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Maximum likelihood, profile likelihood, and penalized likelihood: a primer.

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    This primer explains maximum likelihood estimation for epidemiologists, detailing its use in statistical modeling and its connections to Bayesian methods. It highlights extensions suitable for health research, suggesting they replace standard maximum likelihood.

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    Area of Science:

    • Epidemiology
    • Biostatistics
    • Statistical Modeling

    Background:

    • Maximum likelihood (ML) is a prevalent statistical method in epidemiology.
    • Many epidemiologists lack formal education in ML's conceptual foundations.
    • Existing ML methods may not be optimal for complex observational health research.

    Purpose of the Study:

    • To provide a foundational understanding of maximum likelihood estimation.
    • To introduce advanced ML extensions relevant to epidemiologic research.
    • To compare ML with Bayesian methods and advocate for improved statistical approaches.

    Main Methods:

    • Explanation of the principle of maximum likelihood estimation.
    • Illustration of ML mechanics with a practical example.
    • Discussion of extensions and generalizations of ML for observational data.

    Main Results:

    • Maximum likelihood identifies model parameters that maximize data probability.
    • ML estimators possess desirable large-sample properties under ideal conditions.
    • Extensions offer improved suitability for observational health research compared to standard ML.

    Conclusions:

    • Maximum likelihood is a computationally straightforward yet model-dependent statistical tool.
    • Advanced ML methods and Bayesian connections offer enhanced capabilities for health research.
    • Current ML practices in epidemiology may benefit from adopting these advanced techniques.