A scaled linear mixed model for multiple outcomes

We propose a scaled linear mixed model to assess the effects of exposure an d other covariates on multiple continuous outcomes. The most general form o f the model allows a different exposure effect for each outcome. An importa nt special case is a model that represents the exposure effects using a com mon global measure that can be characterized in terms of effect sizes. Corr elations among different outcomes within the same subject are accommodated using random effects. We develop two approaches to model fitting, including the maximum likelihood method and the working parameter method. A key feat ure of both methods is that they can be easily implemented by repeatedly ca lling software for fitting standard linear mixed models, e.g., SAS PROC MIX ED. Compared to the maximum likelihood method, the working parameter method is easier to implement and yields fully efficient estimators of the parame ters of interest. We illustrate the proposed methods by analyzing data from a study of the effects of occupational pesticide exposure on semen quality in a cohort of Chinese men.