Validation

6 Mar 2011 and updated 7 Nov 2011 with binary equivalence results

The results from Sealed Envelope's power calculators were compared to published sample size calculations. The results are shown in the table below.

Trial Outcome Reference Parameters Reference n Calculator result
Superiority Continuous Julious 2004, 2.1.1 d = 8, σ = 40, α = 5%, β = 10% 527 526
Superiority Continuous Pocock 1983 d = 0.5, σ = 1.8, α = 5%, β = 5% 337 337
Equivalence Continuous Julious 2004, 3.4.3 d = 10, σ = 50, α = 2.5%, β = 10% 651 650
Non-inferiority Continuous Julious 2004, 4.1.1 d = 10, σ = 40, α = 2.5%, β = 10% 338 337
Superiority Binary Pocock 1983 p1 = 90%, p2 = 95%, α = 5%, β = 10% 578 579
Equivalence Binary Julious 2009, 12.1 p = 70%, d = 10%, α = 2.5%, β = 10% 546 546
Equivalence Binary Julious 2009, 12.1 p = 70%, d = 20%, α = 2.5%, β = 10% 137 137
Equivalence Binary Julious 2009, 12.1 p = 90%, d = 5%, α = 2.5%, β = 10% 936 936
Non-inferiority Binary Donner, Example 3 p = 80%, d = 10%, α = 10%, β = 20% 145 145
Non-inferiority Binary Blackwelder, Table 3 p = 90%, d = 20%, α = 5%, β = 10% 39 39
Non-inferiority Binary Blackwelder, Table 3 ps = 60%, pe = 50%, d = 20%, α = 5%, β = 10% 420 420
Non-inferiority Binary Pocock 1983 p = 70%, d = 10%, α* = 5%, β = 20% 332 330
Non-inferiority Binary Pocock 2003 p = 85%, d = 15%, α* = 5%, β = 10% 120 120
* Note: Pocock assumes a 2-sided confidence interval will be produced, so α should be set to 2.5% in the calculator

References

Blackwelder WC. "Proving the Null Hypothesis" in Clinical Trials. Control. Clin. Trials 1982; 3:345-353

Donner A. Approaches to Sample Size Estimation in the Design of Clinical Trials - A Review. Statist. Med. 1984; 3:199-214

Julious SA. Sample sizes for clinical trials with Normal data. Statist. Med. 2004; 23:1921-1986

Julious SA. Estimating Samples Sizes in Clinical Trials. CRC; 2009

Pocock SJ. Clinical Trials: A Practical Approach. Wiley; 1983.

Pocock SJ. The pros and cons of noninferiority trials. Fundam Clin Pharmacol 2003; 17: 483–490