MATS: Inference for potentially Singular and Heteroscedastic MANOVA

In many experiments in the life sciences, several endpoints are recorded per subject. The analysis of such multivariate data is usually based on MANOVA models assuming multivariate normality and covariance homogeneity. These assumptions, however, are often not met in practice. Furthermore, test statistics should be invariant under scale transformations of the data, since the endpoints may be measured on different scales. In the context of high-dimensional data, Srivastava and Kubokawa (2013) proposed such a test statistic for a specific one-way model, which, however, relies on the assumption of a common non-singular covariance matrix. We modify and extend this test statistic to factorial MANOVA designs, incorporating general heteroscedastic models. In particular, our only distributional assumption is the existence of the group-wise covariance matrices, which may even be singular. We base inference on quantiles of resampling distributions, and derive confidence regions and ellipsoids based on these quantiles. In a simulation study, we extensively analyze the behavior of these procedures. Finally, the methods are applied to a data set containing information on the 2016 presidential elections in the USA with unequal and singular empirical covariance matrices

Debt rule federalism: the case of Germany

In 2009, Germany introduced a new debt rule in its federal constitution (Grundgesetz). The socalled ‘debt brake’ prescribes a balanced budget for both the federal level and the states. However, the states have leeway regarding transposition and specification of the national requirements into their own state constitutions and budgetary laws. This analysis presents a comprehensive comparison of the 16 state provisions. We develop an indicator which quantifies the stringency of state rules (Strength of Fiscal Rule Indicator). Two results emerge: First, despite the common constitutional rule at the federal level, the analysis reveals a considerable heterogeneity across German states. Second, several highly indebted states miss the chance to make their fiscal regime more credible. This finding corresponds to the disincentives of the German federation. Due to bailout-guarantees enshrined in German federalism, German states do not have incentives to impress bond markets through particularly strict budgetary rules

Causal inference methods for small non-randomized studies: methods and an application in COVID-19

The usual development cycles are too slow for the development of vaccines, diagnostics and treatments in pandemics such as the ongoing SARS-CoV-2 pandemic. Given the pressure in such a situation, there is a risk that findings of early clinical trials are overinterpreted despite their limitations in terms of size and design. Motivated by a non-randomized open-label study investigating the efficacy of hydroxychloroquine in patients with COVID-19, we describe in a unified fashion various alternative approaches to the analysis of non-randomized studies and apply them to the example study exploring the question whether different methods might have led to different conclusions. A widely used tool to reduce the impact of treatment-selection bias are so-called propensity score (PS) methods. Conditioning on the propensity score allows one to replicate the design of a randomized controlled trial, conditional on observed covariates. Extensions include the doubly robust g-computation, which is less frequently applied, in particular in clinical studies. Here, we investigate the properties of propensity score based methods including g-computation in small sample settings, typical for early trials, in a simulation study. We conclude that the doubly robust g-computation has some desirable properties and should be more frequently applied in clinical research. In the hydroxychloroquine study, g-computation resulted in a very wide confidence interval indicating much uncertainty. We speculate that application of the method might have prevented some of the hype surrounding hydroxychloroquine in the early stages of the SARS-CoV-2 pandemic. R code for the g-computation is provided