Online false discovery rate control for LORD++ and SAFFRON under positive, local dependence.

Online testing procedures assume that hypotheses are observed in sequence, and allow the significance thresholds for upcoming tests to depend on the test statistics observed so far. Some of the most popular online methods include alpha investing, LORD++, and SAFFRON. These three methods have been shown to provide online control of the "modified" false discovery rate (mFDR) under a condition known as CS. However, to our knowledge, LORD++ and SAFFRON have only been shown to control the traditional false discovery rate (FDR) under an independence condition on the test statistics. Our work bolsters these results by showing that SAFFRON and LORD++ additionally ensure online control of the FDR under a "local" form of nonnegative dependence. Further, FDR control is maintained under certain types of adaptive stopping rules, such as stopping after a certain number of rejections have been observed. Because alpha investing can be recovered as a special case of the SAFFRON framework, our results immediately apply to alpha investing as well. In the process of deriving these results, we also formally characterize how the conditional super-uniformity assumption implicitly limits the allowed p-value dependencies. This implicit limitation is important not only to our proposed FDR result, but also to many existing mFDR results.

Personalization in biomedical-informatics: Methodological considerations and recommendations.

Over the last decades there has been an increasing interest in personalization: can we make sure that treatments are effective for individual patients? The quest for personalization affects biomedical informatics in two ways: first, we design systems-for example eHealth applications-that directly interact with patients and these systems might themselves one day be personalized. Hence, we seek effective methods to do so. Second, we design systems that collect the data which will one day be used to personalize treatments: hence, we need to critically consider design requirements that improve the utility of (e.g.,) personal health records for future treatment personalization. By clearly defining personalization and analyzing the effectiveness of different personalization methods this discussion highlights how we should embrace sequential experimentation-as opposed to the traditional randomized trial-if we want to personalize our informatics systems efficiently. Furthermore, we need to make sure that we capture the treatment assignment process in our health records: doing so will greatly increase the utility of the collected data for future personalization attempts.

Sequential asymmetric third order rotatable designs (SATORDs).

Rotatable designs that are available for process/ product optimization trials are mostly symmetric in nature. In many practical situations, response surface designs (RSDs) with mixed factor (unequal) levels are more suitable as these designs explore more regions in the design space but it is hard to get rotatable designs with a given level of asymmetry. When experimenting with unequal factor levels via asymmetric second order rotatable design (ASORDs), the lack of fit of the model may become significant which ultimately leads to the estimation of parameters based on a higher (or third) order model. Experimenting with a new third order rotatable design (TORD) in such a situation would be expensive as the responses observed from the first stage runs would be kept underutilized. In this paper, we propose a method of constructing asymmetric TORD by sequentially augmenting some additional points to the ASORDs without discarding the runs in the first stage. The proposed designs will be more economical to obtain the optimum response as the design in the first stage can be used to fit the second order model and with some additional runs, third order model can be fitted without discarding the initial design.