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Updated: Jul 18, 2025

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Smoothing Lexis diagrams using kernel functions: A contemporary approach.

Philip S Rosenberg1, Adalberto Miranda Filho1, Julia Elrod1

  • 1Biostatistics Branch, National Cancer Institute, Division of Cancer Epidemiology and Genetics, Rockville, MD, USA.

Statistical Methods in Medical Research
|August 25, 2023
PubMed
Summary

This study introduces a new bivariate kernel smoother for analyzing cancer incidence data. The novel truncated model averaging approach improves pattern clarity and trend estimation in Lexis diagrams.

Keywords:
EpidemiologyLexis diagramSurveillanceand End Results Programcancer surveillance researchkernel methodsnonparametric smoothing

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Area of Science:

  • Epidemiology
  • Biostatistics
  • Cancer Surveillance

Background:

  • Lexis diagrams are crucial for cancer surveillance research, displaying event rates by age and period.
  • Stratifying Lexis diagrams by various factors reduces information content, necessitating smoothing methods.
  • Existing methods for smoothing Lexis diagrams have limitations.

Purpose of the Study:

  • To develop a novel bivariate kernel-based smoother for analyzing Lexis diagrams.
  • To improve the clarity of patterns and summary estimates in stratified cancer data.
  • To provide a robust and automatic smoothing approach for cancer surveillance.

Main Methods:

  • Developed a bivariate kernel smoother incorporating singular value decomposition and bias-corrected Akaike information criterion for optimal truncation.
  • Employed model averaging across a panel of candidate kernels with diverse shapes and bandwidths.
  • Validated the approach using a case study of invasive estrogen receptor-negative breast cancer incidence and simulations for 20 cancers.

Main Results:

  • The novel truncated model averaging approach demonstrated superior performance compared to any fixed kernel.
  • The method is fast, automatic, and provides a variance-covariance matrix accounting for model selection.
  • Consistent outperformance was observed across various cancer types.

Conclusions:

  • The truncated model averaging approach is a reliable and effective tool for descriptive cancer surveillance studies.
  • This method enhances the analysis of Lexis diagrams, particularly in stratified datasets.
  • Supports the routine adoption of this advanced smoothing technique in cancer research.