A scaled linear mixed model for multiple outcomes

Area of Science:

• Biostatistics
• Environmental Health
• Epidemiology

Background:

• Assessing the impact of environmental exposures on multiple health outcomes is complex.
• Existing statistical models may not adequately capture correlated outcomes or varying exposure effects.

Purpose of the Study:

• To propose a flexible scaled linear mixed model for analyzing multiple continuous outcomes influenced by exposure and covariates.
• To develop and compare two model-fitting approaches: maximum likelihood and working parameter methods.

Main Methods:

• A scaled linear mixed model accommodating different exposure effects per outcome and correlated outcomes via random effects.
• Implementation using standard linear mixed model software (e.g., SAS PROC MIXED).
• Comparison of maximum likelihood and working parameter fitting methods.

Main Results:

• The working parameter method is easier to implement than maximum likelihood.
• The working parameter method provides fully efficient estimators.
• The model was successfully applied to analyze pesticide exposure and semen quality in Chinese men.

Conclusions:

• The proposed scaled linear mixed model provides a robust framework for analyzing multiple outcomes.
• The working parameter method offers a practical and efficient approach for model fitting.
• This methodology is valuable for occupational exposure studies and other research involving multiple correlated outcomes.