ABSTRACT
This chapter brings both models of unobserved heterogeneity (see Chapter 3) and observed heterogeneity in the form of covariate information (see Chapter 4) together. Let us start with the common nonparametric mixture distribution given as
fi(Q) = m∑ j=1
fi(θj)qj (6.1)
where fi(θj) and Q are as defined in formula (3.8) in Chapter 3. On the other hand, we have modeled available covariate information in Chapter 4 by means of a log-linear model
log θ = η = β0 + β1z1 + ...+ βpzp,
where z1, · · · , zp are covariates expressing information on the study level such as the date of study, the treatment modification, or the location of study. These form via η = β0 + β1z1 + ... + βpzp the linear predictor. It is clear from (6.1) that in the case of m subpopulations with subpopulation-specific relative risks θj , we will have m equations linking the mean structure to the linear predictor:
log θj = ηj = β0j + β1jz1 + ...+ βpjzp. (6.2)
Note that there are nowm coefficient vectors (β0j , · · · , βpj) which create some complexities in making choices for them.
