Joint Bayesian Inference of Genetic Effect Sizes and PK Parameters in Nonlinear Mixed-Effects Models
High-dimensional genetic covariate selection in population pharmacokinetic (PK) models is challenging due to the cohort's restricted size and high correlation among single-nucleotide polymorphisms (SNPs). We propose a fully Bayesian, single-stage framework that jointly infers nonlinear mixed effect model (NLMEM) parameters and SNP effect sizes, providing coherent posterior uncertainty and inclusion summaries within a single model fit. We compare five sparsity-inducing priors -- Spike-and-Slab, Hierarchical Lasso, Regularized Horseshoe, R2--D2, and the $\ell_1$-ball -- calibrated through effect-size and sparsity targets. In simulations, all priors showed low false-discovery rates around $0$--$0.08$ under the null, and recovered the causal signal under the alternative, with peak $F_1$ scores around $0.8$--$0.85$ under reasonable inclusion cutoffs. Spike-and-Slab was especially attractive because it provides analytical posterior inclusion probabilities directly, while among priors requiring tolerance-based proxy inclusion summaries, the $\ell_1$-ball combined similarly strong recovery with the most stable behavior across tolerance values. On genetic and PK data from the ANRS 12154 study in 129 Cambodians living with HIV and receiving nevirapine, posterior predictive checks indicated adequate calibration and PK parameter inference remained stable across priors. While the dominant signal was robust across priors, additional candidate SNPs showed only partial agreement in ranking and more prior-sensitive effect-size estimates. These results support Bayesian variable selection within joint NLMEM as a principled approach for pharmacogenetic analyses when uncertainty quantification and regularization are central.