Interaction Survival Program

Interaction Survival Power/Sample Size

Function

Interaction Survival is a program to calculate either estimates of sample size or power for tests of interaction. Exponential distributions are assumed and are specified as a ratio of the hazard ratio for the treatment effect in stratum 1 to the hazard ratio for 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. An exponentially distributed competing risk is also permitted.

Program Code

The program is written in JavaScript.

Source

The program uses the method of Peterson, B. and George, S.L. (1993). Controlled Clinical Trials, 511-522 but where the expected probability of event for each stratum is calculated using the accrual, follow-up and exponential failure and competing risk assumptions. The total sample size is calculated as follows

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

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

D=log(D₁/D₂)

Where

D_j=l_1j/l_2j is the hazard 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

Accrual time

T, the follow-up time

Competing Risk: the hazard of the competing risk random variable

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)

l₁₁ and l₂₁, the hazard rates for treatment 1 in stratum 1 and 2, respectively, which give the baseline hazard rates for failure.

D₁ and D₂, the hazard ratios between treatment 1 and treatment 2 within each stratum.

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

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