Function for the determination of a grey zone for ordinal diagnostic and screening tests
greyzone(
ref,
test,
pretest.prob = NULL,
criterion.values = c(0.05, 0.95),
return.all = F,
precision = 3
)The reference standard. A column in a data frame or a vector indicating the reference or gold standard. The reference standard must be coded either as 0 (absence of the condition) or 1 (presence of the condition).
The numeric test scores under evaluation. When
mean(test[ref == 0]) > mean(test[ref == 1]) it is assumed that
higher test scores indicate presence of the condition, otherwise that lower
test scores indicate presence of the condition.
The pre-test probability to be used. When NULL, the prevalence found in the sample is used.
The minimum desired values for respectively the negative and positive post-test probability.
Default = FALSE. When TRUE the full table of all results are returned.
Default = 3. Precision used for comparison of the criterion values and the post-test probabilities.
The function returns the lower and upper value of the range of test scores that are considered 'grey' or inconclusive. Only smaller or larger values are considered for a decision. When return.all = TRUE the full table of the results is returned.
This function is proposed by Coste et al. (2003). The current implementation only handles ordinal test values. This functions uses all possible test scores as dichotomous thresholds to calculate Se, Sp, positive and negative likelihood ratios and post-test probabilities. The likelihood ratios are calculated for the accumulated densities of the test scores and indicate the levels of seriousness of the disease for all possible dichotomous thresholds. It uses therefore a cumulative interpretation of the Likelihood Ratios and posttest probabilities. If a test has test scores 1 to 5 (with 5 indicating the largest probability of the disease), Se, positive LR and positive posttest probabilities of the greyzone function uses dichotomous thresholds that concern test results >= 1, >= 2, >= 3, >= 4 and >= 5, while Sp, negative LR and negative posttest probabilities concern test results <= 1, <= 2, <= 3, <= 4 and <= 5. Please note that in these examples values <= 1 respectively <= 5 concern all possible test values and have by definition a dichotomous Sensitivity of 1.
Please note that the definition of a grey zone deviates from the definition of an uncertain interval.
The decision criteria are the required values of post-test probabilities. This has changed in version 0.7. In earlier versions the criteria was a value closest to the criterion, which could produce invalid results. These post-test probabilities of accumulated test scores may require a value over 0.99 or even 0.999 (or under 0.01 or 0.001) to confirm or exclude the presence of a target disease. Only tests of the highest quality can reach such criteria. The default criterion values are .05 and .95 for respectively a negative and positive classification, which may be sufficient for use by clinicians or Public Health professionals for a first classification whether a target disease may be present or not (Coste et al., 2003).
As such the cumulative likelihood ratios differ from the Interval
Likelihood Ratios (see RPV), as proposed by Sonis (1999).
These likelihood ratios are calculated for each given interval of test
scores separately and uses their densities. In contrast to the greyzone
method, Interval Likelihood ratios and interval posttest probabilities
concern the separate intervals, that is in this example, the separate score
1 to 5. Interval likelihood ratios assign a specific value to each level of
abnormality, and this value is used to calculate the posttest probabilities
of disease for each given level of a test (Sonis, 1999). These post-test
probabilities differ strongly from the cumulative post-test probabilities
and criterion values can be much lower, especially when diseases are life
threatening and low-cost treatments are available. See Sonis (1999) for
further discussion of the interval interpretation.
Coste, J., Jourdain, P., & Pouchot, J. (2006). A gray zone assigned to inconclusive results of quantitative diagnostic tests: application to the use of brain natriuretic peptide for diagnosis of heart failure in acute dyspneic patients. Clinical Chemistry, 52(12), 2229-2235.
Coste, J., & Pouchot, J. (2003). A grey zone for quantitative diagnostic and screening tests. International Journal of Epidemiology, 32(2), 304-313.
Sonis, J. (1999). How to use and interpret interval likelihood ratios. Family Medicine, 31, 432-437.
# NOT RUN {
ref=c(rep(0, 250), rep(1, 250))
test = c(rep(1:5, c(90,75,50,34,1)), c(rep(1:5, c(10,25,50,65,100))))
addmargins(table(ref, test))
greyzone(ref, test, ret=TRUE, criterion.values=c(.1, .9))
test = c(rep(14:31, c(0,0,0,0,0,0,3,3,5,7,10,20,30,40,50,24,10,10)),
rep(14:31, c(1,0,0,0,0,0,1,4,4,9, 6,13, 8, 6, 5, 4, 0, 0)))
ref = c(rep(0, 212), rep(1, 61))
barplotMD(ref, test)
addmargins(table(ref, test))
greyzone(ref, test, ret=TRUE, crit=c(.1,.9))
# }
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