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In risk assessment, it is often desired to make inferences on the minimum dose levels (benchmark doses or BMDs) at which a specific benchmark risk (BMR) is attained. The estimation and inferences of BMDs are well understood in the case of an adverse response to a single-exposure agent. However, the theory of finding BMDs and making inferences on the BMDs is much less developed for cases where the adverse effect of two hazardous agents is studied simultaneously. Deutsch and Piegorsch [2012. Benchmark dose profiles for joint-action quantal data in quantitative risk assessment. Biometrics 68(4):1313–22] proposed a benchmark modeling paradigm in dual exposure setting—adapted from the single-exposure setting—and developed a strategy for conducting full benchmark analysis with joint-action quantal data, and they further extended the proposed benchmark paradigm to continuous response outcomes [Deutsch, R. C., and W. W. Piegorsch. 2013. Benchmark dose profiles for joint-action continuous data in quantitative risk assessment. Biometrical Journal 55(5):741–54]. In their 2012 article, Deutsch and Piegorsch worked exclusively with the complementary log link for modeling the risk with quantal data. The focus of the current paper is on the logit link; particularly, we consider an Abbott-adjusted [A method of computing the effectiveness of an insecticide. Journal of Economic Entomology 18(2):265–7] log-logistic model for the analysis of quantal data with nonzero background response. We discuss the estimation of the benchmark profile (BMP)—a collection of benchmark points which induce the prespecified BMR—and propose different methods for building benchmark inferences in studies involving two hazardous agents. We perform Monte Carlo simulation studies to evaluate the characteristics of the confidence limits. An example is given to illustrate the use of the proposed methods. [ABSTRACT FROM AUTHOR]

In risk assessment, it is often desired to make inferences on the risk at certain low doses or on the dose(s) at which a specific benchmark risk (BMR) is attained. At times, dose levels or BMRs are of interest, and some form of multiplicity adjustment is necessary to ensure a valid simultaneous inference. Bonferroni correction is often employed in practice for such purposes. Though relative simple to implement, the Bonferroni strategy can suffer from extreme conservatism (Nitcheva et al., 2005; Al-Saidy et al., 2003). Recently, Kerns (2017) proposed the use of simultaneous hyperbolic and three-segment bands to perform multiple inferences in risk assessment under Abbott-adjusted log-logistic model with the dose level constrained to a given interval. In this paper, we present and compare methods for deriving multiplicity-adjusted upper limits on extra risk and lower bounds on the benchmark dose under Abbott-adjusted log-logistic model. Monte Carlo simulations evaluate the characteristics of the simultaneous limits. An example is given to illustrate the use of the methods. [ABSTRACT FROM AUTHOR]

The hyperbolicconfidence bands for one logistic regression model with restricted predictors have been considered in the statistical literature. At times, one wishes to construct simultaneous confidence bands for comparing several logistic regression models. It seems that Liu's book [Simultaneous Inference in Regression, Chapman & Hall, 2010, Chapter 8] is the only published work that has addressed this problem. Liu suggested simulation-based methods for constructing simultaneous confidence bands for comparing several logistic models, but further research was warranted to assess the conservativeness of the bands. In this paper, we propose a dimension-wise partitioning method to construct a set of simultaneous confidence bands for the comparisons of several logistic regression functions with a pre-specified function in a stepwise fashion. In addition, simulation studies cast new light on the assumption of predetermined testing order for the stepwise procedures presented in this paper and by Hsu and Berger [Stepwise confidence intervals without multiplicity adjustment for dose–response and toxicity studies, J. Amer. Statist. Assoc. 94 (1999), pp. 468–482]. As an illustration, we include an example on the success rate of thrombolysis associated with patient characteristics regarding post-thrombotic syndrome. [ABSTRACT FROM PUBLISHER]

This article presents methods for the construction of two-sided and one-sided simultaneous hyperbolic bands for the logistic and probit regression models when the predictor variable is restricted to a given interval. The bands are constructed based on the asymptotic properties of the maximum likelihood estimators. Past articles have considered building two-sided asymptotic confidence bands for the logistic model, such as Piegorsch and Casella (1988). However, the confidence bands given by Piegorsch and Casella are conservative under a single interval restriction, and it is shown in this article that their bands can be sharpened using the methods proposed here. Furthermore, no method has yet appeared in the literature for constructing one-sided confidence bands for the logistic model, and no work has been done for building confidence bands for the probit model, over a limited range of the predictor variable. This article provides methods for computing critical points in these areas. [ABSTRACT FROM AUTHOR]

