| Name |
Endpoints |
Success Decision Rule |
Significance Level Allocationa |
Family-Wise Overalla |
Advantage(s) |
Disadvantage(s) |
| Bonferroni Correction |
Family – Wise Endpoints (Ek) |
Test each of the k endpoints at the same level (0.05/k) |
0.05/k endpoints |
0.05 |
Easy to compute.
No need to order multiple endpoints beforehand. |
All endpoints tested at same conservative level. |
| Hierarchical Closed Test Procedure |
Primary (E1)
Secondary (E1, E2, …, Ek) |
Test E1 first. If and only if significant, test E2.
Order Ek based on clinical importance. |
0.05 for each sequential endpoint. Process continues until the first time the test is failed. |
NA |
Easy to handle with a large number of endpoints.
All endpoints tested at same 0.05 level if there is a chance to be tested. |
Restrictive: An endpoint as well as the following endpoints will not have a chance to be tested if its previous endpoint fails. |
| Holm’s Step-Down Procedure |
Primary (E1)
Secondary (E1, E2, …, Ek) |
Most conservative a for first endpoint tested. Becomes sequentially less conservative with each endpoint. |
E1α=0.05/k
E2α=0.05/(k-1)
E3α=0.05/(k-2)
Etc. |
0.05 |
No need to order multiple endpoints beforehand.
Understanding relationship among endpoints helpful for selecting efficient test strategy for multiple endpoints. |
Cannotreject H0 if previous H0 is not rejected. |
| Gate keeping Strategies |
Primary (E1)
Secondary (E2, …, Ek)
Tertiary (E3, …, Ek) |
Primary family of hypotheses serves as gatekeeper for secondary and tertiary endpoints. As least one primary endpoint must reach significance to proceed to testing secondary endpoints, etc. |
0.05 |
0.05 |
Increased statistical power when primary endpoint must be met. |
Restrictive: An endpoint as well as the following endpoints will not have a chance to be tested if its previous endpoint fails. |
