# Power calculation for a case-control study with a continuous outcome

We're planning a case-control study, in which we assign subjects to be either cases or controls (based on normal vs low birth weight) and then measure a continuous outcome variable (% body fat) subsequently.

Can anyone point me towards a method for calculating how many cases vs controls we will need. We have an idea of the standard deviation of the outcome variable (% body fat).

Many thanks

Andrew

• To do power analysis you need to specify exactly how the the null hypothesis (no effect) is false. That is, you need to specify an "effect size", which would involve the hypothesized difference in % body fat is there was a small/medium/large effect and an estimate of the variance of the outcome in each group. – Macro Aug 18 '11 at 16:14
• Some information are missing, as suggested already. Also, anticipating dropouts and defining the right hypothesis will change the standard formulae. For an overview, check e.g., Donner, Approaches to sample size estimation in the design of clinical trials–A review, Stat. Med. (1984) 3:199. – chl Aug 18 '11 at 19:50

As I said in my comment, too much information (e.g., expected % of dropouts or missing values, type of matching, one-sided or two-sided hypothesis) is missing to propose a 'magic' formula. So, for general references (apart from classical epidemiological textbook), I would recommend:

• Thanks - the references are very helpful. It was a pointer that I needed rather than a solution! – Andrew Dec 16 '11 at 9:57

Reading about power analysis in any experiment design textbook might answer your question. But here's the general idea: You have a few unknowns relating to power

• Variance
• Sample size
• p-value

So you try to guess what the unknowns are.

1. Run a pilot study so that you can guess what the variance would be.
2. Choose alpha.
3. I feel like I missed one of the unknowns. If I did, you figure that out to.
4. Do the statistical computations in reverse to solve for sample-size. You can also generate random data based on the variance and different sample sizes and then run the statistical computations the normal way, but the analytical approach will probably be easier for the simple design that you have.

And you can of course graph this so you get an idea of how robust your decision is to variations in the variance.