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Power (sample size) calculators

Calculate how big your clinical trial needs to be with our easy to use online calculators.

There are four different sample size calculators - choose the correct one according to the type of clinical trial you are planning (superiority/equivalence) and the nature of the primary outcome variable (binary/continuous). A superiority trial is one where you want to demonstrate that one treatment or intervention is better than another (or better than no treatment/intervention). An equivalence trial is where you want to demonstrate that one treatment is no better or worse than an existing treatment.

Confused?

We can perform power calculations for you if you're not sure how to do it. Please contact us.

Binary outcome equivalence trial

A binary outcome has two categories, such as dead/alive, hospitalisation - yes/no, therapeutic success/failure and so on. This calculator is designed for binary outcomes in parallel group equivalence trials. The percentage of patients that meet the primary outcome definition (e.g. percentage hospitalised) is compared between two randomised groups. You must define a difference between these percentages, d, within which you will accept that the two treatments being compared are equivalent. For example, an existing treatment to prevent hayfever may be effective for 45% of patients. A cheaper alternative has been developed and it is thought that if this alternative is effective in 40% to 50% of patients (i.e. +/- 5%) then it is as good as the existing treatment. In this case d would be 5%. The sample size is chosen so that if the two treatments really are equivalent, there is a good chance (1-beta)% that the (1-alpha)% confidence interval will exclude a difference of more than d.

Significance level (alpha)
Power (1-beta)
Percentage 'success' overall    %
Margin of equivalence, d %

Technical note

Calculation based on the formula: n = f(α, β) × 2 × p × (100 − p) / d2
where p is the percent 'success' overall and f(α, β) = [Φ-1(α/2) + Φ-1(β)]2. Φ-1 is the cumulative distribution function of a standardised normal deviate

Adjustment for cross-overs based on formula: nadj = n × 10,000 / (100 - c1 - c2)2
where c1 and c2 are the percent cross-over in the control and experimental group respectively.

References

Pocock SJ. Clinical Trials: A Practical Approach. Wiley; 1983.
Julious SA. Sample sizes for clinical trials with Normal data. Statist. Med. 2004; 23:1921-1986