Bias correction for estimates from linear excess relative risk models in small case-control studies

Area of Science:

• Epidemiology
• Biostatistics
• Radiation Oncology

Background:

• Epidemiologic studies often use linear excess relative risk (ERR) models to assess radiation dose impact on health outcomes.
• Estimating radiation dose-response relationships for second cancer risk after initial treatment is crucial but challenging.

Purpose of the Study:

• To evaluate small sample bias in maximum likelihood estimates for linear ERR models using location-specific radiation doses.
• To propose and investigate bias correction methods for these estimates.

Main Methods:

• Simulations were used to assess bias in maximum likelihood estimates.
• First and second order jackknife bias corrections were studied.
• Modified score functions under retrospective case-control sampling were derived for direct bias-corrected estimates.

Main Results:

• Substantial upward bias was observed in realistic sample sizes (over 50% relative bias with 75 cases).
• Neither first nor second order jackknife bias correction performed adequately.
• Modified score equation estimates demonstrated significantly improved bias correction and numerical stability.

Conclusions:

• Standard maximum likelihood estimates in linear ERR models are subject to considerable bias with location-specific doses in small studies.
• Modified score functions provide a more reliable approach for bias correction in these scenarios.
• Further refinement may be needed for complete bias elimination, but the proposed method offers substantial improvement.