Interaction Binomial Program

Interaction Binomial Power/Sample Size

Function

Interaction Binomial is a program to calculate either estimates of sample size or power for interaction tests. Alternatives are specified as a ratio of the odds ratio of the treatment effect in stratum 1 vs the odds ratio of the treatment effect in stratum 2. The program allows for unequal sample size allocation in the four cells defined by the two treatment groups and two strata.

Program Code

The program is written in JavaScript.

Source

The program uses the approximate variance of the logarithm of the ratio of odds ratio. Fleiss, J.L. Statistical Rates and Proportions (1981), page 165 provides the variance estimate for an estimated odds ratio. The total sample size is calculated as follows

N = (q(1-a/2)+q(1-b))² * S [1/f_ij*(p_ij*(1-p_ij))]/D²

Where f_ij are the cell frequencies and p_ij are the event probabilities in treatment i and stratum j, q is the inverse normal function, and

D=log(o₁/o₂)

Where

o_j = p_1j(1-p_2j)/(p_2j(1-p_1j)) is the odds ratio for the treatment effect within stratum j

Input Items

The user is prompted for values to the following items. For items that have initial default values set, the values are given in parentheses.

a, the significance level (.05)

One-sided or two-sided test

f₁₁, f₁₂, f₂₁, and f₂₂, the cell frequencies. By way of example, f₁₁ is cell frequency in treatment group 1 and stratum 1. Note that S f_ij =1. (.25 for each cell)

p₁₁ and p₂₁, the event probabilities for treatment 1 in stratum 1 and 2, respectively, which give the baseline probabilities of failure in each stratum.

o₁ and o₂, the odds ratios between treatment 1 and treatment 2 within each of the strata.

1-b, the desired power for sample size estimation, or n, total sample size for power estimation

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