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# Introduction to Biomedical Statistics

Introduction to Biomedical Statistics. Signal Detection Theory. What do we actually “detect” when we say we’ve detected something?. Signal Detection Theory. What do we actually “detect” when we say we’ve detected something? We say we’ve “detected” when a criterion value exceeds a threshold.

## Introduction to Biomedical Statistics

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### Presentation Transcript

1. Introduction to Biomedical Statistics

2. Signal Detection Theory • What do we actually “detect” when we say we’ve detected something?

3. Signal Detection Theory • What do we actually “detect” when we say we’ve detected something? • We say we’ve “detected” when a criterion value exceeds a threshold

4. Signal Detection Theory • examples: • the onset of a light or sound • the presence of an abnormality on x-ray

5. Signal Detection Theory • There are 4 possible situations Target is: Present Absent Present You Respond: Absent

6. Signal Detection Theory • There are 4 possible situations Target is: Present Absent Present You Respond: Absent

7. Signal Detection Theory • There are 4 possible situations Target is: Present Absent Present You Respond: Absent

8. Signal Detection Theory • There are 4 possible situations Target is: Present Absent Present You Respond: Absent

9. Signal Detection Theory • There are 4 possible situations Target is: Present Absent Present You Respond: Absent

10. Signal Detection Theory • There are 4 possible situations Target is: Present Absent Present You Respond: Absent This is the total # of Target Present Trials

11. Signal Detection Theory • There are 4 possible situations Target is: Present Absent Present You Respond: Absent This is the total # of Target Present Trials

12. Signal Detection Theory • Hit Rate (H) is the proportion of target present trials on which you respond “present”

13. Signal Detection Theory • Notice that H is a proportion, so 1 - H gives you the “miss” rate or…

14. Signal Detection Theory • False-Alarm Rate (FA) is the proportion of target absent trials on which you respond “present”

15. Signal Detection Theory • Notice that FA is a proportion. 1 minus FA gives you the correct rejections or …

16. Signal Detection Theory • Signal Detection can be modeled as signal + noise with some detection threshold

17. Signal Detection Theory Noise is normally distributed - Target Absent trials still contain some stimulus Frequency Target Absent Stimulus Intensity

18. Signal Detection Theory Target Present trials contain a little bit extra intensity contributed by the signal Noise is normally distributed - Target Absent trials still contain some stimulus Frequency Target Present Target Absent Stimulus Intensity

19. Signal Detection Theory This is the signal’s contribution Target Present trials contain a little bit extra intensity contributed by the signal Noise is normally distributed - Target Absent trials still contain some stimulus Frequency Target Present Target Absent Stimulus Intensity

20. Signal Detection Theory • We can imagine a static criterion above which we’ll respond “target is present” Criterion Frequency Target Present Target Absent Stimulus Intensity

21. Signal Detection Theory • Notice that H, FA, etc thus have graphical meanings Criterion Frequency Proportion Hits Stimulus Intensity

22. Signal Detection Theory • Notice that H, FA, etc thus have graphical meanings Criterion Frequency Proportion Misses Stimulus Intensity

23. Signal Detection Theory • Notice that H, FA, etc thus have graphical meanings Criterion Frequency Proportion False Alarms Stimulus Intensity

24. Signal Detection Theory • Notice that H, FA, etc thus have graphical meanings Criterion Frequency Proportion Correct Rejections Stimulus Intensity

25. Signal Detection Theory • Notice that as H increases, FA also increases Frequency Criterion H Stimulus Intensity

26. Signal Detection Theory • Notice that as H increases, FA also increases Frequency Criterion FA Stimulus Intensity

27. Signal Detection Theory • d’ (pronounced d prime) is a measure of sensitivity to detect a signal from noise and does not depend on criterion - it is the distance between the peaks of the signal present and signal absent curves • d’ is computed by converting from H and FA proportions into their corresponding Z scores and subtracting Zinv(FA) from Zinv(H) Frequency Stimulus Intensity

