Likelihood Ratios: พื้นฐานความน่าจะเป็นในเชิงเงื่อนไข (Conditional Probability)

🔬 Mathematical Forms

🔸 LR⁺ (Likelihood Ratio for Positive Test)

Definition:

{LR}^{+} = \frac{P (T^{+} ∣ D^{+})}{P (T^{+} ∣ D^{-})}

As raw outcomes:

{LR}^{+} = \frac{True Positive}{False Positive}

As test characteristics:

{LR}^{+} = \frac{Sensitivity}{1 - Specificity}

🔹 LR⁻ (Likelihood Ratio for Negative Test)

Definition:

{LR}^{-} = \frac{P (T^{-} ∣ D^{+})}{P (T^{-} ∣ D^{-})}

As raw outcomes:

{LR}^{-} = \frac{False Negative}{True Negative}

As test characteristics:

{LR}^{-} = \frac{1 - Sensitivity}{Specificity}

🔶 LR⁺ (Likelihood Ratio for a Positive Test)

📌 Definition

The ratio of the probability of a positive test in someone with the disease to the probability of a positive test in someone without the disease.

{LR}^{+} = \frac{P (T^{+} ∣ D^{+})}{P (T^{+} ∣ D^{-})}

🧠 Clinical Interpretation:

LR⁺ tells how much more likely a positive result is in someone with the disease than in someone without the disease.

LR⁺ > 10 → Strong evidence for ruling in disease
LR⁺ ~1 → Test is not useful for confirmation

Structure for LR + :

{LR}^{+} = \frac{\frac{Test Positive}{People with Disease}}{\frac{Test Positive}{People without Disease}} = \frac{True Positive}{False Positive} = \frac{Sensitivity}{1 - Specificity}

🔷 LR⁻ (Likelihood Ratio for a Negative Test)

📌 Definition

The ratio of the probability of a negative test in someone with the disease to the probability of a negative test in someone without the disease.

{LR}^{-} = \frac{P (T^{-} ∣ D^{+})}{P (T^{-} ∣ D^{-})}

🧠 Clinical Interpretation:

LR⁻ tells how much more likely a negative result is in someone with the disease than in someone without the disease.

LR⁻ < 0.1 → Strong evidence for ruling out disease
LR⁻ ~1 → Test is not helpful in exclusion

Structure for LR - :

{LR}^{-} = \frac{\frac{Test Negative}{People with Disease}}{\frac{Test Negative}{People without Disease}} = \frac{False Negative}{True Negative} = \frac{1 - Sensitivity}{Specificity}

Likelihood Ratios: พื้นฐานความน่าจะเป็นในเชิงเงื่อนไข (Conditional Probability)

🔬 Mathematical Forms

🔸 LR⁺ (Likelihood Ratio for Positive Test)

🔹 LR⁻ (Likelihood Ratio for Negative Test)

🔶 LR⁺ (Likelihood Ratio for a Positive Test)

📌 Definition

🧠 Clinical Interpretation:

Structure for LR + :

🔷 LR⁻ (Likelihood Ratio for a Negative Test)

📌 Definition

🧠 Clinical Interpretation:

Structure for LR - :

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