TABLE 4.
Twelve- To 60-Month Outcome of 202 Patients With CC Without EV and Sample Sizes Required to Show A 50%, 34%, and 20% Risk Reduction Using an Ordinal Outcome or Two Different Binary (Time-to-Event) Composite Outcomes Including or Not Development of Varices*
| Observation Time (Months) and n of Patients With Outcome | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Follow-up, months | 12 | 24 | 36 | 48 | 60 | |||||
| Total patients | 202 | 202 | 202 | 202 | 202 | 202 | 202 | 202 | 202 | 202 |
| Outcome (V+/−)† | V+ | V− | V+ | V− | V+ | V− | V+ | V− | V+ | V− |
| 1 = no progression | 194 | 197 | 160 | 185 | 147 | 181 | 142 | 179 | 129 | 172 |
| 2 = varices | 3 | 25 | 35 | 38 | 44 | |||||
| 3 = bleeding | 0 | 5 | 2 | 17 | 2 | 20 | 2 | 22 | 3 | 29 |
| 4 = 1st decomp | 4 | 13 | 16 | 16 | 20 | |||||
| 5 = 2nd decomp | 0 | 1 | 1 | 3 | 3 | |||||
| 6 = death | 1 | 1 | 1 | 1 | 3 | |||||
| Total events | 8 | 5 | 42 | 17 | 55 | 20 | 60 | 22 | 73 | 29 |
| Baseline risk | 0.04 | 0.025 | 0.21 | 0.08 | 0.27 | 0.10 | 0.3 | 0.11 | 0.36 | 0.14 |
| Total sample size required to show a 50% baseline risk reduction with α = 0.05 and power 0.80 | ||||||||||
| Composite endpoint‡,§ | 2,292 | 3,705 | 385 | 1,115 | 285 | 879 | 250 | 793 | 198 | 565 |
| Ordinal outcome ∥ | 2,118 | 354 | 258 | 228 | 176 | |||||
| Total sample size required to show a 34% baseline risk reduction with α = 0.05 and power 0.80 | ||||||||||
| Composite endpoint‡,§ | 5,456 | 8,838 | 892 | 2,638 | 652 | 2,074 | 568 | 1,869 | 442 | 1,322 |
| Ordinal outcome ∥ | 5,314 | 864 | 620 | 548 | 418 | |||||
| Total sample size required to show a 20% baseline risk reduction with α = 0.05 and power 0.80 | ||||||||||
| Composite endpoint† § | 1,7031 | 27,627 | 2,726 | 8,199 | 1,976 | 6,432 | 1,713 | 5,789 | 1,317 | 4,075 |
| Ordinal outcome ∥ | 16,946 | 2,692 | 1,912 | 1,682 | 1,264 | |||||
Differences in sample-size estimates calculated by log-rank (binary) versus ordinal outcome are more marked when varices (without other decompensating event) are considered a nondecompensating event (bolded) and patients are continued in the trial until an overt decompensating event develops.
The ordinal outcome includes six categories: grade 1 = no progression; grade 2 = development of varices; grade 3 = bleeding; grade 4 = nonbleeding decompensation; grade 5 = any second decompensation; and grade 6 = death. The two composite endpoints consider the development of varices being or not being part of the outcome (bold delimited areas denote when varices are not considered a negative outcome).
V+/− denotes inclusion or exclusion of development of varices in the composite endpoint.
Sample size has been estimated according to a reduction of risk of 50%, 34%, and 20% (RRs, 0.5, 0.66, and 0.80) by the sample-size software PASS v.11, using the log-rank test (Freedman) procedure: Input parameters were the proportions of subjects free of the events of interest at the end of follow-up in the two arms, assuming none lost to follow-up. This corresponds to slightly different values of HR and OR according to baseline risks (details in the Supporting Information Appendix).
Sample size needed for cumulative risk comparison, like in the composite endpoint in the example.
Sample size needed for an ordinal outcome (or ordered categorical variable) according to the test for two ordered categorical variables procedure in Pass v.11. As input parameters, we used the proportion of subjects in the six categories at the end of follow-up, assuming none lost to follow-up, and the natural logarithm of the OR for treatment effect.