Randomized test-treatment studies with an outlook on adaptive designs

Background Diagnostic accuracy studies aim to examine the diagnostic accuracy of a new experimental test, but do not address the actual merit of the resulting diagnostic information to a patient in clinical practice. In order to assess the impact of diagnostic information on subsequent treatment strategies regarding patient-relevant outcomes, randomized test-treatment studies were introduced. Various designs for randomized test-treatment studies, including an evaluation of biomarkers as part of randomized biomarker-guided treatment studies, are suggested in the literature, but the nomenclature is not consistent. Methods The aim was to provide a clear description of the different study designs within a pre-specified framework, considering their underlying assumptions, advantages as well as limitations and derivation of effect sizes required for sample size calculations. Furthermore, an outlook on adaptive designs within randomized test-treatment studies is given. Results The need to integrate adaptive design procedures in randomized test-treatment studies is apparent. The derivation of effect sizes induces that sample size calculation will always be based on rather vague assumptions resulting in over- or underpowered study results. Therefore, it might be advantageous to conduct a sample size re-estimation based on a nuisance parameter during the ongoing trial. Conclusions Due to their increased complexity, compared to common treatment trials, the implementation of randomized test-treatment studies poses practical challenges including a huge uncertainty regarding study parameters like the expected outcome in specific subgroups or disease prevalence which might affect the sample size calculation. Since research on adaptive designs within randomized test-treatment studies is limited so far, further research is recommended.

Fern and lycophytes of the Taquari River riparian forests at different stages of succession

Riparian forests are important biodiversity corridors among groups. Such forests were greatly altered or suppressed in the state of Rio Grande do Sul. This study investigates the variation of species richness and distribution of ferns and lycophytes of eighteen study areas at different stages of succession in riparian forests of the Taquari River region. Fern and lycophyte samples were collected using the pathway methodology along the Taquari River during two years. The richness was compared at the different succession stages (advanced remnant formations, intermediate and initial) through analysis of variance and a randomized test, in which about 22 species were recorded: 19 species were at the advanced stage of succession, nine species were at the intermediate stage and seven species were at the initial stage of succession. The average richness was significantly higher in areas at advanced stage of succession. The high value of common species found at intermediate stages highlights the importance of preserving riparian forests at all stages of succession in the Taquari River as alternative for preserving the local biodiversity.

Shortfall risk through Fenchel duality

In this paper, we propose a Fenchel duality approach to study the minimization problem of the shortfall risk. We consider a general increasing and strictly convex loss function, which may be more general than the situation of convex risk measures usually assumed in the literature. We first translate the associated stochastic optimization problem to an equivalent static optimization problem, and then obtain the explicit structure of the optimal randomized test for both complete and incomplete markets. For the incomplete market case, to the best of our knowledge, we obtain for the first time the explicit randomized test, while previous literature only established the existence through the supermartingale optional decomposition approach. We also solve the shortfall risk minimization problem for an insider through the enlargement of filtrations approach.