Hello everyone,
I want to calculate a ratio, but for some measurements, I have
When calculating ratios with a Limit of Detection (LOD) in the denominator, there are a few different approaches that can be used, depending on the specific context and the desired level of accuracy. Here are a few examples:
When the denominator of a ratio includes measurements that are below the limit of detection (LOD), it can be challenging to accurately calculate the ratio. There are several different approaches that can be used to handle this situation, each with its own advantages and limitations.
One common approach is to use a "conservative" assumption, such as assuming that all measurements below the LOD are equal to the LOD or LOD/2. This approach can be useful when the goal is to minimize the potential for overestimating the ratio. However, it can also lead to underestimating the ratio if the actual measurements are significantly higher than the LOD.
Another approach is to use a "maximum likelihood" assumption, which involves estimating the most likely value of the measurement based on the distribution of other measurements. This approach can be more accurate than the conservative approach, but it requires more data and can be more complex to implement.
A third approach is to use Bayesian methods. This method uses Bayes' theorem to update the probability distribution for the denominator value, given the LOD and other information about the measurement. This approach can be useful when there is limited data available, but it can be complex to implement.
In addition to these approaches, it's important to mention that it's also possible to use non-parametric methods such as bootstrap or Monte Carlo simulation to estimate the ratio by simulating the measurements using a probability distribution based on the LOD.
You can find more information and methodological references in the following papers:
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