Non-parametric Estimation for Asymmetrical Concentration Intervals
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Solution Overview
Problem
Existing methods for determining the concentration of low-concentration nucleic acid reference materials, such as those used in genetic testing, often result in inaccurate calculations due to assumptions of normal distribution, which can lead to deviations from actual concentrations, especially when the distribution is bilaterally asymmetrical or discrete, and fail to represent concentration variations accurately.
Innovation Solution
A non-parametric method using percentage points to compute and display product specifications, allowing for accurate representation of concentration intervals irrespective of distribution shape, by setting a target probability and adjusting the interval width to include the desired cumulative probability, ensuring precise representation of low-concentration samples.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a normal distribution method is used to compute concentration specifications, then the calculation is simple and follows a standard statistical approach, but the result deviates from actual concentration when the distribution is bilaterally asymmetrical or discrete (low copy number)
Solution Approach 1:
The patent changes the fundamental parameter of the statistical approach from parametric (normal distribution assumption) to non-parametric (empirical cumulative distribution function). This allows the method to adapt to any distribution shape without assuming normality, thereby resolving the contradiction between computational simplicity and accuracy for low-copy-number samples with discrete or asymmetrical distributions
Solution Approach 2:
Instead of assuming a theoretical distribution shape and fitting data to it (traditional approach), the patent inverts the approach by directly using the empirical cumulative distribution function derived from actual measured data. This inversion eliminates the need to assume normal distribution and directly reflects the actual concentration distribution, improving accuracy while maintaining computational feasibility
2Adaptability or versatility
If a percentage-point method is used to compute concentration specifications, then the method can handle non-normal distributions, but it may produce redundant intervals and less precise concentration estimates
Solution Approach 1:
The patent applies asymmetry by allowing different probability thresholds (α1 and α2) on either side of the median, rather than using symmetric confidence intervals. This enables the method to adapt to asymmetrical distributions commonly found in low-copy-number samples, improving precision by creating non-redundant intervals that accurately reflect the actual data distribution
Solution Approach 2:
The patent introduces dynamic adjustment of interval boundaries based on the actual empirical distribution data. Instead of using fixed percentage points, the method dynamically determines the concentration interval [C1, C2] by finding the range that contains a specified probability mass (1-α) of the empirical distribution, allowing the interval to adapt to the specific shape and characteristics of each dataset
3Ease of manufacture
If the concentration is represented with decimal values (mean ± 2σ), then the representation follows normal distribution theory, but it produces unnatural values for low-concentration samples where copy number should be an integer
Solution Approach 1:
The patent applies local quality by representing concentration differently depending on the local characteristics of the data. For low-copy-number samples where discreteness is significant, it uses integer-based intervals from the empirical distribution. This local adaptation ensures that the representation is both statistically sound and naturally interpretable for the specific context of low-concentration nucleic acid samples
Data Source
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AI summary
Provided is a technique capable of adequately presenting the product specifications of a material sample even when the concentration distribution of the material is asymmetrical. A material sample according to the present disclosure stores a material having variation according to a probability distribution. As the product specifications of the material sample, the representative value of the probability distribution as well as an interval in which the amount of the material is greater than or equal to a target probability on the probability distribution is displayed.