A SIMPLE NONPARAMETRIC APPROACH FOR ESTIMATION AND INFERENCE OF CONDITIONAL QUANTILE FUNCTIONS

In this paper, we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy to implement and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. Our Monte Carlo simulations show that this new estimator compares well with the check-function-based estimator in terms of estimation mean squared error. The bootstrap confidence bands yield adequate coverage probabilities. An empirical example uses a dataset of Canadian high school graduate earnings, illustrating the usefulness of the proposed method in applications.

Multivariate functional additive mixed models

Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary such as precipitation, temperature and wind speeds over time at a given weather station. We propose a multivariate functional additive mixed model (multiFAMM) and show its application to both data situations using examples from sports science (movement trajectories of snooker players) and phonetic science (acoustic signals and articulation of consonants). The approach includes linear and nonlinear covariate effects and models the dependency structure between the dimensions of the responses using multivariate functional principal component analysis. Multivariate functional random intercepts capture both the auto-correlation within a given function and cross-correlations between the multivariate functional dimensions. They also allow us to model between-function correlations as induced by, for example, repeated measurements or crossed study designs. Modelling the dependency structure between the dimensions can generate additional insight into the properties of the multivariate functional process, improves the estimation of random effects, and yields corrected confidence bands for covariate effects. Extensive simulation studies indicate that a multivariate modelling approach is more parsimonious than fitting independent univariate models to the data while maintaining or improving model fit.

Optimal Designs for Comparing Regression Curves: Dependence Within and Between Groups

We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to derive efficient designs we use results from stochastic analysis to identify the best linear unbiased estimator (BLUE) in a corresponding continuous model. It is demonstrated that in general simultaneous estimation using the data from both groups yields more precise results than estimation of the parameters separately in the two groups. Using the BLUE from simultaneous estimation, we then construct an efficient linear estimator for finite sample size by minimizing the mean squared error between the optimal solution in the continuous model and its discrete approximation with respect to the weights (of the linear estimator). Finally, the optimal design points are determined by minimizing the maximal width of a simultaneous confidence band for the difference of the two regression functions. The advantages of the new approach are illustrated by means of a simulation study, where it is shown that the use of the optimal designs yields substantially narrower confidence bands than the application of uniform designs.

Prediction of record values by using quantile regression curves and distortion functions

The purpose of the paper is to provide a general method based on conditional quantile curves to predict record values from preceding records. The predictions are based on conditional median (or median regression) curves. Moreover, conditional quantiles curves are used to provide confidence bands for these predictions. The method is based on the recently introduced concept of multivariate distorted distributions that are used instead of copulas to represent the dependence structure. This concept allows us to compute the conditional quantile curves in a simple way. The theoretical findings are illustrated with a non-parametric model (standard uniform), two parametric models (exponential and Pareto), and a non-parametric procedure for the general case. A real data set and a simulated case study in reliability are analysed.

273 Application of pharmacokinetic-pharmacodynamic modeling to select the optimal dose of ALX148, a CD47 blocker

BackgroundALX148 is a fusion protein comprised of a high-affinity CD47 blocker linked to an inactive immunoglobulin Fc region. Optimal doses selection is increasingly important in clinical setup and can be guided by an assessment of target receptor occupancy (RO) and pharmacodynamics (PD) effect in the site of action. However, direct measurement of RO and PD effect in the tumor tissue is challenging. A mechanistic pharmacokinetic (PK)-PD model was developed to predict CD47 occupancy and PD effect in tumor tissues for ALX148.MethodsThe developed semi-mechanistic PK/RO/PD model describes the PK of ALX148 and its distribution to non-Hodgkin lymphoma tumor tissues (lymph nodes, spleen, and bone marrow). The model includes non-linear clearance of ALX148 due to target CD47 receptor binding and further internalization of the complex. CD47 RO was described on red blood cells and tumor cells taking into account the number of cells and CD47 expression (molecules per cell). Parameters were fitted against clinical PK and in vitro data. In vitro data on stimulation of phagocytosis by ALX148 in the presence of antibodies inducing antibody-dependent cellular phagocytosis (ADCP) was used to estimate the RO-PD relationship. Clinical data on RO in the periphery was used for model validation.ResultsThe model successfully described dose-dependence ALX148 clinical PK and RO data. Predicted trough median CD47 occupancy in the spleen, lymph nodes, and bone marrow during the treatment with 10 mg/kg QW ALX148 was 98% (95% confidence bands: 95%–99%), whereas 30 mg/kg Q2W resulted in 99% CD47 occupancy (95% confidence bands: 98%–99%). ADCP of cancer cells was predicted to be increased by ~1.8 times during the treatment with both regimens of ALX148: 10 mg/kg QW and 30 mg/kg Q2W. Dose 3 mg/kg resulted in the lower induction of ADCP than 10 mg/kg: 1.6 vs 1.8 (p-value < 0.001).ConclusionsThe model was successfully calibrated and validated against both in vitro and clinical data on ALX148. It was predicted that 10 mg/kg QW is an optimal dose of ALX148 to occupy more than 90% of CD47 in the tumor tissues to achieve maximal induction of phagocytosis caused by ADCP stimulating antibodies such as rituximab. This approach can be applied for the optimal dose selection of other anti-CD47 agents taking into account their specific features as binding properties, size, etc.

Lower Heating Value of Jet Fuel from Hydrocarbon Class Concentration Data and Thermo-Chemical Reference Data: An Uncertainty Quantification

A detailed assessment is presented on the calculation and uncertainty of the lower heating value (net heat of combustion) of conventional and sustainable aviation fuels, from hydrocarbon class concentration measurements, reference molecular heats of formation, and the uncertainties of these reference heats of formation. Calculations using this paper’s method and estimations using ASTM D3338 are reported for 17 fuels of diverse compositions and compared against reported ASTM D4809 measurements. All the calculations made by this method and the reported ASTM D4809 measurements agree (i.e., within 95% confidence intervals). The 95% confidence interval of the lower heating value of fuel candidates that are comprised entirely of normal- and iso-alkanes is less than 0.1 MJ/kg by the method described here, while high cyclo-alkane content leads to 95% confidence bands that approach 0.2 MJ/kg. Taking a possible bias into account, the accuracy and precision of the method described in this work could be as high as 0.23 MJ/kg for some samples.

Distributionally Robust Optimization with Confidence Bands for Probability Density Functions

Distributionally robust optimization (DRO) has been introduced for solving stochastic programs in which the distribution of the random variables is unknown and must be estimated by samples from that distribution. A key element of DRO is the construction of the ambiguity set, which is a set of distributions that contains the true distribution with a high probability. Assuming that the true distribution has a probability density function, we propose a class of ambiguity sets based on confidence bands of the true density function. As examples, we consider the shape-restricted confidence bands and the confidence bands constructed with a kernel density estimation technique. The former allows us to incorporate the prior knowledge of the shape of the underlying density function (e.g., unimodality and monotonicity), and the latter enables us to handle multidimensional cases. Furthermore, we establish the convergence of the optimal value of DRO to that of the underlying stochastic program as the sample size increases. The DRO with our ambiguity set involves functional decision variables and infinitely many constraints. To address this challenge, we apply duality theory to reformulate the DRO to a finite-dimensional stochastic program, which is amenable to a stochastic subgradient scheme as a solution method.