## Single Arm Survival Sample Size

Early phase clinical trials often involve an add-on therapy to existing standard therapy in a single arm setting, as a first step before the conduct of succeeding multi-arm trials which could be more expensive and involve complexities such as randomization and double-blinding.

In such a trial the goal is to test safety and to achieve greater confidence in the efficacy of the new therapy even if one can’t provide clear confirmatory evidence of efficacy. One attempts to show some evidence that the new therapy leads to a better survival than a putative standard therapy.

To design an appropriately sized study to assess efficacy one needs estimates of parameters measuring survival for the putative standard therapy and for the survival anticipated for the new therapy/combination. One needs a false positive (alpha) rate or the probability of concluding in favor of new therapy when it is no better than the standard rate and one needs a false negative rate (beta) which is the probability of concluding in favor of the standard therapy when the new therapy does improve survival. Also required are the time it takes to recruit the patients (accrual time) and the time the last patient recruited is followed (follow-up time).

The default example in the calculator involves an alpha level of 10%, a one sided test, a beta of 20% (or power of 80%), a median survival for standard therapy of 15 months, a median survival for the new therapy/combination of 20 months, a drop-out rate of 5% in 12 months, an accrual period of 12 months and a follow-up period of another 12 months. The hazard rates are survival parameters which measure the instantaneous rate of failure and can be obtained from the median survival by entered a probability of 50% and the median time in the first box of the calculator. The exponential drop-out rate is calculated similarly by using a probability of 95% (5% chance of dropping out) at a time of 12 months.

Entering these inputs in the middle box of the calculator produces the results in the bottom box. This study would need 101 patients, patients would need to be enrolled at the rate of 8 to 9 patients per month and there are likely to be about 46 to 56 events in this study.

For some theory on the calculations from Lachin(2000) see the following attachment. The calculations are asymptotically correct (tend to be more accurate as the sample size increases) and there is an assumption of constant hazard rates over time through an exponential distribution.

**Edit the blue cells in the spreadsheet and enter your data and the calculations in the spreadsheet will refresh.**