A review of methods for futility stopping based on conditional power

Conditional power (CP) is the probability that the final study result will be statistically significant, given the data observed thus far and a specific assumption about the pattern of the data to be observed in the remainder of the study, such as assuming the original design effect, or the effect estimated from the current data, or under the null hypothesis. In many clinical trials, a CP computation at a pre‐specified point in the study, such as mid‐way, is used as the basis for early termination for futility when there is little evidence of a beneficial effect. Brownian motion can be used to describe the distribution of the interim Z‐test value, the corresponding B‐value, and the CP values under a specific assumption about the future data. A stopping boundary on the CP value specifies an equivalent boundary on the B‐value from which the probability of stopping for futility can then be computed based on the planned study design (sample size and duration) and the assumed true effect size. This yields expressions for the total type I and II error probabilities. As the probability of stopping increases, the probability of a type I error α decreases from the nominal desired level (e.g. 0.05) while the probability of a type II error β increases from the level specified in the study design. Thus a stopping boundary on the B‐value can be determined such that the inflation in type II error probability is controlled at a desired level. An iterative procedure is also described that determines a stopping boundary on the B‐value and a final test critical Z‐value with specified type I and II error probabilities. The implementation in conjunction with a group sequential analysis for effectiveness is also described. Copyright © 2005 John Wiley & Sons, Ltd.

[1]  John Whitehead,et al.  Stopping clinical trials because of treatment ineffectiveness: a comparison of a futility design with a method of stochastic curtailment , 2003, Statistics in medicine.

[2]  Boris Freidlin,et al.  A comment on futility monitoring. , 2002, Controlled clinical trials.

[3]  Anastasios A. Tsiatis,et al.  Interim Monitoring of Group Sequential Trials Using Spending Functions for the Type I and Type II Error Probabilities , 2001 .

[4]  D L DeMets,et al.  Computations for group sequential boundaries using the Lan-DeMets spending function method. , 2000, Controlled clinical trials.

[5]  John M. Lachin,et al.  Biostatistical Methods: The Assessment of Relative Risks , 2000 .

[6]  S. Emerson,et al.  A Unifying Family of Group Sequential Test Designs , 1999, Biometrics.

[7]  Zhiliang Ying,et al.  A General Theory on Stochastic Curtailment for Censored Survival Data , 1999 .

[8]  R A Betensky,et al.  Early stopping to accept H(o) based on conditional power: approximations and comparisons. , 1997, Biometrics.

[9]  R A Betensky,et al.  Conditional power calculations for early acceptance of H0 embedded in sequential tests. , 1997, Statistics in medicine.

[10]  J. Lanke,et al.  Incorporation of a stopping criterion for futility into the design of a clinical trial with one interim analysis , 1997 .

[11]  Anastasios A. Tsiatis,et al.  Group sequential designs for one-sided and two-sided hypothesis testing with provision for early stopping in favor of the null hypothesis , 1994 .

[12]  J. O'fallon,et al.  Stopping when the experimental regimen does not appear to help. , 1994, Statistics in medicine.

[13]  David M. Reboussin,et al.  Information and information fractions for design and sequential monitoring of clinical trials , 1994 .

[14]  P. Lachenbruch,et al.  The Design and Analysis of Sequential Clinical Trials (2nd ed.). , 1993 .

[15]  D. Zucker,et al.  Sequential monitoring of clinical trials: the role of information and Brownian motion. , 1993, Statistics in medicine.

[16]  Peter Armitage,et al.  16. The Design and Analysis of Sequential Clinical Trials , 1993 .

[17]  M C Wu,et al.  Sequential monitoring for comparison of changes in a response variable in clinical studies. , 1992, Biometrics.

[18]  Margaret S. Pepe,et al.  Two-stage experimental designs : early stopping with a negative result , 1992 .

[19]  B. Davis,et al.  Repeated confidence intervals and prediction intervals using stochastic curtailment , 1992 .

[20]  S. Snapinn,et al.  Monitoring clinical trials with a conditional probability stopping rule. , 1992, Statistics in medicine.

[21]  Barry R. Davis,et al.  Upper bounds for type I and type II error rates in conditional power calculations , 1990 .

[22]  T R Fleming,et al.  Symmetric group sequential test designs. , 1989, Biometrics.

[23]  K K Lan,et al.  The B-value: a tool for monitoring data. , 1988, Biometrics.

[24]  A. Tsiatis,et al.  Approximately optimal one-parameter boundaries for group sequential trials. , 1987, Biometrics.

[25]  J M Lachin,et al.  Evaluation of sample size and power for analyses of survival with allowance for nonuniform patient entry, losses to follow-up, noncompliance, and stratification. , 1986, Biometrics.

[26]  S S Ellenberg,et al.  An efficient design for phase III studies of combination chemotherapies. , 1985, Cancer treatment reports.

[27]  J. Ware,et al.  The futility index. An approach to the cost-effective termination of randomized clinical trials. , 1985, The American journal of medicine.

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

[29]  Anastasios A. Tsiatis,et al.  Repeated Significance Testing for a General Class of Statistics Used in Censored Survival Analysis , 1982 .

[30]  David L. DeMets,et al.  Asymmetric group sequential boundaries for monitoring clinical trials , 1982 .

[31]  D L DeMets,et al.  An aid to data monitoring in long-term clinical trials. , 1982, Controlled clinical trials.

[32]  K. K. Lan,et al.  Stochastically curtailed tests in long–term clinical trials , 1982 .

[33]  J. Lachin.  Introduction to sample size determination and power analysis for clinical trials. , 1981, Controlled clinical trials.

[34]  P. Armitage,et al.  Repeated Significance Tests on Accumulating Data , 1969 .