Micro Statistics Tutorial 04: Power - Can Schering Plough count?

As discussed earlier, there have been concerns raised about the possibility of "functional unblinding" in the ENHANCE trial of the drug Vytorin (ezetimibe/simvastatin-combination).

As the first part of this exercise, let us take a look at the POWER of the ENHANCE trial. There is something slightly odd here (I think). The question is: Can Schering-Plough count?

Power, for neophytes out there, is the probability of rejecting a false statistical null hypothesis. The goal is to allow you to decide (in advance of an experiment)

• How many people (or things) you need to study to answer your question
• How likely it is that your statistical test will be able to detect an effect of a given size

Good experiments must ensure that power is high enough to answer the question. To calculate power we need to know:

• The precise question
• The kind of statistical test that will be used
• The size of the sample (bigger = more power)
• The size of the experimental effects you want to detect (bigger effects need a smaller sample)
• The amount of noise in the measurements (measurement error or biological variability)

Power calculations for the ENHANCE trial were published with the study protocol [Ref 1]. It states:


Although it is possible to perform power calculations taking account of covariates or confounders (such as baseline IMT, center and so on) this is difficult, and no estimated covariate parameters are provided. One therefore has to assume that the power calculations were carried out using conventional methods (a t-test). In the end Schering Plough recruited slightly more patients than their prior power calculation suggested they should recruit as a minimum. However this is not the issue here. They could also claim that this is just a bit of rounding error (see further discussion in comments). This is again irrelevant - the fact remains that it is not possible to add two and two from the numbers they give, or to resuscitate their rather simple calculations. This bypassed the entire system of safeguards that is supposed to check these little details.

So on to the power. Well, as far as my humble brain can establish, Power for N=650 is in fact 88.9%, not 90%.
The required N for 90% Power, 2-tailed alpha 0.05, between group difference of 0.05mm and SD=0.20mm is not N=650.
It is N=674.

A small difference perhaps, but it does tell us something interesting about the process:

1. Perhaps I can't count
2. Perhaps Schering-Plough or Merck can't count
3. Perhaps the authors of the protocol paper didn't read their paper
4. Perhaps peer reviewers didn't back-check anything
5. Perhaps there is something Merck or Schering-Plough aren't telling
6. Perhaps Carrie Smith Cox can only count in units of $28 million

Reference
J. Kastelein, P. Sager, E. de Groot, E. Veltri (2005). Comparison of ezetimibe plus simvastatin versus simvastatin monotherapy on atherosclerosis progression in familial hypercholesterolemia. Design and rationale of the Ezetimibe and Simvastatin in Hypercholesterolemia Enhances Atherosclerosis Regression (ENHANCE) trial. Am Heart J. 2005 Feb;149(2):234-9.

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