{"id":898,"date":"2014-03-23T20:30:43","date_gmt":"2014-03-23T19:30:43","guid":{"rendered":"https:\/\/blogs.bmj.com\/adc\/?p=898"},"modified":"2014-09-12T11:44:42","modified_gmt":"2014-09-12T10:44:42","slug":"gambling-alcohol-and-division","status":"publish","type":"post","link":"https:\/\/blogs.bmj.com\/adc\/2014\/03\/23\/gambling-alcohol-and-division\/","title":{"rendered":"Gambling, alcohol and division."},"content":{"rendered":"

\"\"No, not an average afternoon at the Houses of Parliament, but another in our diagnostics series.
\n<\/span><\/p>\n

Moving yourself from looking at the predictive values of the tests as evaluated, to taking this information but using it in the situation you face, is a case of Bayesian mathematics.
\n<\/span><\/p>\n

Which sounds hard.
\n<\/span><\/p>\n

But its absolutely what you do. Take a serum potassium of 7.8 in a baby who you struggled +++ to get some blood out of, every drop taking minutes to leak from its squealing heel. You may re-test, but you’re unlikely to call ICU on hearing it.
\n<\/span><\/p>\n

What if that same value came back from the central line sample from a child on peritoneal dialysis who presented with vague abdominal pain?
\n<\/span><\/p>\n

There is a different ‘pre-test probability’ \u2013 expectation \u2013 associated with different clinical settings. The same result has a different ‘meaning’ \u2013 chance of being real \u2013 in different settings. However, sensitivity and specificity don’t change lots across different clinically relevant pre-test probability values. And this leads to the ability to use them to move from a known\/estimated pre-test probability of disease, to a post-test value. This needs the use of the likelihood ratio (LR) and, most often, a nomogram.
\n<\/span><\/p>\n

<\/p>\n

\"\"
\n<\/span><\/p>\n

(Fagins nomogram; from http:\/\/www.kardiolab.ch\/<\/a> )
\n<\/span><\/p>\n

With a ruler, you go from your pre-test probability, through the LR in the centre, to read your post-test probability.
\n<\/span><\/p>\n

Likelihood ratios are calculated :
\n<\/span><\/p>\n

Likelihood of finding this result with disease \/ Likelihood of finding this result without disease
\n<\/span><\/p>\n

\n\n\n\n\n\n
\u00a0<\/span><\/td>\nReally diseased\u00a0<\/span><\/td>\nReally not diseased\u00a0<\/span><\/td>\n<\/tr>\n
Test +ve\u00a0<\/span><\/td>\nA\u00a0<\/span><\/td>\nB\u00a0<\/span><\/td>\n<\/tr>\n
Test -ve\u00a0<\/span><\/td>\nC\u00a0<\/span><\/td>\nD\u00a0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

 <\/p>\n

So LR for Test+ is :
\n<\/span><\/p>\n

Likelihood of finding this result with disease [A\/(A+C)] \/ Likelihood of finding this result without disease [B\/(B+D)]
\n<\/span><\/p>\n

And LR for Test- is :
\n<\/span><\/p>\n

Likelihood of finding this result with disease [C\/(A+C)] \/ Likelihood of finding this result without disease [D\/(B+D)]
\n<\/span><\/p>\n

 <\/p>\n

Now this also extends to multi-level tests:
\n<\/span><\/p>\n

\n\n\n\n\n\n\n
\u00a0<\/span><\/td>\nReally diseased\u00a0<\/span><\/td>\nReally not diseased\u00a0<\/span><\/td>\n<\/tr>\n
[Rh] >100\u00a0<\/span><\/td>\nA\u00a0<\/span><\/td>\nB\u00a0<\/span><\/td>\n<\/tr>\n
[Rh]50-99<\/span><\/td>\nC\u00a0<\/span><\/td>\nD\u00a0<\/span><\/td>\n<\/tr>\n
[Rh] <50<\/span><\/td>\nE<\/span><\/td>\nF<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

 <\/p>\n

The LR for serum rhubarb >100 is:
\n<\/span><\/p>\n

Likelihood of finding this result with disease [A\/(A+C+E)] \/ Likelihood of finding this result without disease [B\/(B+D+F)]
\n<\/span><\/p>\n

For [Rh] 50-99
\n<\/span><\/p>\n

Likelihood of finding this result with disease [C\/(A+C+E)] \/ Likelihood of finding this result without disease [D\/(B+D+F)]
\n<\/span><\/p>\n

Etc etc…
\n<\/span><\/p>\n

 <\/p>\n

Armed with this, the ability to convert your diagnostic test numbers into something meaningful should become clinically clear.
\n<\/span><\/p>\n