Does splitting a weekly dose into two half-doses actually flatten the concentration curve?

The argument I keep encountering for splitting a weekly dose into two half-doses three or four days apart is that it lowers the peak and raises the trough, and that a flatter curve means fewer symptoms after each dose and less loss of effect at the end of the week.

That reasoning is standard pharmacokinetics and it is obviously correct for some drugs. What I cannot tell is whether it is correct for these drugs, whose half-lives are around five to seven days. My intuition is that when the dosing interval is roughly one half-life, the curve is already fairly flat and there is not much left to flatten. But intuition is not a calculation.

So: what is the actual peak-to-trough ratio on a weekly schedule for a seven-day half-life compound, what does it become if you split the dose in two, and how do those numbers compare to something where splitting genuinely matters? If somebody can show the general formula rather than one worked case I would prefer that, because I would like to be able to apply it to other compounds.

Not asking anyone what to do. Asking whether the stated mechanism holds.

Steelmanning the split, because there are real arguments for it and they are all different from the one in the question. None of them is about peak-to-trough ratio.

1. Injection volume and local tolerance. This is the strongest of them and it is a tissue argument, not a pharmacokinetic one. Subcutaneous bolus volume relates to local pressure, distension and site reactions. Splitting a large volume across two sites and two occasions halves the volume per site. Whether this matters depends entirely on the volume: at a typical reconstitution concentration a weekly dose in this class is a few hundred microlitres, which is small by any standard, and there is no volume problem to solve. It becomes a real argument at volumes approaching a millilitre or more, which happens with dilute preparations. So it is an argument about reconstitution choices masquerading as an argument about schedules — and the cheaper fix is a more concentrated preparation.

2. Compounds where the interval genuinely does not fit the half-life. The accepted answer's last table row is not hypothetical for the wider research-peptide space. Plenty of peptides have half-lives measured in minutes to hours, and for those the dosing frequency is set by pharmacokinetics rather than by convenience. Reasoning transferred from those compounds to a fatty-acid-acylated, albumin-bound weekly agonist is the actual source of most splitting advocacy, and the transfer is invalid because the whole point of the acylation is to make the interval fit.

3. Distinguishing a real tolerance signal from a scheduling artefact. If somebody reliably has symptoms on days 1 and 2 and none on days 5 to 7, that is at least consistent with a within-week exposure effect, and it is the one presentation where the splitting mechanism is being invoked against evidence rather than in the abstract. It is worth saying clearly that this presentation exists and is reported. It is also worth saying that day 1 and 2 is when Tmax occurs and also when the memory of the injection is freshest, and a log kept prospectively is worth more than a recollection.

4. Nothing about efficacy. I want to be blunt about this one because it is where the advocacy overreaches. Mean exposure is mathematically invariant under splitting, and the pharmacodynamic effects in this class — gastric emptying, satiety signalling, glycaemic effect — respond to sustained exposure over days to weeks rather than to instantaneous concentration. There is no mechanism by which redistributing the same weekly dose increases effect, and claims that splitting improves results are not supported by anything published.

So the honest summary of the case for splitting: one argument that is really about reconstitution volume, one that applies to other compounds, one that applies to a specific symptom pattern, and none about efficacy.

A note on the variability term, since the accepted answer mentions a 30 % coefficient of variation in passing and it deserves a sentence of its own.

The reason the between-person spread matters to this question is not that it makes your own fluctuation unimportant. It is that it makes the population-level fluctuation numbers a poor guide to any individual's curve. The formula 2^(τ/t½) uses your half-life, and half-life is one of the things that varies between people. If someone's effective half-life is five days rather than seven — well within the observed spread — their weekly peak-to-trough ratio is 2^1.4 = 2.64, not 2.00, and their fluctuation index is 1.04 rather than 0.69. That is a 50 % larger swing than the textbook figure.

Which means two things simultaneously, and they are in tension:

• The subgroup for whom the splitting argument is strongest is the subgroup with the shortest half-lives, and that subgroup exists.
• Nobody knows whether they are in it, because half-life is not measurable outside a pharmacokinetic study and nothing you can observe distinguishes a short half-life from ordinary week-to-week variation in appetite and mood.

The nearest available proxy is not very good but it is not nothing: someone whose end-of-interval appetite signal reproducibly returns on the same day of the cycle, week after week, over many weeks, is showing behaviour consistent with a shorter effective half-life. Reproducibility across many cycles is the whole of the evidential weight there — a pattern that holds for three weeks is noise, and a pattern that holds for fifteen is data. This is exactly the kind of observation that is worth bringing to a clinician rather than acting on, since the label-sanctioned response to end-of-interval loss of effect is a dose question and not a schedule question.