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Survival analysis is a statistical method used to analyze time-to-event data, often employed in fields such as medicine, engineering, and social sciences. One of the key challenges in survival analysis is dealing with incomplete data, a phenomenon known as "censoring." Censoring occurs when the event of interest (such as death, relapse, or system failure) has not occurred for some individuals by the end of the study period or is otherwise unobservable, and it might have many different...
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Fast Implementation for Normal Mixed Effects Models With Censored Response.

Florin Vaida1, Lin Liu1

  • 1Department of Family and Preventive Medicine, UC San Diego School of Medicine, La Jolla, CA 92093-0717.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
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Summary
This summary is machine-generated.

This study introduces a faster EM algorithm for mixed effects models with censored data. It improves computation speed significantly by using closed-form expressions, aiding biostatistical analysis.

Keywords:
Detection limitEM algorithmHIV viral loadMaximum likelihoodTruncated multinormal distribution

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Area of Science:

  • Biostatistics
  • Statistical Computing
  • Longitudinal Data Analysis

Background:

  • Mixed effects models are widely used for longitudinal data.
  • Censored responses are common in biostatistical applications, such as HIV viral load.
  • Existing methods for mixed effects models with censored data can be computationally intensive.

Purpose of the Study:

  • To develop a computationally efficient Expectation-Maximization (EM) algorithm for linear and nonlinear mixed effects models with censored response.
  • To improve the speed of maximum likelihood and restricted maximum likelihood estimation.

Main Methods:

  • Proposed an EM algorithm utilizing closed-form expressions in the E-step, avoiding Monte Carlo simulation.
  • Employed formulas for the mean and variance of truncated multinormal distributions.
  • Applied the method to linear and nonlinear mixed effects models, including extensions for variance components, heteroscedastic/autocorrelated errors, and multilevel models.

Main Results:

  • Achieved up to an order of magnitude improvement in computation speed compared to previous methods.
  • Demonstrated the algorithm's applicability through two biostatistical case studies analyzing longitudinal HIV viral load data.
  • Implemented the algorithm in the R package 'lmec'.

Conclusions:

  • The proposed EM algorithm offers a significant computational advantage for analyzing mixed effects models with censored data.
  • The method is versatile, applicable to a broad range of mixed effects models.
  • The R package 'lmec' provides a practical tool for researchers.