StATS: When can I stop my CQI study? (June 6, 2005)

I was asked today about a CQI project where children were being tested for a certain condition, but they never tested positive. This was going on for over a year and there were already 188 cultures and none were positive. Is it safe to hang up your spurs and call it a day?

To decide whether to stop or not depends on how much precision you want or desire.

If you have a rate of 0/188, then you can estimate the 95% confidence interval for the true rate to be somewhere between 0 and 1.6%. That tells you that even after allowing for sampling error, you know the probability is much less than 2%.

Is that small enough, or do you need to make the interval even narrower? You could, for example, collect data on twice as many patients. Then your 95% confidence interval (assuming that all 376 samples are negative) would be somewhere between 0 and 0.8%.

To me it hardly seems worth the trouble to further narrow the confidence interval, but that is just my opinion. You need to balance the cost of additional testing versus the cost of possibly missing a future positive culture.

Another way of looking at it is to ask how much precision do you need? If you want an unreasonable amount of precision, such as requiring that the 95% confidence interval extend up to only 0.1%, then you would need to find all negative results in an unrealistically large sample of 3,000 patients.

If you were quite casual about precision, and believed that an interval that extended up to 20% would be satisfactory, then a casual sample of 15 patients with all negative results would be all that you really need.

I suspect that most people find themselves between those two extremes. Tell me how much precision you are happy with and I will tell you how big a sample size you would need.

Further reading:

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Early stopping.