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Accommodating the Analysis Model in Multiple Imputation for the Weibull Mixture Cure Model: Performance Under

Changchang Xu1,2, Laurent Briollais1,2, Irene L Andrulis2,3

  • 1Division of Biostatistics, Dalla Lana School of Public Health, University of Toronto, Toronto, Canada.

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|March 17, 2026
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Summary

Developing compatible imputation models and penalization methods improves mixture cure (MC) model accuracy for time-to-event data, especially with low event rates. These methods reduce bias and enhance confidence interval coverage in survival analysis.

Keywords:
combined likelihood profile (CLIP)exact conditional distribution (ECD)maximum likelihood (ML)multiple imputation by chained equations (MICE)prognostic biomarkers

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Area of Science:

  • Biostatistics
  • Survival Analysis
  • Medical Informatics

Background:

  • Mixture cure (MC) models are essential for time-to-event data when some individuals never experience the event.
  • Multiple imputation (MI) is used for handling missing data, but model misspecification can lead to inaccurate estimates.
  • Breast cancer studies with incomplete biomarker data necessitate robust statistical methods.

Purpose of the Study:

  • To propose novel imputation models compatible with Weibull proportional hazards mixture cure (PH-MC) analysis models.
  • To evaluate the performance of different imputation models, including an exact conditional distribution (ECD) model, via simulation.
  • To assess the impact of Firth-type penalized likelihood (FT-PL) and combined likelihood profile (CLIP) methods on parameter estimation.

Main Methods:

  • Development of an exact conditional distribution (ECD) imputation model derived from the analysis model likelihood.
  • Simulation studies comparing ECD, a cure indicator approximation (cECD), and a comprehensive simple (CS) model.
  • Incorporation of Firth-type penalized likelihood (FT-PL) and combined likelihood profile (CLIP) into multiple imputation (MI).

Main Results:

  • Multiple imputation (MI) with penalization methods reduced estimation bias and improved confidence interval (CI) coverage compared to complete case analysis.
  • The ECD imputation model demonstrated lower bias and higher CI coverage than cECD and CS models, particularly at lower event rates.
  • While CS models yielded narrower CIs than cECD, they exhibited greater bias and lower coverage.

Conclusions:

  • Compatible imputation models and penalization methods are recommended for mixture cure (MC) modeling, especially in breast cancer prognosis studies.
  • These methods enhance the reliability of statistical analyses involving low event numbers and/or covariate imbalance.
  • The proposed ECD imputation model offers improved accuracy for time-to-event outcome analyses with potential cures.