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Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Epidemiology

Background:

  • Many studies involve outcomes that cannot be directly measured.
  • Indirectly observed outcomes often rely on proxy measures, which can introduce bias.
  • Existing methods may require calibration data or strong assumptions about the outcome-proxy relationship.

Purpose of the Study:

  • To develop a flexible regression framework for analyzing outcomes measured via one or more proxies.
  • To estimate associations between covariates and unobserved outcomes without calibration data.
  • To improve estimation accuracy by aggregating multiple proxies when available.

Main Methods:

  • Utilizing semiparametric transformation models (e.g., Cox proportional hazards regression) for the unobserved outcome.
  • Coupling the regression model with a semiparametric measurement model.
  • Developing a data-driven aggregation method for multiple proxies.

Main Results:

  • The proposed framework effectively estimates associations between covariates and indirectly observed outcomes.
  • The method performs well in finite samples, as shown by simulation studies.
  • Aggregating multiple proxies leads to improved estimation properties.

Conclusions:

  • The developed regression framework offers a robust approach for handling indirectly observed outcomes.
  • The methodology eliminates the need for calibration data and strong functional assumptions.
  • The approach is applicable in various research settings, as demonstrated by case studies.