The 27.1% that a later denominator prints as 49.1%
Showing the misleading chart
Live births as a share of embryo transfers: 49.1% across the national file, and 17.7% even in the oldest age band. The same births as a share of the cycles patients actually started: 27.1% and 3.7%. Of 167,178 cycle starts, 74,901 never reached a transfer — and a rate measured per transfer drops them from the top and the bottom of the fraction at once. Both rates are printed by the same registry, one page apart.
01The claim
These are the national figures for 2023 — every member clinic in the country, patients using their own eggs, the first embryo transfer that follows an egg retrieval. There were 92,277 of them, and the registry publishes what share of each age band ended in the delivery of a living child. Nationally 49.1% did. The axis starts at zero and runs unbroken to 60; every age band in the national file is on it; nothing is sampled, smoothed or projected, and the outcome is a live birth, not a positive pregnancy test and not a clinical pregnancy — though the registry calls a singleton delivered at term the ideal and publishes those too, and 97.5% of the under-35 births were single with 87.5% reaching term. Under 35 the transfer is better than a fair coin, at 53.5%, with 62.5% reaching a clinical pregnancy. At 35 to 37 it is 50.8%, at 38 to 40 it is 46.1%, and even at 41 and 42 more than one transfer in three ends in a birth, at 36.3%. Over 42 it is 17.7%. Age matters and the table says so plainly, but read the index: with under-35 set at 100, the bands run 100, 95, 86, 68 and 33, so across twenty years of age the floor is a third of the ceiling — a threefold spread, not a tenfold one. The procedures behind the figure are printed on the slide too: 167,178 cycle starts, 154,898 egg retrievals, 92,277 first embryo transfers. The chart is drawn on the transfers, because the transfer is the procedure — the moment an embryo is placed, the moment the clinic’s work can be judged, the step whose outcome is least ambiguous. One transfer in, one answer out. And not a rate on the slide is ours: every one of them is printed by the registry.
02The trick
Every number on that slide is right, and the crime is not on the chart — it is in the third table, where the slide prints its own funnel and then picks the last row of it. 167,178 cycle starts. 154,898 retrievals. 92,277 transfers. A rate per embryo transfer is computed only on the cycles that reached a transfer, and 74,901 of them — 44.8% — did not. Some were cancelled before retrieval (3.9% of cycle starts under 35, rising to 15.9% over 42); some produced no embryo suitable to transfer (6.5% of retrievals rising to 41.7%); the rest reached neither a transfer nor the end of the report’s one-year window, a gap the registry publishes without breaking down. A case that fails before the denominator opens leaves the numerator and the denominator together, and so is never counted as a failure at all. Put them back and the same births are 27.1% of the cycles that were started rather than 49.1% of the transfers that happened — and the registry publishes that rate too, on the same page, along with 29.3% per egg retrieval. The lift is not a flat surcharge, and this is the part worth carrying away. It runs ×1.36 under 35, ×1.64 at 35 to 37, ×2.16 at 38 to 40, ×3.21 at 41 to 42 and ×4.78 over 42, because it is largest exactly where the gate rejects most — and the gate rejects 26.4% of starts under 35 and 79.0% over 42. So the denominator does not merely raise the headline; it raises the worst-off group the most, and flattens the very gradient the chart was drawn to show. Per transfer, the best band is 3.0 times the worst. Per intended egg retrieval, it is 10.6 times. That compression is the denominator, not the biology. It is worth keeping distinct from survivorship bias, which it resembles closely. Survivorship takes the cases out of the dataset: the planes that did not come back were never measured. A late denominator leaves them in the dataset and takes them out only of the fraction — here every drop-out is counted, labelled and printed a table away. Note too that the gate can be moved, and that moving it moves the number: a programme that transfers only its strongest embryos, or that stops short of transfer in its hardest cases, raises its per-transfer rate by letting fewer patients through, so the figure improves because more people failed earlier. (Both drawings are our own; the newsletter on the first is invented, and every figure on both is the registry’s, save the all-ages rows and the ratios between published rates.)
03The fix
Denominate at the decision. Nobody buys an embryo transfer: you start a cycle, pay for a cycle and take the drugs for a cycle, so the rate the reader needs is the one measured per cycle started — 27.1% nationally, and 39.4%, 31.0%, 21.3%, 11.3% and 3.7% down the five age bands. The registry says so itself, in its own explanation of what a cycle is, which is that counting each cycle “and not just focusing on the embryo transfer more accurately reflects the treatment burden and costs the patient has endured”. The honest chart here is the two rates drawn side by side on one zero-based axis, with the gate underneath: five bars showing what share of cycle starts never reached a transfer at all — 26.4%, 39.0%, 53.7%, 68.7%, 79.0% — because that panel is the whole explanation in one picture. Keep the late rate as well. It is the right measure for the step it names, and an embryology lab auditing its own bench work needs exactly that number; it simply must never travel alone, and must never wear the plain words “success rate”. Print the funnel beside both, gate by gate, with the count that entered and the count that survived, so the reader can see where the fraction begins rather than having to infer it. Then watch the top of the fraction as well as the bottom, because a report that offers several rates often moves both ends at once. This one publishes five: 49.1% per embryo transfer, 29.3% per egg retrieval and 27.1% per cycle started all share a numerator — births from the first transfer — and differ only in where counting begins; but 35.3% per cycle started counts every transfer from that retrieval within the year, and 54.1% per new patient counts every cycle that patient starts. Those last two are different measurements, not fairer versions of the same one, and the ladder does not run one way. Two habits make it routine. Read the denominator out loud and ask what a case had to do to reach it — “per transfer”, “of those who completed”, “among orders that shipped”, “of students who reached final year” each name a step, and every step before it is a place where cases left. Then ask whether clearing that step was itself part of the outcome; if it was, the rate is measuring the survivors of the thing it claims to measure. And expect the direction rather than discovering it: a later denominator lifts every group, and lifts hardest where the gate rejects most, so a suspiciously compressed spread between groups is the first thing to distrust. Where the late denominator genuinely is the question, keep the finding attached to it. 49.1% is a true fact about embryo transfers and a false one about starting IVF, and the two sentences differ only in where they begin counting.