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fagan(Ben Adarkwa Dwamena)-------------------------------------------------------------------------------

Fagan's bayesian nomogram

Syntax

faganvarlist[ifexp] [inrange] [,{options} *]

Description

fagancreates a plot showing the relationship between the prior probability specified by user over the range 0-1, the likelihood ratio(combination of sensitivity and specificity), and posterior test probability.faganplots an axis on the left with the prior log-odds, an axis in the middle representing the log likelihood ratio and an axis on the right representing the posterior log-odds. Lines are then drawn from the prior probability on the left through the likelihood ratios in the center and extended to the posterior probabilities on the right.

faganrequires a varlist of likelihood ratios positive and negative respectively i.e two or more sets of likelihood ratios.

Options#previs the prior or pretest probability of diseasegrpvar()subgroup variable namelegendopts(#)specify options that affect the plot legend.ysize()andxsize()specify the height and width of plot respectively.

RemarksThe clinical or patient-relevant utility of diagnostic test is evaluated using the likelihood ratios to calculate post-test probability based on Bayes' theorem as follows: Pretest Probability=Prevalence of target condition Post-test probability= likelihood ratio x pretest probability/[(1-pretest probability) x (1-likelihood ratio)]

Assuming that the study samples are representative of the entire population, an estimate of the pretest probability of target condition is calculated from the global prevalence of this disorder across the studies. In this way, likelihood ratios are more clinically meaningful than sensitivities or specificities. This approach would be useful for the clinicians who might use the likelihood ratios generated from here to calculate the post-test probabilities of nodal disease based on the prevalence rates of their own practice population.

Thus, this approach permits individualization of diagnostic evidence. This concept is depicted visually with Fagan's nomograms. When Bayes theorem is expressed in terms of log-odds, the posterior log-odds are linear functions of the prior log-odds and the log likelihood ratios.

The farther the likelihood ratio is from 1, the larger the change will be from the pretest to the posttest probability. One can group likelihood ratios into magnitudes: LR+ > 10 makes large and often conclusive increases in the likelihood of disease LR+ 5-10 makes moderate increases LR+ 2-5 makes small increases LR+ 1-2 makes insignificant increases LR- 0.5-1.0 makes insignificant decreases LR- 0.2-0.5 makes small decreases LR- 0.1-0.2 makes moderate decreases LR- < 0.1 makes large and often conclusive decreases in the likelihood of disease

Examples. use fagan.dta, clear

. fagan lrp lrn, grpvar(test)

. fagan lrp lrn, grpvar(test) pr(0.5)

. fagan lrp lrn, grpvar(test) pr(0.5) scheme(s2color)

AuthorBen A Dwamena, Division of Nuclear Medicine, Department of Radiology, University of Michigan Medical School, Ann Arbor, Michigan. Email bdwamena@umich.edu

Related commands:See Alsofagani (if installed)