Continuous Likelihood Ratios Research Articles

Diagnosis of peanut allergy using continuous likelihood ratios

BackgroundPeanut 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. ObjectiveTo 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. MethodsThe 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. ResultssIgE 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. ConclusionWhen 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.

CONTINUOUS LIKELIHOOD RATIOS TO PREDICT THE PROBABILITY OF A PEANUT REACTION

Introduction Peanut-specific IgE (PsIgE) is used to predict the probability of a reaction using likelihood ratios (LR) which convert pretest to posttest probabilities. While dichotomous (positive or negative) LRs are defined using a cutoff of 0.35, it is better to use a continuous LR which corresponds to each value of PsIgE. This is particularly important when there is only a PsIgE and no history of prior ingestion to rely on. Methods PsIgEs were measured and oral peanut challenges performed on 58 children ages 9 months to 18 years. An ROC curve was determined using SPSS. The slope of the ROC curve, which is the likelihood ratio for each value of PsIgE, was determined by differentiated the ROC curve and used to convert sIgEs to likelood ratios. Results PsIgE ranged from 0 to 23. There were 33 negative and 25 positive oral challenges. The area under the ROC curve was 0.71 (p Conclusions Continuous LRs can provide a more accurate assessment of the probability of a peanut reaction for a given sIgE when the history of peanut ingestion is not known. Additional data points will refine these estimates.

Bayesian analysis using continuous likelihood ratios for identifying pleural exudates

To ascertain if equations that calculate continuous likelihood ratios (CLRs) for pleural exudates improve pleural fluid categorization, especially when false positive or false negative test results are obtained by using Light's criteria. Retrospective review of the clinical and pleural fluid data from a consecutive series of patients with pleural effusion who underwent thoracentesis at the University Hospital Arnau de Vilanova (Lleida, Spain) over an 11-year period. A total of 1490 patients with pleural effusion (298 transudates and 1192 exudates) were recruited into the study. The presence of a transudate or exudate was established by clinical judgment. We examined the comparative diagnostic accuracy of 4 tests (i.e. pleural fluid protein and lactate dehydrogenase (LDH), and pleural fluid to serum protein and LDH ratios) for discriminating between transudates and exudates. Decision thresholds were determined by receiver operating characteristics (ROC) analysis. Equations for calculating CLRs derived from a logistic regression analysis based on a previously described method. Individual pleural fluid tests did not differ in their diagnostic accuracies according to ROC analysis. We calculated CLRs for the elements of Light's criteria and pleural fluid protein, and also illustrated the sequential use of CLRs for determining posttest probabilities. Overall, CLR formulas had marginal performance for the correct categorization of pleural fluid. CLRs provide a probabilistic statement as to the likelihood an effusion is a transudate or exudate. However, clinical judgment is little changed by the application of CLRs, and in doubtful cases a great amount of uncertainty remains. This Bayesian approach is likely to have no major impact on the clinical practice.

Multilevel and Continuous Pleural Fluid pH Likelihood Ratios for Draining Parapneumonic Effusions

Background: Although clinical practice guidelines endorse the use of pleural fluid pH to select patients with parapneumonic effusions for pleural drainage, no studies have reported likelihood ratios for pleural fluid pH. Objectives: We derived and tested the value of continuous likelihood ratios for selecting pneumonia patients for pleural drainage. Methods: Patient level pleural fluid pH results were obtained from a registry of primary studies that assessed the discriminative properties of pH. Multilevel likelihood ratios were calculated for four pH intervals. Continuous likelihood ratios were derived from logistic regression using discrete pH values. Binary, multilevel and continuous likelihood ratios were compared to evaluate the statistical (χ²) and clinical advantages of continuous likelihood ratios. Results: Hundred and ninety-seven pleural fluid pH results were retrieved from published reports and categorized into four pH ordinal intervals. Multilevel likelihood ratios ranged from a low of 0.13 (95% CI, 0.04–0.41) for pH values >7.40 to a high of 15.80 (95% CI, 7.04–35.45) for pH values ≤7.00. Logistic regression derived the following equation for continuous likelihood ratios: exp[–7.168(measured pH – 7.207)]. Continuous likelihood ratios offered more diagnostic information both statistically (p < 0.005) and clinically compared with binary and multilevel likelihood ratios. Conclusions: Analysis of a patient registry allows the derivation of an exponential equation that calculates continuous likelihood ratios for discrete pleural fluid pH values. Continuous likelihood ratios provide more clinically and statistically significant information compared with binary and multilevel likelihood ratios for calculating posttest probabilities of the need to drain parapneumonic effusions.

A meta-analysis derivation of continuous likelihood ratios for diagnosing pleural fluid exudates.

