**One Arm Nonparametric
Survival Sample Size and Power**

**Function**

One Arm Survival is an
interactive program for calculating either estimates of accrual or power for
null and alternative survival functions based on either design specifications
of survival probability or median survival. The test statistic for survival probability
is assumed to be based on the non-parametric estimate of the survival
distribution. For median survival, a Brookmeyer-Crowley like test
assumed. The program also gives large sample expected critical values for
median survival (using Brookmeyer-Crowley) or survival probabilities.

**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 M_{0 }(null
hypothesis median) to the -log(.5),

T=(H(M_{0}
)-(-log(.5))/SE(H(M_{0} )).

**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)
- M
_{0}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.

Back to One Arm Non-Parametric Survival program.