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Abstract:
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In clinical trials comparing survival functions of two groups, the number of events required to achieve the desired power is usually calculated using the method of Freedman (1982) or Schoenfeld (1981). Then, either the sample size or the duration of study that yields the required number of events is calculated; however, their combination is not uniquely determined. Thus, in practice, some combinations are examined considering the enrollment speed, duration, and cost of participants. If a longer duration of study is planned, a small sample size is required because the frequency of observing events increases. On the contrary, if a shorter duration of study is planned, a large sample size is required because the frequency of observing events decreases. We developed a simple graph for sensitivity analysis evaluating the relationship between the sample size and the duration of study under various enrollment speed and treatment effects. We also derived the probability density function of the duration of study, enabling us to evaluate the uncertainty of duration of study under the given sample size.
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