Now Playing: Group-Sequential Tests for Two Hazard Rates (4:56)
The Group-Sequential tests for Two Hazard Rates procedure can be used to determine power, sample size and/or boundaries for group-sequential Z-tests comparing the survival curves of two groups. This methodology assumes an underlying Exponential model.
This procedure is used as the planning tool for determining sample size and initial boundaries. Stage data, as it is obtained, can be evaluated using the companion procedure Group-Sequential Analysis for Two Hazard Rates, found in NCSS. The companion procedure also gives the option for sample-size re-estimation and updated boundaries for current-stage information. In that procedure, simulation can be used to evaluate boundary-crossing probabilities given the current stage results.
Suppose a colorectal cancer study is to be conducted to determine whether a new treatment, following tumor excision, will result in a longer time before tumor recurrence, or, in other words, a lesser hazard rate. The new treatment will be 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 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. It is anticipated that the patients will be accrued as they come, for all 5 years of the study. Accrual is expected to occur at an even rate. The loss hazard rate for both groups is assumed to be 0.03. A power of 0.90 is needed. The assumed hazard rate for the standard approach is 1.75. Researchers wish to examine the sample sizes needed for new approach hazard rates of 1.2, 1.3, and 1.4. Both efficacy and non-binding futility boundaries are intended. 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.
The first report shows the anticipated boundaries.
There are several options for the x-axis for displaying the boundaries graphically.
The Information Report gives the target information and time for each stage, as well as the sample sizes and hazard rates used to calculate those informations.
The alpha- and beta-spending sections show how alpha and beta are anticipated to be spent across the stages.
The boundary probability sections give the estimated probabilities of crossing each of the boundaries.
The final reports show how the different hazard rates affect the needed sample size.
We recommend that you view the companion video for Group-Sequential Analysis for Two Hazard Rates in NCSS. That video shows how to use sample size re-estimation and other stage analyses, as data are collected.