Function

One Arm Survival is an interactive program to calculate either estimates of accrual or power for null and alternative median survival rates assuming an exponential distribution. A cube root transformation of the hazard rate is used in the calculations to get good small sample properties. The program gives critical values for either median survival or survival probabilities from parametric exponential model.

Program Code

The program is written in JavaScript.

Source

Lawless, J. Statistical Models and Methods for Lifetime Data, John Wiley and Sons, 1982.

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. The important normal approximation used in the sample size and power calculations is equation 3.2.7 (page 108) of Lawless.

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.

• Survival probability for for null and alternative at time t. The outcome is assumed to be exponentially distributed. Note, there is a simple connection between survival probabilities and hazard rates for exponential data. The hazard rate is computed as follows:

• Upper and lower critical values for either (median or survival probability). Note, these are based on the parametric exponential estimates. Wider intervals are needed for estimates based on the Kaplan-Meier survival function estimates.