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Non linear mixed effect models are classical tools to analyze non linearlongitudinal data in many fields such as population Pharmacokinetic. Groups ofobservations are usually compared by introducing the group affiliations asbinary covariates with a reference group that is stated among the groups. Thisapproach is relatively limited as it allows only the comparison of thereference group to the others. In this work, we propose to compare the groupsusing a penalized likelihood approach. Groups are described by the samestructural model but with parameters that are group specific. The likelihood ispenalized with a fused lasso penalty that induces sparsity on the differencesbetween groups for both fixed effects and variances of random effects. Apenalized Stochastic Approximation EM algorithm is proposed that is coupled toAlternating Direction Method Multipliers to solve the maximization step. Anextensive simulation study illustrates the performance of this algorithm whencomparing more than two groups. Then the approach is applied to real data fromtwo pharmacokinetic drug-drug interaction trials.

A SAEM Algorithm for Fused Lasso Penalized Non Linear Mixed Effect Models: Application to Group Comparison in Pharmacokinetic