Sufficient Conditions for Some Stochastic Orders of Discrete Random Variables with Applications in Reliability

In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the unimodality of the likelihood ratio for the comparison in some stochastic orders of two discrete random variables. These results have interest in comparing discrete random variables because the sufficient conditions are easy to check when there are no closed expressions for the survival functions, which occurs in many cases. In addition, the results are applied to compare several parametric families of discrete distributions.

A class of two-sample nonparametric statistics for binary and time-to-event outcomes

We propose a class of two-sample statistics for testing the equality of proportions and the equality of survival functions. We build our proposal on a weighted combination of a score test for the difference in proportions and a weighted Kaplan–Meier statistic-based test for the difference of survival functions. The proposed statistics are fully non-parametric and do not rely on the proportional hazards assumption for the survival outcome. We present the asymptotic distribution of these statistics, propose a variance estimator, and show their asymptotic properties under fixed and local alternatives. We discuss different choices of weights including those that control the relative relevance of each outcome and emphasize the type of difference to be detected in the survival outcome. We evaluate the performance of these statistics with small sample sizes through a simulation study and illustrate their use with a randomized phase III cancer vaccine trial. We have implemented the proposed statistics in the R package SurvBin, available on GitHub ( https://github.com/MartaBofillRoig/SurvBin ).

COVID-19 and blood groups: A six-months observational study in Ferrara, Italy

The current literature still gives a little information about the relationships between the ABO blood group system and the immune response to the virus or the different disease outcomes. Hypothesizing the presence of a predisposition by some blood groups to COVID-19, we searched for differences between patients towards the different outcomes of disease.We enrolled 330 inpatients with a diagnosis of COVID-19, determining both their ABO blood group system and Rh factor, collecting demographic, clinical and laboratory data. We searched for relationships with COVID-19 outcomes within an observation period of 180 days (Intensification of Care - IoC, Inhospital death, 180-days mortality). The most frequent ABO blood group was A (45.8%); a minor part was represented by group O (38.8%), B (11.5%), AB (3.9%). As for the Rh factor, 86.7% of patients were Rh-positive. There were no significant differences between blood groups and Rh factors as for age, length of hospital stays (LoS), or Charlson Comorbidity Index (CCI), nor we found significant relationships between the ABO groups and COVID-19 outcomes. A significant relation was found between AB group and IoC (p=0.03) while as for the Rh factor, the patients with Rh factor positive died with less frequency during the stay (p=0.03). Cox regression analyses showed substantial differences in the survival functions concerning the Rh factors. The Rh factor seems to be involved in the 180-day prognosis. The survival functions of patients with Rh factor positive show, in fact, significantly better curves when compared to those with Rh factor negative.

COVID-19 inpatients with gastrointestinal onset: sex and care needs’ differences in the district of Ferrara, Italy

Background COVID-19 is characterized by interstitial pneumonia, but a presentation of the disease with digestive symptoms only may occur. This work was aimed at evaluating: (1) the prevalence of presentation with digestive symptoms only in our cohort of COVID-19 inpatients; (2) differences between patients with and without gastrointestinal onset; (3) differences among males and females with gastrointestinal presentation; (4) outcomes of the groups of subjects with and without gastrointestinal onset. Method We retrospectively divided the patients hospitalized with COVID-19 into two groups: (1) the one with digestive symptoms (DSG) and (2) the other without digestive symptoms (NDSG). We compared the subjects of DSG with those of NDSG and males with females in the DSG group only, in terms of demographics (age, sex), inflammation and organ damage indexes, length of stay, in-hospital and 100-day mortality. Results The prevalence of gastrointestinal symptoms at presentation was 12.5%. The DSG group showed a prevalence of females, and these tended to a shorter hospital stay; DSG patients were younger and with a higher load of comorbidities, but no differences concerning inflammation and organ damage indexes, need for intensification of care, in-hospital and 100-day mortality were detected. Among DSG patients, males were younger than females, more comorbid, with higher serum CRP and showed a longer length of hospital stay. Survival functions of DSG patients, in general, are more favourable than those of NDSG if adjusted for sex, age and comorbidities. Conclusions (1) The prevalence of gastrointestinal presentation among hospitalized COVID-19 patients was 12.5%; (2) DSG patients were on average younger, more comorbid and with a prevalence of females, with a shorter hospital stay; (3) in the DSG group, males had a higher Charlson Comorbidity Score and needed a longer hospital stay; (4) DSG subjects seem to survive longer than those of the NDSG group.

Modeling the probability of occurrence of events

This paper introduces the event-probability function, a measure of occurrence of an event of interest over time, defined as the instantaneous probability of an event at a given time point conditional on having survived until that point. Unlike the hazard function, the event-probability function is a proper probability. This paper describes properties and interpretation of the event-probability function, presents its connection with other popular functions, such as the hazard and survival functions, proposes practical flexible proportional-odds models for estimating conditional event-probabilities given covariates with possibly censored and truncated observations, discusses the theoretical and computational aspects of parameter estimation, and applies the proposed models for assessing mortality in patients with metastatic renal carcinoma from a randomized clinical trial.

The Combined Stop-Loss and Quota-Share Reinsurance: Conditional Tail Expectation-Based Optimization from the Joint Perspective of Insurer and Reinsurer

In the presence of reinsurance, an insurer may effectively reduce its (aggregated) loss by partially ceding such a loss to a reinsurer. Stop-loss and quota-share reinsurance contracts are commonly agreed between these two parties. In this paper, we aim to explore a combination of these contracts. The survival functions of the ceded loss and the retained loss are firstly investigated. Optimizing such a reinsurance design is then carried out from the joint perspective of the insurer and the reinsurer. Specifically, we explicitly derive optimal retentions under a criterion of minimizing a convex combination of conditional tail expectations of the insurer’s total loss and the reinsurer’s total loss. In addition, an estimation procedure and more explanations on numerical examples are also presented to find their estimated values.

Some conditional reliability properties of k-out-of-n system composed of different types of components with discrete independent lifetimes

In this paper, we study reliability properties of k-out-of-n system consisting of l$$(1\le l\le n)$$ ( 1 ≤ l ≤ n ) different types of components with discrete, independent lifetimes. We obtain some conditional survival functions of lifetime of a used system. Next, we use them to calculate two conditional failure probabilities of k-out-of-n systems and show that they are equal to unconditional failure probability of a k-out-of-$$(n-r)$$ ( n - r ) system, $$r<n-k+1$$ r < n - k + 1 . These results are extended versions of the respective ones existing in the literature.