A General Model of Random Variation

A statistical distribution of a random variable is uniquely represented by its normal-based quantile function. For a symmetrical distribution it is S-shaped (for negative kurtosis) and inverted S-shaped (otherwise). As skewness departs from zero, the quantile function gradually transforms into a monotone convex function (positive skewness) or concave function (otherwise). Recently, a new general modeling platform has been introduced, response modeling methodology, which delivers good representation to monotone convex relationships due to its unique “continuous monotone convexity” property. In this article, this property is exploited to model the normal-based quantile function, and explored using a set of 27 distributions.     

Two-Step Residual-Based Estimation of Error Variances for Generalized Least Squares in Split-Plot Experiments

In split-plot experiments, estimation of unknown parameters by generalized least squares (GLS), as opposed to ordinary least squares (OLS), is required, owing to the existence of whole- and subplot errors. However, estimating the error variances is often necessary for GLS. Restricted maximum likelihood (REML) is an established method for estimating the error variances, and its benefits have been highlighted in many previous studies. This article proposes a new two-step residual-based approach for estimating error variances. Results of numerical simulations indicate that the proposed method performs sufficiently well to be considered as a suitable alternative to REML.     

Computational schema on ridge analysis

The purpose of this paper is to revisit the response surface technique ridge analysis within the context of the “trust region” problem in numerical analysis. It is found that these two approaches inherently solve the same problem. We introduce the computational difficulty, termed the “hard case”, which originates in the trust region methods, also exists in ridge analysis but has never been formally discussed in response surface methodology (RSM). The dual response global optimization algorithm (DRSALG) based on the trust region method is applied (with a certain modification) to solving the ridge analysis problem. Some numerical comparisons against a general-purpose nonlinear optimization algorithm are illustrated in terms of examples appearing in the literature     

Statistical Inference of Adaptive Designs with Binary Responses

Adaptive designs of clinical trials are ethical alternatives when the traditional randomization becomes ethically infeasible in desperate medical situations. However, such a design creates a dependency among trial data and its statistical analysis becomes more complex than the analysis for traditional randomized clinical trials. In this article, we examine adaptive designs with dichotomous responses from two treatments and extend some commonly used statistical methods for independent data. Under a regularity condition, the estimated odds ratio and its logarithm are shown to follow asymptotically normal distributions. Moreover, the ordinary goodness-of-fit test statistic for two-by-two contingency tables with dependent data is shown to be asymptotically chi-square distributed. We also discuss the consistency of maximum likelihood estimators of the unknown parameters for a wide class of adaptive designs.     

Sequential Designs for Binary Data with the Purpose to Maximize the Probability of Response

Two kinds of sequential designs are proposed for finding the point that maximizes the probability of response assuming a binary response variable and a quadratic logistic regression model. One is a parametric optimal design approach, and the other one is a nonparametric stochastic approximation approach. The suggested sequential designs are evaluated and compared in a simulation study. In summary, the parametric approach performed very well whereas its competitor failed in some cases.     

A Shiny Update to an Old Experiment Game

ABSTRACT

Games can be a powerful tool for learning about statistical methodology. Effective game design involves a fine balance between caricature and realism, to simultaneously illustrate salient concepts in a controlled setting and serve as a testament to real-world applicability. Striking that balance is particularly challenging in response surface and design domains, where real-world scenarios often play out over long time scales, during which theories are revised, model and inferential techniques are improved, and knowledge is updated. Here, I present a game, borrowing liberally from one first played over 40 years ago, which attempts to achieve that balance while reinforcing a cascade of topics in modern nonparametric response surfaces, sequential design, and optimization. The game embeds a blackbox simulation within a shiny app whose interface is designed to simulate a realistic information–availability setting, while offering a stimulating, competitive environment wherein students can try out new methodology, and ultimately appreciate its power and limitations. Interface, rules, timing with course material, and evaluation are described, along with a “case study” involving a cohort of students at Virginia Tech. Supplementary materials for this article are available online.     

