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Making sense of Diagnostic Information
Dr Carl Thompson
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Non-iatropic Asymptomatic cases
Non-iatropic cases with mild symptoms
Threshold of iatropy
Iatropic cases treated in Primary care
Iatropic hospital cases
Clinical spectrum
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Diagnostic universe
False positive
True positive
False negative
Positive testPositive test
True NegativeTrue Negative
DiseaseDisease
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Diagnostic universe
disease
Present absent
Dx test positive True positives False positives All positives
Negative False negatives True negatives All negatives
All with disease All without disease
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Dx info and probability revision
+
-
Postpositive-test probability of disease
Pre test probability
Post negative test Probability of disease
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scenario5 year old girl presents on the ward via A&E with a
“sore tummy”, feeling “hot” but with clear, non-smelly urine and otherwise OK physiological signs – can you rule out UTI? A colleague says that that clear urine is a good test for ruling out UTIs. You know its not perfect (I.e. some UTIs are missed) how much weight should you attach to the clear urine? Should you order an (expensive) urinalysis and culture just to be on the safe side (bearing in mind that money spent on that is money that could be spent on something else)?
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Pre test probability
• Random patient from given population
• PRE TEST PROB = POPULATION PREVELANCE
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Diagnostic universe
UTI
Present D+ Absent D-
Urine
clarity
Cloudy T+
26 (TP) 23 (FP) All Cloudy
49
Clear
T-3 (FN) 107 (TN) All Clear
urine
110
29 (TP+FN)
All with UTI
130 (FP +TN)
All non UTI
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Sensitivity and specificity (a recap)• Sensitivity P(T+|D+) Sn or TPR (true positive ratio
– 26/29 (0.89/89%)
• Specificity P (T-|D-) Sp or TNR (true negative ratio)– 107/130 (0.82/82%)
• FNR = proportion of patients with disease who have a negative test result– 1-TPR (0.11/11)
• FPR = proportion of patients without the disease who have a positive test result– 1-TNR (0.18/18)
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2 x 2 P revision (steps 1-2 of 4)
Urine UTI NO UTI Row totalStep 1: use prevalence to fix column totals: 18% X 1000
Positive
Negative
Column total 180 820 1000
Step 2: use Sn to fill in disease columns (90% x 180 = 162)
Positive 162
Negative 18
Total by column 180 820 1000
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Step 3: use Sp to fill In no disease columns: (82% x 820 = 805)
Positive 162 148
Negative 18 672
Total by column 180 820 1000
Step 4: compute row totals (162 + 148 = 310)
Positive 162 148 310
Negative 18 672 690 (18/672 = 0.02)
Total by column 180 820 1000
2 x 2 P revision (steps 3-4 of 4)
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Bayes formula Pre test odds x likelihood ratio = post test odds
Nb* pre test ODDS = prevalence/(1-prevalence)Steps when finding is present
–Calculate LR+–Convert prior probability to pretest odds–Use odds ratio form of Bayes’ to calculate posttest odds
Steps when finding is absent–Calculate LR-–Convert prior probability to pretest odds–Use odds ratio form of Bayes’ to calculate posttest odds
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Nomogram
Nb. No need to convert to pre test odds just use P
PD+|T+
PD-|T-
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Path Probability
Operate
Do not operate
Disease present
Disease absent
Disease present
Disease absent
Survive
Operative death
Palliate
Operative deathOperative death
Survive
Survive
No cure
Cure
Cure
No Cure
No cure
Cure
p=.10
p=.90
p=.10
p=.90
p=.90
p=.10
p=.02
p=.98 p=.10
p=.90
p=.10
p=.90p=.90
p=.10
p=.01
p=.99
Try for the cure
Path probability of a sequence of chance events is the product of all probabilities along that sequence
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D+ (180)
T+ (0.9)
P(T+|D+ ieSn)
P(T-|D+ I.e.1-Sn)T- 0.1
D+,T+ (162)
D+,T- (18)P(D+)
D-
P(D-)
P(T+|D- I.e. 1-Sp)
T+ (0.18)D-,T+ (148)
P(T-|D- I.e. Sp)
T- (0.82)D-,T- (672)
T+P(D+|T+)
P(D-|T+)T-
D+,T+
D+,T-P(T+)
T-
P(D-)
P(D+|T-)
D+D-,T+
P(D-|T-)
D-D-,T-
D+
BAYES
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D+
T+
P(T+|D+)
P(T-|D+)T-
D+,T+
D+,T-P(D+)
D-
P(D-)
P(T+|D-)
T+D-,T+
P(T-|D-)
T-D-,T-
T+ (162+148)
D- (148/310)
162
148
T- (18 + 672)
D+ (18/69018
D- (672/690)672
D+ (162/310)
BAYES310
0.52
0.48
690
0.02
0.98
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Pre test P (where do they come from?)
• Dx as opinion revision
– SHOULD be epidemiological data sets
– IS memory and recalled experience
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Heuristics (1)
• Availability: P = ease by which instances are recalled.
– Divide the n of observed cases by the total number of patients seen – makes observed case frequency more available
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Representativeness
• P = how closely a patient represents a larger class of events (typical picture)
– Remember prevalence
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Anchoring and adjustment
• Starting point overly influential (not a problem with epidemiological data of course)
• Cognitive caution is common (Hammond 1966)
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Value induced bias
• Utility is a perception (it’s the bit that goes beyond the facts “which speak for themselves”: cost, benefit, harm, probability)
• The fear of consequences affects decisions: I.e. overestimation of malignancy because of fear of missing case