5c - Paternity Index Calculations

Module Six: Paternity Index Calculations

Introductory Remarks

  • Lecture Context: This lecture is the third in module six focused on paternity index calculations.

  • Previous Content: The last lecture covered:

    • Transmission probabilities

    • Mutations and their impact

    • Power of exclusion

  • Current Goals:

    • Perform paternity index calculations by combining previous knowledge.

    • Recommend reviewing slides 13-14, or slides 13-17 for better understanding during the lecture.

Paternity Index (PI) and Combined Paternity Index (CPI)

  • Paternity Index (PI): Measures the likelihood that a specific individual (alleged father) is the biological parent based on their genetic profile compared to the child.

  • Combined Paternity Index (CPI):

    • For independent loci, CPI is the multiplicative product of individual PI values from all loci examined.

    • Calculation Example:

    • If performing analysis on 10 loci, calculate:
      CPI=PI<em>1×PI</em>2×…×PI10CPI = PI<em>1 \times PI</em>2 \times … \times PI_{10}

    • Interpretation:

    • CPI < 1 indicates support for exclusion, meaning the alleged father is not the biological parent.

    • CPI > 1 indicates support for inclusion; the alleged father is more likely to be the biological father compared to a random unrelated male of the same ethnic group.

  • Example: Using 13 STR loci can yield a CPI, exemplified as 212,390 times more likely that the alleged father is the biological father than a random man of the same ethnic group.

  • Reporting Variations: Laboratories report findings differently, e.g.:

    • An alleged father "cannot be excluded" or the genetic evidence shows that the alleged father is significantly more likely to be the biological father compared to certain population demographics (African American, Caucasian, Hispanic).

Probabilities of Paternity (W)

  • Notation: Probability of paternity may be denoted as W in texts.

  • Calculation Method: Utilizes Bayesian logic for prior probabilities.

  • General formula for probability of paternity:
    Paternity=CPI×priorCPI×prior+(1−prior)Paternity = \dfrac{CPI \times prior}{CPI \times prior + (1 - prior)}

  • Bias Reduction: Setting prior probabilities at 0.5 counters potential biases in results, assuming equal likelihood of being the father or not.

    • When applying it effectively:

    • For a combined paternity index of 50:
      Probability=50×0.550×0.5+0.5Probability = \dfrac{50 \times 0.5}{50 \times 0.5 + 0.5}

    • Result Calculation gives a probability of paternity as approximately 98.04%.

Variations in Prior Probabilities

  • Impact of Prior: Adjusting the prior impacts results more noticeably with lower CPI values:

    • Example with CPI 50:

    • Prior 0.9 yields probability 99.78%

    • Prior 0.1 yields probability 84.75%

  • Higher CPI Effects: The influence of different priors diminishes as CPI increases, thus biasing becomes less impactful.

Reporting Probability of Paternity

  • Standard Report Wording: Laboratories have varying methodologies for articulating results.

    • Example statement: "Assuming a prior probability of 50%… probability of paternity is at least 99.99%" for a given situation.

  • STR Power Analysis:

    • Older core loci reveal mean CPIs and high probabilities, reflecting the strength of STR-based testing.

Parentage Analysis

  • Single Parent Analysis: Involves analysis of one parent (e.g., mother) and child without the second parent's (father’s) genotype,

    • Results often lack power as genetic variability cannot be accounted completely.

  • Statistical Tools: The CODIS software aids in conducting paternity analyses, while Excel can be used for manual calculations.

Worked Example and Cheat Sheet Utilization

  • Worked Examples: Exercise practical applications using genotype patterns to derive paternity indices:

    • Analysis of child (homozygous 5.2/8), mother (homozygous 8/9.2), and alleged father (homozygous 5.2/6.2).

    • Use established patterns from cheat sheets (e.g., slide 14, line 5) to solve.

  • Paternity Index Calculation:

    • The paternity index derived would be PI=0.5frequency(5.2)PI = \frac{0.5}{frequency( 5.2)} resulting in a numerical value indicating inclusion probability.

Mixture Analysis and Mismatches

  • General Mismatch Situation: If typical loci analyzed yield a badly mismatched pair,

    • Use mutation rates and power of exclusion for calculative smoothing.

  • Situational Analysis: Situations can arise that necessitate special formula accounting, especially when one parent’s sample is unavailable.

  • Paternity Index Indicative Values:

    • CPI facilitates a combined understanding of the familial relationships, and mismatches must be carefully interpreted.

Exclusions and Direct Exclusion Analysis

  • Exclusion in Parentage: Define exclusion via analysis across multiple loci, noting that laboratories rarely use single locus mismatches for exclusion draws due to mutation prevalence.

  • Example Generation: Illustrate a case with a singular exclusion scenario and broaden out to reflect on collectivity of findings from multiple loci.

    • Computational adjustments are necessary when considering familial relationships through allele-sharing (AC with AB for child).

Conclusion and Future Learning Points

  • Prepare for Module Seven covering kinship concepts, combining coursework for broader comprehension.

  • Additional supplemental material available for deeper exploration, suggesting avenues for further study in paternity and kinship analysis.