Survival analysis for exhibitor churn puts a date on the risk

Two names come out of the model at 0.55. The sales director wants to know what to do about them, and the honest answer from a binary churn classifier is that both should get a call, which is not an answer, because one of them is going to cancel in nine weeks and the other is going to drift away over three years.

Survival analysis for exhibitor churn exists to answer that. The classifier cannot tell you which is which, because the label it was trained on was a flag. Renewed, or did not renew, at one specific edition. Everything about when has already been thrown away before the model saw the data.

Survival analysis keeps the when. It is not exotic, it has been standard in medical statistics for fifty years, and the version an exhibition business needs can be fitted with logistic regression.

What does a binary churn flag throw away?

A churn flag compresses an exhibitor's whole history into one bit at one moment. Three things go missing.

The first is timing. An account with a 55 per cent chance of leaving at the next renewal and an account with a 55 per cent chance of having left by 2029 are different commercial situations requiring different budgets, and the flag renders them identical.

The second is everyone who has not churned yet. A classifier trained on last edition's outcomes uses accounts that renewed as negative examples, including the account that has been with you for eleven editions and the one in its first. Both are coded zero. The eleven-edition account is carrying information about how long relationships last on your show, and the flag discards it.

The third is the shape of the risk. Exhibitor risk is not flat across tenure. It is high in the first two editions, falls, and then rises again at certain points, usually around a contract expiry or a venue move. A flag averages over all of that.

The three quantities, in exhibition terms

Survival analysis has a small vocabulary and it is worth getting the exhibition translation right once.

The hazard is the probability that an account churns at a given edition, given that it was still exhibiting going into that edition. It is a conditional probability, and the conditioning is the part people skip. A hazard of 0.30 at edition four means 30 per cent of accounts that reached edition four leave at that point.

The survival function is the probability of still being an exhibitor after a given number of editions. It is built from the hazards by multiplying the complements together.

Censoring is what you have for every account still exhibiting at your most recent edition. You know they survived at least this long and you do not know their eventual duration. Treating a censored account as a non-churner biases every duration estimate downward, and treating it as a churner biases everything up. Survival models handle it correctly by design, which is the main reason to use one.

Cox, and what the coefficient actually tells a sales director

Cox published the proportional hazards model in the Journal of the Royal Statistical Society in 1972. The idea is that each account has the same underlying baseline hazard shape over tenure, multiplied up or down by a factor derived from its characteristics.

The output that a commercial team can use is the hazard ratio, which is the exponential of the fitted coefficient. If the coefficient on "reduced space at the last renewal" is 0.47, the hazard ratio is e to the 0.47, which is 1.60. An exhibitor who cut space last time carries 60 per cent more churn hazard at every edition than an otherwise identical exhibitor who did not.

That sentence survives translation into a sales meeting, which the coefficient of a gradient boosted model does not. The Journal of Marketing Analytics published a 2025 study on the predictability and explainability of survival analysis in churn prediction which makes the same case: survival models give individual-level risk profiles that say both who and when, and that timing information is what converts a score into a retention plan.

The proportional part is an assumption, and it is testable. If the hazard ratio for space reduction is 2.1 in a first-edition account and 1.2 in a tenth-edition account, hazards are not proportional and you need an interaction with tenure or a stratified model. Check it before you present anything.

Why does discrete time fit an annual show better?

Cox assumes time is continuous. Exhibitions are not. An exhibitor can only churn at a renewal, and renewals happen once a year, which means your event times are heavily tied and the continuous model spends effort handling a structure that does not exist.

Singer and Willett set out the alternative in the Journal of Educational Statistics in 1993, working from the career paths of 3,941 special educators. Expand each account into one row per edition it was at risk, code the outcome 1 in the edition it churned and 0 otherwise, drop the rows after churn, and fit a logistic regression with tenure entered as a set of dummy variables. The fitted probabilities are the hazards.

