Takayuki Katsube, Toshihiro Wajima
Shionogi & Co., Ltd., Japan
Introduction: Assessing covariate impact on the outcome is important for clinical practice. Inter-individual variability (IIV) for the outcome is commonly variances from individual covariates and from individual random variables which are defined as ETA in NONMEM [1]. A contribution of covariate effect for overall variability of the outcome is expected to describe a covariate impact on the outcome. Variance ratios (Sobol index) are used as a sensitivity index to assess impacts of parameter variability in global sensitivity analyses [2,3]. We reported the variance-based global sensitivity approach would be useful to evaluate covariate effects on outcomes from continuous responses, such as plasma concentrations [4]. In pharmacometric analyses, covariate effects are evaluated for not only continuous response but also categorical response (e.g., pain relief, severity of adverse events).
Objectives: In this study, variance-based global sensitivity approach was applied to categorical response to quantitate contribution of each of covariate effects and random effects on the response.
Methods: Logit transformation is often performed for analyzing categorical response data to transform probability of each measurement from probability scale to non-bounded scale. Logit is used for covariate modeling of categorical response data. The distribution of logit is expected to follow normal distribution, which is favorable to apply the variance-based approach. Therefore, ratios of variance explained by each covariate or by each ETA over the overall variance of logit was used as a sensitivity index. Monte-Carlo simulations were conducted to simulate covariates and ETAs, and then calculate logit based on the model. Variance ratios of logit for each of covariates and ETAs were calculated using soboljansen in R library ”sensitivity” [5]. To assess the variance ratios of logit, an additive model (logit=covariate+ETA) for binary response (0 or 1) was used. For distributions of covariate and ETA, mean of each covariate and ETA was set to 0, and variances of covariate and ETA was set to be variance ratios of 20% to 80% for the covariate. As the 1st set, variances of the covariate were 0.0625 to 1 and variance of ETA was 0.25; as the 2nd set, variances of the covariate were 0.125 to 4 and variance of ETA was 1. An additive model with time-varying function for binary response was also tested. As assessments based on real models, a logistic model of topotecan with individual random variability for ordered categorical severity of neutropenia [6] was used to assess the variance-based approach. In this model, daily AUC was a covariate. A logistic model of pregabalin with individual random variability for ordered categorical pain score [7] was also used for the assessment. In this model, baseline pain score, creatinine clearance, age, and sex were covariates, and time-varying functions were included. Using each of the above models, probabilities of response in subjects with mean covariate and with 95th percentile of covariate were calculated, and differences in probabilities of the responses between both subject population were used to compare with results based on the variance ratios.
Results: In the additive model, the magnitude of variance ratios of logit explained by the covariate corresponded with differences in probabilities of responses between the subjects with mean covariate and with the 95th percentile. The magnitude of absolute variances for the covariate also affected the difference in probabilities. In the additive model with time-varying function, the time-dependent change in variance ratios was consistent with the changes in probabilities of responses between the subjects with mean covariate and with the 95th percentile. In the model of topotecan, the variance ratios explained by daily AUC was approximately 40% and the probabilities of neutropenia grade ≥ 4 was clearly different between the subjects with mean daily AUC and with the 95th percentile. In the model of pregabalin, the variance ratios explained by baseline pain score were 20% to 40% over 24 days of the observation period, and a clear difference in pain scores were observed between the subjects with mean baseline pain score and with the 95th percentile.
Conclusions: The variance ratio was an index to quantify covariate effects on categorical response. The variance-based global sensitivity approach would be useful to assess the impact of covariate effect on categorical response.
References:
[1] Beal SL et al. NONMEM Users Guides. Icon Development Solutions, Ellicott City, Maryland, USA. 1989-2011.
[2] Saltelli A et al. Comput Phys Commun. 2010. 18:259-270.
[3] Zhang XY et al. CPT Pharmacometrics Syst Pharmacol. 2015. 4:69-79.
[4] Katsube T et al. PAGE2019 abstract https://www.page-meeting.org/default.asp?abstract=8819 Stockholm, Sweden.
[5] https://CRAN.R-project.org/package=sensitivity
[6] Mould DR et al. Clin Pharmacol Ther. 2002. 71:334-348.
[7] Byon W et al. J Clin Pharmacol. 2010. 50:803-815.
Reference: PAGE () Abstr 9246 [www.page-meeting.org/?abstract=9246]
Poster: Methodology - Covariate/Variability Models