A Perspective on Standardizing the Predictive Power of Noninvasive Cardiovascular Tests by Likelihood Ratio Computation: 1. Mathematical Principles
Section snippets
Defining Predictive Value In Terms Of Posttest Characteristics
By current conventions, the predictive power of a noninvasive cardiovascular test result is determined by analysis of a representative patient group that is referred for definitive diagnostic evaluation termed an index population2,3,4 The occurrence of disease in the index population is determined by an independently established diagnostic standard such as coronary angiography. The prevalence of disease (PD) is the proportion of the index population expressed as the percentage that has
Defining Predictive Value In Terms Of Sensitivity, Specificity, And Disease Prevalence
The sensitivity and specificity of a test and their complements are termed test performance indices and can be defined on the basis of the posttest characteristics (Figure 2, column 1). The sensitivity (Se) of a test is the quotient of true positives divided by the sum of true positives and false negatives. The complement of sensitivity (1 - Se) is the quotient of false negatives divided by the sum of true positives and false negatives. The specificity (Sp) of a test is the quotient of true
Limitations In Predictive Value Estimates
(3a), (3b) provide a background for analysis of the limitations of the (+)PVd and (-)PVn as measures of the relative power of 2 or more diagnostic tests. Such an analysis will be applied to a comparison of the predictive power of 2 commonly applied noninvasive diagnostic tests for coronary artery disease (CAD), the exercise electrocardiogram (Ex ECG) and the planar exercise thallium scintigram (Ex TI). The sensitivity and specificity levels for this illustration are derived from a meta-analysis
Limitations In Citation Of Sensitivity And Specificity As Measures Of Test Power
In considering the factors in equations (3a) and (3b), it is evident that the predictive power of a positive test result (rule-in power), as expressed in the relationship of (+)PV d to PD, resides in the Se and (1 - Sp), while the predictive power of a negative test result (rule-out power), as expressed in the relationship (-)PVn to PN, resides in the Sp and (1 - Se). Hence, any estimate of positive test power based on the test performance indices must include the Se and (1 - Sp), while any
The Likelihood Ratio As A Composite Measure Of The Predictive Power Of Positive And Negative Test Results
A simplified and easily comprehended expression of the positive and negative predictive power of a noninvasive test is uncovered when sensitivity, specificity, and their complements in equations (3a) and (3b) are consolidated, yielding the following equations:
Considering that the PN term in (4a) is equivalent to (100 - PD) and that the PD term in (4b) is equivalent to (100 - PN), it is apparent that the quotient (Se/1 - Sp)
The Likelihood Ratio As A Probability Odds Measure
A fundamental quality of the likelihood ratio as a measure of predictive power is elucidated when the units of the predictive value equations (6a) and (6b) are converted from a percentage to an odds form (Appendix 3). Conversion to odds: 1 is accomplished by dividing a given percentage in the range 0.0 to <100% by its 100% complement as follows: Odds: 1 = (Percent/100-Percent).)
For a decimal in the range 0.0 to <1.0, conversion to odds: 1 is accomplished by dividing the decimal by its
Estimating The Predictive Power For Combined Test Results
The likelihood ratios provide a convenient means for estimating the power of multiple tests, applied to a common index population. Such an estimate of test power for combined test results is referred to as an effective likelihood ratio (ELR).
The effective likelihood ratios can be estimated by 2 general approaches: (1) calculation of the predicted ELR for disease (predicted ELRd) or for no disease (predicted ELRn) and (2) calculation of the observed ELRd for disease (observed ELRd) or for no
Reconciling Differences In Reported Likelihood Ratio Definition
Weinstein and Fineberg2 define a test likelihood ratio as the ratio of the frequency of a particular test result in those with disease to its frequency in those without disease. In translating this definition in terms of the sensitivity, specificity, and their complements, Sackett7 and Boyko8 have defined the likelihood ratios in the following relationships:
The reader will notice that the LR for a negative test result defined in (b) is
Acknowledgments
The author expresses his appreciation to Professor Fred B. Weissler, professor of mathematics, University of Paris XIII, for his valuable review of a draft of the manuscript and to Julienne M. Montgomery for her able assistance in its preparation.
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2005, American Heart JournalCitation Excerpt :To estimate the predictive power of single tests for predicting the presence or absence of disease, sensitivity, specificity, positive (+) and negative (−) predictive values, accuracy (defined as percentage of true test results, ie, (true positives + true negatives)/total number tests performed), and likelihood ratios [LR] ((+)LR = sensitivity/(1−specificity); (−)LR = specificity/(1−sensitivity)) were calculated considering follow-up data. Standard deviations, 95% confidence limits,30 and odds LR (posttest odds of disease for a positive test = (+)PTOD; posttest odds of no disease for a negative test = (−)PTON)31,32 were also calculated. The same LRs were adopted for estimating the power of combinations of tests, applied in sequence, for predicting the presence or absence of disease (see Appendix A).
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2004, Mayo Clinic ProceedingsCitation Excerpt :However, the large sample of patients studied may reduce selection and geographic differences to some extent. Furthermore, an advantage of using LRs is that the results are less influenced by the prevalence of GCA in different populations.14 Third, all the patients in our study had had temporal artery biopsy; therefore, a decision tree had already been used to decide to proceed with biopsy.
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2002, Archives of Physical Medicine and RehabilitationCitation Excerpt :The LR is preferred15 when expressing test power in terms of its capacity to detect disease for a positive test result (LR+) and to detect the absence of disease for a negative test result (LR−). A test of LR equal to 1.0 has no predictive power, that is, the power of the test is equal to chance alone.13 An LR+ of only 1 to 2 alters posttest probability to a small and rarely important degree, whereas an LR+ that is greater than 10 generates large and conclusive changes in posttest probability, and the relevant test is said to be accurate.15