The practical appeal is that the fitting is done by software everybody already has, the tenure effect comes out as a free-form shape instead of an imposed curve, and time-varying features drop in naturally. An account's days-to-payment in each specific edition sits in that edition's row, which a single-snapshot classifier cannot represent at all. The same families of columns worth building apply here as in any renewal model, and choosing them is G11's subject.

One thing changes about them in this setup, and it is the part that goes wrong quietly. Because each edition gets its own row, any field written during that edition's renewal conversation is now sitting in the row you are trying to predict, so the feature window has to be cut at show close for every row separately (G13).

The cost is data volume. Six hundred and forty exhibitors across five editions expands to somewhere around two thousand account-edition rows, and each account contributes several correlated rows, so standard errors from a naive logistic fit are optimistic. Cluster them by account.

Two accounts at 0.55

Here is the case from the opening, worked through.

Account A has a hazard of 0.30 at the next edition. It survives that edition with probability 0.70. Its cumulative churn probability over two editions is 0.55, which means its survival over two editions is 0.45. So 0.70 multiplied by its second-edition survival equals 0.45, giving second-edition survival of 0.643 and a second-edition hazard of 0.357.

Account B has a hazard of 0.55 at the next edition, surviving with probability 0.45. Its two-edition cumulative churn is 0.60, so two-edition survival is 0.40. Then 0.45 multiplied by its second-edition survival equals 0.40, giving 0.889, and a second-edition hazard of 0.111.

Line them up. Account A goes 0.30 then 0.357, a rising hazard. Account B goes 0.55 then 0.111, a hazard that collapses once the next renewal is past.

Those are opposite problems. Account B has one specific decision coming and everything rides on it, which is consistent with a budget cycle or a stand contract ending, and it wants a named person in the room before the decision date. Account A is drifting, its risk grows the longer nothing changes, and a phone call in renewal week will not touch it. It needs work spread across the year.

A binary classifier reported both as 0.55 and sent both to the same queue.

Reading a curve without over-reading it

Two habits keep survival output honest in a commercial meeting.

Report the cumulative probability at named horizons. Sales directors think in editions, and a raw hazard is a rate per unit time that nobody in the room converts in their head. Give them the probability of loss by the next edition and by the edition after, and let the hazard stay in the model. That pair of numbers is what the rest of a renewal intelligence process gets built on, because a date is what makes a risk score schedulable.

Attach the number of accounts at risk at each tenure point to any curve you show. A survival curve past edition eight built from nineteen accounts will have a dramatic-looking step in it that is one exhibitor leaving. If the at-risk count is on the chart, nobody builds a strategy on it.

Where this stops

The method assumes that the reason an account is censored has nothing to do with its risk, and in an exhibition portfolio that assumption breaks in a specific way.

Suppose you launched a second show three years ago and moved a group of your strongest exhibitors onto a portfolio agreement. Those accounts now look like healthy long-tenure survivors in the data for the original show. Their apparent survival is a consequence of a commercial decision you made, and the model will read it as evidence that accounts of that profile last longer. New accounts of the same profile without the portfolio agreement will be scored too optimistically.

The general form of this is informative censoring, and no amount of model tuning removes it. The fix is to stratify by contract type and report the strata separately, which is less satisfying than one curve and is honest. How far multi edition agreements bend the retention numbers underneath any of this is G38's territory, and it is worth reading before you quote a survival curve to a board.

There is also a hard floor on what any of this can do. Five editions of history gives you at most five hazard estimates, the last of which rests on a small at-risk set. If your show has run three times, fit the model, look at the first two hazards, and say nothing at all about edition six.

Start by building the person-period table for one show. One row per exhibitor per edition they were at risk, columns for tenure, space ratio and the churn outcome for that edition. Fit a logistic regression with nothing but the tenure dummies in it and read the coefficients. That gives you your show's baseline hazard by tenure, which is the shape everything else gets multiplied against, and most teams have never seen it.