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In a randomized clinical trial in the ophthalmology field, I would like to find the R implementation for a linear mixed effects model given by

log(y_ijk) = b0 + b1_j + b2_k + b3_jk + w_i + e_ijk

where y_ijk is an amount of residual antibiotics, b1_j is the effect of structure (j=1 if cornea and j=2 if aquous humor), b2_k are the effects of treatments (k=1,2,3), b3 are interaction effects, w_i are random effects and e_ijk are random errors. We have pairs of observations for each individual (the residual antibiotic is measured in both structures for each subject).

My main difficulty is that the model should incorporate a heteroscedastic structure for the errors, so that the variances are different for each treatment group. In this way,

e_ijk ~ Normal(0,sigma_k),  k = 1,2,3

Thanks

Linus
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Edson Zangiacomi Martinez
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    The package `nlme` has this option, Bates & Pinheiro (2000) describe the implementation of heteroscedastic residuals using this package – Niek Feb 14 '18 at 14:42

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