The arithmetic of a step: what doubling a dose actually asks of you

Consider two steps on the same ladder. Moving from 0.25 mg to 0.5 mg of semaglutide is a doubling. Moving from 1.7 mg to 2.4 mg is an increase of about forty-one per cent. The absolute increments are 0.25 mg and 0.7 mg respectively, so the second looks larger and is in fact the gentler event. Receptor occupancy responds to ratio, not to difference, and every titration ladder in this class is built on tapering ratios for precisely that reason. Almost nobody explains this to the person holding the pen, who reasonably concludes that the steps are getting bigger.

The semaglutide ladder, rung by rung

For weight management, the approved escalation runs 0.25 mg weekly for four weeks, then 0.5 mg, then 1.0 mg, then 1.7 mg, reaching 2.4 mg at week seventeen. For glycaemic indications the ladder is shorter and the maximum lower: 0.25 mg, then 0.5 mg, then 1.0 mg, with a 2.0 mg option added later on the strength of a dedicated dose-comparison study.

Two features are worth noticing. The starting dose is explicitly sub-therapeutic — 0.25 mg is a tolerability rung, not a treatment dose, and describing it as a low dose rather than an initiation dose causes real confusion. And the ratios narrow as the ladder rises: two doublings, then a 1.7-fold step, then a 1.41-fold step.

The 2.4 mg dose was selected on the basis of the phase 2 dose-ranging programme and carried into the STEP trials, where it produced a mean weight reduction of about fifteen per cent at sixty-eight weeks against roughly two and a half per cent on placebo.¹ That is the number the ladder exists to reach, and the ladder itself was never the subject of the trial.

The tirzepatide ladder is a different shape

Tirzepatide begins at 2.5 mg weekly for four weeks, moves to 5 mg, and thereafter increases in 2.5 mg increments at intervals of not less than four weeks, to a maximum of 15 mg. The structural difference from semaglutide is important: after the first doubling the increments are fixed in absolute terms, which means the ratio falls steadily — 1.5-fold, then 1.33, then 1.25, then 1.20.

The practical consequence is that the upper half of the tirzepatide ladder is unusually gentle in proportional terms, and the first step from 2.5 mg to 5 mg is by some distance the most demanding thing the schedule asks. Clinicians we spoke to described the 2.5-to-5 transition as the point at which most early attrition occurs, which is what the ratios predict.

The label also states, in language that repays attention, that 5 mg is a therapeutic dose in its own right and that escalation beyond it should reflect response and tolerability. That is a materially different instruction from a ladder with a fixed destination, and it is closer to how the drug is actually used.²

Why four weeks, precisely

The elimination rate constant of a drug is 0.693 divided by its half-life. Fractional approach to steady state after time t is 1 minus e to the power of minus k times t. For a seven-day half-life this yields about seventy-five per cent of steady state at two weeks, eighty-eight per cent at three, ninety-four per cent at four and ninety-seven per cent at five.

Four weeks is therefore the point at which a once-weekly dose has essentially finished getting stronger. Escalate at two weeks and the person receives the increment written on the pen plus roughly a further quarter of the previous rung still accumulating underneath it. That is not dangerous in any dramatic sense, but it does mean the symptom burden attributed to the new dose is partly the tail of the old one, and it makes the escalation harder to interpret.

For tirzepatide, with a half-life closer to five days, four weeks corresponds to more than five half-lives and the previous rung is fully settled. The same interval is therefore slightly conservative for one molecule and exactly adequate for the other, which is a small illustration of how a shared convention can be right for different reasons.³

The arithmetic of a step

A dose increase should be described as a ratio, because receptor occupancy and the exposure-response relationship are governed by proportional change rather than by absolute milligrams. On the semaglutide weight-management ladder the ratios are 2.00, 2.00, 1.70 and 1.41. On the tirzepatide ladder they are 2.00, 1.50, 1.33, 1.25 and 1.20.

Two consequences follow. The first is that the early rungs are the hard ones, in both ladders, and the widespread expectation that titration gets progressively more difficult is backwards. The second is that a person who has tolerated the doubling at the bottom of the ladder has already survived the largest proportional insult the schedule contains.

There is a third, less obvious consequence for anyone dosing from a multi-dose vial rather than a fixed pen. Fixed-pen users move in the ratios above. Vial users can move in any ratio they like, including ratios small enough to be pharmacologically meaningless and large enough to be foolish. Freedom of increment is the single largest practical difference between pen and vial administration, and the arithmetic is the only guardrail.

Accelerated and decelerated schedules

The evidence on deviating from four-week steps is observational and one-sided. Slower escalation — five, six or eight weeks per rung — is reported by clinicians to reduce early discontinuation, is consistent with the tachyphylaxis data, and has never been randomised against the standard interval in a trial of adequate size. Faster escalation has no supporting rationale we can identify and a clear kinetic argument against it.