The Practical Significance of Measurement Error in Pulmonary Function Testing Conducted in Research Settings

Conventional spirometry produces measurement error by using repeatability criteria (RC) to discard acceptable data and terminating tests early when RC are met. These practices also implicitly assume that there is no variation across maneuvers within each test. This has implications for air pollution regulations that rely on pulmonary function tests to determine adverse effects or set standards. We perform a Monte Carlo simulation of 20,902 tests of forced expiratory volume in 1 second (FEV₁), each with eight maneuvers, for an individual with empirically obtained, plausibly normal pulmonary function. Default coefficients of variation for inter‐ and intratest variability (3% and 6%, respectively) are employed. Measurement error is defined as the difference between results from the conventional protocol and an unconstrained, eight‐maneuver alternative. In the default model, average measurement error is shown to be ～5%. The minimum difference necessary for statistical significance at p < 0.05 for a before/after comparison is shown to be 16%. Meanwhile, the U.S. Environmental Protection Agency has deemed single‐digit percentage decrements in FEV₁ sufficient to justify more stringent national ambient air quality standards. Sensitivity analysis reveals that results are insensitive to intertest variability but highly sensitive to intratest variability. Halving the latter to 3% reduces measurement error by 55%. Increasing it to 9% or 12% increases measurement error by 65% or 125%, respectively. Within‐day FEV₁ differences ≤5% among normal subjects are believed to be clinically insignificant. Therefore, many differences reported as statistically significant are likely to be artifactual. Reliable data are needed to estimate intratest variability for the general population, subpopulations of interest, and research samples. Sensitive subpopulations (e.g., chronic obstructive pulmonary disease or COPD patients, asthmatics, children) are likely to have higher intratest variability, making it more difficult to derive valid statistical inferences about differences observed after treatment or exposure.     

Topics in Microbial Risk Assessment: Dynamic Flow Tree Process

Microbial risk assessment is emerging as a new discipline in risk assessment. A systematic approach to microbial risk assessment is presented that employs data analysis for developing parsimonious models and accounts formally for the variability and uncertainty of model inputs using analysis of variance and Monte Carlo simulation. The purpose of the paper is to raise and examine issues in conducting microbial risk assessments. The enteric pathogen Escherichia coli O157:H7 was selected as an example for this study due to its significance to public health. The framework for our work is consistent with the risk assessment components described by the National Research Council in 1983 (hazard identification; exposure assessment; dose-response assessment; and risk characterization). Exposure assessment focuses on hamburgers, cooked a range of temperatures from rare to well done, the latter typical for fast food restaurants. Features of the model include predictive microbiology components that account for random stochastic growth and death of organisms in hamburger. For dose-response modeling, Shigella data from human feeding studies were used as a surrogate for E. coli O157:H7. Risks were calculated using a threshold model and an alternative nonthreshold model. The 95% probability intervals for risk of illness for product cooked to a given internal temperature spanned five orders of magnitude for these models. The existence of even a small threshold has a dramatic impact on the estimated risk.     

顺应论下中文电视访谈中闪避的变异性研究

闪避作为交际策略的一种,在访谈节目中倍受嘉宾亲睐。在此运用Verschueren的顺应论来探讨访谈类电视节目中,闪避策略的变异性。经过研究发现,在电视访谈节目中,嘉宾主要运用的闪避策略能从以下三个特征来体现顺应论的变异性：改换问题的语境;有意地改变谈话的主题;有意地违返格莱斯的方式准则。在实际的访谈中,三者之间并不是泾渭分明,而是互相交织,它们的交织更多地体现在后两个特征的互相贯穿使用上,而且它们互为因果。     

Uncertainty and Variability in Health-Related Damages from Coal-Fired Power Plants in the United States

The health‐related damages associated with emissions from coal‐fired power plants can vary greatly across facilities as a function of plant, site, and population characteristics, but the degree of variability and the contributing factors have not been formally evaluated. In this study, we modeled the monetized damages associated with 407 coal‐fired power plants in the United States, focusing on premature mortality from fine particulate matter (PM_2.5). We applied a reduced‐form chemistry‐transport model accounting for primary PM_2.5 emissions and the influence of sulfur dioxide (SO₂) and nitrogen oxide (NO_x) emissions on secondary particulate formation. Outputs were linked with a concentration‐response function for PM_2.5‐related mortality that incorporated nonlinearities and model uncertainty. We valued mortality with a value of statistical life approach, characterizing and propagating uncertainties in all model elements. At the median of the plant‐specific uncertainty distributions, damages across plants ranged from $30,000 to $500,000 per ton of PM_2.5, $6,000 to $50,000 per ton of SO₂, $500 to $15,000 per ton of NO_x, and $0.02 to $1.57 per kilowatt‐hour of electricity generated. Variability in damages per ton of emissions was almost entirely explained by population exposure per unit emissions (intake fraction), which itself was related to atmospheric conditions and the population size at various distances from the power plant. Variability in damages per kilowatt‐hour was highly correlated with SO₂ emissions, related to fuel and control technology characteristics, but was also correlated with atmospheric conditions and population size at various distances. Our findings emphasize that control strategies that consider variability in damages across facilities would yield more efficient outcomes.