28. Some Common Biomedical Statistics • Sensitivity • Specificity • Positive Predictive Value • Negative Predictive Value • Likelihood Ratio • Relative Risk • Absolute Risk • Number needed to treat/harm

29. Sensitivity and Specificity • Consider a test for a condition • e.g. Pregnancy test • e.g. Prostate-specific Antigen (Prostate Cancer) • e.g. Ultrasound (Breast Cancer) • These are all signal detection problems

30. Sensitivity and Specificity • Four possible situations: Condition is: Present Absent Present Test Result: Absent

31. Sensitivity and Specificity • Four possible situations: Condition is: Present Absent Present Test Result: Absent

32. Sensitivity and Specificity • Four possible situations: Condition is: Present Absent Present Test Result: Absent

33. Sensitivity and Specificity • Four possible situations: Condition is: Present Absent Present Test Result: Absent

34. Sensitivity and Specificity • Four possible situations: Condition is: Present Absent Present Test Result: Absent

35. Sensitivity and Specificity • Four possible situations: Condition is: Present Absent Present Test Result: Absent This is Total # of Condition Present Cases

36. Sensitivity and Specificity • Four possible situations: Condition is: Present Absent Present Test Result: Absent This is Total # of Condition Absent Cases

37. Sensitivity and Specificity • Four possible situations: Condition is: Present Absent This is Total # of “positive” tests Present Test Result: Absent

38. Sensitivity and Specificity • Four possible situations: Condition is: Present Absent Present Test Result: This is Total # of “negative” tests Absent

39. Sensitivity and Specificity • Sensitivity is the proportion of condition present cases on which the test returned “positive” • Analogous to the hit rate (H) in Signal Detection Theory

40. Sensitivity and Specificity • Specificity is the proportion of condition absent cases on which the test returned “negative” • Analogous to the Correct Rejection rate in Signal Detection Theory

41. Sensitivity and Specificity • Notice that 1 minus the Sensitivity is analogous to the FA of Signal Detection Theory

42. Sensitivity and Specificity • Notice that 1 minus the Sensitivity is analagous to the FA of Signal Detection Theory • Recall that in Signal Detection Theory, as criterion were relaxed both H and FA increased and as criterion were more stringent, H and FA decreased

43. Sensitivity and Specificity • Notice that 1 minus the Sensitivity is analagous to the FA of Signal Detection Theory • Recall that in Signal Detection Theory, as criterion were relaxed both H and FA increased and as criterion were more stringent, H and FA decreased • Sensitivity and Specificity have a similar relationship: as a cut-off value for a test becomes more stringent the sensitivity goes down and the specificity goes up…and vice versa

44. Sensitivity and Specificity • “For detecting any prostate cancer, PSA cutoff values of 1.1, 2.1, 3.1, and 4.1 ng/mL yielded sensitivities of 83.4%, 52.6%, 32.2%, and 20.5%, and specificities of 38.9%, 72.5%, 86.7%, and 93.8%, respectively.” JAMA. 2005 Jul 6;294(1):66-70.

45. Sensitivity and Specificity • Likelihood Ratio is the ratio of True Positive rate to False Positive rate • Loosely corresponds to d’ in that Likelihood ratio is insensitive to changes in criterion

46. Sensitivity and Specificity • If a test is positive, how likely is it that the condition is present? • Positive Predictive Value is the proportion of “positive” test results that are correct

47. Sensitivity and Specificity • Negative Predictive Value is the proportion of “negative” test results that are correct

48. Sensitivity and Specificity • Consider the influence of exposure to some substance or treatment on the presence or absence of a condition • e.g. smoking and cancer • e.g. aspirin and heart disease

49. Sensitivity and Specificity • A similar logic can be applied Disease: Yes No No Exposure: Yes

50. Sensitivity and Specificity • A similar logic can be applied Disease: Yes No This is total # exposure No Exposure: Yes

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