The SEQDESIGN Procedure

Pocock derives the constant boundary on the standardized Z scale to demonstrate the sequential design while maintaining the overall and levels (Pocock, 1977). The resulting boundary tends to stop the trials early with a larger p-value. This boundary is commonly called a Pocock boundary, but Pocock himself does not advocate these boundary values for stopping a trial early to reject the null hypothesis, because large p-values might not be persuasive enough (Pocock and White, 1999). Also, the nominal p-value at the final stage is much smaller than the overall p-value of the design. That is, the trial might stop at the final stage with a small nominal p-value, but the test is not rejected, which might not be easy to justify.

O’Brien-Fleming boundary values are inversely proportional to the square root of information levels on the standardized Z scale (O’Brien and Fleming, 1979). The O’Brien-Fleming boundary is conservative in the early stages and tends to stop the trials early only with a small p-value. But the nominal value at the final stage is close to the overall p-value of the design.

The power family method (Wang and Tsiatis, 1987; Emerson and Fleming, 1989; Pampallona and Tsiatis, 1994) generalizes the Pocock and O’Brien-Fleming methods with a power parameter to allow continuous movement between the Pocock and O’Brien-Fleming methods. The power parameter is for the Pocock method and for the O’Brien-Fleming method.

The unified family triangular method (Kittelson and Emerson, 1999) contains straight-line boundaries on the score scale. For a one-sided trial with early stopping either to reject and to accept the null hypothesis, the method produces a triangular continuation region. The boundary shape is specified with the slope parameter .

The unified family method (Kittelson and Emerson, 1999) extends power family methods to incorporate the triangular method, which contains straight-line boundaries on the score scale.

The Haybittle-Peto method (Haybittle, 1971; Peto et al., 1976) uses a Z value of 3 for the critical values in interim stages and derives the critical value at the final stage. With this method, the final-stage critical value is close to the original design without interim monitoring. The SEQDESIGN procedure extends this method further to allow for different Z or nominal p-values for the boundaries.

Whitehead methods (Whitehead and Stratton, 1983; Whitehead, 1997, 2001) derive the boundary values by adapting the continuous monitoring tests to the discrete monitoring of group sequential tests. With early stopping to reject or accept the null hypothesis in a one-sided test, the derived continuation region has a triangular shape on the score-scaled boundaries. Only elementary calculations are needed to derive the boundary values in Whitehead’s triangular methods. The resulting Type I error probability and power are extremely close but differ slightly from the specified values due to the approximations used in deriving the tests (Jennison and Turnbull, 2000, p. 106). The SEQDESIGN procedure provides the BOUNDARYKEY= option to adjust the boundary value at the final stage for the exact Type I or Type II error probability levels.

The error spending method uses the specified and errors to be used at each stage of the design to derive the boundary values.

The error spending function method uses the error spending function to compute the and errors to be used at each stage of the design and then to derive the boundary values for these errors. The following four error spending functions are available in the SEQDESIGN procedure: