Bayesian hierarchical model of oscillatory cortisol response during drug intervention

Conference poster, 2018

Introduction: Oscillating biomarker response-time courses challenge modelling of drug intervention. A periodically recurring pattern is typically seen for the stress hormone cortisol. This pattern can be captured by mechanism-based turnover models. However, analysing experimental data requires new mathematical techniques. Bayesian hierarchical modelling allows for full quantification of parameter uncer­tainty while also capturing the population aspects typical to nonlinear mixed effects modelling. Inter-occasion variability (IOV) is incorporated in addition to inter-individual variability (IIV).

Objectives:
- Propose a model based workflow for oscillating baseline turnover models including IIV and IOV.
- Apply the workflow to cortisol- and dexamethasone time-series data obtained from horses.
- An additional aim was to predict test performance of a two-sample dexamethasone suppression test-protocol (DST-protocol) [1, 2] in horses.

Methods: Cortisol- and dexamethasone time courses were collected [1]. Four different doses of dexamethasone were given (no drug and 0.1, 1, 10 µg/kg bolus + 0.07, 0.7, 7 µg/kg infusion over three hours). The pharmacokinetic/pharmacodynamic model was adapted from [1]. Cortisol was described by a turnover model with oscillating turnover rate (average baseline kavg, amplitude α, phase-shift t0) and fractional turnover rate kout. Drug intervention was modelled with Hill-type suppression (maximum inhibition Imax, potency IC50, hill coefficient ­n). Dexamethasone exposure was described by a two-compartment model. The model was then extended to a population model by introduction of inter-individual and inter-occasion effects. The final model was inferred from data using a Bayesian framework with the Hamiltonian Monte Carlo algorithm in Stan [3]. Ordinary differential equations were solved analytically for the case of constant drug exposure. The performance of the two-sample DST-protocol was studied by calculation of the specificity of the test. Specificity was predicted by Monte Carlo simulations and compared to two previously published experimental results.

Results: The proposed model described the data well. Estimated ranges for pharmacodynamic parameters were estimated as median (95% credible intervals): kavg = 12.7 (6.44, 23.5) µg L-1 h-1, α = 5.40 (1.38, 17.9) µg L-1 h-1, t0 = -3.71 (-7.54, 0.494) h, kout = 0.315 (0.221, 0.493) h-1, Imax = 0.923 (0.874, 0.965), IC50 = 0.0298 (0.00490, 0.155) µg L-1, n = 1.57 (1.03, 2.61  ). Low precision was found in the standard deviations of the random effect parameters. IIV and IOV present in the data were captured by the model. The average cortisol response level and its amplitude are suppressed with respect to magnitude and variability with increasing exposure to dexamethasone. The maximum and minimum levels of cortisol response were also suppressed by increasing exposure to dexamethasone. Mathematical expressions were derived describing cortisol oscillations with inhibition and were consistent with experimental data. Dependence of predicted specificity on drug administration time and time until measurement was observed. Different levels of variability (IIV and IOV) led to a fraction of healthy subjects with positive test results. The oscillatory behaviour of cortisol response led to an oscillatory pattern in predicted specificity. 

Conclusions:
- New techniques were developed for graphical analysis of the oscillatory cortisol response
- These were successfully applied to equine cortisol data after dexamethasone intervention
- Oscillatory behaviour and level of variability had great impact on the sparse-sample DST-design

References: 
[1] Ekstrand, C. et al. (2015) ‘A quantitative approach to analysing cortisol response in the horse’, Journal of Veterinary Pharmacology and Therapeutics, 39, pp. 255–263. doi: 10.1111/jvp.12276
[2] Carpenter, B. et al. (2017) ‘Stan: A Probabilistic Programming Language’, Journal of Statistical Software, 76(1). doi: 10.18637/jss.v076.i01
[3] Dybdal, N. O. et al. (1994) ‘Diagnostic testing for pituitary pars intermedia dysfunction in horses’, Journal of the American Veterinary Medical Association1, 204, pp. 627–632
[4] Frank, N. et al. (2006) ‘Evaluation of the combined dexamethasone suppression/ thyrotropin-releasing hormone stimulation test for detection of pars intermedia pituitary adenomas in horses.’, Journal of Veterinary Internal Medicine, 20(4), pp. 987–93. doi: 10.1111/j.1939-1676.2006.tb01816.x.