What are the three types of likelihood ratios for continuous outcomes?

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What are the three types of likelihood ratios for continuous outcomes?

With continuous test results, you can quantify how much a specific observed value changes the odds of disease. There are three natural ways to express this evidence. First, value-specific likelihood ratio. For an exact observed value x, the LR is the ratio of how common that value is among diseased people to how common it is among non-diseased people. In symbols, LR(x) = f1(x) / f0(x). This is the most granular use of the data because it uses the full distribution of values, and the post-test odds come from multiplying the pre-test odds by this LR(x). It requires knowing or estimating the distributions under both groups. Second, cutpoint-specific likelihood ratio. If you convert the continuous result into a binary decision using a threshold, you get a single LR associated with crossing that threshold. You obtain LR for values above or below the cutpoint (often called LR+, for values at/above the threshold, and LR−, for values below). These provide a simple, binary update to the odds based on whether the result meets the cutoff. Third, category-specific likelihood ratio. If you group the results into several ranges (categories or bins), you can assign an LR to each category: LR(category) = P(category | disease) / P(category | no disease). This keeps more nuance than a single cutpoint while avoiding the complexity of using the exact value, offering a practical middle ground. The other options don’t capture these distinct ways to handle continuous data: using a general pre/post/prior LR, or labeling LR as “positive,” “negative,” or “combined,” aren’t standard ways to describe LRs for continuous outcomes.

With continuous test results, you can quantify how much a specific observed value changes the odds of disease. There are three natural ways to express this evidence.

First, value-specific likelihood ratio. For an exact observed value x, the LR is the ratio of how common that value is among diseased people to how common it is among non-diseased people. In symbols, LR(x) = f1(x) / f0(x). This is the most granular use of the data because it uses the full distribution of values, and the post-test odds come from multiplying the pre-test odds by this LR(x). It requires knowing or estimating the distributions under both groups.

Second, cutpoint-specific likelihood ratio. If you convert the continuous result into a binary decision using a threshold, you get a single LR associated with crossing that threshold. You obtain LR for values above or below the cutpoint (often called LR+, for values at/above the threshold, and LR−, for values below). These provide a simple, binary update to the odds based on whether the result meets the cutoff.

Third, category-specific likelihood ratio. If you group the results into several ranges (categories or bins), you can assign an LR to each category: LR(category) = P(category | disease) / P(category | no disease). This keeps more nuance than a single cutpoint while avoiding the complexity of using the exact value, offering a practical middle ground.

The other options don’t capture these distinct ways to handle continuous data: using a general pre/post/prior LR, or labeling LR as “positive,” “negative,” or “combined,” aren’t standard ways to describe LRs for continuous outcomes.

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