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Statistical inference in a growth curve quantile regression model for longitudinal data.

Hyunkeun Ryan Cho1

  • 1Department of Biostatistics, University of Iowa, Iowa City, Iowa 52242, U.S.A.

Biometrics
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Summary

This study introduces a flexible polynomial growth curve model to assess treatment effects on outcome distributions over time. The novel approach uses empirical log-likelihood for optimal model selection and robust hypothesis testing in longitudinal data.

Keywords:
Empirical loglikelihoodHypothesis testModel selectionPolynomial regressionQuantile regression

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Area of Science:

  • Biostatistics
  • Longitudinal Data Analysis
  • Statistical Modeling

Background:

  • Assessing treatment effects on outcome distributions over time is crucial in longitudinal studies.
  • Traditional models may lack flexibility in capturing quantile-specific changes.
  • Complexity arises from high-degree polynomial models for adequate data fitting.

Purpose of the Study:

  • To develop a polynomial growth curve quantile regression model for comprehensive treatment effect assessment.
  • To introduce a model selection criterion for identifying optimal polynomial degrees across quantiles.
  • To propose a hypothesis test for evaluating treatment effects on growth curves in longitudinal data.

Main Methods:

  • A polynomial growth curve quantile regression model is proposed.
  • Model selection is based on an empirical log-likelihood criterion.
  • An empirical log-likelihood ratio test statistic is developed for hypothesis testing, incorporating within-subject correlation.

Main Results:

  • The empirical log-likelihood criterion consistently identifies optimal polynomial degrees.
  • The proposed test statistic asymptotically follows a chi-square distribution under the null hypothesis.
  • Simulation studies confirm the test's ability to detect differences in growth curves across quantiles.

Conclusions:

  • The developed model offers a flexible and parsimonious approach to analyze treatment effects on outcome distributions.
  • The empirical log-likelihood method enhances estimation efficiency for quantile regression parameters in growth curve models.
  • The methodology is effectively demonstrated using randomized controlled longitudinal depression data.