One Arm Survival Sample Size and Power

Program Code

The program is written in JavaScript.

Source

Brookmeyer R and Crowley, JJ. A confidence interval for the median survival time. Biometrics, 38, 29-41, 1982.

The formulas are based on the assumptions of uniform accrual over time, no loss to follow-up, exponentially distributed death times.  The tests and intervals are based on the large sample variance of the nonparametric estimate of cumulative hazard function.  For testing the median, a Brookmeyer-Crowley type test is assumed by comparing the cumulative hazard estimate at the M₀  (null hypothesis median) to the -log(.5),

 T=(H(M₀ )-(-log(.5))/SE(H(M₀ )).

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
• T, the length of follow-up period-time from end of accrual to analysis
• a, the significance level (.05)
• One-sided or two sided test (1)
• M₀ and M_a, the median survival times for the null and alternative hypotheses. 
• Survival probabilities for for null and alternative hypotheses at time t. 
• 1-b, the desired power for accrual rate estimation, or n, the sample size for power estimation.
• Upper and lower critical values for either (median or survival probability). Note, these are based on the nonparametric exponential estimates. 

The time specified for survival probability or median survival probabilities specified in the design must be less than the total of accrual and follow-up times.