Micha Mandel

Following evidence of waning immunity against both infection and severe disease after 2 doses of the BNT162b2 vaccine, Israel began administering a 3rd BNT162b2 dose (booster) in July 2021. Recent studies showed that the 3rd dose provides a much lower protection against infection with the Omicron variant compared to the Delta variant and that this protection wanes quickly. However, there is little evidence regarding the protection of the 3rd dose against Omicron (BA.1/BA.2) severe disease. In this study, we estimate the preservation of immunity from severe disease up to 7 months after receiving the booster dose. We calculate rates of severe SARS-CoV-2 disease between groups of individuals aged 60 and above, comparing those who received two doses at least 4 months previously to those who received the 3rd dose (stratified by the time from vaccination), and to those who received a 4th dose. The analysis shows that protection conferred by the 3rd dose against Omicron severe disease did not wane over a 7-month period. Moreover, a 4th dose further improved protection, with a severe disease rate approximately 3-fold lower than in the 3-dose cohorts.

Footwear comparison is used to link between a suspect's shoe and a shoeprint found at a crime scene. Forensic examiners compare the two items, and the conclusion reached is based on class characteristics and randomly acquired characteristics (RACs), such as scratches or holes. An important question concerns the distribution of the location of RACs on shoe soles, which can serve as a benchmark for comparison. This study examines the probability of observing RACs in different areas of a shoe sole using a database of approximately 13,000 RACs observed on 386 outsoles. The analysis is somewhat complicated as the shoes are differentiated by shape and contact surface, and the RACs' locations are subject to measurement errors. A method that takes into account these challenges is presented. All impressions are normalized to a standardized axis to allow for inter‐comparison of RACs on outsoles of different sizes and contact areas, and RACs are localized to one of 14 subareas of the shoe sole. Expected frequencies in each region are assumed to be Poisson distributed with rate parameters that depend on the subarea and the contact surface. Three different estimation approaches are studied: a naive crude approach, a shoe‐specific random effects model, and an estimate that is based on conditional maximum likelihood. It is shown that the rate is not uniform across the shoe sole and that RACs are approximately twice as likely to appear at certain locations, corresponding to the foot's morphology. The results can guide investigators in determining a shoeprint's evidential value.

Background On July 30, 2021, a third (booster) dose of the Pfizer BNT162b2 vaccine was approved in Israel for individuals 60 years or older who had been fully vaccinated (i.e., received two doses) at least five months previously. Here, we estimate the reduction in relative risk for confirmed infection and severe COVID-19 provided by the booster dose. Methods 1,144,690 individuals aged 60y and older who were eligible for a booster dose were followed between July 30 and August 22, 2021. We defined dynamic cohorts where individuals initially belong to the ‘non-booster’ cohort, leave it when receiving the booster dose and join the ‘booster’ cohort 12 days later. Rates of infection and severe COVID-19 outcomes per person-days at risk were compared between the cohorts using Poisson regression, adjusting for possible confounding factors. Results Twelve days or more after the booster dose we found an 11.4-fold (95% CI: [10.0, 12.9]) decrease in the relative risk of confirmed infection, and a >10-fold decrease in the relative risk of severe illness. Under a conservative sensitivity analysis, we find ≈5-fold protection against confirmed infection. Conclusions In conjunction with safety reports, this study demonstrates the effectiveness of a third vaccine dose in both reducing transmission and severe disease and indicates the great potential of curtailing the Delta variant resurgence by administering booster shots.

Worldwide shortage of vaccination against SARS-CoV-2 infection while the pandemic is still uncontrolled leads many states to the dilemma whether or not to vaccinate previously infected persons. Understanding the level of protection of previous infection compared to that of vaccination is critical for policy making. We analyze an updated individual-level database of the entire population of Israel to assess the protection efficacy of both prior infection and vaccination in preventing subsequent SARS-CoV-2 infection, hospitalization with COVID-19, severe disease, and death due to COVID-19. Vaccination was highly effective with overall estimated efficacy for documented infection of 92·8% (CI:[92·6, 93·0]); hospitalization 94·2% (CI:[93·6, 94·7]); severe illness 94·4% (CI:[93·6, 95·0]); and death 93·7% (CI:[92·5, 94·7]). Similarly, the overall estimated level of protection from prior SARS-CoV-2 infection for documented infection is 94·8% (CI:[94·4, 95·1]); hospitalization 94·1% (CI:[91·9, 95·7]); and severe illness 96·4% (CI:[92·5, 98·3]). Our results question the need to vaccinate previously-infected individuals.

