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 test True Negative Disease

Diagnostic universe disease Presentabsent Dx test positive True positivesFalse positives All positives Negative False negativesTrue negatives All negatives All with diseaseAll without disease

Dx info and probability revision + - Postpositive-test probability of disease Pre test probability Post negative test Probability of disease

scenario 5 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 (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) UrineUTINO UTIRow total Step 1: use prevalence to fix column totals: 18% X 1000 Positive Negative Column total Step 2: use Sn to fill in disease columns (90% x 180 = 162) Positive162 Negative18 Total by column

Step 3: use Sp to fill In no disease columns: (82% x 820 = 805) Positive Negative18672 Total by column Step 4: compute row totals ( = 310) Positive Negative (18/672 = 0.02) Total by column 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) zSteps when finding is present –Calculate LR+ –Convert prior probability to pretest odds –Use odds ratio form of Bayes’ to calculate posttest odds zSteps 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 death Survive No cure Cure No Cure No cure Cure p=.10 p=.90 p=.10 p=.90 p=.10 p=.02 p=.98 p=.10 p=.90 p=.10 p=.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+ ( ) D- (148/310) T- ( ) D+ (18/ D- (672/690) 672 D+ (162/310) BAYES

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