In project P6, we examine to what extent the concept of regression models with shared parameters can be used for estimating dose-exposure curves for different genes belong to the same gene group, for example a GO class.

The common way of modelling concentration-response curves for different genes in the same GO class is to estimate the concentration-response curve for each of them separately. Nevertheless, this procedure can be wasteful, since different genes in the same GO class are proven to have similar properties and certain aspects of the concentration-response curves for different genes might be similar, suggesting a borrowing of strength. More precisely, if concentration-response modelling is performed with parametric models one might assume that some parameters of the curves for the different genes are shared, resulting in a more precise estimation of these parameters. Feller et al. (2017) have shown in the context of dose-finding studies that sharing parameters (in connection to the optimal design) improves the statistical inference significantly. Therefore, we want to investigate to what extent the concept of common parameters can be applied when fitting concentration-exposure curves for different genes of the same GO class.

In the first part of this project, we will use model selection to decide which parameters of doseresponse curves are shared by different genes of the same GO class. First, we will apply different classical information criteria, e.g. AIC and BIC (see Konishi and Kitagawa, 2008, among many others), to investigate which parameters should be shared in the parametric models. Note that neither the AIC nor the BIC take into account the goal, when fitting concentration-response curves. The goal might be, e.g., the estimation of the ALEC (absolute lowest effective concentration) or of the area under the curve (AUC). Therefore, we will generalize the focused information criterion defined by Claeskens and Hjort (2003) to the setting of different groups that might share parameters. The focused information criterion aims for the model resulting in the most precise estimation of a predefined one-dimensional parameter in the sense of a minimal mean squared error. Consequently, a moderate misspecification of the model is tolerated if the mean squared error of the resulting estimator of the parameter of interest is small. Following this idea, the information criterion for our setting will take into account both the focus, e.g. the ALEC or the AUC, and the different possibilities to share parameters among the different genes. More precisely, it might be reasonable to tolerate a moderate misspecification in the model of one gene caused by the assumption of common parameters if the resulting estimation of the parameter of interest has a small mean squared error. The performance of this new criterion will be compared to the performance of classical model selection criteria within a simulation study and in application to real data.

In the second part of this project, we will calculate optimal designs for dose-exposure curves with common parameters, where the designs also take the focus, e.g. the estimation of the ALEC or the AUC, into account. Initially, we will assume that the common parameters are perfectly shared without any perturbation and we will derive designs that result in precise estimation of the parameter of interest for each gene. Second, we will follow the idea of the setting of the aforementioned moderate misspecification and will derive designs that can be used to obtain a precise estimation of the parameter of interest under the circumstance that the parameters are not “perfectly” shared. The calculated designs will be compared to designs that are usually used in the joint work with IfADo, both in a simulation study and in conducted experiments.

- Claeskens G, Hjort NL (2003). The focused information criterion. J American Statistical Association. 98, 464, 900-916, doi: 10.1198/016214503000000819.
- Feller C, Schorning K, Dette H, Bermann G, Bornkamp B (2017). Optimal designs for dose response curves with common parameters. The Annals of Statistics 45 (5), 2102-2132, doi: 10.1214/16-AOS1520.
- Konishi S, Kitagawa G (2008). Information criteria and statistical modeling. John Wiley & Sons, New York.