This article presents methods for constructing an asymptotic hyperbolic band under the multiple logistic regression model when the predictor variables are restricted to a specific region . Scheffé's method yields unnecessarily wide, and hence conservative, bands if the predictor variables can be restricted to a certain region. Piegorsch and Casella [Confidence bands for logistic regression with restricted predictor variables. Biometrics. 1988;44:739–750] developed a procedure to build an asymptotic confidence band for the multiple logistic regression model over particular regions. Those regions are shown to be special cases of the region , which was first investigated by Seppanen and Uusipaikka [Confidence bands for linear regression over restricted regions. Scand J Stat. 1992;19:73–81] in the multiple linear regression context. This article also provides methods for constructing conservative confidence bands when the restricted region is not of the specified form. Particularly, rectangular restricted regions, which are commonly encountered in practice, are considered. Two examples are given to illustrate the proposed methodology, and one example shows that the proposed procedure outperforms the method given by Piegorsch and Casella (1988). [ABSTRACT FROM AUTHOR]

Objective: This study examined alignment of subjective balance confidence with Stopping Elderly Accidents, Deaths and Injuries (STEADI) fall risk. Methods: Cross-sectional analysis of 155 community-dwelling adults (60 + y/o) from 2016 to 2018 who completed a STEADI fall assessment. Descriptive statistics, Chi-Square analysis, and biserial point correlations were applied. Results: Adults who overestimate balance confidence, 55.6% (n = 50) reported a fall in the past year, 62.2% (n = 56) were worried about falling, 48.9% (n = 44) felt unsteady when standing/walking, and 70.0% (n = 63) had a score of ≥4 on the Stay Independent Questionnaire (SIQ). Physical performance for these adults were mean TUG score 10.9s (SD = 3.4), mean 30 second chair stands 10.8 (SD = 3.5), and mean 4-stage balance score 3.1 (SD =.76). Discussion: Older adults are more likely to overestimate their subjective balance confidence. Individuals are equally likely to have reported a fall in the past year if they were "at fall risk," regardless of their subjective balance confidence. [ABSTRACT FROM AUTHOR]

Mass shooting incidents have drastically increased in the United States in the last 10 years, with a disproportionate number of incidents occurring in some states. Gun laws vary greatly by state, but little research has been conducted to examine the association between the strength of state gun laws and mass shootings. This study aims to explore the aggregate effect of state gun laws on the rate of mass shooting incidents and fatalities. This was a cross-sectional time series. This study applied the negative binomial generalized linear mixed model to assess the impact of state gun laws restrictiveness—as measured by the total number of active gun laws—on the rate of mass shooting incidents and fatalities. The restrictiveness of state gun laws was significantly associated with the rate of mass shooting fatalities; specifically, for every 1 standard deviation (SD) increase in the state gun law restrictiveness score (i.e. for every additional 27 gun laws in place), the rate of mass shooting fatalities was decreased by 24% (P -value <0.0001), controlling for other predictor variables in the model. However, no significant association was found between the restrictiveness of state gun laws and rate of mass shooting incidents. State gun laws may not decrease the number of mass shooting events, but they appear to help reduce the number of deaths when these mass shootings occur. Better data collection on mass shootings and further research on the impacts of specific gun laws are needed to help understand the effectiveness of gun laws and inform law-based interventions. [ABSTRACT FROM AUTHOR]

Mass shootings (incidents with four or more people shot in a single event, not including the shooter) are becoming more frequent in the United States, posing a significant threat to public health and safety in the country. In the current study, we intended to analyze the impact of state-level prevalence of gun ownership on mass shootings—both the frequency and severity of these events. We applied the negative binomial generalized linear mixed model to investigate the association between gun ownership rate, as measured by a proxy (i.e., the proportion of suicides committed with firearms to total suicides), and population-adjusted rates of mass shooting incidents and fatalities at the state level from 2013 to 2022. Gun ownership was found to be significantly associated with the rate of mass shooting fatalities. Specifically, our model indicated that for every 1-SD increase—that is, for every 12.5% increase—in gun ownership, the rate of mass shooting fatalities increased by 34% (p value < 0.001). However, no significant association was found between gun ownership and rate of mass shooting incidents. These findings suggest that restricting gun ownership (and therefore reducing availability to guns) may not decrease the number of mass shooting events, but it may save lives when these events occur. [ABSTRACT FROM AUTHOR]