Had an issue understanding this concept for quite some time and finally figured out. Sharing some details that helped me (attached as word doc as well since tables may not appear clearly)
How cut-0ff values affect PPV and NPV
The text in bold (italics) is from an explanation I found online and the rest is smth that I put together to understand the concept better
Consider the following hypothetical example: measurement of high endorphin levels in SpRs in Anaesthesia has been found to be associated with success in the final FRCA examination. A sample of SpRs is tested before the examination resulting in a range of endorphin values. The data are examined and an arbitrary cut-off point for endorphin levels is chosen above which most of the candidates passed with few failures. Despite choosing the cut-off value in such a way that the maximum possible number of SpRs is correctly classified, we may find that 10% of the cohort with endorphin levels above the cut-off level failed the exam (false positives) and 15% of the cohort with endorphin levels below the cut-off level passed the exam (false negatives).
Let say for e.g
N=100 doctors
Cut-off value for endorphin = 200
doc will pass if endorphin level above 200
doc will fail if endorphin level below 200
Exam passed Exam failed Total
Endorphin test + ve 54 (TP) 6 (FP) 10% 60 docs had endorphin ≥ 200
Endorphin test -ve 6 (FN) 15% 34 (TN) 40 docs had endorphin ≤ 200
100
If the cut-off point is raised, there are fewer false positives but more false negatives—the test is highly specific but not very sensitive. Similarly, if the cut-off point is low, there are fewer false negatives but more false positives—the test is highly sensitive but not very specific
The 6 (FP) people who actually failed the exam most likely had endorphin levels just slightly above 200. So if we raised the cut-off from 200 to 230 (for e.g) then probably all the 6 would correctly reflect that they failed (i.e. will become TN and that FP will disappear or decrease). But this would mean there could be more false negatives showing up.
Similarly the 6 (FN) people who actually passed the exam most likely had endorphin levels just slightly below 200. So if we lowered the cut-off from 200 to 170 (for e.g) then all the 6 would correctly reflect that they passed (i.e. will become TP and that FN will disappear or decrease). But this would mean there could be more false positives showing up.
Bottom Line:
If we raise cut-off
False positives decreases
False negatives increases
If FP ↓ then specificity increases (FP is in denominator in formula)
If FN ↑then sensitivity decreases (based on formula)
If FP ↓ then PPV increases (based on formula)
If FN ↑then NPV decreases (based on formula)
If we lower cut-off
False negatives decreases
False positives increases
If FN ↓ then sensitivity increases (based on formula)
If FP ↑then sensitivity decreases (based on formula)
If FN ↓ then NPV increases (based on formula)
If FP ↑then PPV decreases (based on formula)
How cut-0ff values affect PPV and NPV
The text in bold (italics) is from an explanation I found online and the rest is smth that I put together to understand the concept better
Consider the following hypothetical example: measurement of high endorphin levels in SpRs in Anaesthesia has been found to be associated with success in the final FRCA examination. A sample of SpRs is tested before the examination resulting in a range of endorphin values. The data are examined and an arbitrary cut-off point for endorphin levels is chosen above which most of the candidates passed with few failures. Despite choosing the cut-off value in such a way that the maximum possible number of SpRs is correctly classified, we may find that 10% of the cohort with endorphin levels above the cut-off level failed the exam (false positives) and 15% of the cohort with endorphin levels below the cut-off level passed the exam (false negatives).
Let say for e.g
N=100 doctors
Cut-off value for endorphin = 200
doc will pass if endorphin level above 200
doc will fail if endorphin level below 200
Exam passed Exam failed Total
Endorphin test + ve 54 (TP) 6 (FP) 10% 60 docs had endorphin ≥ 200
Endorphin test -ve 6 (FN) 15% 34 (TN) 40 docs had endorphin ≤ 200
100
If the cut-off point is raised, there are fewer false positives but more false negatives—the test is highly specific but not very sensitive. Similarly, if the cut-off point is low, there are fewer false negatives but more false positives—the test is highly sensitive but not very specific
The 6 (FP) people who actually failed the exam most likely had endorphin levels just slightly above 200. So if we raised the cut-off from 200 to 230 (for e.g) then probably all the 6 would correctly reflect that they failed (i.e. will become TN and that FP will disappear or decrease). But this would mean there could be more false negatives showing up.
Similarly the 6 (FN) people who actually passed the exam most likely had endorphin levels just slightly below 200. So if we lowered the cut-off from 200 to 170 (for e.g) then all the 6 would correctly reflect that they passed (i.e. will become TP and that FN will disappear or decrease). But this would mean there could be more false positives showing up.
Bottom Line:
If we raise cut-off
False positives decreases
False negatives increases
If FP ↓ then specificity increases (FP is in denominator in formula)
If FN ↑then sensitivity decreases (based on formula)
If FP ↓ then PPV increases (based on formula)
If FN ↑then NPV decreases (based on formula)
If we lower cut-off
False negatives decreases
False positives increases
If FN ↓ then sensitivity increases (based on formula)
If FP ↑then sensitivity decreases (based on formula)
If FN ↓ then NPV increases (based on formula)
If FP ↑then PPV decreases (based on formula)
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