Likelihood ratios of quantitative laboratory results in medical diagnosis: The application of Bézier curves in ROC analysis

Likelihood Ratios as Value Proposition for Diagnostic Laboratory Tests

The clinical and health economic value of clinical laboratory diagnostics has been debated increasingly in recent years without resulting in practical recommendations for measuring the effectiveness of diagnostic tests. One way to achieve such a goal could be to enrich the mere data of laboratory test results with additional information about their likelihood ratios for diagnosis. The diagnostic significance of test results can be judged subjectively based on the experience of the treating physician or expressed objectively in the form of likelihood ratios. The provision of likelihood ratios by the laboratory would increase the impact of laboratory diagnostics in healthcare and thus have positive economic value. Consequently, likelihood ratios should be taken into account in reimbursement strategies.

Diagnosis of peanut allergy using continuous likelihood ratios

BACKGROUND

Peanut allergy (PA) is associated with an economic and psychological burden on patients and families. Its diagnosis includes tests for peanut specific immunoglobulin E (sIgE), the values of which usually are categorized as positive or negative using a predefined cutoff (usually 0.35 kU/L). With the use of Bayes' theorem, this categorization can be replaced with a continuous interpretation of sIgE, which accounts for the prevalence of PA and history of ingestion.

OBJECTIVE

To evaluate a method for estimating the likelihood ratio (LR) for each value of sIgE by performing a pilot investigation with the results of oral food challenges. The LR could be used to estimate the probability of PA.

METHODS

The outcomes of oral food challenges and serum IgE values from 117 children seen in an allergy clinic between January 2017 and November 2019 were obtained. Polynomial regression of the receiver operation characteristics curve was used to determine an LR for each value of sIgE. Linear regression was used to estimate an LR for each value of sIgE.

RESULTS

sIgE ranged from less than 0.1 kU/L to 35 kU/L. Bayes' theorem and a receiver operation characteristics curve were used to estimate LRs for each value of peanut sIgE. The value of IgE associated with an LR of 1 was 0.22 kU/L, which is comparable to other studies that used a value of 0.35 kU/L to separate positive from negative results.

CONCLUSION

When combined with estimates of pretest probability, this method should permit the development of computerized decision-making algorithms to estimate the probability that a patient has PA.

A simplified method to approximate a ROC curve with a Bézier curve to calculate likelihood ratios of quantitative test results

In order to calculate likeli hood ratios (LR) values for quantitative test results, a distribution-independent algorithm based on Bézier curves is proposed. Receiver operating characteristic (ROC) analysis provides the LR as the slope of the tangent to the ROC curve at the point corresponding to the test result.

• Here, we make use of cubic Bézier curves defined by Bernstein polynomials of degree 3.

• A simplified method to adjust a Bézier curve to a ROC curve is presented

• The crucial advantage of this procedure is that Bézier curves are constructed by tangents to the ROC curve, whose slopes immediately provide the LR of a specific point on the curve.

The perspective on standardisation and harmonisation: the viewpoint of the EASI president

Standardisation of immuno-assays for autoantibodies is a major challenge. Although multiple organisations participate in the generation of internationally accepted standards, adequate standardisation of assays has not yet been achieved. Harmonisation may offer an alternative approach to better align requesting, testing, reporting and interpretation of autoimmune diagnostics. The European Autoimmunity Standardisation Initiative (EASI) was founded to facilitate both standardisation as well as harmonisation of autoantibody tests, but over the years the focus has drifted away from standardisation in favour of harmonisation. In the current paper the options for harmonisation are highlighted.

The likelihood ratio and its graphical representation

Diagnostic tests are important clinical tools. Bayes’ theorem and Bayesian approach are important methods for interpreting test results. The Bayesian factor, the so-called likelihood ratio, has not always been well-understood. In this article, we try to discuss the likelihood ratio and its value for a specific test result, a positive or negative test result, and a range of test results, along with their graphical representations.

Application of Bézier Curves for Calculating Likelihood Ratios for Plasma Amyloid-β Biomarkers for Alzheimer's Disease

Introduction: Alzheimer's disease, being the most frequent cause of dementia in elderly people, still is difficult to diagnose and to predict its occurrence. The clinical application of biomarkers for diagnosis of Alzheimer's disease has been restricted so far to the analysis of proteins in the cerebrospinal fluid like amyloid β₁₋₄₂ and p-tau. However, in a recently published nature letter it has been shown that the high-performance measurement of amyloid-β in plasma alone could provide a method well suited for a broad clinical application. The study uses ROC analysis to evaluate the clinical significance of the method but it does not provide likelihood ratios (LR) of the measured results.

Methods: In this article, a newly developed method is used to calculate LRs for any measurement result of a study by approximation of the ROC curves using Bézier curves. Such LRs provide an estimation of the clinical significance of any particular test result by applying Bayes' theorem: Pretest odds for disease multiplied by the LR of the test result give the posttest odds.

Results: The application of the Bézier curve approximation to the data of the plasma amyloid-β study is demonstrated. To generalize the calculation of LRs for all test results, a relation between the test results and the points on the Bézier curve with their LRs is established.

Discussion: The application of Bézier curves in ROC analysis allows calculating LRs for all individual test results when measuring amyloid-β biomarkers for Alzheimer's disease.