What can be said with confidence is that the cost of going slower is bounded and calculable: a longer time to target exposure, and therefore a later arrival at the efficacy plateau. Because the plateau itself sits at sixty weeks or beyond, adding four or eight weeks to the escalation phase is a small fraction of the treatment course. The cost of going faster is a higher probability of discontinuation, and discontinuation costs the entire effect.

That asymmetry is the strongest thing the Journal is willing to say on the subject. It is an argument from consequence rather than from trial data, and we flag it as such rather than dressing it as a finding.⁴

The shape of the curve, stated numerically

Across the programmes the exposure-response relationship for weight is approximately log-linear over the lower and middle range and flattens above it, while the relationship for gastrointestinal adverse events is closer to linear in dose and does not flatten in the same range. That divergence is the ceiling.

In glycaemic endpoints the flattening is even more pronounced. HbA1c reduction in the tirzepatide diabetes programme differed by roughly a quarter of a percentage point between the 5 mg and 15 mg arms in the head-to-head against semaglutide, which is a small difference against a threefold dose range.⁵ For a person whose objective is glycaemic control rather than weight, the argument for the upper rungs is correspondingly weaker.

The general point is that the class has two dose-response curves running in parallel and only one of them flattens. Any discussion of escalation that quotes the efficacy curve without the tolerability curve is quoting half a graph, which is how the top of the ladder came to be treated as an obvious destination.

Non-standard concentrations and the errors they cause

Compounded and grey-market preparations are frequently supplied at concentrations that do not correspond to any licensed presentation. That is not in itself a quality problem, but it removes every mental shortcut a person may have acquired, and it interacts badly with escalation.

The recurring error is arithmetic rather than clinical: a person who has learned that a particular volume equals a particular dose changes vial, keeps the volume, and changes the dose without intending to. We have seen this reported in both directions and at magnitudes exceeding a full rung on the ladder.

Two habits protect against it. Recompute the volume-to-dose conversion whenever the vial changes, from the stated content and the reconstitution volume, rather than carrying the old figure forward. And write the result down somewhere attached to the vial, because the calculation is easy and the recall is not. The Journal covers the underlying arithmetic in the injection-practice file; the point here is that changing vials mid-titration converts a titration decision into a units problem, and units problems are where the largest errors in this field occur.

How the Journal reports dose figures

Three conventions govern the numbers in this file. Weight-change figures are quoted with the estimand named, because the treatment-policy and trial-product analyses in the obesity programmes differ by two to three percentage points and secondary coverage habitually mixes them. Doses are quoted as the weekly amount, not as a pen volume or a unit count, because volume and units depend on concentration and concentration varies. And where a figure derives from a responder analysis rather than a primary endpoint, we say so.

Where we describe practice rather than evidence, the text says so explicitly. A substantial part of what is known about titration in this class is craft knowledge held by clinicians, and reporting it is legitimate journalism. Presenting it as trial data is not.

Nothing in this file is medical advice. The Journal does not recommend doses, schedules, products or suppliers. Several compounds discussed here are sold for research use only and are not approved for human use in any jurisdiction. Decisions about treatment belong with a licensed clinician who has examined the person concerned.

A short glossary, because the terms get swapped

Initiation dose: the first rung, chosen for tolerability and generally sub-therapeutic. Not a low treatment dose. Target dose: the dose a protocol or prescriber intends to reach. Maintenance dose: the dose continued once the intended effect is achieved. Maximum approved dose: the highest dose in the label, set by the studied range and the tolerability ceiling.

Escalation interval: the time between increments. Hold: deliberately remaining at a rung beyond the standard interval. Re-titration: re-ascending after exposure has been substantially cleared. Dose-limiting: describing an effect severe enough to prevent escalation, which is a property of the person and the dose jointly, not of the drug alone.

Steady state: the condition in which drug entering the body equals drug leaving it. Accumulation ratio: steady-state average concentration divided by first-dose average concentration. Precision here matters more than it sounds: a large share of the correspondence this desk receives about titration turns out on inspection to be a disagreement about which of these words the writer meant.

Five things about titration nobody can currently answer

First, the optimal escalation interval. No adequately powered randomised comparison of intervals at a fixed target dose exists for any molecule in this class.

Second, the optimal hold duration for a person who has not adapted at four weeks. Practice ranges from four to twelve weeks on no comparative evidence at all.

Third, the lowest maintenance dose that preserves a result. The withdrawal trials compared full dose with nothing.

Fourth, whether tolerability at one rung predicts tolerability at the next. Clinicians assume it does, plausibly, and the published dose-ranging data is not analysed in a way that answers the question.

Fifth, whether any measurable baseline characteristic predicts the ceiling. Nothing published does so usefully, which mirrors the situation for efficacy: mean behaviour in this class is well characterised and individual variation is not.⁶

The Journal lists these not as a complaint about researchers but as a map of where confident advice is currently outrunning its evidence. Anyone offering a precise answer to any of the five is offering an opinion, and should be read as doing so.

What follows this file in the department is the other half of the same problem: not how to raise the dose, but what to do about the symptoms that decide whether raising it is possible at all. Titration and tolerability are one subject examined from two ends, and the second end is where most people actually live.