Optimal designs for comparing curves

Designs for the simultaneous inference of concentration-response curves

BACKGROUND

An important problem in toxicology in the context of gene expression data is the simultaneous inference of a large number of concentration-response relationships. The quality of the inference substantially depends on the choice of design of the experiments, in particular, on the set of different concentrations, at which observations are taken for the different genes under consideration. As this set has to be the same for all genes, the efficient planning of such experiments is very challenging. We address this problem by determining efficient designs for the simultaneous inference of a large number of concentration-response models. For that purpose, we both construct a D-optimality criterion for simultaneous inference and a K-means procedure which clusters the support points of the locally D-optimal designs of the individual models.

RESULTS

We show that a planning of experiments that addresses the simultaneous inference of a large number of concentration-response relationships yields a substantially more accurate statistical analysis. In particular, we compare the performance of the constructed designs to the ones of other commonly used designs in terms of D-efficiencies and in terms of the quality of the resulting model fits using a real data example dealing with valproic acid. For the quality comparison we perform an extensive simulation study.

CONCLUSIONS

The design maximizing the D-optimality criterion for simultaneous inference improves the inference of the different concentration-response relationships substantially. The design based on the K-means procedure also performs well, whereas a log-equidistant design, which was also included in the analysis, performs poorly in terms of the quality of the simultaneous inference. Based on our findings, the D-optimal design for simultaneous inference should be used for upcoming analyses dealing with high-dimensional gene expression data.

Identifying alert concentrations using a model-based bootstrap approach

The determination of alert concentrations, where a pre-specified threshold of the response variable is exceeded, is an important goal of concentration-response studies. The traditional approach is based on investigating the measured concentrations and attaining statistical significance of the alert concentration by using a multiple t-test procedure. In this paper, we propose a new model-based method to identify alert concentrations, based on fitting a concentration-response curve and constructing a simultaneous confidence band for the difference of the response of a concentration compared to the control. In order to obtain these confidence bands, we use a bootstrap approach which can be applied to any functional form of the concentration-response curve. This particularly offers the possibility to investigate also those situations where the concentration-response relationship is not monotone and, moreover, to detect alerts at concentrations which were not measured during the study, providing a highly flexible framework for the problem at hand.

Immune Determinants of Viral Clearance in Hospitalised COVID-19 Patients: Reduced Circulating Naïve CD4+ T Cell Counts Correspond with Delayed Viral Clearance

Virus-specific cellular and humoral responses are major determinants for protection from critical illness after SARS-CoV-2 infection. However, the magnitude of the contribution of each of the components to viral clearance remains unclear. Here, we studied the timing of viral clearance in relation to 122 immune parameters in 102 hospitalised patients with moderate and severe COVID-19 in a longitudinal design. Delayed viral clearance was associated with more severe disease and was associated with higher levels of SARS-CoV-2-specific (neutralising) antibodies over time, increased numbers of neutrophils, monocytes, basophils, and a range of pro-inflammatory cyto-/chemokines illustrating ongoing, partially Th2 dominating, immune activation. In contrast, early viral clearance and less critical illness correlated with the peak of neutralising antibodies, higher levels of CD4 T cells, and in particular naïve CD4+ T cells, suggesting their role in early control of SARS-CoV-2 possibly by proving appropriate B cell help. Higher counts of naïve CD4+ T cells also correlated with lower levels of MIF, IL-9, and TNF-beta, suggesting an indirect role in averting prolonged virus-induced tissue damage. Collectively, our data show that naïve CD4+ T cell play a critical role in rapid viral T cell control, obviating aberrant antibody and cytokine profiles and disease deterioration. These data may help in guiding risk stratification for severe COVID-19.

Optimal Designs for Comparing Regression Curves: Dependence Within and Between Groups

We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to derive efficient designs we use results from stochastic analysis to identify the best linear unbiased estimator (BLUE) in a corresponding continuous model. It is demonstrated that in general simultaneous estimation using the data from both groups yields more precise results than estimation of the parameters separately in the two groups. Using the BLUE from simultaneous estimation, we then construct an efficient linear estimator for finite sample size by minimizing the mean squared error between the optimal solution in the continuous model and its discrete approximation with respect to the weights (of the linear estimator). Finally, the optimal design points are determined by minimizing the maximal width of a simultaneous confidence band for the difference of the two regression functions. The advantages of the new approach are illustrated by means of a simulation study, where it is shown that the use of the optimal designs yields substantially narrower confidence bands than the application of uniform designs.

Lessons learned from IDeAl - 33 recommendations from the IDeAl-net about design and analysis of small population clinical trials

BACKGROUND

IDeAl (Integrated designs and analysis of small population clinical trials) is an EU funded project developing new statistical design and analysis methodologies for clinical trials in small population groups. Here we provide an overview of IDeAl findings and give recommendations to applied researchers.

METHOD

The description of the findings is broken down by the nine scientific IDeAl work packages and summarizes results from the project's more than 60 publications to date in peer reviewed journals. In addition, we applied text mining to evaluate the publications and the IDeAl work packages' output in relation to the design and analysis terms derived from in the IRDiRC task force report on small population clinical trials.

RESULTS

The results are summarized, describing the developments from an applied viewpoint. The main result presented here are 33 practical recommendations drawn from the work, giving researchers a comprehensive guidance to the improved methodology. In particular, the findings will help design and analyse efficient clinical trials in rare diseases with limited number of patients available. We developed a network representation relating the hot topics developed by the IRDiRC task force on small population clinical trials to IDeAl's work as well as relating important methodologies by IDeAl's definition necessary to consider in design and analysis of small-population clinical trials. These network representation establish a new perspective on design and analysis of small-population clinical trials.

CONCLUSION

IDeAl has provided a huge number of options to refine the statistical methodology for small-population clinical trials from various perspectives. A total of 33 recommendations developed and related to the work packages help the researcher to design small population clinical trial. The route to improvements is displayed in IDeAl-network representing important statistical methodological skills necessary to design and analysis of small-population clinical trials. The methods are ready for use.