventory-depletion date. It does not account for prescription-approval delays, shipping windows, refrigeration constraints, or per-pharmacy lead times - it's a planning hint, not a guaranteed deadline.

• GI-tolerance forecast is a population pattern (NOT a personal prediction)

  The 'GI tolerance forecast' projects each dose-up in a titration plan as a rough-patch window: peak day +5 from the dose-up, resolves by day +14. Intensity is bucketed from the relative dose increase: <50% = mild, 50-100% = moderate, ≥100% = rough. These offsets reflect the population pattern of GLP-1 GI side effects reported in the STEP and SURMOUNT trial families. Inter-individual variability is enormous (interquartile range often spans 'barely noticed' to 'had to pause titration'); the forecast is a population pattern, not a personal prediction.

• Cost calculator assumes a fixed per-vial price

  The Refill cost card divides cost-per-vial by vial mg capacity to produce $/mg, then multiplies by weekly mg to project $/week, $/month, and $/year. It assumes the same vial price across the full year of refills - it does not model insurance reimbursement, manufacturer coupons, bulk-order discounts, or compounded vs. branded pricing differences. The $/year number is `$/week × 52` exactly (no leap-week handling).

Formulas used

Each output is derived from one of the formulas below. They run client-side, so what you see in the calculator is what the math actually does.

1. 1. Doses per week

   doses_per_week = 7 / interval_days

2. 2. Mg per injection

   mg_per_injection = weekly_mg / doses_per_week

3. 3. Volume per dose

   volume_mL = mg_per_injection / concentration_mg_per_mL

4. 4. Weekly mL

   weekly_mL = weekly_mg / concentration_mg_per_mL

5. 5. U-100 syringe units (estimate)

   units = volume_mL * 100

6. 6. Vial volume (mL)

   vial_volume_mL = vialSize (when unit = mL) OR vialSize / concentration_mg_per_mL (when unit = mg)

7. 7. Doses per vial

   doses_per_vial = floor(vial_volume_mL / volume_mL)

8. 8. Days of supply

   days_of_supply = doses_per_vial * interval_days

9. 9. Decay constant

   k = ln(2) / t_half

10. 10. Concentration over time

    C(t) = sum over past doses of dose_mg * e^(-k * (t - t_dose))

11. 11. Time to ~95% steady state

    t_95 = 4.32 * t_half

12. 12. Accumulation ratio per interval

    ratio = 1 / (1 - e^(-k * tau))

13. 13. Steady-state mean body load (companion)

    mean_load_mg = mg_per_injection / (k * tau)

14. 14. Steady-state systemic mean (bioavailability-adjusted)

    systemic_mean_mg = mg_per_injection * F / (k * tau)

15. 15. Missed-dose trough sensitivity

    trough_drop_fraction = 1 - e^(-k * tau)

16. 16. Missed-dose decision (per-drug cutoff)

    action = hours_late <= drug.rescheduleIfHoursLateAtMost ? 'take-now' : 'skip'

17. 17. Drug-switch equivalent dose (weight-loss-effect mapping)

    to_equivalent_mg = nearest_tier(toDrug.tiers, interpolate_pct(fromDrug.tiers, fromWeeklyMg))

18. 18. Refill order-by date

    order_by = startDate + (lastDoseNumber + 1) × intervalDays - leadTimeDays

19. 19. GI-tolerance window per dose-up

    window = { start: phaseStart, peak: phaseStart + 5d, end: phaseStart + 14d }

20. 20. Cost breakdown

    cost_per_mg = cost_per_vial / vial_mg_capacity ; cost_per_week = cost_per_mg × weekly_mg

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