Without sufficient data, as in the case of rare events, a plausible statistical model, coupled with reasonable sensitivity analyses, may enlighten the DSMB's interpretation of the observations. In this section, we present a number of procedures as examples of our approach. The procedures share some simple features. First, they identify a sentinel event. Next, they establish a statistical method for monitoring subsequent occurrences of that event. The method must exclude any occurrence of the sentinel event that led to the monitoring. Furthermore, the method should have reasonably high power. It should be statistically unbiased, but its Type 1 error rate may be set at a one-sided level higher than the conventional 0.025.
For individual events, we may consider (a) the number of nonevents until the kth event or (b) the time until the next (or kth) event. For groups of patients in whom the sentinel "event" is an unexpectedly high rate, we can use (c) the event rate in the future patients.
Various statistical models suggest themselves: for individual events the negative binomial model or a binomial sequential probability ratio test is natural for problem (a) whereas the exponential or gamma distribution is appropriate for problem (b). Normal models lend themselves to problem (c).
The remainder of this section deals with two specific examples of the approach. In the first example (Section 4.4.1), all subjects have the same follow-up time and all events occur in the treated group (or the monitoring is based only on the treated group). The second example (Section 4.4.2) provides an approach when the follow-up times differ and we are comparing the occurrences of the event in the treated group to a historical rate or to the control group.
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