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The clinical value of diagnostic tests A well-explored but underdeveloped continent

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### The clinical value of diagnostic testsA well-explored but underdeveloped continent

### The clinical value of diagnostic testsThe diagnostic test and some neglected aspects of its statistical evaluation.

Plan of my talk

J. Hilden : March 2006

Some aspects were covered in my seminar spring 2003

Plan of my talk

Historical & ”sociological” observations

Clinicometric framework

Displays and measures of diagnostic power

Appendix: math. peculiarities

Plan of my talk

Historical & ”sociological” observations

”Skud & vildskud”

- Diagnostic vs. therapeutic research

- 3 key innovations & some pitfalls

Clinicometric framework

Displays and measures of diagnostic power

Appendix: math. peculiarities

Trials concern what happens observably

…concern 1st order entities (mean effects)

Diagnostic activities aim at changing the doc’s mind

…concern 2nd order entities (uncertainty / “entropy” change)

A quantitative framework for diagnostics is much harder to devise than for therapeutic trials.CONSORT >> 10yrs >> STARD

CC ~1993 CC ~2003

In the 1970s

medical decision theory established itself

– but few first-rate statisticians took notice.

Were they preoccupied with other topics, … Cox, prognosis, … trial follow-up ?

Sophisticated models became available for describing courses of disease conditionally on diagnostic data.

Fair to say that they themselves remained

‘a vector of covariates’ ?

Early history

Yerushalmy ~1947:

studies of observer variation*

Vecchio:

/:BLACK~WHITE:/ Model 1966

- simplistic but indispensable

- simple yet often misunderstood?!

Warner ~1960:

congenital heart dis. via BFCI

* important but not part of my topic today

Other topics not mentioned

Location (anatomical diagnoses)

and multiple lesions

Monitoring, repeated events, prognosis

Systematic reviews & meta-analyses

Interplay between diagnostic test data & knowledge from e.g. physiology

Tests with a therapeutic potential

Non-existence of ”prevalence-free”

figures of merit

Patient involvement, consent

BFCI (Bayes’ Formula w. Conditional Independence**)

”based on the assumption of CI”:

what does that mean?

Do you see why it was misunderstood?

** Indicant variables independent cond’lly on pt’s true condition

BFCI (Bayes’ Formula w. Conditional Independence)

”Bayes based on the assumption of CI”

- what does that mean?

- ”There is no ”Bayes Theorem” without CI”
- ”The BFCI formulae presuppose CI

(CI is a necessary condition for correctness)”

No, CI is a sufficient condition; whether it is

also necessary is a matter to be determined

– and the answer is No.

Counterexample: next picture !

Joint conditional distribution of two tests* in two diseases (red, green)

*with 3 and 2 test qualitative outcomes

Vecchio’s /:BLACK&WHITE:/ Model 1966

Common misunderstandings:

- ”The sensitivity and specificity are properties of the diagnostic test [rather than of the patient population]”
- They are closely connected with the ability of the test to rule out & in

True only when the ”prevalence” is intermediate

Plan of my talk

Historical & ”sociological” observations

Clinicometric framework

Displays and measures of diagnostic power

Appendix: math. peculiarities

You cannot discuss Diagnostic Tests without:Some conceptual framework*

A Case, the unit of experience in the clinical disciplines,

is a case of a Clinical Problem, defined by the who-how-where-why-what of a clinical encounter

– or Decision Task.

We have a case population or:

case stream (composition!) with a case flow (rate, intensity).

*Clini[co]metrics, rationel klinik, …

Examples

Each time the doc sees the patient we have a new encounter / case, to be compared with suitable ”statistical” precedents – and physio- & pharmacology.

Prognostic outlook at discharge from hospital: a population of cases = discharges, not patients (CPR Nos.).

Danish Citizen No.

Diagnosis?

Serious diagnostic endeavours are always action-oriented

– or at least counselling-oriented –

i.e., towards what should be done so as to influence the future (action-conditional prognosis).

The ”truth” is either

- a gold standard test (”facitliste”), or
- syndromatic (when tests define the ”disease,*” e.g. rheum. syndromes, diabetes)

*in clinimetrics there is little need for that word!

Example

The acute abdomen:

there is no need to discriminate between appendicitis and non-app. (though it is fun to run an ”appendicitis contest”)

What is actionwise relevant is the decision: open up or wait-and-see?

In clinical studies the choice of sample, and of the variables on which to base one's prediction, must match the clinical problem as it presents itself at the time of decision making. In particular, one mustn't discard subgroups (impurities?) that did not become identifiable until later: prospective recognizability !

