**Purpose.**:
Almost all uveal melanomas showing chromosome 3 loss (i.e., monosomy 3) are fatal. Randomized clinical trials are therefore needed to evaluate various systemic adjuvant therapies. Conventional trial designs require large numbers of patients, which are difficult to achieve in a rare disease. The aim of this study was to use existing data to estimate how sample size and study duration could be reduced by selecting high-risk patients and adopting multistage trial designs.

**Methods.**:
We identified 217 patients with a monosomy 3 melanoma exceeding 15 mm in basal diameter; these patients had a median survival of 3.27 years. Several trial designs comparing overall survival were explored for such a population. A power of 0.90 to detect a hazard ratio of 0.737 was set, and recruitment of 16 patients per month was assumed.

**Results.**:
A suitable single-stage study would require 960 patients and a duration of 76 months. A two-stage design with an interim analysis based on 852 patients after 53.3 months would have a 50% probability of stopping because no statistically significant treatment effect is seen. Encouraging but inconclusive results would require a further 108 patients and prolongation of the study to 77.2 months. A multistage design would have a 43% probability of stopping before 47 months having recruited 759 patients.

**Conclusions.**:
Prospects for clinical studies of systemic adjuvant therapy for uveal melanoma are enhanced by multistage trial designs enrolling only high-risk patients.

^{ 1 }Despite systemic treatment, such disease is usually fatal within a year of becoming symptomatic. With some other cancers, survival is improved by systemic adjuvant therapy directed at undetectable micrometastases in high-risk patients. Previous clinical trials in uveal melanoma have not shown statistically significant benefit of adjuvant therapy, but they had inadequate sample sizes and included patients with low risk of metastatic disease.

^{ 2,3 }

^{ 4 }Many patients will not enroll because they live far from the center or are too elderly. Many are lost to follow-up because involvement in the study is too onerous or because they die of unrelated disease. The feasibility of such trials could be enhanced by excluding patients with only a small risk of metastatic death, which is now possible through genetic typing of uveal melanomas.

^{ 5 }Metastatic disease from choroidal melanoma occurs almost exclusively in patients whose primary tumor shows chromosome 3 loss or class 2 gene expression profile (i.e., metastasizing uveal melanoma). Survival time in these patients correlates inversely with clinical stage of disease and with histological grade of malignancy.

^{ 5 }

*i*th interim analysis, there will be an upper limit for continuation, u

*, and a lower limit, $\u2113$*

_{i}*. If the test statistic exceeds u*

_{i}*, the trial is stopped because the treatment is beneficial; if it is less than $\u2113$*

_{i}*, the trial is stopped for futility. Otherwise the trial continues to the next interim analysis. A variety of sequential methodologies have been developed, and here we adopt the “boundaries approach.”*

_{i}^{ 6 }The designs presented here have been constructed so that their expected sample sizes are appreciably smaller than both the corresponding fixed sample size and the expected sample sizes of other two-stage and multistage approaches.

**Figure 1.**

**Figure 1.**

*k*interim analyses will be conducted. We set $\u2113$

*= u*

_{k}*, so that the trial is certain to be conclusive and stop at the last analysis (if not before). The stopping limits were calculated to achieve fixed risks of type I and type II errors. We took the Kaplan-Meier curves shown in Figure 1 as representative of survival in the controls. The designs were constructed with a power of 90% to detect a probability of surviving beyond 3.27 years being 0.60 in the treated group (compared with 0.50 for placebo) as superior to control at the 5% (two-sided) level if the hazards of death are proportional over time. The advantage defined here corresponds to a hazard ratio of 0.737.*

_{k}^{ 7 }

^{ 8 }that is easily extended to two-stage and multistage designs. The sample size and study duration required to produce these deaths were determined by the method described in Appendix 2 of Whitehead.

^{ 9 }We assumed that 16 patients per month are recruited for 5 years and followed up until sufficient deaths are observed.

_{1}, then the trial is stopped to declare the novel treatment significantly superior to control. Otherwise, the trial is continued until a second and final analysis. At the final analysis, the log-rank statistic is computed from all available data, and if it exceeds a second critical value u

_{2}, it is concluded that the novel treatment is superior. The design is constructed so that the number of deaths at the interim analysis would be one half the number at the final analysis (should the trial continue to that stage).

