Why events per variable is a floor, not a sample-size target
Why the distinction matters
Power asks whether a prespecified clinically important effect can be detected under stated assumptions. Precision asks how narrow an interval may be. A parameter-count floor asks whether the proposed model may be too unstable to fit or transport. These are different questions, so a floor cannot replace the first two.
Count parameters, not labels
A categorical predictor with several levels, a spline, an interaction or a time-varying effect uses more than one fitted parameter. Estimate the number of outcome events for binary or time-to-event models, the event fraction, and the total usable sample; missing data and rare categories matter even when the headline count appears adequate.
Do not turn a historical threshold into a target
A fixed threshold such as ten events per parameter performs differently across outcome frequencies, predictor distributions and model strengths. For prediction-model development, use criteria addressing overfitting, calibration and precision of the overall risk. For a primary effect estimate, use an effect- or precision-based calculation suited to that estimand, then compare it with the model-capacity check.
When the available dataset is fixed
State the number of eligible people and observed or plausibly expected events, simplify the prespecified model if scientifically defensible, and report the attainable precision. Do not back-calculate observed power from the fitted effect or present an event-count floor as if it established a detectable clinical difference.
How Mallard's code fits
The R and Python power-plan code labels logistic events-per-parameter and linear subjects-per-parameter results as floors. Its generic rule-of-thumb route says what inputs and follow-up sizing method are still required; it does not certify a final sample size.
Clinical example
A registry analysis proposes a logistic model for a rare adverse event with many candidate predictors. The team counts all fitted parameters and expected events, recognizes that the proposed model may be unstable, and narrows the model before comparing the event count with a clinically meaningful effect-based or prediction-model calculation. No single events-per-parameter threshold can settle that choice.
What to watch out for
Events-per-parameter and subjects-per-parameter rules are screening floors, not effect-based power or a final sample-size target. Counting named variables instead of fitted parameters can understate model complexity.
- Minimum sample size for developing a multivariable prediction model: PART II - binary and time-to-event outcomes (opens in a new tab) · Stat Med · doi 10.1002/sim.7992
- Sample size for binary logistic prediction models: Beyond events per variable criteria (opens in a new tab) · Stat Methods Med Res · doi 10.1177/0962280218784726
- How Many Subjects Does It Take To Do A Regression Analysis (opens in a new tab) · Multivariate Behav Res · doi 10.1207/s15327906mbr2603_7