Delta-Cq Confidence Estimation Using Noise Models
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Quantitative PCR measurements require normalization to compare gene expression across samples, but existing methods lack precision in determining confidence intervals for delta-Cq values, especially with low material yields, leading to unreliable test results and potential need for repeated measurements.
Innovation Solution
A method that calculates confidence intervals for delta-Cq values by constructing a noise model from training PCR data, incorporating a lower bound to ensure finite variance, allowing for reliable estimation even with low material yields, and using this information to improve decision-making in patient treatment.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If the delta-Cq method is used for normalization, then gene expression can be compared across samples, but the precision and reliability of test results deteriorate when material yield is low
Solution Approach 1:
The patent introduces a lower bound parameter (LB) that changes the mathematical treatment of delta-Cq calculations. When material yield is low and replicates are undetected, the lower bound parameter transforms the infinite variance problem into a finite variance solution by constraining the delta-Cq value to be at least LB, thereby maintaining measurement precision across all material yields
Solution Approach 2:
The patent performs preliminary calculation of confidence intervals and lower bounds before final test result determination. By pre-calculating the distribution of true delta-Cq values and determining confidence intervals in advance, the system can assess reliability before reporting results, allowing for proactive decision-making about repeated measurements
2Reliability
If repeated measurements are performed to improve confidence, then test result reliability improves, but time consumption and productivity deteriorate
Solution Approach 1:
The patent implements a feedback mechanism that calculates confidence intervals and lower bounds for each measurement and uses this information to determine whether repeated measurements are necessary. The system feeds back the reliability assessment to the decision-making process, allowing clinicians to understand the precision of individual measurements before determining if repetition is needed, thereby avoiding unnecessary repeated measurements
Solution Approach 2:
The system performs preliminary reliability assessment by calculating confidence intervals and lower bounds before final test result reporting. This preliminary action allows the system to predict whether a single measurement suffices or if repetition is needed, eliminating the need for blind repeated measurements and reducing time consumption
3Measurement precision
If a lower bound is introduced to ensure finite variance, then measurement precision improves for low material yield samples, but the complexity of calculations increases
Solution Approach 1:
The patent introduces a lower bound parameter (LB) that simplifies the mathematical treatment of low material yield samples. By changing the parameter space to constrain delta-Cq values to be at least LB, the system transforms complex infinite variance calculations into manageable finite variance calculations, improving precision without excessive complexity
Solution Approach 2:
The patent applies the lower bound constraint partially - only when material yield is low and replicates are undetected. For normal samples with sufficient material yield, the standard delta-Cq calculation is used without the lower bound constraint. This partial application avoids unnecessary complexity in most cases while providing enhanced precision when needed
Data Source
Figure 1~2
Figure 3~4
Figure 5
AI summary
The invention describes how to estimate delta-Cq values from measured (raw-) Cq values gained from PCR measurements and how to calculate confidence intervals for them. This is realized by the following processing steps: A noise model, which might be constructed on some training PCR data, calculates the distribution of the true target material concentration of a single well for an observed measurement results. Said distribution is calculated for all types of measurement results including "Numeric" raw-Cq values as well as Cq being "Undetected", which denotes that no fluorescence signal was detected during all cycles and thus corresponds to no or very few target molecules. Based on this distribution information from several replicate wells of a gene of interest and several replicate wells of one or more reference genes the distribution of the true delta-Cq value is calculated. In order to come out with a finite variance of the delta-Cq value (which so far would not be the case if all replicates are "Undetected") a lower bound is defined on the delta-Cq value. This lower bound is chosen so small that no useful information about the clinical implications is lost but so large that even for samples with low total material yield a reliable estimation of the delta-Cq value is possible.