How many hemiarthroplasties do you perform a year?
low volume
medium volume
high volume
How fast do you learn?
λ = learning curve (≈ 60 patients)A higher λ means a faster climb to proficiency, so fewer patients before the excess risk fades. Excess risk fades as skill builds, essentially gone at full proficiency — about 3/λ patients, well past simply being able to perform the operation. Default 0.05 ≈ 60 patients; slower ≈ 0.03 (100 patients); faster ≈ 0.10 (30 patients). At the far right (0.20) that's ≈ 15 patients — faster than the evidence supports.
How much previous experience do you have?
n₀ = head start, in equivalent cases (an estimate) 0 = new to this technique | ~25 = substantial transferable experience | 50 = extensive, near-proficient before the first case. A rough estimate of how far relevant prior experience has carried you along this curve — there is no exact way to know it.
How large is the benefit?
NNT = number needed to treat to prevent one dislocation Patients treated with the new approach to gain one additional good outcome. Higher NNT = smaller benefit. The default (100) is favorable to the new technique — more than much of the current evidence supports.
How serious is a complication?
Wh = Weight of harm (complication severity) Weight of a learning-curve complication relative to one unit of benefit. Anchored to the reoperation-probability ratio (≈3).
How to read this
- Each line is one surgeon, at the annual case volume shown.
- The line is a running tally of benefit minus harm across all the patients treated. Below zero, the learning-curve harm so far outweighs the benefit; above zero, the new technique is ahead.
- The dot marks break-even — where the new technique pulls even with the established one.
- The shaded band is the stretch where adoption is still a net loss.
- Lower-volume surgeons stay in that band far longer.
Why this is a conservative test. The model favors the new technique by design: it grants the benefit, charges all the learning-curve harm to the new approach, and ignores both what the established approach did well and the cost of switching. So a net loss at low volume is a conservative result, not a rigged one.
About n₀ (experience). A rough guess, in case-equivalents, of how far your prior experience has already carried you up this technique's curve. It can't be known exactly. It's here to show how much the break-even point shifts with experience — not to pin down your number.
Where the numbers come from. The shape of the learning curve follows published CUSUM studies of surgical proficiency. Fixed values: one unit of benefit per prevented event; a serious approach-related complication (periprosthetic femoral fracture or deep infection) occurs in 7% of the earliest cases, falling to 2% once proficient.
About n₀ (experience). A rough guess, in case-equivalents, of how far your prior experience has already carried you up this technique's curve. It can't be known exactly. It's here to show how much the break-even point shifts with experience — not to pin down your number.
Where the numbers come from. The shape of the learning curve follows published CUSUM studies of surgical proficiency. Fixed values: one unit of benefit per prevented event; a serious approach-related complication (periprosthetic femoral fracture or deep infection) occurs in 7% of the earliest cases, falling to 2% once proficient.
The model. U(n) = ∑i=1n [ B(i) − H(i) ], summed over cases.
Break-even case n* solves U(n*) = 0; break-even time = n* / V.
B(i) = Wb / NNT (per-case benefit) ·
H(i) = (Pmax − Pbase) · e−λ(i + n₀) · Wh (per-case learning-curve harm)Break-even case n* solves U(n*) = 0; break-even time = n* / V.