Interim analysis (September 13, 1999)
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Dear Professor Mean, I'm going on a job interview and I know one of the questions they will ask me is about interim analysis. What should I tell them? -- Harried Howard
Dear Harried, Tell them that you rely on Professor Mean for all your statistical advice. That will clinch the job for you. What? They've never heard of Professor Mean? Are you sure you really want to work there?
Interim analysis is analysis of the data at one or more time points prior to the official close of the study with the intention of possibly terminating the study early. There are several things to keep in mind with an interim analysis.
In a study where you expect the new therapy to be better than placebo, for example, you might want to stop the study as soon as you have enough evidence that the new therapy is better. There are ethical reasons (you want to minimize the number of subjects getting the placebo) and economic reasons (you don't to spend extra money after enough evidence has been accumulated).
Stopping because the new therapy is better is the most common reason for interim analysis, though there are others. Sometimes you might want to end a study early if a substantial number of patients experience serious side effects. Other times, you may want to end a study early because the evidence clearly shows that the results at the end of the trial are likely to be negative. This approach is sometimes called futility analysis.
If you want to run one or more interim analyses, you need to realize that there is no free lunch. If you apply the traditional test at both the middle and the end of the study, you increase the chance of Type I error (a false positive finding). You can (and should) make adjustments to prevent this, but then you end up requiring a greater amount of evidence, both at the middle and at the end of the study.
The two classic approaches to interim analysis are the Pocock method and the O'Brien-Fleming method. Both approaches require equally spaced intervals. This means that if two interim and one final analyses are planned, then the first interim analysis occurs after exactly one third of the data has been collected and the second interim analysis occurs after exactly two thirds of the data have been collected. Recently, a more flexible approach, the alpha spending function, has been developed for unequally spaced intervals.
A standard study would wait until all the data was collected and would declare the new therapy to be effective if the p-value were less than .05. Let's assume that we want two interim and one final analysis.
The Pocock procedure uses the same cut-off for both the interim and final analyses. With two interim and one final analysis, we would declare the new therapy to be effective if the p-value is less than 0.022 at any of the analysis times.
The O'Brien-Fleming method uses a very strict cut-off at first, then relaxes this cut-off over time. At the first interim analysis, you would conclude that the new therapy is effective if the p-value is less than 0.005. At the second interim analysis, you would compare the p-value to 0.014. At the end of the study, you would compare the p-value to 0.045.
Both approaches pay a penalty at the final analysis, but notice that the O'Brien-Fleming method, which has stricter standards earlier, has much less of a penalty at the planned conclusion of the study.
Harried Howard wants to make an impression during his job interview by giving a simple explanation of what interim analysis (or a group sequential trial) is. Professor Mean explains the interim analysis is a statistical analysis at one or more time points prior to the official end of the study with the intention of ending the study early if there is sufficient evidence of efficacy. He explains that you have to pay a price with an interim analysis, by living with a smaller alpha level at the end of your study. He then characterizes two simple approaches to interim analysis by Pocock and O'Brien-Fleming.