Do we need a perfect basic structural model before exploring the covariate model? Example with enoxaparin
Bergès A (1), Laporte S (1), Girard P (5), Epinat M (2), Zufferey P (3), Alamartine E (4), Decousus H (1,2), Mismetti P (1,2) for the PROPHRE-75 study Group*.
1) Clinical Pharmacology Dpt., 2) Dpt. of Internal Medicine, 3) Anesthesiology Dpt., and 4) Nephrology Unit, all from the Thrombosis Research Group (EA3065), University Hospital of Saint-Etienne, France. 5) EA3738 CTO, Lyon, France. * Supported by a grant from PHRC 2001.
Background: Major bleeding complications with low-molecular-weight heparin (LMWH) treatment have been reported from pharmacovigilance, randomised and observational studies, especially in elderly patients. An accumulating effect in patients with renal impairment was referred to explain this phenomena, because of the exclusive kidney elimination route of LMWH. As a result, monitoring anti-factor Xa activity is recommended in special situations, even without clear knowledge of normal targeted range. A population pharmacokinetic study was conducted to estimate distribution parameters of anti-Xa activity in the elderly and factors yielding in a potential between-subject variability.
Methods: We conducted a prospective study in a cohort of consecutive patients older than 75 years and treated with 4000 IU subcutaneous injection of enoxaparin once daily for medical or surgical venous thrombo-embolism prophylaxis. Dosing history and sparse samplings for anti-factor Xa activity were collected throughout the duration of treatment. Additional data included, weight, gender, age, renal function, medical history and concomitant medication. Population parameters and inter-individual variability were estimated using NONMEM® V program (ADVAN2 and ADVAN4). Model validation will be performed by using a posterior predictive check.
Results: Anti-Xa activity was available in 189 patients receiving enoxaparin for the prevention of venous thrombo-embolism (160 medical and 29 orthopaedic patients). Mean age (± sd) was 82 ± 5 years, 21% of patients had body weight lower than 55 kg; 49% presented severe or moderate renal impairment according to creatinine clearance estimated by Cockcroft and Gault formula lower than 50 ml/min. An average of 2.4 measurements of anti-Xa levels per patient was available; anti-Xa levels varied from 0.05 to 1.0 IU/ml. A large panel of population pharmacokinetic models were tested using FOCE INTERACTION in NONMEM but all presented the same fitting problem on population prediction: according to the graphical approach, the measured anti-Xa activities were systematically predicted below 0.5 IU/ml even when the observed values were up to 1.0 IU/ml. Several paths were explored without any fit improvement:
i) changing the structural model (one, two, or three-compartment model) [1,2], the absorption model (first-order and zero-order) or introducing non-linear Michaelis-Menten elimination;
ii) changing the error model from multiplicative to additive or mixed error model;
iii) using transformation both sides with logarithm-transformed data and prediction;
iv) adding anti-factor Xa endogenous baseline activity [1-3];
v) omitting or replacing data below the LOQ [4].
Conclusion: Nearly all evaluated models were already described in the literature without any consensus [1-2, 5-6]. In fact, the choice of model seems to be dosage regimen-dependant (curative or prophylactic treatment), design-dependant (sparse or rich data), and drug-dependant (tinzaparin or enoxaparin). The best model found in this PK study, according to objective function, was a two-compartment model with a first-order absorption, without endogenous activity. However this model was unsatisfactory in predicting higher activities above 0.5 IU/ml which represented only 13% of the total number of measured activities, but could potentially be related with higher bleeding risks.
Other model improvements are actually explored as mixture models, between patient variability of residual variance and integration of covariates. The issues that have to be fixed are the following: which other model improvement can be added to correct the systematic prediction error? Do we need to have a perfect basic structural model before exploring the covariate model? Once correct model for anti-Xa activity in the elderly will be identified and qualified using posterior predictive check, it will be used for dose adjustment recommendation and/or optimisation.
References:
1. Green B et al. Br J Clin Pharmacol 2004; 59: 281-90.
2. Barrett JS et al. Int J Clin Pharmacol Ther 2001; 39: 431-46.
3. Schoemaker E & Cohen A, Br J Clin Pharmacol 1996; 42: 283-90.
4. Duval V & Karlsson M, Pharmaceutical Res 2002; 19: 1835-40.
5. Bruno R et al. Br J Clin Pharmacol 2003; 56: 407-14.
6. Hulot JS et al. Ther Drug Monit 2004; 26: 305-10.