Construction of a continuous stopping boundary from an alpha spending function.

Lan and DeMets (1983, Biometrika 70, 659-663) proposed a flexible method for monitoring accumulating data that does not require the number and times of analyses to be specified in advance yet maintains an overall Type I error, alpha. Their method amounts to discretizing a preselected continuous boundary by clumping the density of the boundary crossing time at discrete analysis times and calculating the resultant discrete-time boundary values. In this framework, the cumulative distribution function of the continuous-time stopping rule is used as an alpha spending function. A key assumption that underlies this method is that future analysis times are not chosen on the basis of the current value of the statistic. However, clinical trials may be monitored more frequently when they are close to crossing the boundary. In this situation, the corresponding continuous-time boundary should be used. Here we demonstrate how to construct a continuous stopping boundary from an alpha spending function. This capability is useful in the design of clinical trials. We use the Beta-Blocker Heart Attack Trial (BHAT) and AIDS Clinical Trials Group protocol 021 for illustration.

[1]  D O Scharfstein,et al.  The use of simulation and bootstrap in information-based group sequential studies. , 1998, Statistics in medicine.

[2]  Anastasios A. Tsiatis,et al.  Sequential methods for parametric survival models , 1995 .

[3]  D L DeMets,et al.  Interim analysis: the alpha spending function approach. , 1994, Statistics in medicine.

[4]  H. Waskin,et al.  A controlled trial of trimethoprim-sulfamethoxazole or aerosolized pentamidine for secondary prophylaxis of Pneumocystis carinii pneumonia in patients with the acquired immunodeficiency syndrome. AIDS Clinical Trials Group Protocol 021. , 1992, The New England journal of medicine.

[5]  Michael A. Proschan,et al.  Effects of assumption violations on type I error rate in group sequential monitoring , 1992 .

[6]  Christopher Jennison,et al.  An improved method for deriving optimal one-sided group sequential tests , 1992 .

[7]  N L Geller,et al.  On the choice of times for data analysis in group sequential clinical trials. , 1991, Biometrics.

[8]  J. S. D. Cani,et al.  Group sequential designs using a family of type I error probability spending functions. , 1990, Statistics in medicine.

[9]  D L DeMets,et al.  Changing frequency of interim analysis in sequential monitoring. , 1989, Biometrics.

[10]  D. Siegmund,et al.  Approximate Exit Probabilities for a Brownian Bridge on a Short Time Interval, and Applications. , 1989 .

[11]  David L. DeMets,et al.  Design and analysis of group sequential tests based on the type I error spending rate function , 1987 .

[12]  D. Siegmund.  Sequential Analysis: Tests and Confidence Intervals , 1985 .

[13]  James Durbin,et al.  The first-passage density of a continuous gaussian process to a general boundary , 1985, Journal of Applied Probability.

[14]  C. Jennen,et al.  Second-Order Approximations to the Density, Mean and Variance of Brownian First-Exit Times , 1985 .

[15]  K. K. Lan,et al.  Discrete sequential boundaries for clinical trials , 1983 .

[16]  Thomas Sellke,et al.  Sequential analysis of the proportional hazards model , 1983 .

[17]  Eric V. Slud,et al.  Two-Sample Repeated Significance Tests Based on the Modified Wilcoxon Statistic , 1982 .

[18]  H. R. Lerche,et al.  First exit densities of Brownian motion through one-sided moving boundaries , 1981 .

[19]  P. O'Brien,et al.  A multiple testing procedure for clinical trials. , 1979, Biometrics.

[20]  S. Pocock.  Group sequential methods in the design and analysis of clinical trials , 1977 .

[21]  C. W. Gear,et al.  Numerical initial value problem~ in ordinary differential eqttations , 1971 .