Recent Advances in Design and Analysis of Screening Experiments with Applications in Healthcare

Screening designs that do not allow estimation of all effects of interest are often compared under one or more heuristic criteria that in some way measure their proximity to an unattainable orthogonal design. Such criteria do not directly measure a design's quality in terms of screening. To address this disconnect, we develop an optimal design framework to maximize the lasso's sign recovery probability. The proposed criteria have varying amounts of prior knowledge about the model's parameters. We show that an orthogonal design is an ideal structure when the signs of the active factors are unknown. When the signs are assumed known, we show that a design whose columns exhibit small, positive correlations are ideal. These conclusions are based on a new approximate design framework. From this justification, we propose a computationally-efficient design search algorithm that filters through optimal designs under different heuristic criteria to select the one that maximizes the sign recovery probability under the lasso. 

In some experimental situations, there is a natural grouping of factors. Prior knowledge may indicate that active two-factor interactions only occur within groups of factors. Designs of variable resolution (Lin ,2012) were introduced for such situations. However, main effects from one group in a design of variable resolution may be aliased with non-negligible two-factor interactions from another group. In this talk, we introduce robust designs of variable resolution which ensure main effects are robust to non-negligible interactions that occur within groups of factors. Constructions are provided for a number of situations and connected to other recent designs.  

There is increasing recognition that the order of administration of drugs in drug combination studies can markedly affect the outcome. Similarly, manufactured products are often sequentially produced and the final quality frequently depends on the order of assembly. Order-of-addition experiments account for the order of administration of the components, and they are quite prevalent, yet research in this area is quite limited, especially in the screening situations where there are more components to choose. We present a series of models for order-of-addition screening experiments and study their properties. We illustrate these models on a drug combination experiment which studies combinations of three antibiotics and two chemotherapy drugs in order to eliminate intracellular microbes. 

For a designed experiment with many factors, when observations are expensive, it is common that the number of model effects is much larger than the number of observations. A design for such a problem is known as a supersaturated design. Experiments that use such designs are intended to differentiate between a few factors that can explain most of the differences in a response variable and the factors that are unimportant. Various methods of analysis have been proposed for such experiments, but correctly identifying the few important factors is very challenging because, typically, many models will fit the data approximately equally well. We will discuss some of the challenges and how identifying the important factors may be improved by considering multiple fitted models.