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.

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.²

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.³

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.⁴ 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.

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.

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.