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Log Likelihood Ratio Formula:
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Log Likelihood Ratio (LLR) is the natural logarithm of the Positive Likelihood Ratio (PLR). It provides a measure of how much more likely a positive test result is in individuals with the condition compared to those without the condition, expressed on a logarithmic scale.
The calculator uses the LLR formula:
Where:
Explanation: The natural logarithm transformation of PLR provides a symmetric scale that is often more interpretable in statistical analyses.
Details: LLR is used in diagnostic test evaluation, evidence-based medicine, and statistical modeling to quantify the diagnostic value of a test result on a logarithmic scale.
Tips: Enter the Positive Likelihood Ratio value (must be greater than 0). The calculator will compute the natural logarithm of the input value.
Q1: What is the range of LLR values?
A: LLR can range from negative infinity to positive infinity. Positive values indicate the test result is more likely in diseased individuals, while negative values indicate it's more likely in non-diseased individuals.
Q2: How is LLR interpreted in diagnostic testing?
A: LLR values further from zero (in either direction) indicate stronger diagnostic evidence. Larger positive values suggest stronger rule-in potential, while larger negative values suggest stronger rule-out potential.
Q3: What is the relationship between LLR and probability?
A: LLR can be used to update pre-test probabilities to post-test probabilities using Bayesian principles through logarithmic odds transformations.
Q4: Are there different types of logarithms used?
A: While natural logarithm (base e) is most common, some applications may use base 10 or base 2 logarithms. This calculator uses natural logarithm.
Q5: When is LLR preferred over PLR?
A: LLR is often preferred in statistical modeling and meta-analyses because it provides a symmetric scale and better normal distribution properties.