OPTION 1

Comparative Clinical Trial with Loss to Follow-up and a Period of Continued Observation

Ref: Rubinstein LV, Gail MH and Santner TJ: Planning the duration of a comparative clinical trial with loss to follow-up and a period of continued observation. J. Chron. Dis. 1981, Vol 34, pp 469-479.

The program computes required sample size, trial duration or statistical power for an accrual trial design. The program assumes that trial follow-up data will be analyzed with the Mantel-Haenszel (logrank) test for comparing survival curves. The program allows for loss to follow-up during the trial and allows the planner to reduce the total number of cases required by introducing a period of continued observation after the end of patient accrual.

The program makes the following assumptions:

  1. Patients are accrued uniformly into the trial at a rate of N per time unit for a total of T time units. Patients are randomized with equal probability to either the control or experimental group. After the accrual period, patients are followed for a period of 'tau' time units of 'continued observation'.
  2. The survival time distribution for the control group is exponential with hazard rate, lambda, specified by the user. However, these calculations are reasonably accurate for Weibull distributions with increasing or decreasing hazards. The hazard rate ratio (controls/experimental) determines the alternative hypothesis 'delta'. It is assumed the experimental treatment will improve survival so that delta is > 1.
  3. The loss to follow-up rates can be different for the control and experimental groups and are assumed independent of each other and of the entry times and deaths. Losses refer to true withdrawals and not those censored administratively by the accrual of participants over a period of time rather than instantaneously. Administrative censoring is accommodated by the assumption of uniform accrual and, therefore, uniform censoring.

The program computes the accrual periods, the accrual rate, the power or ratio of hazards. Three of these must be specified and the fourth is computed.