Christian Bartels, Bruno Bieth, Thomas Dumortier, Xinting Wang, Jing Yu
Novartis Pharma AG, Basel, Switzerland
Introduction:
Exposure-response relations for time to event data are often analyzed with non-parametric (Kaplan Meier) or semi-parametric (Cox regression) methods. These methods have their limitations. Population pharmacokinetic–pharmacodynamic (PKPD) modelling can overcome some of the limitations.
Objectives:
- Using data from the CANTOS trial (Ridker 2017), evaluate the potential of PKPD modeling in characterizing the exposure-response relationship for time to event data relative to simpler non-parametric or semi-parametric methods.
- Use the PKPD model to estimate the efficacy of the drug when all patients had strictly adhered to treatment, i.e., assess the treatment method effectiveness estimand (Sheiner and Rubin, 1995).
- Position the PKPD estimate of the method effectiveness within statistical causal inference framework (Robins, 2000; Daniel, 2018; Rogers, 2019).
Methods:
We performed a series of exposure-response analyses for the CANTOS trial (Ridker 2017). The CANTOS trial studied anti-inflammatory therapy with Canakinumab for atherosclerotic disease, and involved 10,061 patients with previous myocardial infarction. The primary efficacy endpoint was nonfatal myocardial infarction, nonfatal stroke, or cardiovascular death (MACE). The analyses extended from non-parametric Kaplan-Meier estimates, over semi-parametric proportional hazard methods (linear Cox regression) towards more detailed characterizations using full parametric non-linear population PKPD models for time to first MACE event.
With both modeling approaches (linear Cox and non-linear PKPD), base models were first established that described the baseline hazard as well as baseline covariates. The base models were then expanded by evaluating different exposure-response relationships. For the PKPD models, direct and indirect models were considered. For the linear Cox models, different linear relationships were evaluated including step functions and linear splines.
The models were qualified for simulations based on plots of martingale residuals, visual predictive checks and precision of parameter estimates. In addition, the final model was positioned within a series of alternative models via comparisons of their diagnostic plots, their values of the objective function and their parameter estimates. Importantly, the alternative models included sensitivity analyses to assess potential selection/immortality biases.
Simulations based on the qualified model, corresponding to g-computation in terms of statistical causal inference, were used to assess method effectiveness.
Non-parametric and semi-parametric analyses have been implemented using the survival package in R. The parametric modeling was performed with NONMEM, using R to generate the model diagnostics.
Results:
The non-parametric and semi-parametric linear analyses provided strong evidence for exposure-response on clinical primary and secondary endpoints and gave an initial characterization of the shape of the exposure-response, which seemed to be non-linear.
Nevertheless, some limitations are inherent to these analyses:
- It remains challenging to assess the shape of the exposure-response curves in a continuous manner, since non-linear shapes cannot be evaluated.
- Longitudinal aspects are not being characterized such as the effect of missing a dose.
- These models are not well suited for simulation purposes, e.g., to evaluate different dosing regimens.
Instead, the use of longitudinal non-linear population PKPD analyses gave a more detailed characterization of the exposure-response relationship by estimating EC50, the maximal possible response and by exploring time dependence of the clinical response, as well as incorporating all the dosing records.
Population PKPD modeling provided a framework for robust simulations giving the opportunity to explore further the dose-exposure-response relationship, to assess different dosing regimens and to estimate method effectiveness.
Conclusions:
Standard descriptions of time to event data using semi-parametric (Cox regression) models might be enough to characterize exposure response in most cases. Describing data in a more detailed longitudinal manner using parametric PKPD methods gives additional insights into shape of the exposure response, describes the progression of the clinical endpoints over time, and it enables simulations. . Simulations from the PKPD model adjusted for confounders correspond to g-computations and can provide valid statistical causal inference estimates of method effectiveness.
References:
[1] Daniel, R.M., 2018. G-Computation Formula. Wiley StatsRef: Statistics Reference Online, pp.1-10.
[2] Ridker, P.M., Everett, B.M., Thuren, T., MacFadyen, J.G., Chang, W.H., Ballantyne, C., Fonseca, F., Nicolau, J., Koenig, W., Anker, S.D. and Kastelein, J.J., 2017. Antiinflammatory therapy with canakinumab for atherosclerotic disease. New England Journal of Medicine, 377(12), pp.1119-1131.
[3] Robins, J.M., Hernan, M.A. and Brumback, B., 2000. Marginal structural models and causal inference in epidemiology.
[4] Rogers, J.A., 2019. Causa Nostra: the potentially legitimate business of drawing causal inferences from observational data. CPT: pharmacometrics & systems pharmacology.
Reference: PAGE 28 (2019) Abstr 8922 [www.page-meeting.org/?abstract=8922]
Poster: Methodology - New Modelling Approaches