Statistical methods for comparison to placebo in active-control trials
There has been a proliferation of active-control clinical trials comparing experimental therapies with standard ones (active control). In such cases, one often wants to know how the experimental therapy would have performed if it had been compared directly to placebo. This comparison requires 1. The observed effectiveness of experimental treatment compared to the active-control, and 2. The estimated effectiveness of the active-control therapy versus placebo (often obtained from a meta-analysis). If these two estimates apply to a common subpopulation, then two additional measures can be derived: 3. The estimated effectiveness of the experimental therapy relative to placebo, and 4. The estimated fraction of effect preserved by the experimental therapy. All four of these estimates can be described by point estimates, confidence intervals, and associated p-values. Our calculations have shown that if we use the conventional methods to compute the fraction of effect preserved based on the addition of confidence intervals, we dramatically increase the sample size required for studies of the experimental treatment versus standard therapy. As newer therapies become the standard therapies, we can expect that we will have a sequence of comparisons required to estimate the effect of the newest therapy relative to placebo, and this can be estimated using a generalization of the methodology just described. This comparison addresses the issue of "drift" (the risk that a series of active-control trials might push the general therapy in the wrong direction by accepting therapies that are worse than previously approved therapy). The problem of combining evidence from studies with several different treatment arms is also generalization of the methodology described previously. The solution to the problem requires that we assume that all of the odds ratios between the various treatments remain constant (1). We illustrate the method with an example from data on thrombolytics.
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