Funnel Plot calculator

Compare units fairly with a funnel plot: rates against volume inside control limits that narrow as volume grows. Exact binomial limits, overdispersion adjustment, and risk-adjusted O/E funnels.

What it does

Plots each unit against the amount of information behind it, inside control limits that narrow as that grows. From unit-level rows it compares crude rates against volume; from case-level rows it fits a risk model, compares each unit's observed events with the events expected for ITS patients, and plots the ratio against the expected count.

When to use it

You have one row per unit — hospital, centre, surgeon, region — with a count of events and the denominator it came from, and you want a fair comparison that does not punish small units for being noisy.

Alternatives

How to read the output

The funnel shape
The limits narrow as volume grows, because a large unit's rate is pinned down much more precisely than a small one's. That shape is the whole point. A small unit near the top of the chart may be comfortably inside its limits, while a large unit closer to the target sits outside. That is correct, and it is why this replaces a league table rather than decorating one.
The target line
The pooled rate across all units — total events over total volume — not the average of the unit rates. Averaging the rates would let a 30-case unit count as much as a 1,000-case one in setting the benchmark.
Points outside the limits
A unit whose rate is more extreme than chance comfortably explains, given its volume. With many units, some will fall outside by chance alone — 1 in 20 outside the 95% band is expected, which is why the 99.8% band is the one usually acted on.
Overdispersion (φ)
Whether units vary by more than binomial chance allows. When they do, the limits are widened and the chart says so. Overdispersion usually means real differences in casemix or data quality that the chart cannot see. Widened limits make the plot honest, not the underlying comparison fair.
O/E ratio (risk-adjusted mode)
Observed events divided by the events expected for that unit's patients. 1 means exactly as many as predicted; 1.2 means 20% more. This is not a rate and must not be described as one. Two units with the same O/E can have very different death rates, because their patients differ — which is the entire point.
Expected events on the horizontal axis
Precision comes from expected events, not from patients. A large unit full of low-risk patients can sit further left — with wider limits — than a smaller unit full of high-risk ones. That is correct, not a bug. Few expected events means little information about the unit, however many patients passed through.
The internal standard
The risk model is fitted across all the units on the chart, so the benchmark comes from this dataset rather than from outside it. Every unit helps set the standard it is judged against, so a poor unit slightly raises the bar for everyone and slightly flatters itself. And the ratios are relative: they cannot say whether the group as a whole is doing well.
What the model was given
Adjustment only accounts for the risk factors you selected. Unmeasured severity does not disappear because a model was fitted. A unit taking sicker patients in ways your columns do not capture will still look worse.

How this calculator is validated · Which statistical test should I use?