A geometric characterization of cc-optimal designs for heteroscedastic regression

We consider the common nonlinear regression model where the variance, as well as the mean, is a parametric function of the explanatory variables. The $c$-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of $c$-optimal designs in this context is presented, which generalizes the classical result of Elfving [Ann. Math. Statist. 23 (1952) 255--262] for $c$-optimal designs. As in Elfving's famous characterization, $c$-optimal designs can be described as representations of boundary points of a convex set. However, in the case where there appear parameters of interest in the variance, the structure of the Elfving set is different. Roughly speaking, the Elfving set corresponding to a heteroscedastic regression model is the convex hull of a set of ellipsoids induced by the underlying model and indexed by the design space. The $c$-optimal designs are characterized as representations of the points where the line in direction of the vector $c$ intersects the boundary of the new Elfving set. The theory is illustrated in several examples including pharmacokinetic models with random effects.Comment: Published in at http://dx.doi.org/10.1214/09-AOS708 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A geometric characterization of c-optimal designs for heteroscedastic regression

We consider the common nonlinear regression model where the variance as well as the mean is a parametric function of the explanatory variables. The c-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of c-optimal designs in this context is presented, which generalizes the classical result of Elfving (1952) for c-optimal designs. As in Elfving's famous characterization c-optimal designs can be described as representations of boundary points of a convex set. However, in the case where there appear parameters of interest in the variance, the structure of the Elfving set is different. Roughly speaking the Elfving set corresponding to a heteroscedastic regression model is the convex hull of a set of ellipsoids induced by the underlying model and indexed by the design space. The c-optimal designs are characterized as representations of the points where the line in direction of the vector c intersects the boundary of the new Elfving set. The theory is illustrated in several examples including pharmacokinetic models with random effects. --c-optimal design,heteroscedastic regression,Elfving's theorem,pharmacokinetic models,random effects,locally optimal design,geometric characterization

Optimal designs for random effect models with correlated errors with applications in population pharmacokinetics

We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In the present paper a new approach is introduced to determine efficient designs for nonlinear least squares estimation which addresses the problem of correlation between observations corresponding to the same subject. We use asymptotic arguments to derive optimal design densities, and the designs for finite sample sizes are constructed from the quantiles of the corresponding optimal distribution function. It is demonstrated that compared to the optimal exact designs, whose determination is a hard numerical problem, these designs are very efficient. Alternatively, the designs derived from asymptotic theory could be used as starting designs for the numerical computation of exact optimal designs. Several examples of linear and nonlinear models are presented in order to illustrate the methodology. In particular, it is demonstrated that naively chosen equally spaced designs may lead to less accurate estimation.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS324 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bestimmung c-optimaler Versuchspläne in Modellen mit zufälligen Effekten, mit Anwendungen in der Pharmakokinetik

Medizinische Studien im Bereich der Pharmakokinetik basieren in vielen Fällen auf speziellen Modellen mit zufälligen Effekten, den sogenannten Populationsmodellen. In solchen Studien werden jeweils mehrere Messungen an einer Anzahl verschiedener Patienten durchgeführt. Aus dem Blickwinkel der optimalen Versuchsplanung führt dies zu methodischen Schwierigkeiten, da der zufällige Effekt sowohl eine parameterabhängige Varianz der Beobachtungen als auch teilweise korrelierte Daten zur Folge hat. Auf diese Weise sind zwei der Schlüsselannahmen klassischer Versuchsplanungsliteratur verletzt. Es ist das Ziel dieser Arbeit, die bestehende Methodik so anzupassen und zu ergänzen, dass auch diese Situationen betrachtet werden können. Da die wichtigsten zu schätzenden Kenngrößen in der Pharmakokinetik bestimmte Summengrößen der Parameter sind (z.B. die Fläche unter der Konzentrationskurve eines Präparates) wird der Schwerpunkt dieser Arbeit auf c-optimalen Designs liegen, die die optimale Schätzung solcher Größen erlauben. Im einzelnen wird zunächst die geometrische Repräsentation optimaler Designs nach Elfving (1952) so verallgemeinert, dass die beschriebene Situation abgedeckt ist. Im zweiten Schritt wird die Äquivalenztheorie nach Kiefer (1974) und Pukelsheim (1993) auf das spezifische Modell angewendet. Dritter Schritt ist die Anpassung multplikativer Algorithmen zur numerischen Bestimmung optimaler Designs in dieser Situation, und als letztes Ergebnis wird das Konzept asymptotisch optimaler Designs auf einen speziellen Fall korrelierter Beobachtungen angewendet

