An update from the JSM 2006 - Seattle

0.0
0
200
400
600
800
Cumulative Sample Size
How to calculate these ε’s?
• These conditional rejection probabilities can be calculated conveniently under various adaptations using EaSt (Cytel Software)
• Interval Estimation for the treatment difference δ is explained in Mehta’s slides
200
400
600
Cumulative Sample Size
What if we want to make a change?
At an interim look we may want to: • Increase in sample size • Increase number of looks • Change the shape of the spending
• At present our license expired and we are updating it!
• I promise an example delivered to you when our license is upgraded
…Example to come!!!
What about Estimation?
function for remaining looks • Change inclusion criteria
BUT: can we do this without inflating Type I error? Can we estimate the Rx effect at the end?
We Want Change!
• Select desired power for study, sample size, overall Type I error rate
• Select a spending function for Type I error that reflects how much “alpha” we want to spend at each look
• If at some look L in a K-look trial, we want to make a design change, we need to consider ε:
•This is referred to as the conditional rejection probability. •Zj, bj are values of test statistic and boundary at look J. •Any change to the trial at look L must preserve ε for the modified trial (Muller & Schafer)
• The spending function determines our rejection boundaries for test statistics computed at each analysis → example…
Example…
• Suppose we choose two interim looks + final analysis
4.0
Original Design Boundaries
Accumulated Data
Modified Study Boundaries
3.5
S ta n d a r d iz e d T e s t S ta tis tic
3.0
2.5
Reject Ho
2.0
1.5
1.0
0.5 Such changes are fine, provided ε=0.255 for modified trial
• Sample size of 600 with interim looks at n=200, 400
• Overall Type I error = 0.05 • Want fairly conservative
boundaries early, with some alpha left for final analysis…
Reject Ho
CondiCtioondnitioanlalRReejejcetiocntPiroobnabPilityroatbN=a40b0i=li0t.y255at N=400 → 0.255
200
400
600
Cumulative Sample Size
Modified Design to Four-look Larger Study (N=800)
Three-look Sequential Boundary for Rejection of Ho
S ta n d a r d iz e d T e s t S ta tis tic
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
0
Original Design Boundaries Accumulated Data
process looks like…
Βιβλιοθήκη Baidu
Three-look Sequential Boundary for Rejection of Ho
S ta n d a r d iz e d T e s t S ta tis tic
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
0
Reject Ho
An update from the JSM 2006 - Seattle
Ryan Woods – January 8, 2007
Case 1: Change in Trial Design…
Review of Sequential Hypothesis Testing:
• We choose a number of interim looks