A mechanistic latent variable model for estimating drug concentrations in the male genital tract: a case study in drug kinetics

The purpose of this study is to develop statistical methodology to facilitate indirect estimation of the concentration of antiretroviral drugs and viral loads in the prostate gland and the seminal vesicle. The differences in antiretroviral drug concentrations in these organs may lead to suboptimal concentrations in one gland. Suboptimal levels of the antiretroviral drugs may not be able to fully suppress the virus in that gland, leading to a source of sexually transmissible virus and increasing the chance of selecting for a drug-resistant virus. This information may be useful for selecting an antiretroviral drug regimen that will achieve optimal concentrations in the genital tract glands. Using fractionally collected semen ejaculates, Lundquist (Acta Physiol. Scand. 1949; 19:1-95) measured levels of surrogate markers in each fraction that are uniquely produced by specific male accessory glands. To determine the original glandular concentrations of the surrogate markers, Lundquist solved a simultaneous series of linear equations. This method has several limitations. In particular, it does not yield a unique solution, it does not address measurement error, and it does not provide population-averaged estimates after taking into account inter-subject variability in the parameters. To cope with these limitations, we developed a mechanistic latent variable model based on the physiology of the male genital tract and surrogate markers. We employ a Bayesian approach and perform a sensitivity analysis on the distributional assumptions on the random effects and priors. The model and Bayesian approach are validated on experimental data where the concentration of a drug should be (biologically) differentially distributed between the two glands. In this example, the Bayesian model-based conclusions are found to be robust to model specification and this hierarchical approach leads to more scientifically valid conclusions than the original methodology. In particular, unlike existing methods, the proposed model-based approach was not affected by a common form of outliers.