Efficient algorithms for calculating optimal designs in pharmacokinetics and dose finding studies

Random effects models are widely used in population pharmacokinetics and dose finding studies. In such models the presence of correlated observations (due to shared random effects and possibly residual serial correlation) usually makes the explicit determination of optimal designs diffcult. In this paper we develop a class of multiplicative algorithms for the numerical calculation of optimal experimental designs in such situations. In particular we demonstrate its application in a concrete example of a cross-over dose finding trial. Additionally, we show that the methodology can be modified to determine optimal designs where there exist some requirements regarding the minimal number of treatments for several (in some cases all) experimental conditions. AMS Subject Classi cation: 62K0

A geometric characterization of c-optimal designs for regression models with correlated observations

We consider the problem of optimal design of experiments for random effects models, especially population models, where a small number of correlated observations can be taken on each individual, while the observations corresponding to different individuals can be assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving (1952) from the case of uncorrelated data can be adapted to the problem of selecting optimal sets of observations for the n individual patients. The theory is demonstrated in a linear model with correlated observations and a nonlinear random effects population model, which is commonly used in pharmacokinetics

Semi-automatic 3D-volumetry of liver metastases from neuroendocrine tumors to improve combination therapy with 177Lu-DOTATOC and 90Y-DOTATOC

PURPOSEPatients with neuroendocrine tumors (NET) often present with disseminated liver metastases and can be treated with a number of different nuclides or nuclide combinations in peptide receptor radionuclide therapy (PRRT) depending on tumor load and lesion diameter. For quantification of disseminated liver lesions, semi-automatic lesion detection is helpful to determine tumor burden and tumor diameter in a time efficient manner. Here, we aimed to evaluate semi-automated measurement of total metastatic burden for therapy stratification.METHODSNineteen patients with liver metastasized NET underwent contrast-enhanced 1.5 T MRI using gadolinium-ethoxybenzyl diethylenetriaminepentaacetic acid. Liver metastases (n=1537) were segmented using Fraunhofer MEVIS Software for three-dimensional (3D) segmentation. All lesions were stratified according to longest 3D diameter >20 mm or ≤20 mm and relative contribution to tumor load was used for therapy stratification.RESULTSMean count of lesions ≤20 mm was 67.5 and mean count of lesions >20 mm was 13.4. However, mean contribution to total tumor volume of lesions ≤20 mm was 24%, while contribution of lesions >20 mm was 76%.CONCLUSIONSemi-automatic lesion analysis provides useful information about lesion distribution in predominantly liver metastasized NET patients prior to PRRT. As conventional manual lesion measurements are laborious, our study shows this new approach is more efficient and less operator-dependent and may prove to be useful in the decision making process selecting the best combination PRRT in each patient

Synergy of retinoic acid and BH3 mimetics in MYC(N)-driven embryonal nervous system tumours

Background Certain paediatric nervous system malignancies have dismal prognoses. Retinoic acid (RA) is used in neuroblastoma treatment, and preclinical data indicate potential benefit in selected paediatric brain tumour entities. However, limited single-agent efficacy necessitates combination treatment approaches. Methods We performed drug sensitivity profiling of 76 clinically relevant drugs in combination with RA in 16 models (including patient-derived tumouroids) of the most common paediatric nervous system tumours. Drug responses were assessed by viability assays, high-content imaging, and apoptosis assays and RA relevant pathways by RNAseq from treated models and patient samples obtained through the precision oncology programme INFORM (n = 2288). Immunoprecipitation detected BCL-2 family interactions, and zebrafish embryo xenografts were used for in vivo efficacy testing. Results Group 3 medulloblastoma (MBG3) and neuroblastoma models were highly sensitive to RA treatment. RA induced differentiation and regulated apoptotic genes. RNAseq analysis revealed high expression of BCL2L1 in MBG3 and BCL2 in neuroblastomas. Co-treatments with RA and BCL-2/XL inhibitor navitoclax synergistically decreased viability at clinically achievable concentrations. The combination of RA with navitoclax disrupted the binding of BIM to BCL-XL in MBG3 and to BCL-2 in neuroblastoma, inducing apoptosis in vitro and in vivo. Conclusions RA treatment primes MBG3 and NB cells for apoptosis, triggered by navitoclax cotreatment