_{1}, u

_{2}, and the number of deaths at the interim analysis. The required type I error rate (0.05, two-sided) and power (0.90) provide two equations that must be satisfied.

_{1}= 2.54 and u

_{2}= 2.01. Both u

_{1}and u

_{2}are more stringent than the value 1.96 used in the single-stage design. Table 1 presents further properties of the design.

**Table 1.**

**Table 1.**

Hazard Ratio | Probability of Stopping at Interim | Expected Final Sample Size | Expected Final Duration (Months) |

1 | 0.506 | 905 | 65.1 |

0.858 | 0.207 | 938 | 72.2 |

0.737 | 0.425 | 914 | 67.1 |

*i*th of which the standardized log-rank statistic Z

*would be computed and compared with the upper limit, u*

_{i}*, and the lower limit, $\u2113$*

_{i}*, as described above. This primary interim analysis requires: patient code number, recruitment date, date of death or date of last known status, and treatment arm.*

_{i}^{ 6,10 }an asymmetric design which stops for futility if no evidence that the novel treatment is superior is apparent. Following,

^{ 10 }it can be established that the boundary points are given by the following equations: These boundary points are listed in Table 2, together with the number of deaths (d

*) that determine the timing of the*

_{i}*i*th interim analysis. Also shown are the probabilities of stopping on the upper boundary at or before each interim analysis, for the null hazard ratio of 1, the alternative hazard ratio of 0.737, and the intermediate value of 0.858. Corresponding probabilities for the lower boundary are also shown. A plot of $\u2113$

*√(15*

_{i}*i*) and u

*√(15*

_{i}*i*) against the number of deaths (not shown) reveals the triangular shape that gives the test its name.

**Table 2.**

**Table 2.**

Interim | d _{i} | ℓ _{i} | u _{i} | Probability of Stopping at ith Interim or Before on the Upper Boundary for Hazard Ratio | Probability of Stopping at ith Interim or Before on the Lower Boundary for Hazard Ratio | ||||

1 | 0.858 | 0.737 | 1 | 0.858 | 0.737 | ||||

1 | 60 | −2.514 | 3.950 | 0.000 | 0.000 | 0.003 | 0.006 | 0.001 | 0.0001 |

2 | 120 | −1.016 | 3.047 | 0.001 | 0.014 | 0.085 | 0.155 | 0.032 | 0.004 |

3 | 180 | −0.207 | 2.695 | 0.004 | 0.051 | 0.267 | 0.427 | 0.115 | 0.013 |

4 | 240 | 0.359 | 2.514 | 0.008 | 0.104 | 0.461 | 0.657 | 0.223 | 0.028 |

5 | 300 | 0.803 | 2.409 | 0.012 | 0.163 | 0.622 | 0.808 | 0.334 | 0.044 |

6 | 360 | 1.173 | 2.346 | 0.016 | 0.222 | 0.740 | 0.895 | 0.435 | 0.060 |

7 | 420 | 1.493 | 2.307 | 0.020 | 0.277 | 0.821 | 0.942 | 0.521 | 0.075 |

8 | 480 | 1.777 | 2.285 | 0.023 | 0.322 | 0.870 | 0.964 | 0.586 | 0.088 |

9 | 540 | 2.035 | 2.274 | 0.024 | 0.351 | 0.893 | 0.973 | 0.625 | 0.097 |

10 | 600 | 2.271 | 2.271 | 0.025 | 0.362 | 0.900 | 0.975 | 0.638 | 0.100 |

**Table 3.**

**Table 3.**

Interim | Sample Size at Interim | No. of Months Until Interim |

1 | 491 | 31 |

2 | 640 | 40 |

3 | 759 | 47 |

4 | 868 | 54 |

5 | 960 | 61 |

6 | 960 | 67 |

7 | 960 | 73 |

8 | 960 | 79 |

9 | 960 | 87 |

10 | 960 | 97 |

**Table 4.**

**Table 4.**

Hazard Ratio | Expected Final Sample Size | Expected Final Duration (Months) |

1 | 832 | 54.2 |

0.858 | 906 | 64.4 |

0.737 | 874 | 59.2 |

**Figure 2.**

**Figure 2.**

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