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Predicting health outcomes like smoking cessation from longitudinal data requires careful interpretation of scalar-on-function regression models. This study offers practical guidelines for understanding the joint relationship between time-varying data and outcomes.

Keywords:
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Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Predicting distal outcomes from longitudinal data is crucial in health research.
  • Scalar-on-function regression is a method for analyzing such relationships.
  • Interpreting the fitted coefficient function in these models presents unique challenges.

Purpose of the Study:

  • To provide practical guidelines for interpreting scalar-on-function regression coefficients.
  • To clarify the distinction between joint and marginal relationships in longitudinal analysis.
  • To illustrate interpretation methods using a smoking cessation study.

Main Methods:

  • Semiparametric scalar-on-function regression was employed.
  • The study focused on the interpretation of the fitted coefficient regression function.
  • Data from a smoking cessation study was used for illustration.

Main Results:

  • The fitted coefficient function represents a joint relationship between time points and the outcome.
  • Misinterpretation can arise if treated as a marginal or cross-sectional relationship.
  • Guidelines were developed to aid practitioners in correct interpretation.

Conclusions:

  • Accurate interpretation of scalar-on-function regression is essential for valid scientific conclusions.
  • The provided guidelines facilitate understanding the complex temporal relationships in longitudinal data.
  • This work enhances the application of functional data analysis in health-related research.