Data collection

Purity vs. representativeness:A meticulously filtered case stream ('proven infarctions') may be needed for patho- and pharmaco-physiological research, but is inappropriate as a basis for clinical decision rules [incl. cost studies].

Data collection

Consecutivity as a safeguard against selection bias.Standardization: (Who examines the patient? Where? When? With access to clin. data?)Gold standard … the big problem !! w. blinding, etc.Safeguards against change of data after the fact.

Data collection

STARD !

”Discrepant analysis”

If the outcome is FALSE negative or positive,

you apply an ”arbiter” test

”in order to resolve the discrepant finding,”

i.e. a 2nd, 3rd, … reference test.

If TRUE negative or positive, accept !

~ The defendant decides who shall be allowed to give testimony and when

Digression…Randomized trials of diagn. tests

…theory under development

Purpose & design: many variants

Sub(-set-)randomization, depending on the pt.’s data so far collected.

”Non-disclosure”: some data are kept under seal until analysis. No parallel in therapeutic trials!

Main purposes…

…Randomized trials of diagn. tests

- when the diagnostic intervention is itself potentially therapeutic;
- when the new test is likely to redefine the disease(s) ( cutting the cake in a completely new way );
- when there is no obvious rule of translation from the outcomes of the new test to existing treatment guidelines;

4) when clinician behaviour is part of the research question…

…end of digression

Plan of my talk

Historical & ”sociological” observations

Clinicometric framework

Displays and measures of diagnostic power

Appendix: math. peculiarities

Displays & measures of diagnostic power

- The Schism – between:
- ROCography
- VOIography

ROCography

~ classical discriminant analysis / pattern recognition

Focus on disease-conditional distribution of test results (e.g., ROC)

AuROC (the area under the ROC) is popular … despite 1991 paper

VOI (value of information)

~ decision theory.

VOI = increase in expected utility afforded by an information source such as a diagnostic test

Focus on posttest conditional distribution of disorders, range of actions and the associated expected utility – and

– its preposterior quantification.

Less concerned with math structure, more with medical realism.

VOI

Do we have a canonical guideline?

1) UTILITY

2) UTILITY / COST

Even if we don't have the utilities

as actual numbers, we can use this

paradigm as a filter:

evaluation methods that violate it are

wasteful of lives or resources.

Stylized utility (pseudo-regret functions) as a (math. convenient) substitute.

VOI

Def. diagnostic uncertainty as expected regret

(utility loss, relative to if you knew what ailed the pt.)

Diagnosticity measures (DMs):

Diagnostic tests

should be evaluated in terms of

pretest-posttest difference

in diagnostic uncertainty.

Auxiliary quantities like sens and spec

… go into the above.

…so much as to VOIprinciples

Diagnosticity measures and auxiliary quantities

Sens (TP), spec (TN): nosografic distrib.

PVpos, Pvneg: diagnostic distr.|test result

Youden’s Index: Y = sens + spec – 1 =

1 – (FN) – (FP)

= det(nosog. 2X2) =

(TP)(TN)–(FP)(FN)

= 2(AuROC – ½)

AuROC =

[sens+spec] / 2

ROC

Y = 1

FN

TP

Y = 0

BLACK&WHITE

FP

TN

Diagnosticity measures and auxiliary quantities

Sens, spec nosografic distribution

LRpos, LRneg = slopes of segments

The ”Likelihood ratio” term is o.k. when diagnostic

hypotheses are likened to scientific hypotheses

ROC

Y = 1

FN

neg

pos

TP

Y = 0

BLACK&WHITE

FP

TN

Diagnosticity measures and auxiliary quantities

«Utility index» = (sens) xY.

... is nonensense

ROC

Y = 1

FN

TP

Y = 0

BLACK&WHITE

FP

TN

Diagnosticity measures and auxiliary quantities

DOR (diagnostic odds ratio) =

[(TP)(TN)] / [(FP)(FN)]

= infinity in this example

even if TP is only 0.0001. ... careful!

ROC

Y = 1

FN

Y = 0

BLACK&WHITE

TP

FP = 0

TN

Utility-based evaluation in general

∫(pdy + qdx )mina{ (LaDpdy +La,nonDqdx)/(pdy + qdx) }

is how it looks when applied to the ROC

(which contains the required information about

the disease-conditional distributions).

*

The area under the ROC (AuROC) is misleading

You have probably seen my

counterexample* before.

Assume D and non-D

equally frequent and also

utilitywise symmetric …

*Medical Decision Making 1991; 11: 95-101

Historical & ”sociological” observations

Clinicometric framework

Displays and measures of diagnostic power

Appendix: math. peculiarities

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