Events per Variable and the Minimum Sample Size for Regression

The events-per-variable (EPV) rule says a logistic or Cox regression model needs at least 10 outcome events for every candidate predictor variable in the model. It is one of the most-cited rules of thumb in applied biostatistics, and one of the most misapplied — misapplied because ‘events’ is not the same thing as sample size, and because the field has since produced a real replacement for the flat rule rather than just critiques of it.

What EPV actually counts

EPV is events divided by predictors, not observations divided by predictors. For a binary logistic model, an ‘event’ is a case in the minority outcome category — if 40 of 800 patients in a cohort had the outcome, EPV is calculated against 40, not 800, however large the full sample looks. For a Cox proportional-hazards model, the same logic applies to the number of observed events (deaths, relapses, whatever the endpoint is), not the number of subjects entered into the analysis, since censored subjects contribute much less information to estimating the hazard than an observed event does. See Logistic Regression (the Logit Model) and The Cox Proportional Hazards Model for how each model actually estimates its coefficients from that count.

‘Predictors’ counts every parameter the model has to estimate — each continuous variable as one, each categorical variable as (levels − 1), and each interaction term separately. A 4-level categorical predictor with two interaction terms can silently cost 5 or 6 degrees of freedom, not one. Undercounting this is a common way a model that looks like it clears EPV 10 on paper does not.

Where the rule came from

The EPV 10 heuristic traces to a 1996 Journal of Clinical Epidemiology simulation study by Peduzzi, Concato, Kemper, Holford and Feinstein, which tested logistic regression models across a range of simulated EPV values and found that below roughly 10 events per variable, coefficient estimates, standard errors and confidence-interval coverage all became unreliable in ways that mattered for inference. It was a genuinely useful, easy-to-apply finding, and it became the default sample-size sanity check taught in most applied-statistics and epidemiology curricula for the following two decades.

The problem is that it was derived from one family of simulation scenarios and generalized far beyond them. It says nothing about how many predictors a study actually needs, how strong they are expected to be, how well the intended model is expected to discriminate or calibrate, or what the outcome prevalence is — it is a single fixed ratio applied regardless of what the model is being built to do.

What replaced it: sample size driven by the model’s target performance

Riley, Snell, Ensor, Burke, Harrell, Moons and Collins published the current standard reframing in Statistics in Medicine in 2019 (“Minimum sample size for developing a multivariable prediction model: Part II – binary and time-to-event outcomes”), building on earlier work by van der Ploeg, Austin and Steyerberg (2014) that had already shown EPV 10 performs inconsistently across scenarios — sometimes badly under-sampling, sometimes badly over-sampling, relative to what the model actually needs. Riley and colleagues replaced the single ratio with sample-size targets tied directly to how well the model is expected to perform, calculated from criteria including:

• Shrinkage of predictor effects — a global shrinkage factor of at least 0.9, keeping relative-scale overfitting (predictor coefficients that look stronger in this sample than they really are) within an acceptable bound.
• Absolute agreement between apparent and adjusted model fit — no more than a 0.05 gap between the model’s apparent Nagelkerke R² and its optimism-adjusted value, bounding absolute-scale overfitting the way the shrinkage target bounds the relative scale.
• Precise estimation of the overall outcome risk — enough events that the model’s estimate of the population’s average event rate itself has an acceptably narrow margin of error, independent of how well any individual predictor performs.

Because these targets depend on the model’s anticipated Cox-Snell R² and the outcome’s prevalence rather than a flat ratio, the required EPV varies by design — Riley and colleagues’ own worked examples show the calculated minimum ranging from roughly EPV 5 to EPV 23 depending on those inputs, both sides of the old EPV 10 line. A model targeting a rare outcome with a handful of already well-established, moderately strong predictors can legitimately need less than 10 events per variable to hit these targets; a model with many candidate predictors of uncertain strength, or a target performance level pitched deliberately high, can legitimately need much more. This is calculated with the pmsampsize package (available for both R and Stata, from the same author group), not looked up on a fixed-ratio table.

Where EPV 10 is still useful, and where it fails

The flat rule is not wrong so much as incomplete. It remains a reasonable, near-zero-cost early sanity check — if a proposed model is nowhere close to EPV 10, that is still worth noticing before doing any real design work. Where it actively misleads:

• Predictor selection studies. EPV 10 was derived for estimating coefficients in an already-specified model, not for data-driven variable selection (stepwise, LASSO, or similar) across many candidate predictors, where far more events are typically needed to get a stable final model — see Stepwise Regression: Why Reviewers Reject It for the related, and larger, problem with selection procedures themselves.
• High- or low-prevalence outcomes. A study can have thousands of subjects and still have a thin event count if the outcome is rare (or, mirrored, if the ‘non-event’ category is rare) — total N is not a proxy for EPV in either direction.
• Prediction models being built for external validation and later use, where the actual quantity that matters is future calibration and discrimination performance, which the Riley criteria target directly and EPV does not.

Practical checklist before finalizing sample size

1. Confirm the outcome and count actual events, not total N — for Cox models, count observed events, not enrolled subjects.
2. Count parameters honestly: categorical levels minus one, every interaction term separately.
3. Run EPV 10 as a first-pass sanity check, not a final answer.
4. If the model is a prediction model intended for calibration/discrimination use (not just coefficient estimation in an already-fixed model), calculate the Riley et al. (2019) criteria directly — via pmsampsize in R or Stata — using an anticipated Cox-Snell R² from prior literature or a pilot model.
5. If the design is fixed and the question is instead “what could this achieved sample actually detect,” that is a different calculation — see Sensitivity Power Analysis, not an EPV check.

Frequently asked questions

Is EPV the same as sample size?

No. Sample size is total observations; EPV is the count of outcome events (the minority-category count for a binary outcome, or observed events for a survival outcome) divided by the number of predictor parameters. A large sample with a rare outcome can still have a low EPV.

Does the EPV 10 rule still apply to modern prediction modelling?

As a rough, upfront sanity check it is still commonly used, but the field’s current reference standard for calculating a defensible minimum sample size for a multivariable prediction model is the Riley et al. (2019) performance-based criteria, not a fixed EPV ratio — those criteria have shown the correct EPV for a given study can reasonably sit well below or well above 10, depending on the anticipated model performance and outcome prevalence.

How do I count events for a Cox model with censoring?

Count observed (uncensored) events only — subjects who are censored before experiencing the outcome do not count toward the EPV numerator, even though they contribute to the total sample size and to partial-likelihood estimation in other ways.

What if my study already has a fixed, unchangeable sample size?

Then the forward-looking sample-size question does not apply, and neither does EPV as a planning tool — the relevant calculation becomes what the achieved sample was capable of detecting. See Sensitivity Power Analysis: Finding the Minimum Detectable Effect Size.

For the broader relationship between significance level, power, sample size and effect size that both the classic EPV rule and the newer performance-based criteria sit inside, see Power Analysis and Sample Size Calculation. For regression fundamentals and how coefficients and their standard errors are actually estimated, see Regression Analysis: Assumptions, Interpretation, and How to Report It and How to Interpret an Odds Ratio.