The goal of phase II clinical trials is to evaluate the therapeutic efficacy of a new drug. Some investigators want to use the time-to-event endpoint as the primary endpoint of the phase II study to see the improvement of the therapeutic efficacy of a new drug in median survival time. Recently, median event time test (METT) has been proposed to provide a simple and straightforward rule which compares the observed median survival time with the prespecified threshold. However, median survival time would not be observed during the trial if the drug performs well and indeed cures most patients or if the accrual rate is so fast. To address the issues in clinical practice, we first propose a percentile event time test (PETT), which generalizes METT to any percentile of the survival time, and develop data-driven monitoring for phase II clinical trial designs based on PETT. We evaluate the performance of the method through simulations and illustrate the proposed method with a trial example.

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient computational algorithm for this class is presented that easily scales to thousands of observations and features. We prove minimax optimal convergence bounds for this class under a weak compatibility condition. In addition, we characterize the rate of convergence when this compatibility condition is not met. Finally, we also show that the optimal penalty parameters for structure and sparsity penalties in our framework are linked, allowing cross-validation to be conducted over only a single tuning parameter. We complement our theoretical results with empirical studies comparing some existing methods within this framework.

A common problem faced in clinical studies is that of estimating the effect of the most effective (e.g. the one having the largest mean) treatment among k(≥2) available treatments. The most effective treatment is adjudged based on numerical values of some statistic corresponding to the k treatments. A proper design for such problems is the so-called \"Drop-the-Losers Design (DLD)\". We consider two treatments whose effects are described by independent Gaussian distributions having different unknown means and a common known variance. To select the more effective treatment, the two treatments are independently administered to n1 subjects each and the treatment corresponding to the larger sample mean is selected. To study the effect of the adjudged more effective treatment (i.e. estimating its mean), we consider the two-stage DLD in which n2 subjects are further administered the adjudged more effective treatment in the second stage of the design. We obtain some admissibility and minimaxity results for estimating the mean effect of the adjudged more effective treatment. The maximum likelihood estimator is shown to be minimax and admissible. We show that the uniformly minimum variance conditionally unbiased estimator (UMVCUE) of the selected treatment mean is inadmissible and obtain an improved estimator. In this process, we also derive a sufficient condition for inadmissibility of an arbitrary location and permutation equivariant estimator and provide dominating estimators in cases, where this sufficient condition is satisfied. The mean squared error and the bias performances of various competing estimators are compared via a simulation study. A real data example is also provided for illustration purpose.

This paper derives a macroeconomic resilient control framework that provides the optimal feedback fiscal and monetary policy responses in response to a potentially large negative external incident. We simulate the model for the U.S. under the conditions that prevailed throughout the 2020 economic crisis that occurred due to the government lockdown that was caused by the coronavirus pandemic. We develop a discrete-time soft-constrained linear-quadratic dynamic game under a worst-case design with multiple disturbances. Within this context, we introduce a resilience feedback response and compare the case where the policymakers counter in response the external incident with the case when they do not counter. This framework is especially applicable to large-scale macroeconomic tracking control models and wavelet-based control models when formulating the magnitudes of the policy changes necessary for the unemployment rate and national output variables to maintain acceptable tracking errors in the periods following a major disruption. Our policy recommendations include the maintenance of \"rainy day\" funds at appropriate levels of government to mitigate the effects of large adverse events.

We consider the problem, arising in nuclear spectroscopy, of estimating peak areas in the presence of a baseline of unknown shape. We analyze a procedure that chooses the baseline to be as smooth as is consistent with the data and note that the estimates have a certain minimax optimality. Expressions are developed for the systematic and random errors of the estimate, and some large sample approximations are derived. Procedures for choosing a smoothing parameter are developed and illustrated by simulations.

We present properties some new derivations of properties of a nonlinear version of a minimax tree network location problem. The provide necessary and sufficient conditions for optimality, a means of computing the optimum objective function value, and a means of constructing the unique optimum location.

