Sample size for logistic regression (events per variable)

A feasibility check for adjusted analyses: does your dataset carry enough outcome events to support the number of predictors in your model?

Method & formula

For a binary outcome, the effective sample size is the number of participants in the rarer outcome category — the events. The classical rule of thumb requires at least 10 events per candidate predictor (Peduzzi 1996): five predictors at a 20% event rate means ≥ 50 events, so ≥ 250 participants.

Treat this as a floor, not a target. The events-per-variable rule checks feasibility; it does not guarantee a stable or well-calibrated model. The modern approach (Riley et al., Stat Med 2019; van Smeden et al.) derives the required sample from the anticipated model performance, outcome prevalence, and number of parameters — and usually asks for more. Categorical predictors count once per estimated coefficient (a 4-category variable spends 3), and any predictor you considered counts, not just those that survived selection.

Source: Peduzzi P, et al. A simulation study of the number of events per variable in logistic regression analysis. J Clin Epidemiol 1996;49:1373–79 · Riley RD, et al. Minimum sample size for developing a multivariable prediction model. Stat Med 2019;38:1276–96.

Inputs, explained

Number of predictors/covariates: All candidate model terms, counting k−1 for a k-category variable, plus any interactions. Variables screened out during selection still count.
Event rate: The expected proportion with the outcome. If more than half have the outcome, the events are the participants without it — use 1 minus the rate.

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