The trial presented in the preceding example was not designed with an asymmetric rule for stopping in the face of negative results. It was partly for this reason that the data monitoring committee and investigators considered several methods of analysis before reaching a decision to stop the trial. Although there will sometimes be special circumstances that require analyses not specified a priori, it is preferable to determine in advance whether the considerations for stopping are asymmetric in nature and, if so, to include an appropriate asymmetric stopping rule in the initial protocol design.

Computer packages (East, Cytel Software Corp., Cambridge, MA; and PEST3, MPS Research Unit, University of Reading; Reading, UK) are available to help with the design of studies using any of the rules discussed in Section 2 (see Emerson [42] for a review). Alternatively, one may modify a ''standard'' symmetric rule (e.g., O'Brien-Fleming boundaries) by retaining the upper boundary for early stopping due to positive results but replacing the lower boundary to achieve a more appropriate rule for stopping due to negative results. It is often the case that this will alter the operating characteristics of the original plan so little that no additional iterative computations are required.

To illustrate this, suppose one had designed a trial to test the hypothesis H0: 5 = 0 versus 5 > 0 to have 90% power versus the alternative HA: 5 = ln(1.5) with a one-sided a of 0.025, using a Fleming et al. (10) rule with three interim looks. Such a design would require interim looks when there had been 66,132, and 198 events, with final analysis at 264 events. From Table 1a of Fleming et al. (10), one such rule would be to stop and conclude that the treatment was beneficial if the standardized logrank statistic Z exceeded 2.81 at the first look, 2.74 at the second look, or 2.67 at the third look. The null hypothesis would be rejected at the end of the trial if Z exceeded 2.02. If a symmetric lower boundary were considered inappropriate, one might choose to replace it by simply testing the alternate hypothesis HA: 5 = ln(1.5) versus 5 < ln(1.5) at some small significance level (e.g., a = 0.005) at each interim look (this suggestion is adapted from the monitoring rules in SWOG Protocol SWOG-8738, an advanced disease lung cancer trial). In the framework of Section II, this rule is asymptotically equivalent to stopping if the standardized Z is < -0.93 at the first look, or < -0.25 at the second look, or <0.28 at the third look (a fact that one does not need to know to use the rule, since the alternative hypothesis can be tested directly using standard statistical software, e.g., SAS Proc PHREG [43]). It follows that if the experimental treatment adds no additional benefit to the standard regimen, there would be a 0.18 chance of stopping at the first look, a 0.25 chance of stopping at the second look, and a 0.22 chance of stopping at the third look (Table 1). Adding this rule does not significantly change the experiment-wise type I error rate (a = 0.0247) and would only lower the power to detect a treatment effect of 5a = ln(1.5) from 0.902 to 0.899.

Following Wieand et al. (21), an alternative but equally simple way to modify the symmetric Fleming et al. boundaries would be simply to replace the lower Z-critical values with zeroes at each interim analysis at or beyond the halfway point. Using this approach, if the experimental arm offered no additional benefit to that of the standard regimen, the probability of stopping at the first look would be very small (0.0025), but the probability of stopping at the second look would be 0.4975, and at the third look would be 0.10 (Table 1). Again no special program is needed to implement this rule, and its use has a negligible effect on the original operating characteristics of the group sequential procedure (a = 0.0248, power = 0.900).

No. of events |
Probability of Stopping If Treatments are Equivalent |
Probability of Stopping Under Alternative S = 1.5 | ||

SWOG |
WSO |
SWOG |
WSO | |

66 |
0.18 |
0.0025 |
0.005 |
0.000 |

132 |
0.25 |
0.4975 |
0.004 |
0.010 |

198 |
0.22 |
0.10 |
0.003 |
0.001 |

WSO, Wieand, Schroeder, O'Fallon (21). SWOG, Southwest Oncology Group.

WSO, Wieand, Schroeder, O'Fallon (21). SWOG, Southwest Oncology Group.

The decision of which rule to use will depend on several factors, including the likelihood that patients will still be receiving the treatment at the time of the early looks and whether it is likely that the experimental treatment would be used outside the setting of the clinical trial before its results are presented. To illustrate this, we consider two scenarios.

Scenario 1: The treatment is being tested in an advanced disease trial where the median survival with conventional therapy has been 6 months and the alternative of interest is to see if the experimental treatment results in at least a 9-month median survival. Under the assumption of constant hazards, this is equivalent to the hypothesis SA = ln(1.5). Suppose one would expect the accrual rate to such a study to be 150 patients per year. If one designed the study to accrue 326 patients, which would take 26 months, one would need to follow them for slightly less than 4.5 additional months to observe 264 deaths if the experimental regimen offers no additional benefit to the standard regimen or an additional 7.5 months if S = SA = ln(1.5). If the experimental treatment offers no additional benefit, one would expect 146 patients to have been entered when 66 deaths have occurred, 227 patients to be entered when 132 deaths have occurred, and 299 patients to have been entered when 198 deaths have occurred (Table 2). Early stopping after 66 deaths have occurred would prevent 180 patients from being entered to the trial and stopping after 132 deaths would prevent 99 patients from being entered. Thus, the potential benefit of stopping in the face of negative results would be to prevent a substantial number of patients from receiving the apparently ineffective experimental regimen, in addition to allowing early reporting of the results (the savings in time for reporting the results would be approximately 19, 12, and 7 months according to whether the trial stopped at the first, second, or third look, respectively).

Scenario 2: The treatment is being tested in an adjuvant trial where the expected hazard rate is 0.0277 deaths/person-year, corresponding to a 5-year survival rate of slightly more than 87%. If one is now looking for an alternative SA

Table 2 Effect of Early Stopping on Accrual and Reporting Time

No. of Patients No. of Patients to be Time until Final Accrued Accrued Analysis (mo)

Table 2 Effect of Early Stopping on Accrual and Reporting Time

No. of Patients No. of Patients to be Time until Final Accrued Accrued Analysis (mo)

Advanced |
Adjuvant |
Advanced |
Adjuvant |
Advanced |
Adjuvant | |

Disease |
Disease |
Disease |
Disease |
Disease |
Disease | |

No. of Events |
Trial |
Trial |
Trial |
Trial |
Trial |
Trial |

66 |
146 |
1975 |
180 |
625 |
19 |
36 |

132 |
227 |
2600 |
99 |
0 |
12 |
24 |

198 |
299 |
2600 |
27 |
0 |
7 |
12 |

264 |
326 |
2600 |
0 |
0 |
0 |
0 |

= ln(1.5) (which would roughly correspond to increasing the 5-year survival rate to 91%) and if the accrual rate was approximately 800 patients per year, a reasonable plan would be to accrue 2600 patients, which would take approximately 39 months, and to analyze the data when 264 deaths have occurred, which should occur approximately 66 months after initiation of the trial, if the experimental regimen offers no additional benefit to the standard regimen (75 months after initiation if 5 = 5A = ln{1.5}). With this accrual and event rate, 1975 of the expected 2600 patients will have been entered by the time 66 events have occurred if the experimental regimen offers no additional benefit to the standard regimen (Table 2). The second and third looks would occur approximately 3 and 15 months after the termination of accrual, so early stopping after these analyses would have no effect on the number of patients entering the trial, although it could permit early reporting of the results. The savings in time for reporting the results would be approximately 36, 24, and 12 months according to whether the trial stopped at the first, second, or third look, respectively. If there is little likelihood that the therapy will be used in future patients unless it can be shown to be efficacious in the current trial, there may be little advantage to reporting early negative results, and one might choose not to consider early stopping for negative results at any of these looks.

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