Previous studies of one-facility minimax location problems are extended by permitting the cost of travel to be given by any (strictly) increasing, continuous function of travel distance. Previous solution procedures for the rectilinear distance problem in the plane and for the problem on a tree network are extended to these general cost functions.

The \'clinical target distribution\' (CTD) has recently been introduced as a promising alternative to the binary clinical target volume (CTV). However, a comprehensive study that considers the CTD, together with geometric treatment uncertainties, was lacking. Because the CTD is inherently a probabilistic concept, this study proposes a fully probabilistic approach that integrates the CTD directly in a robust treatment planning framework. First, the CTD is derived from a reported microscopic tumor infiltration model such that it explicitly features the probability of tumor cell presence in its target definition. Second, two probabilistic robust optimization methods are proposed that evaluate CTD coverage under uncertainty. The first method minimizes the expected-value (EV) over the uncertainty scenarios and the second method minimizes the sum of the expected value and standard deviation (EV-SD), thereby penalizing the spread of the objectives from the mean. Both EV and EV-SD methods introduce the CTD in the objective function by using weighting factors that represent the probability of tumor presence. The probabilistic methods are compared to a conventional worst-case approach that uses the CTV in a worst-case optimization algorithm. To evaluate the treatment plans, a scenario-based evaluation strategy is implemented that combines the effects of microscopic tumor infiltrations with the other geometric uncertainties. The methods are tested for five lung tumor patients, treated with intensity-modulated proton therapy. The results indicate that for the studied patient cases, the probabilistic methods favor the reduction of the esophagus dose but compensate by increasing the high-dose region in a low conflicting organ such as the lung. These results show that a fully probabilistic approach has the potential to obtain clinical benefits when tumor infiltration uncertainties are taken into account directly in the treatment planning process.

We construct robust designs for nonlinear quantile regression, in the presence of both a possibly misspecified nonlinear quantile function and heteroscedasticity of an unknown form. The asymptotic mean-squared error of the quantile estimate is evaluated and maximized over a neighbourhood of the fitted quantile regression model. This maximum depends on the scale function and on the design. We entertain two methods to find designs that minimize the maximum loss. The first is local - we minimize for given values of the parameters and the scale function, using a sequential approach, whereby each new design point minimizes the subsequent loss, given the current design. The second is adaptive - at each stage, the maximized loss is evaluated at quantile estimates of the parameters, and a kernel estimate of scale, and then the next design point is obtained as in the sequential method. In the context of a Michaelis-Menten response model for an estrogen/hormone study, and a variety of scale functions, we demonstrate that the adaptive approach performs as well, in large study sizes, as if the parameter values and scale function were known beforehand and the sequential method applied. When the sequential method uses an incorrectly specified scale function, the adaptive method yields an, often substantial, improvement. The performance of the adaptive designs for smaller study sizes is assessed and seen to still be very favourable, especially so since the prior information required to design sequentially is rarely available.

The system of wireless sensor networks is high of interest due to a large number of demanded applications, such as the Internet of Things (IoT). The positioning of targets is one of crucial problems in wireless sensor networks. Particularly, in this paper, we propose minimax particle filtering (PF) for tracking a target in wireless sensor networks where multiple-RSS-measurements of received signal strength (RSS) are available at networked-sensors. The minimax PF adopts the maximum risk when computing the weights of particles, which results in the decreased variance of the weights and the immunity against the degeneracy problem of generic PF. Via the proposed approach, we can obtain improved tracking performance beyond the asymptotic-optimal performance of PF from a probabilistic perspective. We show the validity of the employed strategy in the applications of various PF variants, such as auxiliary-PF (APF), regularized-PF (RPF), Kullback-Leibler divergence-PF (KLDPF), and Gaussian-PF (GPF), besides the standard PF (SPF) in the problem of tracking a target in wireless sensor networks.