Two Arm Survival Sample Size and Power
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
The user is prompted for values to the following items. For items that have initial
default values set, the values are given in parentheses.
- The length of follow-up period-time from the end of accrual to the analysis time
significance level (.05)
- n1/(n1+n2), the proportion of patients in the standard
- 1-sided or 2-sided test (1-sided)
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:
- The proportion of the total sample in each stratum, if there is more than one stratum.
- The hazard ratio, 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