# Two Arm Survival Sample Size and Power

Program Code

Two Arm Survival is written in JavaScript.

Source

Bernstein D and Lagakos SW (1978). Sample size and power determination for stratified clinical trials. Journal of Statistical Computation Simulation 8:65-73.

The formulas are based on the assumptions of uniform accrual over time, no loss to follow-up, exponentially distributed death times, and use of the exponential MLE test.

Running the Program

The user is prompted for the type of calculation to be performed, either estimate sample size required or estimate power, input type survival proportion or hazard rates, and the number of strata (maximum 6). The default is to estimate the sample size, using hazard rates for a single stratum. The user is then prompted for the input listed below. All input must be in terms of the same time units. Some input items have initial default values.

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.

• Length of accrual period
• The length of follow-up period-time from the end of accrual to the analysis time
• n1/(n1+n2), the proportion of patients in the standard group (.5)
• a, the significance level (.05)
• 1-sided or 2-sided test (1-sided)
• The proportion of the total sample in each stratum, if there is more than one stratum.
• The hazard rate, l 0 or the survival proportion, S0(t), for the standard arm. For survival proportions, the proportion surviving, S(t), to a given time, t, is requested. The survival time units entered must be consistent with the accrual rate time units. Note, since the outcome is assumed to be exponentially distributed, there is a simple connection between survival proportions (S(t)) and hazard rates (l ). The hazard rate is computed as follows:

l=-ln(S(t))/t

• The hazard ratio, l 0/l x, is required. If a survival proportion for the experimental group is to be assumed, it must be converted to the user to a hazard ratio to input into the program using the above formula.
• 1-b, the desired power for accrual rate estimation, or the accrual rate per unit time for power estimation.

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