The New England Journal of Statistics in Data Science

Designing longitudinal studies is generally a very challenging problem because of the complex optimization problems. We show the popular nature-inspired metaheuristic algorithm, Particle Swarm Optimization (PSO), can find different types of optimal exact designs for longitudinal studies with different correlation structures for different types of models. In particular, we demonstrate PSO-generated D-optimal longitudinal studies for the widely used Michaelis-Menten model with various correlation structures agree with the reported analytically derived locally D-optimal designs in the literature when there are only 2 observations per subject, and their numerical D-optimal designs when there are 3 and 4 observations per subject. We further show the usefulness of PSO by applying it to generate new locally D-optimal designs to estimate model parameters when there are 5 or more observations per subject. Additionally, we find various optimal longitudinal designs for a growth curve model commonly used in animal studies and for a nonlinear HIV dynamic model for studying T-cells in AIDS subjects. In particular, c-optimal exact designs for estimating one or more functions of model parameters (c-optimality) were found, along with other types of multiple objectives optimal designs.

In addition to scientific questions, clinical trialists often explore or require other design features, such as increasing the power while controlling the type I error rate, minimizing unnecessary exposure to inferior treatments, and comparing multiple treatments in one clinical trial. We propose implementing adaptive seamless design (ASD) with response adaptive randomization (RAR) to satisfy various clinical trials’ design objectives. However, the combination of ASD and RAR poses a challenge in controlling the type I error rate. In this paper, we investigated how to utilize the advantages of the two adaptive methods and control the type I error rate. We offered the theoretical foundation for this procedure. Numerical studies demonstrated that our methods could achieve efficient and ethical objectives while controlling the type I error rate.

The supersaturated design is often used to discover important factors in an experiment with a large number of factors and a small number of runs. We propose a method for constructing supersaturated designs with small coherence. Such designs are useful for variable selection methods such as the Lasso. Examples are provided to illustrate the proposed method.

The performance of a learning technique relies heavily on hyperparameter settings. It calls for hyperparameter tuning for a deep learning technique, which may be too computationally expensive for sophisticated learning techniques. As such, expeditiously exploring the relationship between hyperparameters and the performance of a learning technique controlled by these hyperparameters is desired, and thus it entails the consideration of design strategies to collect informative data efficiently to do so. Various designs can be considered for this purpose. The question as to which design to use then naturally arises. In this paper, we examine the use of different types of designs in efficiently collecting informative data to study the surface of test accuracy, a measure of the performance of a learning technique, over hyperparameters. Under the settings we considered, we find that the strong orthogonal array outperforms all other comparable designs.

In the interest of business innovation, social network companies often carry out experiments to test product changes and new ideas. In such experiments, users are typically assigned to one of two experimental conditions with some outcome of interest observed and compared. In this setting, the outcome of one user may be influenced by not only the condition to which they are assigned but also the conditions of other users via their network connections. This challenges classical experimental design and analysis methodologies and requires specialized methods. We introduce the general additive network effect (GANE) model, which encompasses many existing outcome models in the literature under a unified model-based framework. The model is both interpretable and flexible in modeling the treatment effect as well as the network influence. We show that (quasi) maximum likelihood estimators are consistent and asymptotically normal for a family of model specifications. Quantities of interest such as the global treatment effect are defined and expressed as functions of the GANE model parameters, and hence inference can be carried out using likelihood theory. We further propose the “power-degree” (POW-DEG) specification of the GANE model. The performance of POW-DEG and other specifications of the GANE model are investigated via simulations. Under model misspecification, the POW-DEG specification appears to work well. Finally, we study the characteristics of good experimental designs for the POW-DEG specification. We find that graph-cluster randomization and balanced designs are not necessarily optimal for precise estimation of the global treatment effect, indicating the need for alternative design strategies.

The crossover models and interference models are frequently used in clinical trials, agriculture studies, social studies, etc. While some theoretical optimality results are available, it is still challenging to apply these results in practice. The available theoretical results, due to the complexity of exact optimal designs, typically require some specific combinations of the number of treatments (t), periods (p), and subjects (n). A more flexible method is to build integer programming based on theories in approximate design theory, which can handle general cases of $(t,p,n)$. Nonetheless, those results are generally derived for specific models or design problems and new efforts are needed for new problems. These obstacles make the application of the theoretical results rather difficult. Here we propose a new algorithm, a revision of the optimal weight exchange algorithm by [1]. It provides efficient crossover designs quickly under various situations, for different optimality criteria, different parameters of interest, different configurations of $(t,p,n)$, as well as arbitrary dropout scenarios. To facilitate the usage of our algorithm, the corresponding R package and an R Shiny app as a more user-friendly interface has been developed.

Systems with both quantitative and qualitative responses are widely encountered in many applications. Design of experiment methods are needed when experiments are conducted to study such systems. Classic experimental design methods are unsuitable here because they often focus on one type of response. In this paper, we develop a Bayesian D-optimal design method for experiments with one continuous and one binary response. Both noninformative and conjugate informative prior distributions on the unknown parameters are considered. The proposed design criterion has meaningful interpretations regarding the D-optimality for the models for both types of responses. An efficient point-exchange search algorithm is developed to construct the local D-optimal designs for given parameter values. Global D-optimal designs are obtained by accumulating the frequencies of the design points in local D-optimal designs, where the parameters are sampled from the prior distributions. The performances of the proposed methods are evaluated through two examples.

Controlled experiments are widely applied in many areas such as clinical trials or user behavior studies in IT companies. Recently, it is popular to study experimental design problems to facilitate personalized decision making. In this paper, we investigate the problem of optimal design of multiple treatment allocation for personalized decision making in the presence of observational covariates associated with experimental units (often, patients or users). We assume that the response of a subject assigned to a treatment follows a linear model which includes the interaction between covariates and treatments to facilitate precision decision making. We define the optimal objective as the maximum variance of estimated personalized treatment effects over different treatments and different covariates values. The optimal design is obtained by minimizing this objective. Under a semi-definite program reformulation of the original optimization problem, we use a YALMIP and MOSEK based optimization solver to provide the optimal design. Numerical studies are provided to assess the quality of the optimal design.

We address the estimation of the Integrated Squared Error (ISE) of a predictor $\eta (x)$ of an unknown function f learned using data acquired on a given design ${\mathbf{X}_{n}}$. We consider ISE estimators that are weighted averages of the residuals of the predictor $\eta (x)$ on a set of selected points ${\mathbf{Z}_{m}}$. We show that, under a stochastic model for f, minimisation of the mean squared error of these ISE estimators is equivalent to minimisation of a Maximum Mean Discrepancy (MMD) for a non-stationary kernel that is adapted to the geometry of ${\mathbf{X}_{n}}$. Sequential Bayesian quadrature then yields sequences of nested validation designs that minimise, at each step of the construction, the relevant MMD. The optimal ISE estimate can be written in terms of the integral of a linear reconstruction, for the assumed model, of the square of the interpolator residuals over the domain of f. We present an extensive set of numerical experiments which demonstrate the good performance and robustness of the proposed solution. Moreover, we show that the validation designs obtained are space-filling continuations of ${\mathbf{X}_{n}}$, and that correct weighting of the observed interpolator residuals is more important than the precise configuration ${\mathbf{Z}_{m}}$ of the points at which they are observed.