see also:

• Medical statistical analysis;
• journal club;
• study designs

mathematical risk = when we don’t know what the outcome is, but we do know the distribution of the outcomes

mathematical uncertainty = when we don’t know what the outcome is, and we don’t know the distribution of outcomes

David Newman's lecture - "Health Care's Most Critical Reform: The Doctor" - highlighting how the medical profession continues with disproven and even harmful therapies - a must watch for all clinicians

• is this test relevant to my practice?

• was there an independent, blind comparison with a reference (“gold”) standard?
• was the diagnostic test evaluated in an appropriate spectrum of patients (like those to whom it would be offered in practice)?
• was the reference standard applied regardless of the result?

• what were the results?
  • see below for sensitivity, specificity, etc.
• how precise were the results?
  • were the results expressed with a range or confidence interval?
• were likelihood ratios presented or data provided to calculate them?

• will the test be available, affordable, accurate & reliable in my setting?
• if the test is not available, are there sufficient details to enable it to be replicated?
• can you generate a clinically sensible estimate of your patient's pre-test probability?
• will the resulting post-test probabilities affect your management & help your patient?
• would the consequences of this test help your patient?

• For each diagnostic test, we need to know the following characteristics:

• ie. % of all +ve cases picked up by the test
• ie. 100 - (% false negatives);
• thus, = (case positives + test positives) x 100 / (case positives)
• ie. = true positives x 100/ case positives

• ie. % of all +ve tests that were case +ve;
• ie. 100 - (% false positive);
• thus, = (case negatives + test negatives) x 100 / (case negatives);
• ie = true negatives x 100 / case negatives
• NB. in determining the cut-off point in a test, there is always a trade off between sensitivity & specificity (see below);

• ie. chance of a +ve test reflecting true presence of dis.;
• ie. (case positives + test positives) x 100 / (test positives)
• ie. a / (a + b)
• or using sensitivities (s), specificity (sp) and pre-test probability of disease (y) in percentages:
  • = (s x y/100) / [(s x y/100)+(100-y)-(sp(100-y)/100)]

• ie. chance of a -ve test reflecting true absence of dis.;
• ie. (case negatives + test negatives) x 100 / (test negatives);
• ie. d / (c + d)
• or using sensitivities (s), specificity (sp) and pre-test probability of disease (y) in percentages:
  • = [(sp(100-y)/100] / [(y-(s x y/100)) + (sp(100-y)/100)]

• because they are based on a ratio of sensitivity & specificity they do not vary in different populations and settings
• they can be used directly at the individual patient level to determine a post-test probability based on a pre-test probability
• Worster, A. Carpenter, CR. A Brief Note on Likelihood Ratios Canadian Journal of Emergency Medicine, 2008 September;10(5) 441-442

• This nomogram can also be used to determine the range of pre-test probabilities between which performance of the test may be useful, below which, wait & see is best, & above which, immediate treatment may be warranted. To use this need to know the threshold of post-test probability of disease at which you will decide to treat the disease;
• Nomogram for using Likelihood Ratios (LRs) to convert pre-test probabilities into post-test probabilities for diagnostic test results with a known LR
• Drag the blue arrows to the values you have for your patient's pre-test probability (%) and the test result's LR, and read off the post test probability from the red arrow on the right.

• = probability of +ve test in those with disease / probability of +ve test in those without disease
• ie. true positive rate / false positive rate
• ie. = (a/[a+c]) / (b/[b+d])
• ie. = sensitivity / (1 - specificity)
• thus stress ECG for IHD with sens.71% spec.73% has LR+ of 2.6 and LR- of 0.4
• for CT-PA for PE, assuming sens 80% & spec. 90% then has LR+ of 8 and LR- of 0.2

• = probability of -ve test in those with disease / probability of -ve test in those without disease
• = false negative rate / true negative rate
• = (a/[a+c]) / (b/[b+d])
• = (1- sensitivity) / specificity

• Will a +ve result increase our pretest prob. of disease presence significantly or will a neg. result increase our pre-test prob. of absence significantly?
• Would we prefer to over-treat rather than under-treat?
  • eg. if we know a pt with “typical” ischaemic PIC has 90% likelihood of having CAD, then performing a stress ECG test (eg. sens.71% spec.73%) on this pt. may not significantly increase our diagnostic accuracy to change our management:
    • ie. stress ECG +ve → PPV 96% → likely to have CAD;
    • -ve → NPV 21% → no CAD unlikely!!
    • however, if we had not known the pre-test prob .of disease (90%), then +ve result would have helped but a -ve result would not have helped!
• THUS we need to have an idea of pre-test probability of the presence of disease as well to interpret the result.

• availability of, & time duration to perform test;
• cost of test;
• invasiveness of test & possible complications;

• see first, do no harm

• Aust Presc 2008 - Interpreting risks and ratios in therapy trials