Prediction of power of test of discrete covariates in population analyses and influence of design: application to gender effect in joint pharmacokinetic models of nucleoside analogs and their active metabolites
Caroline Bazzoli , Sylvie Retout , France Mentré
INSERM U738 and Université Paris Diderot, Paris, France.
Objectives: To predict power of test of gender effect and to study the influence of design in population pharmacokinetic (PK) analyses of nucleoside reverse transcriptase inhibitors (NRTI) and their active metabolite using joint pharmacokinetic models.
Methods: Methodology for design evaluation and optimization in nonlinear mixed effects models has been extended for models with parameters quantifying influence of discrete covariates [1, 2]. The predicted standard error (SE) from the computation of the Fisher information matrix (MF) is used to predict the power of the Wald test of a discrete covariate as well as the number of subjects needed to achieve a given power. We apply this development on multiple response PK models: the joint population model of zidovudine (ZDV) and its active metabolite ZDV-TP and the joint population model of lamivudine (3TC) and its active metabolite 3TC-TP [3]. Results from clinical trials suggest that there may be clinically important gender differences in antiretroviral PK, especially on intracellular concentrations of NRTI [4, 5]. Data are obtained from the COPHAR2-ANRS 111 trial in 75 naïve HIV patients receiving oral combination of ZDV and 3TC, as part of their HAART treatment. Four blood samples per patient were taken after two weeks of treatment to measure the concentrations at steady state at 1, 3, 6 and 12 hours. Intracellular concentrations were measured in 62 patients, 11 patients had 4 samples the remaining had 1 or 2 samples at 3h and/or 12h. Using the SAEM algorithm implemented in the MONOLIX software [6], we estimate the PK parameters of ZDV and 3TC and their active metabolites including in each model a gender effect on the apparent clearance of the metabolite. Using PFIM 3.2, a new extension of PFIM [7, 8], we then compute the expected power to detect the gender effect with the initial design and thus, we predict the number of subjects needed to achieve a power of 80% for the test. Influence of optimized design on the power and the number of subjects needed from the whole matrix of population parameters from both responses is studied.
Results: The apparent metabolite clearance of ZDV-TP increases by 30 % for male compare to female, although not significant (p=0.162). With the initial design and a type I error of 5%, an expected power of 31% is computed to detect this gender effect. To achieve a power of 80%, 273 subjects would be needed to detect such an increase with the same sampling design. An optimized design using PFIM 3.2 yields a greater power. Regarding 3TC and 3TC-TP, because a very small decrease of 3% of the clearance of the metabolite in male is found we do not investigate further the power of this test.
Conclusions: We illustrate the consequence of the choice of the design and the number of patients needed to achieve a given power of the Wald test of discrete covariate for complex PK models, i.e. accommodating several responses. This approach can also be applied to compute power of test of absence of effect of covariates, i.e. using an equivalence test, given "equivalence" limits.
References:
[1] Retout S, Mentré F. Further developments of the Fisher information matrix in nonlineari mixed effects models with evaluation in population pharmacokinetics. Journal of Biopharmaceutical Statistics, 2003; 13(2):209-27.
[2] Retout S, Comets E, Samson A, Mentré F. Design in nonlinear mixed effects models: Optimization using the Federov-Wynn algorithm and power of the Wald test for binary covariates. Statistics in Medicine, 2007; 26(28):5162-79.
[3] Bazzoli C, Benech H, Rey E, Retout S, Tréluyer JMT, Salmon D, Duval X, Mentré F and the COPHAR2- ANRS 111 study group. Pharmacokinetics of zidovudine, lamivudine and their active metabolites in HIV patients using joint population models. 10th International Workshop on Clinical Pharmacology of HIV Therapy, 2009; (Poster).
[4] Anderson PL, Kakuda TN, Kawle S, Fletcher CV. Antiviral dynamics and sex differences of zidovudine and lamivudine triphosphate concentrations in HIV-infected individuals. AIDS, 2003; 17(15):2159-68.
[5] Aweeka FT, Rosenkranz SL, Segal Y, Coombs RW, Bardeguez A, Thevanayagam L, Lizak P, Aberg J, Watts DH; NIAID AIDS Clinical Trials Group. The impact of sex and contraceptive therapy on the plasma and intracellular pharmacokinetics of zidovudine. AIDS, 2006; 20(14):1833-41.
[6] www.monolix.org
[7] www.pfim.biostat.fr
[8] Bazzoli C, Retout S, Comets E, Le Nagard H, Mentré F. New features for population design evaluation and optimization with R functions: PFIM Interface 3.1 and PFIM 3.2. PAGE meeting, 2009; (Software demonstration).
