Conversation with Merlin · Sun Dec 10 2023

Please explain me bellow point? 1. definition of probability index and combind index 2. how do we calculate them and 3 what is the cutoff to discriminate unrelated people from half sibling

Certainly! Let's address each point step by step:

  1. Definition of Probability Index and Combined Index:

    • Probability Index (PI): The Probability Index, often used in paternity testing, measures the likelihood that a genetic marker in an individual is inherited from a particular person. It is calculated by comparing the frequency of the marker in the general population with the frequency of the marker in a specific population, such as potential fathers.
    • Combined Index: The Combined Index is the product of the Probability Index values for each genetic marker examined in the DNA testing. It provides an overall assessment of the likelihood that the tested individuals are related as compared to unrelated individuals.
  2. How do we calculate them:

    • Probability Index (PI) is calculated using the formula: PI = 1 / (2 * (1 - frequency in population)).
    • For example, if a marker is found in 10% of the population, the PI would be: PI = 1 / (2 * (1 - 0.10)) = 1 / (2 * 0.90) = 1 / 1.8 = 0.56.
    • The Combined Index is determined by multiplying the individual Probability Index values together for all the genetic markers tested. For example, if the PI values for three markers are 0.56, 0.70, and 0.45, the Combined Index would be 0.56 * 0.70 * 0.45 = 0.1764.
  3. Cutoff to discriminate unrelated people from half-siblings:

    • The cutoff to discriminate unrelated people from half-siblings in paternity testing is typically based on the Combined Index value. Different testing laboratories may have slightly different cutoff values, but generally, a Combined Index value above a certain threshold (e.g., 100) indicates a high likelihood of a biological relationship, while a value below the threshold suggests unrelatedness.
    • It's important to note that the specific cutoff value and interpretation may vary between different testing methods and laboratories, so consulting with a genetics professional or testing provider is recommended for accurate assessment.

I hope this explanation helps clarify the concepts of Probability Index, Combined Index, and the cutoff for discriminating unrelated people from half-siblings in paternity testing. If you have any further questions or if there's anything else you'd like to understand better, feel free to ask!

please explain more about Combined Paternity Index and Probability of paternity and the difference between unrelated people and half sibling. please introduce me some reference with examples to calculate this indexes for ABI 17 marker kit

The Combined Paternity Index (CPI) and the Probability ofernity (POP) are critical concepts in paternity testing, distinguishing related and unrelated individuals. Let's discuss each concept and their differences, followed by an introduction to references and examples for calculating these indexes specifically using the ABI 17 marker kit.

  1. Combined Paternity Index (CPI):

    • The Combined Paternity IndexCPI) is a statistic used in the analysis of DNA profiles to determine paternity. It is calculated by multiplying the individual Probability Index (PI) values for each genetic marker examined in the DNA testing when comparing a child's DNA to that of potential father. The CPI provides an overall assessment of the likelihood that the potential father is the biological father.
  2. Probability of Paternity (POP):

    • The Probability of Paternity (POP) is the that a tested man is the biological father of a particular child, given the DNA profiles of both individuals. It's calculated based on the comparison of the genetic markers between the alleged father and the child. The higher the POP, the more likely it that the tested man is the biological father.
  3. Difference between Unrelated People and Half-Siblings:

    • In paternity testing, the Combined Paternity Index and Probability of Paternity are used to discriminate between unrelated individuals and potential half-siblings. The CPI and POP are significantly higher when the tested individuals are biological relatives, such as father and child, as compared to unrelated individuals. The genetic similarities between half-siblings are typically than those between a biological father and child, resulting in lower CPI and POP values for half-s compared to father-child relationships.

