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

We have looked for a randomised comparison of escalation intervals — same molecule, same target dose, four-week steps against two-week steps or six-week steps — and we cannot find one of any size. There are protocol amendments, there are post-hoc tolerability analyses, and there is a great deal of clinical convention. What there is not, thirty million prescriptions into this class, is a trial that answers the single most frequently asked practical question about it. The Journal regards that as the most striking evidence gap in the field, and we intend to keep saying so.

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.

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.