Likelihood Ratios

[AZ7]

So a Positive Likelihood Ratio is a ratio that represents the likelihood of having the disease given a positive test result.
Positive Predictive Value is the probability that a disease is present given a positive test result.
Isn't probability and likelihood the same thing? Whats the difference between Predictive values and Likelihood ratios?

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[Transposony]

While Predictive Value uses values from "rows" Likelihood ratio uses "columns" for calculation purposes.
For example:
Positive Likelihood ratio = SEN / FP rate (1- SPEC)

 

[Phloston]

So a Positive Likelihood Ratio is a ratio that represents the likelihood of having the disease given a positive test result.
Positive Predictive Value is the probability that a disease is present given a positive test result.
Isn't probability and likelihood the same thing? Whats the difference between Predictive values and Likelihood ratios?

I'll answer this quite broadly in a way that may or may not be beneficial here.

PPV would be the probability that a positive result means the person actually has the disease. NPV would be the probability a negative test result means the person actually doesn't have the disease.

(+)LR = sensitivity / 1-specificity

And you know what sensitivity and specificity are.

So therefore (+)LR = probability of testing positive if you have the disease / the probability of testing positive if you don't have the disease

That's epic, I know.

So therefore (+)LR tells you the clinical usefulness a positive result has. If the ratio is high, a positive result is very useful. If an individual has a low pretest probability, a positive result means he or she likely has the disease. As far as I'm aware LR bridges pretest and post-test probability.

 

[AshNiffler]

Jesus.

 

[AZ7]

@Phloston
But how would both of these be differentiated in a question stem? For example, if a patient takes a diagnostic test and ends with with the positive result, isn't asking the probability of them having the disease the same as asking the likelihood of them having the disease?

 

[Jabbed]

I neither know nor care what any of it actually means. This is my brutish method of interpreting the result.

Patient is being evaluated for disease x (pre-test probability of disease is 25%)

Test comes back positive:
LR(+) values of 2, 5, and 10 increase the risk of disease probability by 15%, 30%, and 45%

Test comes back negative:
LR(-) values of 0.5, 0.2, and 0.1 decreases the risk of disease probability by 15%, 30%, and 45%

So if pre-test probability is 25% and the LR(+) ratio is 5, a positive test result in this patient indicates a post-test probability of 55% chance of disease. Conversely if it had been negative with LR(-) 0.2, probability of disease is virtually 0%.

 

[Jabbed]

And to answer your original question, PPV does not consider pre-test probability. For that reason, you have to decide if the pretest probability is sufficiently high enough before considering the value of PPV with regards to a positive test result. This is largely why talking about the PPV of a test is often useless.

 

[dempty]

@Phloston
But how would both of these be differentiated in a question stem? For example, if a patient takes a diagnostic test and ends with with the positive result, isn't asking the probability of them having the disease the same as asking the likelihood of them having the disease?

Probability and likelihood are not the same thing, in a technical sense. In common use, the terms are synonymous.

 

[AZ7]

Thanks !

 

[Pholston]

Whats the difference between Predictive values and Likelihood ratios?

Predictive values depend on the prevalence of the disease in the population tested.
Likelihood Ratios depends on sensitivity & specificity and are independent of prevalence.

LR > 1 indicates an increased probability
LR < 1 indicates a decreased probability
LR = 1 indicates that the test result does not change the probability of disease

 

[navigator]

I neither know nor care what any of it actually means. This is my brutish method of interpreting the result.

Patient is being evaluated for disease x (pre-test probability of disease is 25%)

Test comes back positive:
LR(+) values of 2, 5, and 10 increase the risk of disease probability by 15%, 30%, and 45%

Test comes back negative:
LR(-) values of 0.5, 0.2, and 0.1 decreases the risk of disease probability by 15%, 30%, and 45%

So if pre-test probability is 25% and the LR(+) ratio is 5, a positive test result in this patient indicates a post-test probability of 55% chance of disease. Conversely if it had been negative with LR(-) 0.2, probability of disease is virtually 0%.

I'm kinda stumped by this explanation. I get the general concept that a high PLR (say, 15) means it's 15x more likely the patient has the disease than doesn't have the disease if tested positive. It also makes sense that if there's low pretest probability but a positive test and a high PLR, the patient very likely (or almost certainly) has the disease.

But how do you relate the PLR to changes in disease probability from pretest probability, as you did here?

 

[Rahas]

Because the results of the test increase the information you have about the patients condition, and allow you to more accurately predict the probability.

 

[Rahas]

eg if I asked you to guess the Step 1 score of a random medical student, you might go with 230. If I told you he was amongst the top 10 students in his class, you might guess 250. If I told you all his practice NBMEs were 260+, your estimate would lie in the same region. The only thing changing here is the amount of information you have. As it increases, so does the accuracy of your guessing