Cross-validation for linear model with unequal variances in genomic analysis.

Area of Science:

• Genomics
• Biostatistics
• Clinical Trials

Background:

• Genomic studies identify genes for predictive models in clinical trials.
• Predictive models aid treatment response identification but require validation.
• Existing methods like Shao's (1993) assume equal variances, limiting applicability.

Purpose of the Study:

• To extend Shao's cross-validation method for linear models with unequal variances.
• To develop and evaluate novel re-sampling methods for genomic data with heterogeneous variances.
• To provide a validated approach for predictive model development in clinical settings.

Main Methods:

• Extension of Shao's cross-validation for linear models with unequal variances.
• Development of two novel re-sampling methods to address variance heterogeneity.
• Simulation studies to assess the performance of proposed methods with finite samples.

Main Results:

• The proposed methods effectively account for variance heterogeneity in linear models.
• Simulations demonstrated the finite sample performance of the new re-sampling techniques.
• The methods were illustrated using a breast cancer research example.

Conclusions:

• The extended method provides a robust approach for predictive model validation with genomic data.
• The proposed re-sampling methods enhance the reliability of predictive models in the presence of unequal variances.
• This work supports the use of validated predictive models in clinical development, particularly in oncology.