You are dosing into a feedback loop. Exogenous hormone suppresses endogenous secretion, so the measured concentration is the drug plus a baseline that moves in response to it [1,2]. Start from turnover (indirect response), not a direct-effect model [3,4], and add an explicit feedback term when modeling the axis itself [5] (see pharmacodynamics).
Baseline is rhythmic, so sampling time is a covariate. Testosterone follows a circadian rhythm, most pronounced in younger men [6,7]; in premenopausal women LH, FSH, estradiol and progesterone vary across the menstrual cycle [8,9]. A pre-dose sample drawn at an arbitrary hour is one point on a rhythm, not a baseline [10,11].
Response outlasts exposure. Steroids act through nuclear receptors and gene transcription [12], so endpoints such as luteinising hormone, spermatogenesis and prostate specific antigen move on the timescale of the affected system, not of plasma concentration [1,13].
Flip-flop is the norm. Depot injections, implants, transdermal systems and vaginal rings make the formulation set the input rate [14,15]. For non-removable depots absorption is slower than elimination, so the apparent terminal half-life belongs to the vehicle [16,17].
Mechanistic extrapolation. PBPK dominates here, predicting how CYP3A inducers such as efavirenz or rifampicin lower ethinylestradiol and progestin exposure, and whether dose adjustment preserves contraceptive efficacy [18,19].
References
[1]
Bi Y, Perry PJ, Ellerby M, Murry DJ. Population pharmacokinetic/pharmacodynamic modeling of depot testosterone cypionate in healthy male subjects. CPT: Pharmacometrics & Systems Pharmacology 2018;7:259–68.
https://doi.org/10.1002/psp4.12287.
[2]
Pastuszak AW, Bush M, Curd L, Vijayan S, Priestley T, Xiang Q, et al. Population pharmacokinetic modeling and simulations to evaluate a potential dose regimen of testosterone undecanoate in hypogonadal males. The Journal of Clinical Pharmacology 2021;61:1618–25.
https://doi.org/10.1002/jcph.1939.
[3]
Pechstein B, Nagaraja NV, Hermann R, Romeis P, Locher M, Derendorf H. Pharmacokinetic-pharmacodynamic modeling of testosterone and luteinizing hormone suppression by cetrorelix in healthy volunteers. The Journal of Clinical Pharmacology 2000;40:266–74.
https://doi.org/10.1177/00912700022008937.
[4]
Snelder N, Drenth HJ, Riber Bergmann K, Wood ND, Hibberd M, Scott G. Population pharmacokinetic-pharmacodynamic modelling of the relationship between testosterone and prostate specific antigen in patients with prostate cancer during treatment with leuprorelin. British Journal of Clinical Pharmacology 2019;85:1247–59.
https://doi.org/10.1111/bcp.13891.
[5]
Tornøe CW, Agersø H, Senderovitz T, Nielsen HA, Madsen H, Karlsson MO, et al. Population pharmacokinetic/pharmacodynamic (
PK/
PD) modelling of the hypothalamic-pituitary-gonadal axis following treatment with
GnRH analogues. British Journal of Clinical Pharmacology 2007;63:648–64.
https://doi.org/10.1111/j.1365-2125.2006.02820.x.
[6]
Brambilla DJ, Matsumoto AM, Araujo AB, McKinlay JB. The effect of diurnal variation on clinical measurement of serum testosterone and other sex hormone levels in men. The Journal of Clinical Endocrinology & Metabolism 2009;94:907–13.
https://doi.org/10.1210/jc.2008-1902.
[7]
Diver MJ, Imtiaz KE, Ahmad AM, Vora JP, Fraser WD. Diurnal rhythms of serum total, free and bioavailable testosterone and of
SHBG in middle-aged men compared with those in young men. Clinical Endocrinology 2003;58:710–7.
https://doi.org/10.1046/j.1365-2265.2003.01772.x.
[8]
Stricker R, Eberhart R, Chevailler MC, Quinn FA, Bischof P, Stricker R. Establishment of detailed reference values for luteinizing hormone, follicle stimulating hormone, estradiol, and progesterone during different phases of the menstrual cycle on the
Abbott ARCHITECT analyzer. Clinical Chemistry and Laboratory Medicine 2006;44:883–7.
https://doi.org/10.1515/cclm.2006.160.
[9]
Röblitz S, Stötzel C, Deuflhard P, Jones HM, Azulay D-O, Graaf PH van der, et al. A mathematical model of the human menstrual cycle for the administration of
GnRH analogues. Journal of Theoretical Biology 2013;321:8–27.
https://doi.org/10.1016/j.jtbi.2012.11.020.
[11]
Bhasin S, Brito JP, Cunningham GR, Hayes FJ, Hodis HN, Matsumoto AM, et al. Testosterone therapy in men with hypogonadism: An
Endocrine Society clinical practice guideline. The Journal of Clinical Endocrinology and Metabolism 2018;103:1715–44.
https://doi.org/10.1210/jc.2018-00229.
[12]
Burris TP, Solt LA, Wang Y, Crumbley C, Banerjee S, Griffett K, et al. Nuclear receptors and their selective pharmacologic modulators. Pharmacological Reviews 2013;65:710–78.
https://doi.org/10.1124/pr.112.006833.
[13]
Gisleskog PO, Hermann D, Hammarlund-Udenaes M, Karlsson MO. A model for the turnover of dihydrotestosterone in the presence of the irreversible 5
\(\alpha\)-reductase inhibitors
GI198745 and finasteride. Clinical Pharmacology & Therapeutics 1998;64:636–47.
https://doi.org/10.1016/S0009-9236(98)90054-6.
[14]
Francis J, Mngqibisa R, McIlleron H, Kendall MA, Wu X, Dooley KE, et al. A semimechanistic pharmacokinetic model for depot medroxyprogesterone acetate and drug-drug interactions with antiretroviral and antituberculosis treatment. Clinical Pharmacology & Therapeutics 2021;110:1057–65.
https://doi.org/10.1002/cpt.2324.
[16]
Kuan IHS, Wright DFB, Duffull SB. The influence of flip-flop in population pharmacokinetic analyses. CPT: Pharmacometrics & Systems Pharmacology 2023;12:285–7.
https://doi.org/10.1002/psp4.12909.
[18]
Lewis GJ, Ahire D, Taskar KS. Physiologically-based pharmacokinetic modeling of prominent oral contraceptive agents and applications in drug–drug interactions. CPT: Pharmacometrics & Systems Pharmacology 2024;13:563–75.
https://doi.org/10.1002/psp4.13101.
[19]
Adeojo LW, Patel RC, Sambol NC. A physiologically-based pharmacokinetic simulation to evaluate approaches to mitigate efavirenz-induced decrease in levonorgestrel exposure with a contraceptive implant. Pharmaceutics 2024;16:1050.
https://doi.org/10.3390/pharmaceutics16081050.