In evaluating pleural effusions, clinicians perform thoraceninstance, recommend measuring pleural fluid-to-serum albumin gradients when patients with congestive heart failure have tesis and pleural fluid analysis most often by Light’s criteria to establish the exudative or transudative nature of the effuan exudative effusion by Light’s criteria (7). A Bayesian approach addresses these limitations of binary sion (1). Light’s criteria (2) dichotomize effusions into exudative or transudative categories with the use of three pleural testing strategies (10). Rather than diagnosing the presence or absence of a condition, a Bayesian strategy uses test results test criteria: pleural fluid-to-serum protein ratio, pleural fluid lactate dehydrogenase (LDH) concentration, and pleural fluidto generate likelihood ratios that increase or decrease a clinician’s pretest estimate of the probability of disease. Likelito-serum LDH ratio. Several other pleural fluid test criteria have similar diagnostic accuracies as compared with each of hood ratios represent the likelihood that a positive test result would be found in a patient with as opposed to without the individual tests within Light’s criteria (3). These criteria include pleural fluid cholesterol, pleural fluid-to-serum cholesdisease (10). Likelihood ratios are usually calculated using a single test result cutoff point. These binary likelihood ratios terol ratio, pleural fluid protein, and pleural fluid-to-serum have values above 1 for test results that increase the likelialbumin gradient. All of these tests dichotomize effusions into hood of an exudative effusion and values below 1 that deexudative or transudative categories by determining whether crease the likelihood. We previously published multilevel the test results are above or below a single cutoff point. likelihood ratios for pleural fluid test criteria commonly used Problems exist, however, with these pleural fluid test criteria to diagnose exudative pleural effusions (11). Multilevel likelias commonly used in clinical practice. First, dichotomizing hood ratios are calculated by using two or more cutoff points effusions into exudates and transudates by using a single for the range of possible test results. These multiple cutoff cutoff point loses much of the information contained in pleupoints demarcate test result intervals that are each associated ral fluid tests, which generate continuous numeric results (4). with a different likelihood that the patient has an exudative Test results just beyond and those extremely beyond a cutoff effusion. Although breaking up continuous test result values point are treated the same in that both establish the presence into ordinal intervals with multiple cutoff points improves of an exudative effusion. This binary diagnostic strategy exdiagnostic precision as compared with using a single cutoff plains why Light’s criteria frequently misclassify as exudates point, they only provide an average value for the range of the pleural effusions associated with congestive heart failure likelihood ratios that exist within each of the test result inter(5–7), which usually have borderline pleural fluid test results vals (4). A more precise diagnostic approach would calculate when in the exudative range. It also contributes to the misclassian exact likelihood ratio for each possible discrete pleural fluid fication that occurs in 1 to 10% of patients with malignant test result. Such discrete likelihood ratios are called continuous pleural effusions who appear to have transudative effusions likelihood ratios (12). Methods for calculating continuous likeby Light’s criteria (8). Second, combining two or more tests lihood ratios have been reported for very few conditions. using a single cutoff point for each test, as done by Light’s In this study, we analyze with logistic regression a multicencriteria, increases sensitivity but decreases specificity because ter registry of pleural fluid test values from patients with estabonly one of the tests needs to be positive to define an exudative lished diagnoses to derive equations that calculate continuous effusion (9). Finally, the lower specificity caused by combining likelihood ratios for pleural fluid test criteria for exudative several criteria encourages physicians to commonly order addieffusions. We also compare continuous likelihood ratios with tional—and usually unnecessary—pleural fluid tests when inimultilevel and binary likelihood ratios to determine whether tial test results do not fit clinical circumstances. Experts, for continuous likelihood ratios provide statistically significant and clinically important advantages.

Multilevel and Continuous Pleural Fluid pH Likelihood Ratios for Evaluating Malignant Pleural Effusions

Expert consensus recommends testing pleural fluid for pH to assist the selection of patients with malignant pleural effusions for pleurodesis. Although published studies report an association between pleural fluid pH and patient outcomes after pleurodesis, clinicians have no definitive information on how to use pH to select patients for pleurodesis. Thus, we quantitatively assessed different methods for deriving likelihood ratios from pleural fluid pH and evaluated the potential role of pH in selecting patients for pleurodesis. MEDLINE, systematic reviews, article reference lists, and contact with primary authors. Studies that assessed the impact of pleural fluid pH on survival and pleurodesis failure rates among patients with malignant pleural effusions. Primary authors provided their data in electronic spreadsheets. Retrieved data sets included survival and pleurodesis failure rates for 417 patients and 433 patients, respectively. Binary, multilevel, and continuous likelihood ratios were calculated to estimate the likelihood of death within 3 months of pleurodesis or pleurodesis failure rates. Values for the likelihood ratios were compared for each of the three strategies, and relative clinical and statistical significance were assessed. Pleural fluid pH had marginal performance for identifying patients with < 3-month anticipated survival; binary likelihood ratios provided as much information as the multilevel and continuous strategies. Likelihood ratios for identifying patients likely to fail pleurodesis were clinically useful. Continuous likelihood ratios provided statistically more information as compared with the multilevel and binary strategies. Pleural fluid pH has marginal value for estimating death within 3 months of pleurodesis, and binary likelihood ratios (cut point </= 7.20) perform as well as the other strategies assessed. Pleural fluid pH provides more useful information for estimating the likelihood of pleurodesis failure for which continuous likelihood ratios provide the most information as compared with binary or multilevel likelihood ratios.

Likelihood ratios for continuous test results—making the clinicians' job easier or harder?

Clinicians' paradigms for considering diagnostic test results require decisions based on the actual test value. However, when the test result is reported on a continuous scale each possible outcome may not result in unique actions. To simplify decision making, clinicians often break down the continuous scale into dichotomous or ordered outcomes. Likelihood ratios, reported with the test outcome, help summarize the impact of diagnostic tests. Although commonly applied to dichotomous outcomes, likelihood ratios can also be applied to ordinal or continuous results. This application allows investigators to consider the effect of clinically simplifying continuous data into dichotomous or ordinal categories. The parameters of a simple logistic regression equation summarize continuous likelihood ratios, evaluate covariates, generate likelihood ratio lines, and help assess the statistical significance of more complex models. Having visually inspected likelihood ratio lines and considered statistical differences, the investigator should choose the test report format that best accounts the realities driving clinical decisions.