The identification of peaks or maxima in probability densities, by mode testing or bump hunting, has become an important problem in applied fields. This task has been approached in the statistical literature from different perspectives, with the proposal of testing procedures which are based on kernel density estimators or on the quantification of excess mass. However, none of the existing proposals provides a satisfactory performance in practice. In this work, a new procedure which combines the previous approaches (smoothing and excess mass) is presented and compared with the existing methods, showing a superior behaviour. A real data example on philatelic data is also included for illustration purposes.

In several applied fields, multimodality assessment is a crucial task as a previous exploratory tool or for determining the suitability of certain distributions. The goal of this paper is to present the utilities of the R package multimode, which collects different exploratory and testing non-parametric approaches for determining the number of modes and their estimated location. Specifically, some graphical tools (SiZer map, mode tree or mode forest) are provided, allowing for the identification of mode patterns, based on the kernel density estimation. Several formal testing procedures for determining the number of modes are described in this paper and implemented in the multimode package, including methods based on the ideas of the critical bandwidth, the excess mass or using a combination of both. This package also includes a function for estimating the modes locations and different classical data examples that have been considered in mode testing literature.

The evidence of an association between Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS) and chronic herpesviruses infections remains inconclusive. Two reasons for the lack of consistent evidence are the large heterogeneity of the patients' population with different disease triggers and the use of arbitrary cutoffs for defining seropositivity. In this work we re-analyzed previously published serological data related to 7 herpesvirus antigens. Patients with ME/CFS were subdivided into four subgroups related to the disease triggers: S0-42 patients who did not know their disease trigger; S1-43 patients who reported a non-infection trigger; S2-93 patients who reported an infection trigger, but that infection was not confirmed by a lab test; and S3-48 patients who reported an infection trigger and that infection was confirmed by a lab test. In accordance with a sensitivity analysis, the data were compared to those from 99 healthy controls allowing the seropositivity cutoffs to vary within a wide range of possible values. We found a negative association between S1 and seropositivity to Epstein-Barr virus (VCA and EBNA1 antigens) and Varicella-Zoster virus using specific seropositivity cutoff. However, this association was not significant when controlling for multiple testing. We also found that S3 had a lower seroprevalence to the human cytomegalovirus when compared to healthy controls for all cutoffs used for seropositivity and after adjusting for multiple testing using the Benjamini-Hochberg procedure. However, this association did not reach statistical significance when using Benjamini-Yekutieli procedure. In summary, herpesviruses serology could distinguish subgroups of ME/CFS patients according to their disease trigger, but this finding could be eventually affected by the problem of multiple testing.

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Background The current COVID-19 outbreak represents a most serious challenge for societies worldwide. It is endangering the health of millions of people, and resulting in severe socioeconomic challenges due to lock-down measures. Governments worldwide aim to devise exit strategies to revive the economy while keeping the pandemic under control. The problem is that the effects of distinct measures are not well quantified.Methods This paper compares several suppression approaches and potential exit strategies extending the classic epidemic SEIR model into a SPQEIR model. This allows to assess the effect of individual and combined approaches on epidemic decline. In addition to peak flattening, we also estimate the time to zero infectious associated with each strategy, and their corresponding reproduction number. Finally, the paper provides an online tool that allows researchers and decision makers to interactively simulate diverse scenarios with our model. FindingsWhile rapid and strong lock-down is an effective pandemic suppression measure, a combination of other strategies such as social distancing, active protection and removal can achieve similar suppression synergistically. Strength and type of intervention measures matter to achieve effective and rapid epidemic suppression.Interpretation Pursuing one intervention strategy alone requires its full enhancement. On the contrary, aiming at synergistic scenarios could impact epidemic decline with analogous effect and timing, with milder individual effort. This quantitative understanding can support the establishment of midand long-term interventions, in particular towards phase 2.