Could you explain figure 7.9?
In part A, the LR+ appears to be large and the LR- appears to be small.
In part B, the LR- appears to be small and the LR- appears to be large.
I understand why the LRs change based on the prevalence of circumcision, but do not understand why part A and part B would give you the same OR if OR=LR+/LR-.
Thanks!
Hi All,
Dr. Newman explained this to me and asked me to post the explanation. Here goes:
Figure 7.9A represents a country where most boys are circumcised. Figure 7.9B represents a country where most boys are NOT circumcised. In both countries, the relationship between circumcision and having a UTI is the same (the OR is the same). In both countries, the odds of getting a UTI are 10 times as high in uncircumcised boys as in circumcised boys.
In a country where most boys are circumcised (7.9A), the prior probability of a UTI is low. If a boy is indeed circumcised (Test Result -), you gain no information, your LR- is small, and your posttest prob is not very different from your pretest prob. If the boy is NOT circumcised, your LR+ is large (this information makes him way more likely to have a UTI than the general population), and your posttest prob has greatly increased.
The opposite is true where most boys are NOT circumcised. LR+ is small (no new information) and LR- is large (makes it way less likely a boy has a UTI).
The length of the arrows in the figure represent the magnitude of the LOGARITHM of the LRs, and the direction represents the sign of the LOGARITHM of the LRs. An OR is division, therefore working on the logarithmic scale it is subtraction.
LR+/LR- becomes log(LR+) - log(LR-)
When we subtract LR- (a negative number given the arrow pointing down), it is like adding the absolute values of both arrows. Adding the length of both arrows gives you the same total length of the OR arrow: the same relationship between UTI and circumcision in population in A and B.
Thanks Jean! Right on!
The only clarification I would add is that when Jean referred to LR- being large or small, she is referring to the absolute value of log(LR-). So a "small" LR- would be close to 1 and a "large" LR- would be close to zero.
Tom
I'm still not completely sure I understand this.
I have always thought of LR+/- and sensitivity/specificity as test characteristics independent of the disease prevalence (pretest probability). In this thinking, a positive test is less helpful in a high disease prevalent situation because the pretest probability (and odds) is higher, NOT because the LR+ is smaller. For example, a test with LR+ 10 when pretest odds is low (1:10 -> 10:10, so you've gone from ~9% to 50% post test probability), versus when pretest odds is high (9:1 -> 90:1, so going from 90% to 99%).
But I can see mathematically that if you change the disease prevalence and keep the ODDS fixed, then all the test characteristics sens/spec and LR+/- must change, as explained by Jean.
I'm just not sure I get what kind of real-life situation this describes (i.e. why would the odds be the same? We have done many problem sets calculating PPV/NPV in different pretest probabilities, and all have assumed sens/spec/LR+/- were inherent properties of the test).
The key to the circumcision example in Box 7.3 and Figure 7.9 is the direction of causality. Usually we have Disease causing Test result; in this case we have risk factor causing disease.
Since we've mostly been dealing with test results rather than disease causes, we've been OK assuming LR don't change much (except in all of the situations we've described) with prevalence.
This is why LR are not got for risk factors and OR are not good for test results.
I've updated Box 7.3 to clarify these points and I uploaded it right under Chapter 7. Let us know if you are still confused.
Tom
