Now Playing: Group-Sequential Analysis for Two Hazard Rates (6:39)
The Group-Sequential Analysis for Two Hazard Rates procedure is used to test the difference of two hazard rates in stages using group-sequential methods. This methodology assumes an underlying Exponential model. Unless the stage boundaries are entered directly, the stage boundaries are defined using a specified spending function. One- or two-sided tests may be performed with the option of binding or non-binding futility boundaries. Futility boundaries are specified through a beta-spending function.
Sample size re-estimation, based on current-stage sample sizes and parameter estimates, may also be obtained in this procedure.
At each stage, the current and future boundaries are calculated based on the accumulated information proportion. Conditional and predictive power for future stages is also given.
Suppose that a colorectal cancer study is conducted to determine whether a new treatment, following tumor excision, will result in a longer time before tumor recurrence (or lesser hazard rate). The new treatment is compared to the current standard treatment. The response for each patient is time, in years, before recurrence. A one-sided test with alpha equal to 0.025 is used. The MLE-based Z-Test for comparing two hazard rates will be used.
The new treatment is assigned to Group 1, and the standard is assigned to Group 2.
The design calls for five stages of one year each, if the final stage is reached. The current stage is the 2nd stage, or end of year 2. In the design phase, a needed power of 0.90 called for 505 patients per group if the final stage is reached, based on assumed hazard rates of 1.40 and 1.75 for the new and standard treatments, respectively. Both efficacy and non-binding futility boundaries are implemented. The efficacy spending function used is the O’Brien-Fleming analog. The Gamma beta-spending function with gamma parameter 1.5 is used for futility. Accrual is intended to be steady over the 5-year period of the study. Loss hazard rates of 0.03 for both groups are anticipated.
The report shows that no boundary has been crossed at the 2nd stage.
The boundaries have been adjusted to the actual proportion of the total information that has been accumulated.
Only a very small portion of alpha has been spent.
The conditional powers to show a difference by the end of the study are quite high, if the current difference in hazard rates holds.
The Boundary Probabilities sections indicate high probabilities that the efficacy boundary will be crossed in stage 3 or 4, assuming the underlying hazard rate difference holds.
At the end of the 3rd year of the study, the procedure is run again. The stage 3 boundaries are calculated based on the current information proportion. The stage 3 efficacy boundary has been crossed, indicating that the null hypothesis of equal hazard rates can be rejected at the 0.025 level. The stage results and descriptive statistics give useful summary information.
In order to obtain a Kaplan-Meier survival curve plot, the data must be converted into a form that can be used in the Kaplan-Meier Curves (Log-rank Tests) procedure.
To do this:
Rows with blank end times should be identified as censored.
Blank end times must be filled in with the current stage time.
And, an Elapsed Time column should be created by subtracting start times from end times.
When these steps are taken, the Kaplan-Meier Curves (Log-rank Tests) procedure can be run to generate a Kaplan-Meier survival curve.