= Surgical complication count versus patient incidence
<Surgical complication count versus patient incidence> distinguishes the number of postoperative events from the number of people who experience at least one event. A person can have several <postoperative complications>. Counting events and counting affected patients therefore answer different questions, even with the same follow-up period.
Let $N$ be the number of operated patients with complete observation through a specified time, and let $K_i$ be the number of qualifying events for patient $i$. Then
$$
E=\sum_{i=1}^N K_i,\qquad
N_{\mathrm{affected}}=\sum_{i=1}^N\mathbf 1_{\{K_i\ge1\}},\qquad
\widehat p=\frac{N_{\mathrm{affected}}}{N}.
$$
Here $E$ is an event count, $\widehat p$ estimates the proportion experiencing at least one complication during the specified period, and $E/N$ is mean events per patient. Unlike $\widehat p$, the last quantity can exceed one.
For an original example, one 100-patient cohort has 40 events concentrated among 20 people. Another has 40 events, each in a different person. Both have $0.40$ events per patient, but their patient incidences are $20\%$ and $40\%$. Neither summary alone reveals severity, persistence or how closely events cluster in time.
The <Clavien-Dindo classification> adds severity information, but a highest-grade-per-patient summary still discards multiplicity. In the original validation paper, the most severe complication was registered when a patient had more than one. That is an explicit patient-level severity convention, rather than a count of every complication.<Classification of Surgical Complications: A New Proposal With Evaluation in a Cohort of 6336 Patients and Results of a Survey by Daniel Dindo and others>[Patients and Methods, Validation of the Modified Classification in a Cohort of 6336 Patients]{ref}
Time and denominators must be specified. With 40 events over $3000$ patient-days, the event rate is $40/3000\approx0.0133$ per patient-day; it is not a $1.33\%$ probability for each individual day. With incomplete follow-up, simple affected-patient proportions require further assumptions or methods accounting for observation time and competing events. <Recurrent postoperative event analysis> also has to account for dependence between several events in the same patient, rather than treating them as independent extra patients.
A reproducible comparison therefore defines the qualifying <postoperative complication>, observation window, patient denominator, event-counting rule and severity summary together. The original classification separately distinguishes complications from inherent sequelae and failure to cure, so those categories should not silently be added to the same numerator.<Classification of Surgical Complications: A New Proposal With Evaluation in a Cohort of 6336 Patients and Results of a Survey by Daniel Dindo and others>[Methods and Definitions of Complications, Definition of Negative Outcome]{ref}
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