The Mann–Whitney test is a commonly used non-parametric alternative of the two-sample t-test. Despite its frequent use, it is only rarely accompanied with confidence intervals of an effect size. If reported, the effect size is usually measured with the difference of medians or the shift of the two distribution locations. Neither of these two measures directly coincides with the test statistic of the Mann–Whitney test, so the interpretation of the test results and the confidence intervals may be importantly different. In this paper, we focus on the probability that random variable X is lower than random variable Y. This measure is often referred to as the degree of overlap or the probabilistic index; it is in one-to-one relationship with the Mann–Whitney test statistic. The measure equals the area under the ROC curve. Several methods have been proposed for the construction of the confidence interval for this measure, and we review the most promising ones and explain their ideas. We study the properties of different variance estimators and small sample problems of confidence intervals construction. We identify scenarios in which the existing approaches yield inadequate coverage probabilities. We conclude that the DeLong variance estimator is a reliable option regardless of the scenario, but confidence intervals should be constructed using the logit scale to avoid values above 1 or below 0 and the poor coverage probability that follows. A correction is needed for the case when all values from one sample are smaller than the values of the other. We propose a method that improves the coverage probability also in these cases.

Multi-state models provide an extension of the usual survival/event-history analysis setting. In the medical domain, multi-state models give the possibility of further investigating intermediate events such as relapse and remission. In this work, a further extension is proposed using relative survival, where mortality due to population causes (i.e. non-disease-related mortality) is evaluated. The objective is to split all mortality in disease and non-disease-related mortality, with and without intermediate events, in datasets where cause of death is not recorded or is uncertain. To this end, population mortality tables are integrated into the estimation process, while using the basic relative survival idea that the overall mortality hazard can be written as a sum of a population and an excess part. Hence, we propose an upgraded non-parametric approach to estimation, where population mortality is taken into account. Precise definitions and suitable estimators are given for both the transition hazards and probabilities. Variance estimating techniques and confidence intervals are introduced and the behaviour of the new method is investigated through simulations. The newly developed methodology is illustrated by the analysis of a cohort of patients followed after an allogeneic hematopoietic stem cell transplantation. The work has been implemented in the R package mstate.

In many haematological diseases, the survival probability is the key outcome. However, when the population of patients is rather old and the follow-up long, a significant proportion of deaths cannot be attributed to the studied disease. This lessens the importance of common survival analysis measures like overall survival and shows the need for other outcome measures requiring more complex methodology. When disease-specific information is of interest but the cause of death is not available in the data, relative survival methodology becomes crucial. The idea of relative survival is to merge the observed data set with the mortality data in the general population and thus allow for an indirect estimation of the burden of the disease. In this work, an overview of different measures that can be of interest in the field of haematology is given. We introduce the crude mortality that reports the probability of dying due to the disease of interest; the net survival that focuses on excess hazard alone and presents the key measure in comparing the disease burden of patients from populations with different general population mortality; and the relative survival ratio which gives a simple comparison of the patients' and the general population survival. We explain the properties of each measure, and some brief notes are given on estimation. Furthermore, we describe how association with covariates can be studied. All the methods and their estimators are illustrated on a sub-cohort of older patients who received a first allogeneic hematopoietic stem cell transplantation for myelodysplastic syndromes or secondary acute myeloid leukemia, to show how different methods can provide different insights into the data.

During the first wave of the COVID-19 pandemic in spring 2020, Slovenia was among the least affected countries, but the situation became drastically worse during the second wave in autumn 2020 with high numbers of deaths per number of inhabitants, ranking Slovenia among the most affected countries. This was true even though strict non-pharmaceutical interventions (NPIs) to control the progression of the epidemic were being enforced. Using a semi-parametric Bayesian model developed for the purpose of this study, we explore if and how the changes in mobility, their timing and the activation of contact tracing can explain the differences in the epidemic progression of the two waves. To fit the model, we use data on daily numbers of deaths, patients in hospitals, intensive care units, etc., and allow transmission intensity to be affected by contact tracing and mobility (data obtained from Google Mobility Reports). Our results imply that though there is some heterogeneity not explained by mobility levels and contact tracing, implementing interventions at a similar stage as in the first wave would keep the death toll and the health system burden low in the second wave as well. On the other hand, sticking to the same timeline of interventions as observed in the second wave and focusing on enforcing a higher decrease in mobility would not be as beneficial. According to our model, the ‘dance’ strategy, i.e., first allowing the numbers to rise and then implementing strict interventions to make them drop again, has been played at too-late stages of the epidemic. In contrast, a 15–20% reduction of mobility compared to pre-COVID level, if started at the beginning and maintained for the entire duration of the second wave and coupled with contact tracing, could suffice to control the epidemic. A very important factor in this result is the presence of contact tracing; without it, the reduction in mobility needs to be substantially larger. The flexibility of our proposed model allows similar analyses to be conducted for other regions even with slightly different data sources for the progression of the epidemic; the extension to more than two waves is straightforward. The model could help policymakers worldwide to make better decisions in terms of the timing and severity of the adopted NPIs.

Studies on the serum biomarkers of granulomatous inflammation and pulmonary interstitial disease in intrathoracic sarcoidosis have shown conflicting results. We postulated that differences in the concentrations of serum biomarkers can be explained by the heterogenous patterns of sarcoidosis seen on thoracic HRCT. Serum biomarker levels in 79 consecutive patients, newly diagnosed with intrathoracic sarcoidosis, were compared to our control group of 56 healthy blood donors. An analysis was performed with respect to HRCT characteristics (the presence of lymph node enlargement, perilymphatic or peribronchovascular infiltrates, ground-glass lesions, or fibrosis), CXR, and disease extent. Serum levels of CXCL9, CXCL10, CTO, and CCL18 were statistically significantly increased in all patients compared to controls. Serum levels of CA15.3 were statistically significantly increased in all patients with parenchymal involvement. SAA was increased in patients with ground-glass lesions while SP-D levels were statistically significantly increased in patients with lung fibrosis. Only SP-D and CA15.3 showed a significant correlation to interstitial disease extent. In conclusion, we found that sarcoidosis patients with different HRCT patterns of intrathoracic sarcoidosis have underlying biochemical differences in their serum biomarkers transcending Scadding stages. The stratification of patients based on both radiologic and biochemical characteristics could enable more homogenous patient selection for further prognostic studies.