Reference and Examples for ABI 17 Marker Kit:

  • The ABI 17 marker kit is a specific set of genetic markers in DNA testing for paternity determination. When using this kit the calculation of CPI and POP values is based on the allele frequencies of the 17 genetic markers and the comparison of these markers between the tested individuals.
  • For detailed examples and reference calculations using the ABI 17 marker kit, it's recommended to refer to the specific guidelines and documentation provided by the testing laboratory or DNA testing kit manufacturer. These references typically include step-by-step instructions, calculations, and interpretation guidelines tailored to the specific genetic markers and testing methodology used in the ABI 17 marker kit.

I hope this explanation provides a clearer understanding of Combined Paternity Index, Probability of Paternity, and their application in discerning relationships in paternity testing. If you need further information on calculations or specific references for the ABI 17 kit, feel free to inquire for more details.

please tell me how can we calculate Probability of Paternity (POP) with an example

Certainly! The Probability of Paternity (POP) can be calculated using genetic markers from the tested child and the potential father. The process involves comparing the genetic profiles of the child and the alleged father, and then calculating the likelihood that the tested man is the biological father based on these profiles. Here's a step-by-step example of how to calculate the Probability of Paternity:

  1. Obtain Genetic Profiles:

    • Gather the genetic profiles of the child and the alleged father. These profiles consist of alleles (variants of a gene) at specific genetic markers, such as STR (Short Tandem Repeat) loci or SNPs (Single Nucleotide Polymorphisms).
  2. Determine Alleles at Genetic Markers:

    • Identify the alleles present at each genetic marker for both the child and the alleged father. For example, at a specific genetic marker, the child might have alleles 12 and 15, while the alleged father might have alleles 10 and 15.
  3. Calculate the Combined Probability of Exclusion:

    • The Combined Probability of Exclusion (CPE) is calculated by determining the combined likelihood that the alleged father would not be the biological father based on the non-matching alleles at each genetic marker: CPE = (1 - Frequency of Child's Alleles) * (1 - Frequency of Alleged Father's Alleles) for each marker, and then multiply the results for all markers.
  4. Derive the Relative Probability:

    • The Relative Probability (RP) is then calculated using the Combined Probability of Exclusion (CPE): RP = 1 - CPE
  5. Calculate the Probability of Paternity:

    • Finally, the Probability of Paternity (POP) is determined by considering both the Relative Probability and the prior odds of paternity (typically assumed to be 0.5 for most cases): POP = RP / (RP + (1 - RP) / Prior Odds)

Example: Let's consider a hypothetical scenario using a single genetic marker. Assume the child has alleles 12 and 15, while the alleged father has alleles 10 and 15. The frequencies of these alleles in the relevant population are 0.3, 0.2, 0.1, and 0.4, respectively.

  • For the Combined Probability of Exclusion (CPE) and Relative Probability (RP), you would calculate: CPE = (1 - 0.3) * (1 - 0.4) = 0.7 * 0.6 = 0.42 RP = 1 - 0.42 = 0.58

  • Assuming a prior odds of 0.5, you can then calculate the Probability of Paternity (POP): POP = 0.58 / (0.58 + (1 - 0.58) / 0.5) ≈ 0.853

This example demonstrates a simplified calculation for a single genetic marker. In actual paternity testing, multiple genetic markers are examined, and the combined results contribute to the overall Probability of Paternity.

I hope this example helps illustrate the calculation of the Probability of Paternity. If you have any further questions or if there's anything else you'd like to understand better, feel free to ask!

please introduce paper for these formula and calculations

The calculations and formulas for the Probability of Paternity (POP) and related concepts in paternity testing are based on principles of population genetics and statistical analysis of DNA profiles. These principles are widely documented and discussed scientific literature, technical manuals, and research papers related to forensic genetics and paternity testing. Here are a few reference papers and sources where you can find in-depth discussions and applications of these calculations:

  1. "Forensic DNA Typing" by John M Butler:

    • This authoritative book provides comprehensive coverage of DNA analysis and interpretation, including detailed discussions on the principles and calculations involved in paternity testing. It serves as an excellent reference for understanding the scientific basis of DNA testing and the relevant statistical methodologies.
  2. "Population Genetics for Forensic Scientists" by Ford and Balding:

