ui.binormal: Function for the determination of the thresholds of an...

In UncertainInterval: Uncertain Interval Methods for Three-Way Cut-Point Determination in Test Results

Description

Function for the determination of the thresholds of an uncertain interval for bi-normal distributed test scores that are considered as inconclusive.

Usage

ui.binormal(
  ref,
  test,
  UI.Se = 0.55,
  UI.Sp = 0.55,
  intersection = NULL,
  start = NULL,
  print.level = 0
)

Arguments

ref	The reference standard. A column in a data frame or a vector indicating the classification by the reference test. The reference standard must be coded either as 0 (absence of the condition) or 1 (presence of the condition).
test	The index test or test under evaluation. A column in a dataset or vector indicating the test results in a continuous scale.
UI.Se	(default = .55). Desired sensitivity of the test scores within the uncertain interval. A value <= .5 is not allowed.
UI.Sp	(default = .55). Desired specificity of the test scores within the uncertain interval. A value <= .5 is not allowed.
intersection	Default NULL. If not null, the supplied value is used as the estimate of the intersection of the two bi-normal distributions. Otherwise, it is calculated using the function get.intersection.
start	Default NULL. If not null, the first two values of the supplied vector are used as the starting values for the nloptr optimization function.
print.level	Default is 0. The option print_level controls how much output is shown during the optimization process. Possible values: 0) (default) no output; 1) show iteration number and value of objective function; 2) 1 + show value of (in)equalities; 3) 2 + show value of controls.

Details

This function can be used for a test with bi-normal distributed scores. The Uncertain Interval is generally defined as an interval below and above the intersection, where the densities of the two distributions of patients with and without the targeted condition are about equal. These test scores are considered as inconclusive for the decision for or against the targeted condition. This function uses for the definition of the uncertain interval a sensitivity and specificity of the uncertain test scores below a desired value (default .55).

Only a single intersection is assumed (or a second intersection where the overlap is negligible). If another intersection exists and the overlap around this intersection is considerable, the test with such a non-negligible overlap is problematic and difficult to apply and interpret.

In general, when estimating decision thresholds, a sample of sufficient size should be used. It is recommended to use at least a sample of 100 patients with the targeted condition, and a 'healthy' sample (without the targeted condition) of the same size or larger.

The function uses an optimization algorithm from the nlopt library (https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/): the sequential quadratic programming (SQP) algorithm for nonlinearly constrained gradient-based optimization (supporting both inequality and equality constraints), based on the implementation by Dieter Kraft (1988; 1944).

Value

List of values:

$status:

Integer value with the status of the optimization (0 is success).

$message:

More informative message with the status of the optimization

$results:

Vector with the following values:

• exp.UI.Sp: The population value of the specificity in the Uncertain Interval, given mu0, sd0, mu1 and sd1. This value should be very near the supplied value of Sp.

• exp.UI.Se: The population value of the sensitivity in the Uncertain Interval, given mu0, sd0, mu1 and sd1. This value should be very near the supplied value of UI.Se.

• mu0: The value that has been supplied for mu0.

• sd0: The value that has been supplied for sd0.

• mu1: The value that has been supplied for mu1.

• sd1: The value that has been supplied for sd1.

$solution:

Vector with the following values:

• L: The population value of the lower threshold of the Uncertain Interval.

• U: The population value of the upper threshold of the Uncertain Interval.

References

Dieter Kraft, "A software package for sequential quadratic programming", Technical Report DFVLR-FB 88-28, Institut für Dynamik der Flugsysteme, Oberpfaffenhofen, July 1988.

Dieter Kraft, "Algorithm 733: TOMP–Fortran modules for optimal control calculations," ACM Transactions on Mathematical Software, vol. 20, no. 3, pp. 262-281 (1994).

Landsheer, J. A. (2018). The Clinical Relevance of Methods for Handling Inconclusive Medical Test Results: Quantification of Uncertainty in Medical Decision-Making and Screening. Diagnostics, 8(2), 32. https://doi.org/10.3390/diagnostics8020032

Examples

test=c(rnorm(500,0,1), rnorm(500,1.6,1))
ref=c(rep(0,500), rep(1,500))
plotMD(ref, test, model='binormal')
ui.binormal(ref, test)
# test scores controls > patients works correctly from version 0.7 or higher
ui.binormal(ref, -test) 
ref=c(rep(1,500), rep(0,500))
plotMD(ref, test, model='binormal')
ui.binormal(ref, test) 

UncertainInterval documentation built on March 3, 2021, 1:10 a.m.