One-Sided Logistic Regression Sample Size Calculator

Example Data Table

Formula Used

This calculator uses a Wald style approximation for one-sided logistic regression planning.

p1 = OR × p0 / (1 - p0 + OR × p0)

p̄ = (1 - q)p0 + q p1

β = |ln(OR)|

N = (Z1-α + Zpower)² / [p̄(1 - p̄) × q(1 - q) × β²]

N adjusted = N / (1 - R²)

N final = max(dropout adjusted N, events per variable N)

Here, p0 is baseline event probability. OR is the target odds ratio. q is the exposure proportion. R squared is the estimated prediction overlap from other covariates.

How to Use This Calculator

1. Enter the one-sided alpha level.
2. Enter the desired statistical power.
3. Add the baseline event probability for the reference group.
4. Enter the target odds ratio you want to detect.
5. Add the expected exposed proportion.
6. Set covariate R squared when predictors are correlated.
7. Enter predictor count and events per variable target.
8. Add design effect, dropout, and safety multiplier.
9. Press the calculate button.
10. Download CSV or PDF results when needed.

Planning One-Sided Logistic Regression Studies

Why Sample Size Matters

Logistic regression is used when the outcome has two states. Common outcomes include disease, failure, response, and approval. A one-sided test is used when the research question has direction. The study may only need evidence for an increase. It may only need evidence for a decrease. This choice must be made before data collection.

Inputs That Control Precision

The baseline event rate is very important. Rare outcomes need more observations. Very common outcomes can also reduce information. The target odds ratio also changes the sample sharply. A small effect needs a larger study. A strong effect needs fewer observations. Power controls the chance of detecting the planned effect. Alpha controls the one-sided false positive risk.

Covariates And Adjustment

Logistic models often include several predictors. These predictors may share information with each other. That overlap is represented by the R squared adjustment. A higher value increases the required sample size. This calculator also checks events per variable. That rule helps reduce unstable estimates. It is useful when the event rate is low.

Design And Dropout

Real studies may use clusters, repeated sites, or complex sampling. The design effect expands the calculated sample. Dropout also increases the starting recruitment target. A safety multiplier can add another conservative buffer. These options make the result more practical. They also help during protocol writing.

Reading The Result

The final sample is the largest required value. It compares power needs with events guidance. Expected events and non-events are also displayed. Exposed and unexposed counts help check feasibility. Treat the answer as a planning estimate. For final trials, confirm assumptions with a statistician.

FAQs

What is a one-sided logistic regression test?

It tests whether a predictor changes odds in one planned direction. The direction should be chosen before data collection. It is not suitable when either increase or decrease would be important.

What does the odds ratio mean?

The odds ratio compares event odds between groups or predictor levels. A value above one means higher odds. A value below one means lower odds.

Why is baseline event probability needed?

The event rate affects available information. Very rare or very common events provide less balance. That usually increases the needed sample size.

What is the exposure proportion?

It is the expected share of participants with the main predictor present. Balanced exposure near 0.50 often gives stronger information than very uneven exposure.

What does covariate R squared mean?

It represents how much the main predictor is explained by other covariates. More overlap reduces independent information. The calculator increases sample size when this value rises.

Why include events per variable?

Logistic regression needs enough outcome events for stable estimates. Events per variable gives a practical lower bound, especially when several predictors are planned.

Can I use this for continuous predictors?

This version is mainly arranged for binary exposure planning. For continuous predictors, use a suitable predictor variance and a coefficient based on the chosen unit change.

Is this a final clinical trial calculation?

It is a planning estimate. Final trial design may need simulations, interim rules, clustering details, missing data assumptions, and expert statistical review.