Okay, I agree with you, but it’s an understandable mistake. Let’s quickly review the idea of likelihood ratios. A positive likelihood ratio is defined at Sn / (1-Sp) where Sn is the sensitivity of the diagnostic test and Sp is the specificity. For a diagnostic test with a very high specificity, you get a very large ratio, because you are putting a really small value in the denominator. For Sp=0.99, for example, you would end up getting a positive likelihood ratio of 50 or more (assuming that Sn is at least 0.5).

The positive likelihood ratio is a measure of how much the odds of disease are increased if the diagnostic test is positive.

A negative likelihood ratio is defined as as (1-Sn) / Sp. For a diagnostic test with a very large sensitivity, the negative likelihood ratio is very close to zero. For Sn=0.99, the likelihood ratio is going to be 0.02 or smaller, assuming that Sp is at least 0.5.

The negative likelihood ratio is a measure of how much the odds of disease are decreased if the diagnostic test is negative.

The two likelihood ratios should remind you of the acronyms SpIn and SnOut. SpIn means that if specificity is large, then a positive diagnostic test is good at ruling in the disease. This isn’t always the case, sadly, and for many diagnostic tests, the next step after a positive test is not to treat the disease, but to double check things using a more expensive or more invasive test.

SnNout means that if the sensitivity is large, then a negative diagnostic test is good at ruling out the disease. You can safely send the patient home in some settings, or start looking for other diseases in different settings.

That sounds great, but sometimes you are very concerned about false negatives, and you don’t want to send someone home if they actually have the disease. If you are worried about a cervical fracture, ruling out the fracture and sending someone home might lead to paralysis or death if you have a false negative. So you want to be very sure of yourself in this setting.

Now with regard to the comment above, I think it is just a case of careless language. When the authors say “large negative likelihood ratio”, they should have said “extreme negative likelihood ratio” meaning a likelihood ratio much much smaller than one. I’ve done it myself when I talk about a correlation of -0.8 as being a “big” correlation because it is very far away from zero.

We tend to shy away from words like “small” when we talk about a negative likelihood ratio being much less than 1, because “small” in some people’s minds means “inconsequential” when the opposite is true. When I am careful in my language, I try to use the word “extreme” to mean very far away from the null value (1 for a likelihood ratio or 0 for a correlation) rather than “large” or “small”.

The Likelihood Ratio Slide Rule.

The Likelihood Ratio Slide Rule is a pocket sized device that allows you to calculate the post test probability of disease after a positive or negative result on a medical diagnostic test. It is loosely based on the Fagan Nomogram (Fagan TJ. NEJM 1975, Jul 31; 293(5): 257). This poster will show practical uses of the slide rule, including estimating positive and negative predictive values for varying disease prevalence levels and calculating a range of pre-test probabilities for which a diagnostic test is unnecessary. You can pick up one of these slide rules at the poster session while supplies last.

This slide rule was originally developed in 2002 and described on my website at www.pmean.com/08/sliderule.html.

In future blog entries, I will update and revise that page and share more details about this slide rule and how it works.

There are many ways to validate. I’m guessing here, but I suspect that you want to compare your algorithm, which is simple, cheap, or fast, to a gold standard measure of diabetes. The gold standard is something that has been around for a while and is well trusted by doctors, but it may be a lot more expensive or time consuming that what you are proposing.

Establishing validity in this framework is typically done by establishing that your sensitivity and specificity are large enough. You want to select a sample size so that the confidence intervals for sensitivity and specificity are reasonably narrow. A key statistic here is the proportion of patients in your sample that will have diabetes according to your gold standard.

Psychologists use terms like “criterion validity” or “predictive validity” in this case, though I am always a bit unclear on their terminology. That’s probably more of a limitation on my intellectual capacity than a criticism of their definitions.

Note that there is no “power” involved in this calculation. The reason for this is that validity is not something that is easily reduced to a simple hypothesis test.

If you want more details, I talk about sample sizes needed for a study of a diagnostic test at http://www.pmean.com/04/SampleSizeDiagnostic.html