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Goodness-of-Fit Testing for a Regression Model With a Doubly Truncated Response.

Jacobo de Uña-Álvarez1

  • 1Department of Statistics and Operations Research, Universidade de Vigo, Vigo, Spain.

Biometrical Journal. Biometrische Zeitschrift
|December 17, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces new statistical tests to address selection bias in doubly truncated data, common in survival analysis and epidemiology. These methods improve regression modeling accuracy for time-to-event data.

Keywords:
epidemiologyinterval samplingmodel selectionrandom truncationsurvival analysis

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Area of Science:

  • Statistics
  • Survival Analysis
  • Epidemiology

Background:

  • Interval sampling in survival analysis and epidemiology can lead to doubly truncated event times.
  • This double truncation induces selection bias, rendering ordinary statistical methods inconsistent.

Purpose of the Study:

  • To introduce novel goodness-of-fit procedures for regression models with doubly truncated response variables.
  • To develop statistically sound methods for analyzing data affected by interval sampling or other double truncation designs.

Main Methods:

  • Construction of a marked empirical process based on weighted residuals.
  • Establishment of the weak convergence of this empirical process.
  • Derivation of Kolmogorov-Smirnov- and Cramér-von Mises-type tests.
  • Development of a bootstrap approximation for practical implementation.

Main Results:

  • The proposed goodness-of-fit tests are derived from the established weak convergence of the marked empirical process.
  • Simulation studies demonstrate the performance of the new tests.
  • The methods are applied to model selection for AIDS incubation time, considering age at infection.

Conclusions:

  • The introduced procedures provide a statistically consistent approach to regression modeling with doubly truncated data.
  • The developed tests offer a practical solution for analyzing data affected by selection bias in survival analysis and epidemiology.
  • The application to AIDS incubation time highlights the utility of these methods in real-world epidemiological research.