Asuka Suzuki
Teikyo University Graduate School of Public Health, Japan
Introduction: The likelihood ratio test is typically conducted to evaluate whether a candidate covariate should be included into or excluded from the model in population pharmacokinetic (PPK) analysis. For example, the relationship between a dichotomous characteristic of patients and clearance of a drug to be evaluated. Recently, we proposed a method for a covariate selection in PPK analysis when a sampling schedule does not cover the entire time-concentration curve, and hence enough observations were not obtained in a specific time windows that is “information rich” regarding specific PK parameters (e.g. clearance) [1]. Based on the equation derived by Wang [2], we proposed an approximation of deviance that enables to calculate a new statistic, the difference of “pseudo” deviances (or OFV, objective function value, in NONMEM), by creating individual components of deviance for any time points added to cover a time region without observations. However, a method to determine a reasonable rejection criterion has been needed, because the proposed statistic no longer follows the chi-square distribution.
Objectives: To compare the power of the proposed method that uses the pseudo difference of OFV as statistic and the rejection region determined with a parametric bootstrap, with the power of the usual likelihood ratio test using the difference of OFVs.
Methods: The blood drug concentration profiles from the virtual population were simulated for different sampling designs using a 1-compartment model with first-order absorption with inter-individual variability in the distribution volume and the clearance, assuming exponential error models respectively. The simulation settings are as follows: the number of subjects is 70 and half of subjects have the characteristic that affects the clearance of the test drug (i.e. a typical individual value in one-half of the subjects was 0.7 times of the other half); a sampling schedule of each scenario differed in the pattern of deletion of sampling points mainly in the latter part of a time-concentration curve (1, 3, 6, 9, 12, 18, 24, 36, 48, 60 and 72 h after dosing), intended to dare make an unfavorable situation lacking information about clearance; a sampling schedule of each scenario is same for all subjects. For each of the simulated datasets, a difference of pseudo OFV was calculated and simultaneously a rejection criterion was determined from the 5 percentile of the distribution of differences of pseudo OFVs that was created by parametric bootstrap using a set of estimated PPK parameters under the null hypothesis. As a comparison, the usual likelihood test was performed based on the critical value of 3.84; the upper 5 percent point of chi-square distribution of df = 1. The power to reject the null hypothesis under the various sampling design was calculated. NONMEM 7.5 and SAS 9.4 were used.
Results: Some of the conditions are presented here. In the setting that sampling time points are 1, 3, 6 and12, the power to reject the null hypothesis was 0.52 when the proposed method was used, compared to the power of 0.72 of a likelihood test that is the usually applied. Although the results are preliminary, the absolute value of the pseudo OFV difference increases when the set of arbitrarily added time points used to calculate the pseudo OFV and the simulation settings such as the number of patients were changed. Since the rejection criterion did not change at these times, the proposed method may improve the power of covariate selection under some conditions.
Conclusions: With the proposed method, we obtained the rejection criterion that is needed to adopt the robust covariate selection method to real data analysis under the sampling schedule that lacks “information rich” observations. The proposed covariate selection method fail to show the improvement yet the power in the likelihood ratio test about whether a candidate of a dichotomous patients’ characteristic contributes to the inter-individual variety of a certain PK parameter.
References:
[1] Nemoto A. A Robust Covariate Selection Method for the Limited Sampling Design in Population Pharmacokinetic Analysis. The 6th International Symposium on Biopharmaceutical Statistics. Kyoto Japan. August 26-30, 2019.
[2] Wang Y. Derivation of Various NONMEM Estimation Methods. J Pharmacokinet Pharmacodyn. 2007;34(5):575-93.
Reference: PAGE 29 (2021) Abstr 9876 [www.page-meeting.org/?abstract=9876]
Poster: Methodology - Covariate/Variability Models