Footwear comparison is used to link between a suspect's shoe and a footprint found at a crime scene. Investigators compare the two items using randomly acquired characteristics (RACs), such as scratches or holes. However, to date, the distribution of RAC characteristics has not been investigated thoroughly, and the evidential value of RACs is yet to be explored. An important question concerns the distribution of the location of RACs on shoe soles, which can serve as a benchmark for comparison. The location of RACs is modeled here as a point process over the shoe sole and a data set of 386 independent shoes is used to estimate its rate function. The analysis is somewhat complicated as the shoes are differentiated by shape, level of wear and tear and contact surface. This paper presents methods that take into account these challenges, either by using natural cubic splines on high resolution data, or by using a piecewise-constant model on larger regions defined by experts' knowledge. It is shown that RACs are likely to appear at certain locations, corresponding to the foot's morphology. The results can guide investigators in determining the evidential value of footprint comparison.

The proportionality principle is an international humanitarian law requirement intended to constrain the use of military force in order to protect civilians in armed conflicts. This research experimentally assesses the reliability of its application by legal and moral experts (in 11 countries), by military officers (in two countries) and by laypeople. Reliability was evaluated according to three criteria: inter-expert convergence; sensitivity to relevant factors; and robustness – relative (lack of) susceptibility to biases. Unlike laypeople, experts and military officers performed well on the sensitivity criterion and manifested an appropriate understanding of the principle at the abstract level. However, both groups of experts failed to reach reasonable judgment convergence. These findings cast doubt on the reliability of the protection provided to civilians during warfare, even when warring parties attempt to abide by the proportionality principle.

Quantifying the strength of gunshot residue (GSR) evidence requires scientific knowledge about the number of particles expected to be found on individuals who were or were not involved in a shooting. However, controlled experiments demand expensive resources in terms of microscope time and labor, which restricts the data of most studies to only a small group of individuals. We suggest a novel method that exploits data collected routinely on suspects during the daily work of forensic laboratories. These observational data relate to both persons who were involved in a shooting and innocent individuals. We suggest a mixture approach with different models for the number of gunshot residue particles in each group and develop an iterative algorithm to estimate the probabilities of observing the evidence under the defense proposition that the suspect is innocent and under the prosecution assumption that he is not. The method is applied to data of more than 500 suspects collected by the Israel National Police Division of Identification and Forensic Science. The analysis shows that the probability of finding three or more GSR particles on the hands of innocent suspects is very small, less than 1.5 in 1000 cases. Our new method enables researchers to use data on real cases, possibly supplemented by experimental data, in order to estimate the probabilities of a given GSR finding under the defense and prosecution propositions.

Right‐truncated data arise when observations are ascertained retrospectively, and only subjects who experience the event of interest by the time of sampling are selected. Such a selection scheme, without adjustment, leads to biased estimation of covariate effects in the Cox proportional hazards model. The existing methods for fitting the Cox model to right‐truncated data, which are based on the maximization of the likelihood or solving estimating equations with respect to both the baseline hazard function and the covariate effects, are numerically challenging. We consider two alternative simple methods based on inverse probability weighting (IPW) estimating equations, which allow consistent estimation of covariate effects under a positivity assumption and avoid estimation of baseline hazards. We discuss problems of identifiability and consistency that arise when positivity does not hold and show that although the partial tests for null effects based on these IPW methods can be used in some settings even in the absence of positivity, they are not valid in general. We propose adjusted estimating equations that incorporate the probability of observation when it is known from external sources, which results in consistent estimation. We compare the methods in simulations and apply them to the analyses of human immunodeficiency virus latency.

Sufficiency, Conditionality and Invariance are basic principles of statistical inference. Current mathematical statistics courses do not devote much teaching time to these classical principles, and even ignore the latter two, in order to teach modern methods. However, being the philosophical cornerstones of statistical inference, a minimal understanding of these principles should be part of any curriculum in statistics. The scaled uniform model is used here to demonstrate the importance and usefulness of the conditionality principle, which is probably the most basic and less familiar among the three.