Making sense of Diagnostic Information Dr Carl Thompson.

Making sense of Diagnostic Information

Dr Carl Thompson

Non-iatropic Asymptomatic cases

Non-iatropic cases with mild symptoms

Threshold of iatropy

Iatropic cases treated in Primary care

Iatropic hospital cases

Clinical spectrum

Diagnostic universe

False positive

True positive

False negative

Positive testPositive test

True NegativeTrue Negative

DiseaseDisease

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

Dx info and probability revision

+

-

Postpositive-test probability of disease

Pre test probability

Post negative test Probability of disease

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)?

Pre test probability

• Random patient from given population

• PRE TEST PROB = POPULATION PREVELANCE

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

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)

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

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)

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

Nomogram

Nb. No need to convert to pre test odds just use P

PD+|T+

PD-|T-

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

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

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

Pre test P (where do they come from?)

• Dx as opinion revision

– SHOULD be epidemiological data sets

– IS memory and recalled experience

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

Representativeness

• P = how closely a patient represents a larger class of events (typical picture)

– Remember prevalence

Anchoring and adjustment

• Starting point overly influential (not a problem with epidemiological data of course)

• Cognitive caution is common (Hammond 1966)

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