Stopping rules for interim analysis

In Chapter 10 we spoke extensively about the dangers of multiple testing and the associated inflation of the type I error. Methods were developed to control that inflation and account for multiplicity in an appropriate way. 

One area that we briefly mentioned was interim analysis, where we are looking at the data in the trial as it accumulates. The method due to Pocock (1977) was discussed to control the type I error rate across the series of interim looks. The Pocock methodology divided up the 5 per cent type I error rate equally across the analyses. So, for example, for two interim looks and a final analysis, the significance level at each analysis is 0.022. For the O Brien and Fleming (1979) method most of the 5 per cent is left over for the final analysis, while the first analysis is at a very stringent level and the adjusted significance levels are 0.00052, 0.014 and 0.045. 

These two methods are the most common approaches seen in pharmaceutical applications. A third method, which we see used from time to time, is due to Haybittle (1971) and Peto et al. (1976). Here a significance level of 0.001 is used for each of the interims, again leaving most of the 5 per cent left over for the final analysis. For two interims and a final, the adjusted significance level for the final analysis is in fact 0.05 to two decimal places, for three interims we have 0.049 left over . Clearly these methods have little effect on the final evaluation, but associated with that there is also little chance of stopping at an interim stage. 

Each of these methods assumes that the analyses take place at equally spaced intervals. So, for example, if the total sample size is 600 and we are planning two interims and a final, then the interims should take place after 200 and 400 

Statistical Thinking for Non-Statisticians in Drug Regulation Richard Kay 2007 John Wiley Sons, Ltd ISBN 978-0-470-31971-0 

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