    • This book delves into the theoretical underpinnings of population genetics and its application in forensic science, including calculations related to parentage testing. It offers thorough explanations of the statistical concepts involved in paternity testing calculations3. "The Evaluation of Forensic DNA Evidence" by National Research Council (NRC):
    • This report published by the National Research Council provides insights into the interpretation and statistical analysis of forensic DNA evidence, including discussions on pat testing and the calculations involved. It offers a rigorous examination of the statistical principles underlying DNA evidence interpretation.
  3. "Genetics and of Quantitative Traits" by Michael Lynch and Bruce Walsh:

    • This book is a valuable resource for understanding quantitative genetics and statistical analysis of genetic, including population genetics principles that underpin paternity testing calculations. It provides detailed discussions of genetic analysis and related statistical methodologies.

When seeking scholarly references for the formulas and calculations related to Probability of Paternity and other paternity testing concepts, scientific journals such as Forensic Science International, Journal of Forensic Sciences, and Genetics in Medicine are also excellent sources for detailed research articles and discussions in the field of forensic genetics and DNA analysis.

These should provide in-depth discussions and detailed explanations of the formulas and calculations involved in paternity testing, thus valuable insight into the scientific basis of the Probability of Paternity and related concepts. If you need more specific recommendations or further assistance, feel free to ask for additional details.

in there any excell sheet to use for this calculation

Yes, there are several Excel spreadsheets and software tools available for performing paternity testing calculations, including the Probability of Paternity and related genetic analysis. These tools are designed to streamline the calculations and provide a user-friendly interface for entering genetic data and obtaining the relevant statistical results. Here are a few resources where you can find Excel sheets or software for paternity testing calculations:

  1. Online Resources:

    • Some laboratories and academic institutions provide online calculators for paternity testing, often in the form of web-based tools. These calculators allow users to input genetic data and obtain the Probability of Paternity and related results.
  2. Laboratory Software:

    • Many DNA testing laboratories utilize specialized software for genetic analysis and paternity testing calculations. Some of these laboratories may offer access to their software tools, which can provide comprehensive functionality for paternity testing and DNA analysis.
  3. Commercial Software:

    • There are commercial software packages available for forensic DNA analysis that include modules for paternity testing calculations. These software tools are designed for professionals in forensic genetics and DNA testing and often provide advanced features for data analysis and interpretation.
  4. Excel Templates:

    • While specific Excel spreadsheets for paternity testing calculations may not be widely available, some academic or scientific publications related to forensic genetics may provide Excel templates or examples for understanding the principles and basic calculations involved in paternity testing.

When looking for an Excel sheet or software tool for paternity testing calculations, it's important to ensure that the tool aligns with recognized standards and guidelines in forensic genetics and DNA analysis. Additionally, consulting with professionals in the field of forensic genetics or DNA testing may provide valuable insights into the availability of relevant software tools and resources.

If you require further assistance in locating specific software or Excel tools for paternity testing calculations, please feel free to ask for additional guidance or details about your specific requirements.

please introme me some excell sheet to calculate

I don't have the ability to provide specific Excel sheets directly. However, you can often find Excel templates or spreadsheets for paternity testing calculations by searching online academic databases, forensic science resources, or professional genetics forums and websites. Additionally, some genetic analysis software providers may offer Excel-based tools as part of their packages. When searching for such resources, it's essential to ensure that any Excel sheet you use aligns with recognized scientific standards and guidelines for paternity testing calculations.

If you have access to academic or institutional libraries, you may also find scholarly articles, books, or technical manuals that include examples and templates for paternity testing calculations using Excel.

When using any Excel sheet for paternity testing calculations, it's important to verify the accuracy and applicability of the formulas and methods used, especially in the context of forensic genetics and DNA analysis.

If you need assistance with specific aspects of paternity testing calculations or require further guidance on locating Excel sheets for this purpose, feel free to ask for additional help or details on a particular area of interest.