Pharmacogenetics and population pharmacokinetics: impact of the design on three tests using the SAEM algorithm

Abstract

Pharmacogenetics is now widely investigated and health institutions acknowledge its place in clinical pharmacokinetics. Our objective is to assess through a simulation study, the impact of design on the statistical performances of three different tests used for analysis of pharmacogenetic information with nonlinear mixed effects models: (i) an ANOVA to test the relationship between the empirical Bayes estimates of the model parameter of interest and the genetic covariate, (ii) a global Wald test to assess whether estimates for the gene effect are significant, and (iii) a likelihood ratio test (LRT) between the model with and without the genetic covariate. We use the stochastic EM algorithm (SAEM) implemented in MONOLIX 2.1 software. The simulation setting is inspired from a real pharmacokinetic study. We investigate four designs with N the number of subjects and n the number of samples per subject: (i) N = 40/n = 4, similar to the original study, (ii) N = 80/n = 2 sorted in 4 groups, a design optimized using the PFIM software, (iii) a combined design, N = 20/n = 4 plus N = 80 with only a trough concentration and (iv) N = 200/n = 4, to approach asymptotic conditions. We find that the ANOVA has a correct type I error estimate regardless of design, however the sparser design was optimized. The type I error of the Wald test and LRT are moderatly inflated in the designs far from the asymptotic (<10%). For each design, the corrected power is analogous for the three tests. Among the three designs with a total of 160 observations, the design N = 80/n = 2 optimized with PFIM provides both the lowest standard error on the effect coefficients and the best power for the Wald test and the LRT while a high shrinkage decreases the power of the ANOVA. In conclusion, a correction method should be used for model-based tests in pharmacogenetic studies with reduced sample size and/or sparse sampling and, for the same amount of samples, some designs have better power than others.

Fig 1

Mean simulated concentration-time curve and allocation of the sampling times within each of the designs N=40/n=4, N=80/n=2, N=100/n=4,1 and N=200/n=4 (separated by solid horizontal lines): the vertical lines denote the four possible sampling times, the dashed horizontal lines join samples within the same group and the circles size is proportional to the sample size within each elementary design.

Fig 2

Concentrations (ng/mL) simulated for the designs N=40/n=4 (left), N=80/n=2 (center) and N=100/n=4,1 (right) for a representative data set under H₀ (top) and a representative one under H₁ (bottom). Solid lines represent the subjects CC while dashed and dotted lines represent the subjects CT and TT for the exon SNP₁, respectively. For the N=100/n=4,1 design, circles represent the subjects CC while triangles and plus represent the subjects CT and TT for the exon SNP₁, respectively.

Fig 3

(a) Boxplot of shrinkage on V/F from M_base obtained with SAEM on the 1000 data sets simulated under H₀ (grey) and H₁ (black) for the designs N=40/n=4, N=80/n=2, N=100/n=4,1 and N=200/n=4, (b) type I error for the ANOVA on the log-parameters versus the empirical shrinkage on V/F for the designs N=40/n=4 (○), N=80/n=2 (△), N=100/n=4,1 (+) and N=200/n=4 (×) simulated under H₀, (c) Corrected power of the ANOVA on the log-parameters versus the empirical shrinkage on V/F for the designs N=40/n=4 (○), N=80/n=2 (△) and N=100/n=4,1 (+) simulated under H₁.

Fig 4

(a) Boxplot of the estimated standard errors (SE) and corresponding empirical SE (dotted line) obtained with SAEM for β₁ and β₂ on the 1000 data sets simulated under both H₀ (grey) and H₁ (black) for the N=40/n=4, N=80/n=2, N=100/n=4,1 and N=200/n=4 designs, (b) Wald test type I error versus the ratio of the median SE over the empirical SE for β₂ for the designs N=40/n=4 (○), N=80/n=2 (△), N=100/n=4,1 (+) and N=200/n=4 (×) simulated under H0, (c) Wald test corrected power versus the empirical SE for β₂ for the designs N=40/n=4 (○), N=80/n=2 (△) and N=100/n=4,1 (+) simulated under H1.

Fig 5

Histograms of the likelihood ratio test (LRT) statistics above the theoretical threshold (5.99) obtained with SAEM under H₀ for the N=40/n=4, N=80/n=2, N=100/n=4,1 and N=200/n=4 designs. The dotted curve corresponds to the density of a χ² with 2 degrees of freedom.

Fig 6

Standard errors versus the estimates for β₁ and β₂ obtained with FOCE-I in NONMEM version V (a) and (b) and SAEM in MONOLIX version 2.1 (c) and (d) for the design N=40/n=4 simulated under H₁. Note that β_FOCE–I1 and β_FOCE–I2 correspond respectively to e^β_SAEM1 and e^β_SAEM2, therefore the scales are different.