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Counting methods (EM algorithm) in human pedigree analysis: linkage and segregation analysis

J Ott

    Annals of Human Genetics
    |May 1, 1977
    PubMed
    Summary
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    This study introduces a method for computing derivatives of human pedigree data likelihood. This enables iterative solutions for linkage and segregation analysis using maximum likelihood estimation (MLE) methods, extending existing counting techniques.

    Area of Science:

    • Genetics
    • Statistical Genetics
    • Computational Biology

    Background:

    • Human pedigree data analysis is crucial for understanding genetic inheritance patterns.
    • Traditional methods for linkage and segregation analysis can be computationally intensive.
    • Maximum Likelihood Estimation (MLE) is a standard statistical approach for parameter estimation.

    Purpose of the Study:

    • To develop a computationally efficient method for analyzing human pedigree data.
    • To facilitate the calculation of derivatives for likelihood functions in genetic analysis.
    • To extend existing statistical methods for parameter estimation in genetic studies.

    Main Methods:

    • Formulating the likelihood of human pedigree data to enable derivative computation.

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  • Applying these derivatives to derive equations for maximum likelihood estimates.
  • Utilizing an iterative approach for solving these equations, extending Smith's (1957) counting methods.
  • Classifying these procedures within the framework of Expectation-Maximization (EM) algorithms for incomplete data.

    • Main Results:

    • The likelihood function for human pedigree data can be structured for derivative computation.
    • This structure leads to elegant equations for maximum likelihood estimates.
    • The proposed iterative solution method is efficient for parameter estimation.
    • The methods are shown to be a specific application of general EM algorithms.

    Conclusions:

    • The developed method provides an efficient way to compute derivatives for human pedigree data.
    • This facilitates iterative solutions for linkage and segregation analysis.
    • The approach unifies existing counting methods under the umbrella of EM algorithms for incomplete data analysis.